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1 Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2015 Development of Real-Time Voltage Stability Monitoring Tool for Power System Transmission Network Using Synchrophasor Data Md Kamrul Hasan Pulok Follow this and additional works at the FSU Digital Library. For more information, please contact

2 FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING DEVELOPMENT OF REAL-TIME VOLTAGE STABILITY MONITORING TOOL FOR POWER SYSTEM TRANSMISSION NETWORK USING SYNCHROPHASOR DATA By MD KAMRUL HASAN PULOK A Dissertation submitted to the Department of Electrical & Computer Engineering in partial fulfillment of the requirements for the degree of Master of Science 2015 Copyright 2015 Md Kamrul Hasan Pulok. All Rights Reserved.

3 Md Kamrul Hasan Pulok defended this dissertation on July 13, The members of the supervisory committee were: Md Omar Faruque Professor Directing Thesis Chris S. Edrington Committee Member Lukas Graber Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements. ii

4 To my parents and wife. iii

5 ACKNOWLEDGMENTS Many thanks are due to many people. First of all, I am very grateful to my supervisor, Dr. Md Omar Faruque for giving me the opportunity to work with him and guiding me to accomplish this research. I am also grateful to my committee members, colleagues, friends and family. Thanks a lot to all of you. iv

6 TABLE OF CONTENTS List of Tables viii List of Figures Abstract xiii 1 Introduction Motivation and Objective Technologies Used/Developed in this Thesis Phases of the Research Organization of the Chapters Synchrophasor Technology Introduction to Synchrophasor Basic Principle of Phasor Basic Principle of Synchrophasor Comparison of SCADA and Synchrophasor technology Applications of Synchrophasor Applications in Wide Area Monitoring Systems (WAMS) Applications of PMU in Power System Protection and Control IEEE Standard for Synchrophasor Modeling of the IEEE C PMU P-Class PMU Model M-Class PMU Model PSCAD FFT (Fast Fourier Transformation) Model Simulation Results TVE Evaluation Results FE Evaluation Results Phasor Data Concentrator (PDC) Introduction Setup of PDC Server Discussion Voltage Stability Analysis Introduction Basics of Voltage Stability Algorithms to Identify Voltage Instability Margin Voltage Stability Indices Voltage Stability Boundary in P-Q Plane Temperature Impact on Voltage Stability Simulation Setup Simulation Results and Analysis Voltage Stability Indices Results ix v

7 3.5.2 Results of Voltage Stability Boundary in the P-Q Plane Analysis of Results Results of Temperature Impact Study on Voltage Stability Discussion Algorithm For Optimal PMU Placement Introduction Network Observability Analysis Proposed Algorithm to Identify Optimum PMU Locations Developed GUI Tool PMU Placement Optimization Result Discussion Real-Time Dynamic State Estimation Introduction Theoretical Background Basic Principle of Linear State Estimation Solution to the Linear State Estimation Methodology Formulating Matrices Simulation Model and Test Setup Results Discussion Real-time Voltage Stability Monitoring Tool Introduction Features of the Developed Tool Simulation Results Conclusion and Future Work Key Contributions of This Thesis Future Work Conclusion Appendices A Configuration of Open-PDC 73 A.1 Installation of OpenPDC A.2 Configuring PMU Devices in OpenPDC B Configuration of Microsoft SQL Server 2012 Database 80 C Interfacing MATLAB with SQL Server Database 90 C.1 Setting up the Real-time Interface C.2 Importing Data Using MATLAB Database Explorer GUI C.3 Importing Data Using MATLAB Command and Scripting vi

8 D MATLAB Code of Optimal PMU Placement Algorithm 102 D.1 Graphical User Interface (GUI) Design D.2 MATLAB Code of Optimal PMU Placement Identifier Tool E MATLAB Code of Voltage Stability Monitoring Tool 110 E.1 Code of MATLAB function initializehistoricdata.m E.2 Code of MATLAB function UpdateTopologyMatrix H.m E.3 Code of MATLAB function RealTimeStability.m E.4 Code of MATLAB function SE.m E.5 Code of MATLAB function CalculateVSI.m E.6 Code of MATLAB function Draw Stability Boundary.m Bibliography Biographical Sketch vii

9 LIST OF TABLES 2.1 P-Class Model Design Parameters M-Class Model Design Parameters PMU Placement Results for IEEE 39 Bus Comparison of PMU placements for IEEE test systems Computational time comparison with [55] PMU configurations for voltage measurements PMU configurations for current measurements B.1 The formation of zmatrix with PMU PointIDs viii

10 LIST OF FIGURES 1.1 List of the technologies used in this study Block diagram of the technologies used in this study Comparison between PMU vs. SCADA measurements [10] Growing phase angle difference between Cleveland and Michigan during the August 14, 2003 blackout in the Eastern Interconnection [9] Application of PMUs at Wide Area Monitoring System (WAMS) Functional block diagram of PMU model [12] Three phase PMU signal processing model [5] P-class filter coefficients M-class filter coefficients TVE Comparison of the simulated PMU Models FE Comparison of the simulated PMU Models PDC network in power system Home screen of OpenPDC software A simple two bus power system with PMUs Voltage stability boundary in a P-Q Plane Run-time view of the IEEE 39 Bus system in single line diagram Voltage at each bus (case-1) Active power & reactive power of generators (case-1) VSI and VCPI for selected 5 transmission lines (case-1) VSI and VCPI for selected 5 transmission lines (case-2) line ranking comparison by VSI and VCPI (at 140% load, case-1) VSI and VCPI comparsion at line 2t1: Top Plot : VSI vs. VCPI; Bottom plot: Ratio comparison of P,Q,S to see which type of power got limited Voltage Stability Boundary of line 2t1, 1t39 & 16t ix

11 3.11 Operating point trajectory in P-Q plane for varying loading, Left chart: line 2t1; Right chart: line 1t VSI value comparison (20 C vs. 75 C) Bus test system Addition stage of proposed PMU placement optimization algorithm Reduction stage of proposed PMU placement optimization algorithm GUI developed for optimum PMU placement identifier tool PMU locations of IEEE 39 Bus System SCADA System State Estimation block diagram [61] Transmission π-line model for calculating line flows One-line diagram of a fictitious 4 bus system Block diagram of simulation and test setup for the SE tool One line diagram of IEEE 39 Bus system Flow chart of real-time state estimation process State estimation error distribution Functional block diagram and process flow of VSM tool Home screen of voltage stability monitoring tool : Disconnected mode Home screen of voltage stability monitoring tool : Connected mode One-line Diagram view of voltage stability monitoring tool A.1 Database type selection during the installation of OpenPDC A.2 Configuration of Historian instances A.3 Connection String A.4 The names of the PMU streaming standards supported by OpenPDC A.5 PMU connection configuration window of OpenPDC (step-1) A.6 PMU connection configuration window of OpenPDC (step-2) A.7 List of PMU measurements for Graphical Real-time visualization x

12 B.1 Connect to Server window of Microsoft SQL Server Management Studio B.2 Home screen of Microsoft SQL Server Management Studio B.3 Executing a new query to create a table named TimeSeriesMeasurement B.4 Script-1: To create a table named TimeSeriesMeasurement B.5 Script-2: for Selecting Latest 1000 Rows from TimeSeriesMeasurement table B.6 Retrieval result of Latest 1000 measurement in SQL server B.7 Contents of dbo.measurement Table in SQL server B.8 Types of measurement data stored for each PMU device (example for PMU6 14T13). 86 B.9 Script-3: for creating RequiredMeasurements table B.10 Script-4: for populating data in RequiredMeasurements table B.11 The contents of dbo.requiredmeasurements Table B.12 Script 5: for creating Z Matrix table B.13 Script-6: for Updating the Z Matrix Table B.14 Partial view of the contents of Z Matrix Table C.1 Compatibility requirement of MATLAB database toolbox [67] C.2 Creating New Data source using MATLAB Database explorer C.3 ODBC Data Source Administrator dialog box C.4 Create a New Data Source dialog box C.5 Microsoft SQL Server DSN Configuration, step C.6 Microsoft SQL Server DSN Configuration, step C.7 Microsoft SQL Server DSN Configuration, step C.8 Microsoft SQL Server DSN Configuration, step C.9 Connecting to SQL server using MATLAB Database explorer GUI C.10 Common connection failure error message C.11 After successful connection with SQL server, all tables and selected table values are appeared in Database explorer xi

13 C.12 Matlab Cell Array variable in Workspace after Data Import C.13 Auto generated script by Database explorer GUI D.1 GUIDE design of the optimal PMU placement identifier tool D.2 Complete GUI of PMU placement identifier tool xii

14 ABSTRACT Intelligent and effective monitoring of power system stability in control centers is one of the key issues in smart grid technology to prevent unwanted power system blackouts. Voltage stability analysis is one of the most important requirements for control center operation in smart grid era. With the advent of Phasor Measurement Unit (PMU) or Synchrophasor technology, real time monitoring of voltage stability of power system is now a reality. This work utilizes real-time PMU data to derive a voltage stability index to monitor the voltage stability related contingency situation in power systems. The developed tool uses PMU data to calculate voltage stability index that indicates relative closeness of the instability by producing numerical indices. The IEEE 39 bus, New England power system was modeled and run on a Real-time Digital Simulator that stream PMU data over the Internet using IEEE C protocol. A Phasor data concentrator (PDC) is setup that receives streaming PMU data and stores them in Microsoft SQL database server. Then the developed voltage stability monitoring (VSM) tool retrieves phasor measurement data from SQL server, performs real-time state estimation of the whole network, calculate voltage stability index, perform real-time ranking of most vulnerable transmission lines, and finally shows all the results in a graphical user interface. All these actions are done in near real-time. Control centers can easily monitor the systems condition by using this tool and can take precautionary actions if needed. xiii

15 CHAPTER 1 INTRODUCTION 1.1 Motivation and Objective It is always desired to have a high utilization of power system infrastructure, but from technical perspectives, particularly from the system stability point of view, higher utilization means higher vulnerability to system collapse. Thus, power system engineers always face the challenge of implementing proper and effective techniques for analyzing, monitoring and predicting possible voltage collapses in the system prior to its occurrence. Voltage stability analysis is one of the important monitoring tools for control center operation in smart grid era. There are a lot of advanced monitoring technologies available in this digital communication era, but their capabilities in monitoring or predicting power system health is still limited. SCADA (Supervisory Control and Data Acquisition) system is the main infrastructure used at the control center operation of power system. Even though Synchrophasor technology which can provide measurements in very high resolution using the fast digital communication is available, it s usage in the power system utilities is still limited. Traditional SCADA measurements are not suitable for real-time analysis of voltage stability, since the measurements are unsynchronized among the nodes and they are very slow (sampling time is 2 10s). On the other hand, the PMU devices can provide synchronized measurements by which synchronized comparison throughout the network is possible. And the sampling time of measurements can be in milliseconds range. Thus PMU technology provides the opportunity to perform real-time voltage stability analysis. One of the major objectives of this research is to use Synchrophasor (PMU) technology to analyze real-time voltage stability of a large power system transmission network. There are substantial research work reported on voltage stability analysis, but most of them are limited in theoretical level. This research focuses to implement a suitable voltage stability analysis algorithm and visualize the stability condition of the network in real-time in a graphical user interface (GUI). Since PMU devices are expensive, it is not economically efficient to install PMUs at every bus or substation. So another research objective is to develop a very fast and efficient algorithm to identify minimum and optimum number of PMUs and their placement 1

16 in the power system network. Thus having limited number of direct measurements from the PMU devices, it is necessary to perform state estimation. There are quite a number of algorithm available in the literature to perform state estimation. But most of the methods are unsuitable for real-time state estimation, as they involve iterative solution of nonlinear equations. So this research focuses on the development of a state estimation technique that is suitable for the implementation of realtime state estimation. In summary, the research objective is to develop real-time voltage stability monitoring tool which can be utilized for control center operation. The motivation of this research is to use available advanced technologies for the advancement of power system with the goal of achieving smart grid. 1.2 Technologies Used/Developed in this Thesis In this research, a lot of novel technologies are used as shown in Fig Since the objective of this research is to develop a real-time voltage stability monitoring tool, real-time digital simulation is a prerequisite of this research. So this study utilizes the facility of Real-time digital simulation tools available at CAPS (Center for Advanced Power Systems) laboratory. This laboratory has state-ofthe-art Real-time digital simulator (RTDS ) consisting 14 racks [1]. In this study, two racks are utilized for the whole simulation. The next technology used in this study is Synchrophasor (PMU) technology [2]. The advantage of PMU is that it can provide synchronized voltage and current phasor measurements over the Internet (Chapter-2). And the resolution and data streaming rate of these measurements are very high compared to the traditional SCADA (Supervisory Control and Data Acquisition) measurements. This provides the technological advantage to implement realtime dynamic analytical tools in power system for which PMU devices are considered as smart-grid devices. However, PMU devices are very expensive and it is economically inefficient to deploy PMU devices at every substation. In this study, a novel algorithm is proposed to identify minimum PMU requirements and optimal location of PMUs in a power system network (Chapter-4). A dedicated graphical user interface (GUI) has been developed and tested it s performance with other algorithms available in the literature. Also a Phasor data concentrator (PDC) is configured in the CAPS laboratory using OpenPDC and Microsoft SQL server. The function of PDC server is to store streaming PMU measurements in a database server in real-time and to provide a realtime interface of the data to other tools like state estimator. The next technology used in this 2

17 Real-time Digital Simulation (RTDS ) Technology Synchrophasor (PMU) Technology Novel Algorithm for Optimal PMU Placement Real-time Dynamic State Estimation Real-time Voltage Stability Visualization Figure 1.1: List of the technologies used in this study study is Real-time Dynamic State estimation. Since PMUs are installed in limited number of bus locations of the network, the direct voltage and current measurements are not available throughout the power system. Thus state estimation is performed to estimate voltage magnitude and phase angle of all of the buses throughout the power system. Once estimated voltages of all the buses are available, they can be utilized to perform many contingency analysis. There are many algorithms available in the literature to perform state estimation (Chapter-5). But most of the state estimation methods are either static or quasi-static. These methods use the measurements from SCADA system which needs to solve nonlinear equations in iterative algorithm. However, since PMU devices can measure states (voltage and phase angle) directly, the state estimation of other buses can be done by solving linear equations. Thus real-time implementation of state estimation is possible by using exclusive PMU measurements. In this research, a real-time state estimator tool with graphical user interface(gui) has been developed. The next step in this study is Real-time Voltage Stability Visualization. In this study, two indexing method of voltage stability 3

18 are compared using real-time digital simulation and the suitable algorithm for real-time voltage stability margin visualization was identified. Also the performance of voltage stability boundary in P-Q plane is evaluated and used in the voltage stability monitoring tool. A dedicated graphical user interface (GUI) has been developed for real-time voltage stability monitoring tool which uses real-time state estimated voltages to calculate voltage stability index and voltage stability boundary for each transmission line (Chapter-6). Then it visualizes the results in the GUI using charts. Also it performs real-time ranking of the transmission lines showing the list of weakest lines to strongest lines. 1.3 Phases of the Research Fig. 1.2 illustrates the phases of the research according to which this research study progressed. Since this research involves usage of various technologies, different phases required it s own literature review and studies. The target of phase-1 is to prepare the real-time digital simulation model of IEEE 39 Bus system. In this phase, a complete simulation model of the test system (IEEE 39 Bus system) is prepared in RTDS and validated the model performance by comparing it with the PSS E model results. Since PMUs need to be connected to the bus locations of the RTDS model, identifying the location of the PMUs required another intensive study. In this phase, the algorithm to identify optimum PMU placements are developed along with GUI. Then according to the results of this PMU placement identifier tool for IEEE 39 bus system, the PMUs are configured in RTDS model. Then the streaming capability of the PMUs of RTDS are tested and finally a working RTDS simulation model with PMU streaming capability are developed in phase-1. In phase-2, the research objective was to set up a phasor data concentrator ( PDC ) in the laboratory. One of the primary requirements of PDC is that it needs to be capable of receiving and processing incoming streaming PMU measurements over the Internet. Then it should time align all the PMU measurements and store in a database. All of this functions need to be performed in real-time. In this phase, OpenPDC has been used as PMU data handler and Microsoft SQL server has been used as database server. The database server is needed to facilitate real-time data reading by the voltage stability monitoring tool. In phase-3, a lot of literature review has been performed to identify best suitable state estimation algorithm for real-time implementation. In this phase, real-time state estimator tool was developed and it s performance was tested. MATLAB was used 4

19 Figure 1.2: Block diagram of the technologies used in this study to implement the state estimation algorithm and develop the GUI tool. The most challenging part of this phase was to interface MATLAB with SQL server. This was challenging since data transfer between this two need to be real-time (with minimum possible time lagging). In phase- 4, algorithms to analyze real-time voltage stability are implemented in MATLAB using the state estimated voltages. Various test cases are studied in this phase and performance are evaluated. In phase-5, the focus was to develop a user friendly, feature rich graphical user interface of voltage stability monitoring tool. 5

20 1.4 Organization of the Chapters The chapters of this thesis are organized according to the technologies used and phases of the research. Since a lot of literature reviews are performed related to requirements at different phases of the research, related state-of-the-art researches are explained in related chapters. Chapter-2 represents the explanation of Synchrophasor technology. It contains the description of basic working principle of PMU, difference compared to SCADA and the applications of this devices in power system. The simulation model built for PMU according to the IEEE standard are also presented in this chapter and a comprehensive performance analysis between PMU classes are provided. A brief description of PDC - phasor data concentrator is also provided in this chapter. Chapter-3 contains the literature review of voltage stability analysis. It also contains the description of the simulation setup and the results of real-time voltage stability analysis of IEEE 39 Bus system. A comparative analysis with simulation results are provided among voltage collapse proximity indicator (VCPI), voltage stability index (VSI) and voltage stability boundary in P-Q plane. In chapter-4 literature review for optimal PMU placement are provided. It contains the theoretical background of network observability analysis. In this chapter, detailed explanation of the proposed algorithm to identify optimum PMU placement are provided. Chapter-5 explains the state estimation technique along with theoretical background. The methodology used in this study to perform real-time state estimation are also presented in this chapter. A comprehensive result with analysis are provided in the results section of this chapter. The detailed explanation of the developed voltage stability monitoring tool is given in Chapter-6. It basically contains the description of the features available in the developed GUI with detailed illustrations. Then the conclusion and possible future work of this thesis are given in chapter-7 which also have a brief description of the major contributions of this research. 6

21 CHAPTER 2 SYNCHROPHASOR TECHNOLOGY 2.1 Introduction to Synchrophasor Synchrophasor is Synchronized Phasor Measurement Unit, also known as PMU- Phasor Measurement Unit. PMU devices are considered as one of the prominent components of the upcoming smart grid era. One of the primary requirements of smart grid is gathering power system s state information through very fast digital communication. PMU devices provide the foundation of gathering very fast metered data as it can provide time synchronized sub-second phasor measurement data of the system. The term smart grid covers a range of devices and systems that leverage recent advances in digital technology and communications to improve the efficiency, performance, and reliability of the existing electric power system infrastructure. The term Smart Grid not only focuses on the advancements of distribution systems but also on the enhancements to the transmission system. Phasor measurement units, or PMUs, are a new Smart technology which is now widely in use in transmission network. The concept of phasor is not new. It was 1893 when Charles Proteus Steinmetz presented a paper on simplified mathematical description of the waveforms of alternating current electricity, and he named his representation as phasor [3]. However the concept to calculate real time phasor measurement is comparatively very new. It was 1988 when Dr. Arun G. Phadke and Dr. James S. Thorp at Virginia Tech invented phasor measurement units (PMU) that are synchronized to an absolute time reference provided by the global positioning system (GPS) [2 4]. Early prototypes of the PMU were built at Virginia Tech, and Macrodyne built the first PMU (model-1690) in 1992 [2]. The first PMU standard developed by IEEE was in 1995 and the latest version is known as C , IEEE Standard for Synchrophasor Measurements for Power Systems which is released in December 2011 [5]. After the invention of PMU technology, numerous application of PMUs are found in the literature [7]-[11]. The use of PMUs can be broadly categorized in two categories: (1) Wide Area Monitoring Systems (WAMS) and (2) Power System Protection and Control. In 2014, IEEE has 7

22 published a report named Use of synchrophasor measurements in protective relaying applications [7]. A detailed list of practical applications of PMUs at different areas can be found in the report. PMU devices can measure phase and sequence values of voltage and current at critical intersecting locations, normally in substations on a power grid. Since these measurements are precisely synchronized, synchronized comparison of two quantities is possible in real time. The PMU monitored buses are preselected through various algorithms to make the the power system network under study to be fully or optimally observable. PMU measurements are streamed through Internet or other communication protocol to a control center where a database server is present. This database server is known as Phasor Data Concentrator (PDC). This PDC can be either on-site or at centralized locations. The phasor data is then transmitted to a regional monitoring system which is maintained by the local Independent System Operator (ISO). These ISO s will monitor phasor data from individual PMU s to provide information for establishing controls on power flow from multiple energy generation sources (nuclear, coal, wind, etc.) [2]. In this chapter, the basic working principle of synchrophasor are explained. In section 2.2, a comparative study of SCADA and PMU technology are provided followed by the applications of synchrophasor in section 2.3. Design standard provided by IEEE is also described in section 2.4 followed by description of developed simulation model of IEEE P-Class and M-Class synchrophasor in section 2.5. The simulation results with comprehensive analysis are given in section 2.6. The explanation of PDC server is provided in section Basic Principle of Phasor IEEE defined Phasor as Phasor is complex equivalent of a sinusoidal wave quantity such that the complex modulus is the cosine wave amplitude, and the complex angle (in polar form) is the cosine wave phase angle [5]. An AC waveform can be mathematically represented by equation (2.1). A(t) = A m cos(ωt+φ) (2.1) Equation (2.1) is commonly represented as the Phasor as shown in equation (2.2). A = Am 2 e jφ = Am 2 (cosφ+jsinφ) = A r +ja i (2.2) Where the magnitude Am 2 is the root-mean-square (RMS) value of the waveform, and the subscripts r and i signify real and imaginary parts of a complex value in rectangular components. The value 8

23 of φ depends on the time scale, particularly where t = 0. It is important to note that this phasor is defined for the angular frequency ω rad/s; evaluation with other phasors must be done with the same time scale and frequency [5] Basic Principle of Synchrophasor According to IEEE standard [5], Synchrophasor is defined as A Phasor calculated from data samples using a standard time signal as the reference for the measurement. In simple language, Phasors is a quantity with magnitude and phase of a sinusoidal wave. And when Phasors are calculated with reference to a common time source, i.e. synchronized measurements of phasors are called Synchrophasor. The term PMU is commonly used for Synchrophasor. Basically PMU is a phasor measurement unit which gives synchrophasor data. A PMU is an electronic device that uses state-of-the-art digital signal processors that can measure 50/60Hz AC waveforms (voltages and currents). An analog to digital converter for each phase are used to digitize AC waveforms and then passes through FIR filter. A GPS clock is used to synchronize the whole process. Along with phasors, line frequencies and rate of change of frequency (ROCOF) are also calculated by the PMU at each site. The resultant time tagged phasors can be transmitted to a local or remote database server (PDC), typically at rates up to 60 samples per second. 2.2 Comparison of SCADA and Synchrophasor technology SCADA stands for Supervisory Control and Data Acquisition that consists of meter reading and equipment status reporting. These data are then compiled and formatted in a control center where a control room operator can make supervisory decisions to adjust or override normal RTU (Remote Terminal Unit) (PLC) controls. A historian or database management system is also maintained to allow trend analysis and other analytical auditing [8]. The advantages of PMU measurements over traditional SCADA measurements include: ❼ Higher sampling frequency ❼ The ability to provide direct measurement of power system states (i.e., the voltage magnitude and angle). The PMU devices may have very high sampling frequency. And these devices can capture system changes at a higher resolution, allowing for more accurate monitoring of power systems 9

24 and faster remedial actions. In general, PMU can send measurements at the rate of 20, 30, 60 samples per second based on device configuration. On the other hand, SCADA system presents system wide data on all generators and substations at every 2 to 10 seconds [2]. Figure 2.1 depicts the comparison of SCADA and PMU voltage measurements in response to a disturbance in a network [10]. The first thing noticeable from the figure is that PMU measurements are very precise and captures dynamic conditions of the waveform, whereas SCADA measurements misses dynamic information of the voltage waveform. It is also noticeable that PMU device captured the disturbance event ahead of time than SCADA system. Traditional SCADA/EMS systems are based on steady Figure 2.1: Comparison between PMU vs. SCADA measurements [10] state power flow analysis, and therefore cannot observe the dynamic characteristics of the power system. Synchrophasor technology is considered as the MRI of the power system as it can provide very high resolution measurements. Certainly this technology overcomes the limitations of the old X-ray quality visibility that traditional SCADA-based systems provide [9]. 2.3 Applications of Synchrophasor Since PMUs provide very fast time synchronized measurement, it offers wide area visibility of the system as measurements are globally comparable. This, in turn, facilitates the capability for distributed sensing and coordinated control action. The calculation of phase angle difference throughout the network is very important. We know, for DC circuits, power flows from high 10

25 voltage to low voltage. Whereas in AC circuits, power flows from a higher voltage phase angle to a lower voltage phase angle. The larger the phase angle difference between the source bus and the sink bus, the greater the power flow through the transmission line connected between these two buses. However if the phase angle difference become more than 90, the system is close to possible instability. The Figure 2.2 shows the growing phase angle difference between Cleveland and Figure 2.2: Growing phase angle difference between Cleveland and Michigan during the August 14, 2003 blackout in the Eastern Interconnection [9] Michigan during the August 14, 2003 blackout in the Eastern Interconnection [9]. It is observable from the figure that the phase angle difference was increasing and when it went beyond 90, the whole system collapsed. So it is evident that having synchronized phase angle measurement data, various type of advanced contingency analysis are possible. Since PMU devices can provide phase and sequence measurements of voltage and current, they have various aspects of usage. One aspect of usage is for wide area monitoring purposes for control center operation. Another aspect of usage is for power system protection and control purposes. In the following subsections the application in both aspects of usage are described. 11

26 2.3.1 Applications in Wide Area Monitoring Systems (WAMS) One of the major advantages of PMU data is that it can be used for wide area monitoring systems of modern smart grid architecture. WAMS master station receive the dynamic data sent from the PMU, save data into real-time and historical database, analyze data, and display these dynamic information on the man-machine interface, to make the dispatcher know the dynamic state of power system in real time. This function provides the alarm function using sound, display, and other means to remind the dispatcher noticing and handling. In study [11], the WAMS is categorized as shown in the block diagram (Fig. 2.3). WAMS Target Phenomena Thermal Islanding Stability Detection Frequency Stability Rotor Angle Stability Voltage Stability Intentional Oscillatory Transient Steady-State Ambient Transient Figure 2.3: Application of PMUs at Wide Area Monitoring System (WAMS) PMU measurements have substantial usage in stability monitoring under WAMS. Load carrying ability of AC transmission lines are limited by thermal constraints, voltage constraints, dynamic angle constraints, steady state angle constraints. WAMS applications provide a way of monitoring the proximity of the stability limits and constraints. Following stability monitoring can be obtained in WAMS using PMU data: ❼ Voltage stability index monitoring and prediction 12

27 ❼ Line thermal monitoring ❼ Ambient and transient power oscillation monitoring ❼ Power oscillation monitoring ❼ Power damping monitoring ❼ Phase angle monitoring ❼ Wide area frequency monitoring Applications of PMU in Power System Protection and Control PMU measurements with high accuracy time stamping are in use of number of protective relaying and control applications. According to [7], synchrophasor data are in use for following protection and control applications: ❼ Power swing detection and protection ❼ Load shedding under Remedial Action Schemes (RAS). ❼ Synchrophasor assisted Black Start ❼ Automatic Generator Shedding ❼ Fault location identification ❼ Bus differential relaying ❼ Line differential protection ❼ Fine tuning of line parameters ❼ Synchrophasor application to controlled islanding ❼ Detection of power system inter-area oscillations ❼ Synchrophasor-based Line Backup Protection 13

28 2.4 IEEE Standard for Synchrophasor There is a standard for synchrophasor technology published by the IEEE Power & Energy Society and it is known as IEEE Std C [5]. This standard is a revision of IEEE Std C The title of the standard is IEEE Standard for Synchrophasor Measurements for Power Systems. Definitions of synchrophasor, frequency, and rate of change of frequency (ROCOF) measurement are provided in the standard. The specifications and requirements for this measurement device are provided considering the system s steady state and dynamic conditions. It also specifies the time tag and synchronization requirements. According to this standard, a phasor measurement unit (PMU) can be a stand-alone physical unit or a functional unit within another physical unit. According to IEEE standard C , there are two performance classes of PMU, namely P-Class and M-Class. P-class PMUs can provide very fast response as there are no explicit filtering. The targeted applications of P-class PMU are for those which require fast response such as in protection applications. On the other hand, M-class PMUs can provide robust measurements as they are invulnerable to the aliased signals, however the response can be comparatively lower than P-class PMUs. The targeted applications of M-class PMU are for those which require greater precision but is not a problem for little reporting delay. Such applications can be found in measurement applications [5]. 2.5 Modeling of the IEEE C PMU Figure 2.4 shows the signal processing steps within the PMU. The voltage and current signals are passed through front-end anti-aliasing filter so that high frequency interference signals are eliminated. In this study, sixth order Butterworth low pass filter is Figure 2.4: Functional block diagram of PMU model [12] 14

29 used as front-end anti-aliasing filter. Then the signals are digitized using a A/D converter at a fixed sampling rate which is synchronized with GPS (Global Positioning System) clock. GPS clock can provide coordinated universal time (UTC) which have precision level in microsecond resolution. The digitized signals are then go through complex multiplication with the nominal frequency carrier which gives the real and imaginary components of the phasor. These components are then passed through a back-end performance class filter which give required accuracy under dynamic conditions. The back-end performance class filter can be either P-class or M-class filter, which are basically a FIR (Finite Impulse Response) filter. The difference between P-class and M-class is in the FIR filter design considerations which are explained in next subsections. After getting the filtered phasor components, frequency, rate of change of frequency (ROCOF), real & reactive power are calculated. At the i th sample time of a single phase signal x i, the synchrophasor estimate X(i) is given by equation (2.3). X(i) = 2 Gain N 2 k= N 2 x i+k W (k) exp( j(i+k) tω 0 ) (2.3) Gain = N 2 W (k) (2.4) k= N 2 Where ω 0 = 2πf 0,f 0 is the nominal power system frequency (50Hz or 60Hz) N = FIR filter order (number of filter taps is equal to N +1) t = 1/Samplingf requency x i = Sample of the waveform at time t = i t, where the time t = 0 coincides with a 1s rollover W (k) = Low-pass filter coefficients (depending on P or M class filter). Figure 2.5 shows complete three phase PMU signal processing model. By using the the symmetrical component transformation, positive sequence component is calculated. From the positive sequence component, the frequency is calculated from the rate of change of phase angle. In this algorithm, latest four phase angles are considered and their weighted differences are calculated by using (2.5). Higher weight is given to the latest phase angle in this algorithm. The benefit of this algorithm is that it smooths out the frequency estimate. F(i) = {6[θ(i) θ(i 1)]+3[θ(i 1) θ(i 2)]+[θ(i 2) θ(i 3)]}/[20π t] (2.5) 15

30 Figure 2.5: Three phase PMU signal processing model [5] where θ(i) is the angle of the i th positive sequence estimate X(i),θ(i 1) is the angle of the previous estimate, etc. The rate of change of the frequency (ROCOF) is estimated using the equation (2.6). The final synchrophasor is calculated using the equation (2.7). DF(i) = [ F(i) F(i 1)]/ t (2.6) [ ( )] π(f F(i)) ˆX = X(i)/ sin 2f 0 Where, F(i) = Deviation of frequency from nominal frequency computed at point i as shown in equation (2.5). Two simulation model, one is P-Class PMU and another is M-Class PMU model, are built in RSCAD software and the time step used was 50µs. In both models, sixth order Butter-worth low-pass filter with cut-off frequency at one half of sampling frequency is used as a front-end antialiasing filter. All other blocks (Fig. 2.4) are same except the back-end performance class filter. The detailed design considerations of both model are given in next subsections P-Class PMU Model The key design parameters of P-Class model is shown in Table I. The coefficients of FIR filter for P-Class PMU were calculated according to equation (2.8). Figure 2.6 shows the calculated filter coefficients based on Table 2.1 design parameters and equation (2.8). (2.7) 16

31 VALUE SAMPLE NUMBER Figure 2.6: P-class filter coefficients Table 2.1: P-Class Model Design Parameters Name Formula Value Sampling Rate or Sample per cycle N s 15 Sampling Frequency f s = f 0.N s 900Hz Sampling time t = 1/f s FIR Filter order N = 2(N s 1) 28 Filter Taps N Butterworth filter cutoff frequency f s /2 450Hz W(k) = ( 1 2 N +2 k ) (2.8) where k = N/2 : N/2 (integer values only) and N = Filter order M-Class PMU Model The M-Class model has key design parameters shown in Table 2.2. The coefficients of FIR filter for M-Class PMU were calculated according to equation (2.9). where k = N/2 : N/2 N = Filter order ( W(k) = sin 2π 2F ) fr f s k 2π 2F h(k) (2.9) fr f s k 17

32 F fr = Low pass filter reference frequency from Table C.1 of [5] h(k) = Hamming function W(0) = 1 (note when k = 0,W = 0/0, which is not a number and must be replaced by 1) VALUE -0.2 SAMPLE NUMBER Figure 2.7: M-class filter coefficients Table 2.2: M-Class Model Design Parameters Name Formula Value Sampling Rate or Sample per cycle N s 16 Sampling Frequency f s = f 0.N s 960Hz Sampling time t = 1/f s FIR Filter order N = 2(N s 1) 96 Filter Taps N Butterworth filter cutoff frequency f s /2 480Hz Low pass filter ref. frequency F fr PSCAD FFT (Fast Fourier Transformation) Model To compare the P-class and M-class PMU performance we considered the performance of existing PSCAD FFT model which also provides the phasors. The existing FFT model in PSCAD/EMTDC is based on the standard FFT technique, which computes the DFT(Discrete Fourier Transformation) of the signal [13]. In this model, DFT of size p is divided into two smaller DFTs of size p/2; Then two outputs from the even-indexed inputs and the odd-indexed inputs are combined to 18

33 produce the complete DFT. This FFT model has an optional anti-aliasing filter and a frequency tracker which can be enabled or disabled based on the application. Along with the fundamental component of the signal, this model can also measure harmonics from 2 nd to 255 th, where the sampling rate is automatically increased accordingly from 16 to 512 samples/cycle depending on the number of harmonics required. 2.6 Simulation Results The performance of modeled PMUs are to be evaluated using the concept of Total Vector Error (TVE) and Frequency Error (FE) defined in the IEEE standard [5]. TVE is the measurement of magnitude errors which can be calculated based on equation (2.10). FE is the measurement of frequency errors which can be calculated based on equation (2.11). TVE(n) = x a(n) x m (n) x a (n) 100 (2.10) FE(n) = f a (n) f m (n) (2.11) Wherex a (n),x m (n)arethemagnitudeoftheactualandthemeasuredphasorsrespectively. f a (n),f m (n) are the actual and the measured frequencies respectively TVE Evaluation Results Figure 2.8 shows the TVE comparison of the simulated models. According to the IEEE standard [5], the standard limit of TVE error is 1%. It can be observed from figure 2.8 that, PSCAD model has very minimal error, less than 0.07% and meet the performance limit. P-class model also passes the performance limit in both study. P-Class model TVE is less than 0.01% which is significantly good. In case of M-Class model, we found that TVE meets error limit for all frequencies except 55 and 65Hz. In that case the error was around 1.4% FE Evaluation Results Figure 2.9 shows the FE comparison. The standard limit of FE is 0.005Hz [5]. The PSCAD model failed to meet standard requirement as shown in the figure. Both P-class and M-class model passed the standard requirement. It is found that M-class model doesn t have any error. Which means the M-class PMU model is very robust in frequency measurement. 19

34 Figure 2.8: TVE Comparison of the simulated PMU Models Figure 2.9: FE Comparison of the simulated PMU Models 20

35 2.7 Phasor Data Concentrator (PDC) Introduction Phasor Data concentrator (PDC) is a system which receives phasor measurements from remote phasor measurement units(pmus) through a communication medium and stores data in a database management system. IEEE has published a guide for phasor data concentrator which is named IEEE Guide for Phasor Data Concentrator Requirements for Power System Protection, Control, and Monitoring (IEEE Std C TM 2013) [14]. According to the guideline, the function of the PDC is data handling, processing and storage. One of the major functions of the PDC is to time-synchronize phasor data from multiple PMUs to produce a real-time, time-aligned output data stream [15]. The PDC has the function to synchronize phasor measurements by aligning the timetag of the measurements and create a system wide time-series measurement set. The PDC can have additional features [9]. It can flag measurements based on the results of various quality inspection on the incoming phasor measurements. It has the monitoring system to provide information on the overall measurement system s performance like latency, data quality, frame rate etc. PDCs can also receive measurements from other PDCs by which multiple layers of concentration can be implemented as shown in Fig The figure illustrates the basic formation of phasor network which consists of multiple combination of PMUs and PDCs in a power system network. Typically PMUs are connected at major substations in transmission network and transmit the measurements in real-time over the Internet or other communication medium like fiber optic network. PMU measurements are then collected in a local PDC which may be located at the utility control center where the data are aggregated in a database management system. In addition, many local PDCs belonging to different utilities can also be connected to a centralized PDC. This provides the aggregation of phasor measurements across the utilities [9]. The centralized PDC sometimes also known as super PDC Setup of PDC Server In this study, a PDC with database server has been set up at the CAPS (Center for Advanced Power Systems) laboratory. To set up a PDC server following functional elements are required: 1. Phasor Data handler and processor 2. Storage of data in a database server 21

36 Figure 2.10: PDC network in power system An open source PDC software named OpenPDC [16] has been used as Phasor Data handler and processor. The PMU measurements are streamed over the Internet from the simulation model. The OpenPDC software receives those streaming measurement data, synchronizes all the PMU measurements by their time-tag and process as time-series measurements. As database server, Microsoft SQL server 2012 has been used. The configuration in OpenPDC software has been made in such a way that the phasor measurements are stored by OpenPDC in SQL server in real-time in a time-series measurement table. Fig shows the home screen of OpenPDC software. In the appendix a detailed procedure of PDC server (OpenPDC and Microsoft SQL server) configuration is provided. 22

37 Figure 2.11: Home screen of OpenPDC software 2.8 Discussion In this study, P-Class and M-Class PMU model are simulated and performance are compared according to IEEE standard performance evaluation criterion. It is found that in general, P-Class PMU model performed better than M-Class model. So in the rest of the studies of this thesis P-class PMU model has been used. A PDC server has been setup using OpenPDC and Microsoft SQL server to store phasor measurements in real-time for further usage of the data for real-time state estimation and voltage stability analysis. 23

38 CHAPTER 3 VOLTAGE STABILITY ANALYSIS 3.1 Introduction Intelligent and effective monitoring of power system stability in control centers is one of the key issues in smart grid technology to prevent unwanted power system blackouts. Voltage stability analysis is one of the important monitoring tools for control center operation in smart grid era. With the advent of Phasor Measurement Unit (PMU) technology, real time monitoring of voltage stability of power system is now a reality. It is always desired to have a high utilization of power system infrastructure, but from technical perspectives, particularly from the system stability point of view, higher utilization means higher vulnerability to system collapse. Thus power system engineers always face the challenge of implementing proper and effective techniques for analyzing, monitoring and predicting possible voltage collapses in the system prior to its occurrence. A review of the literature on techniques [17] [30] to study voltage collapse reveals that various analytical tools based on different concepts have been proposed to predict power system collapse due to voltage instability. By utilizing real time Synchrophasor measurement data, various methods [22] [30] are reported to visualize and analyze voltage instability condition. A classification of available algorithms is available in [31] [32] where two broad categories were proposed: Jacobian matrix based VSI and System variable based VSI. The study [32] categorized some of the indices like test function [38], second order index [39], tangent vector [40] into Jacobian matrix based VSI. System variable based VSIs are identified like Voltage Collapse Proximity Index (VCPI) [17], Voltage Stability Index (VSI) [27], Voltage Controllability Index (VCI) [41]. Many studies can be found in the literature on comparison among voltage stability indices [31] [34]. Since most of them are based on offline simulation tools, the effectiveness of those are not fully validated and not well understood, especially how they will behave in a real-world power system. The main objective of this chapter is to explain the effectiveness of various voltage stability indices with comprehensive simulation results. The simulation is performed on-line using real-time 24

39 PMU data. In this study, the IEEE 39 bus system is used as the test system that runs on RTDS in real-time and a combination of hardware and software was used to implement the PMU on the RTDS that streams real-time PMU data over the Internet. Data streamed through PMU were used to evaluate the effectiveness of two voltage stability indices -VCPI [17], VSI [27] and voltage stability boundaries [35] [36]. The objective of the study is to identify effective method of Voltage stability analysis which will be used in the real-time voltage stability monitoring tool with graphical visualization. In this chapter, the theoretical background of voltage stability is provided in section 3.2. In section 3.3, the algorithms to analyze voltage stability are explained. Simulation setup and simulation results are presented in section 3.4 and section 3.5 respectively. The comparative study with comprehensive analysis among voltage stability analysis algorithms are also presented in section 3.5 followed by discussion in section Basics of Voltage Stability There is a study conducted by IEEE/CIGRE Joint Task Force on Stability Terms and Definitions which provided a very good definition on voltage stability [43]. According to the paper the term Voltage stability is defined as follows: Voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition. It depends on the ability to maintain/restore equilibrium between load demand and load supply from the power system. Instability that may result occurs in the form of a progressive fall or rise of voltages of some buses. The study also defined the term Voltage collapse as follows: Voltage collapse the process by which the sequence of events accompanying voltage instability leads to a blackout or abnormally low voltages in a significant part of the power system. The most common phenomenon of voltage instability is the progressive drop of bus voltage. However the risk of overvoltage instability can also be possible [43]. One of the most common reasons for voltage instability is the high load demand. With the increase of load demand, the voltage tends to decrease. In response to this decrease of voltage, distribution voltage regulators 25

40 and tap-changing transformers tend to operate so that voltage increases. Power consumed by the increased loads tends to be restored by the action of motor slip adjustment. Restored loads, increase the reactive power consumption which leads to further voltage reduction. Thus it increases the stress on the high voltage network. This scenario can aggravate further when voltage instability appear in the network due to load dynamics attempt to restore the power consumption beyond the capability of the transmission network and the connected generation [43]. The vulnerability of voltage stability is increased when a disturbance increases the reactive power demand beyond the adequate capacity of the available reactive power resources. Themostcommonresultofvoltageinstabilityislossofloadinanareaortrippingoftransmission lines or other elements by their protective systems. This can lead to loss of synchronism of some generators which may lead to cascading outages and blackouts. The stable operation of power system could be possible at low voltage by the operation of transformer tap change or intentional and unintentional load shedding. 3.3 Algorithms to Identify Voltage Instability Margin Voltage Stability Indices One of the main reasons of voltage collapse is the inability of power system to supply reactive power. A sudden system wide sharp voltage decline is observed when a system reaches to a critical load and unable to maintain its generation and transmission. This sharp voltage decline phenomenon is recognized as voltage collapse. There are many methods [17]-[30] to measure voltage stability of a power system. A formulation to measure Voltage Collapse Proximity Indicator (VCPI) was described in [17]. The concept of this formulation is based on maximum transferable power through a line. Fig. 3.1 depicts a simplified two bus power system model with PMU connected at both ends. The paper used four separate formulas to represent VCPI as shown in (3.1) (3.4). VCPI(1) = P r P max = VCPI(2) = Q r Q max = VCPI(3) = P l P l(max) = V 2 s Z V 2 s Z P r cosφ 4cos 2 ( θ φ V 2 s Z Q r sinφ 4cos 2 ( θ φ P l 2 ) (3.1) 2 ) (3.2) cosθ 4cos 2 ( θ φ 2 ) (3.3) 26

41 Figure 3.1: A simple two bus power system with PMUs VCPI(4) = Q l Q l(max) = where P r = Active power at the receiving end Q r = Reactive power at the receiving end V s = Sending end voltage Z θ = Line impedance Z l φ = Load impedance P l = Active power loss in the line Q l = Reactive power loss in the line. V 2 s Z Q l sinθ 4cos 2 ( θ φ 2 ) (3.4) The numerator in equation (3.1) represents the receiving end real power which depends on the system parameters, network topology, interconnections and load of the system. The denominator represents the maximum power that can be transferred to the receiving end at a particular instant. The higher the value of VCPI (a value of 1 means voltage collapse situation), the vulnerable the system is to voltage collapse. Since this VCPI algorithm has four separate indices, it will give four separate indices for each line in any situation. Gong et al. [27] proposed Voltage Stability Index (VSI) formulation whose main concept is also based on maximum transferable power. But in this case it considers three maximum transferable power and express stability condition in one index. Ref. [25] also gave similar formulation with slight modifications which is mentioned below. By neglecting parallel admittance (Y) of transmission line as depicted in Fig. 3.1, the expression for transmitted active power P r and reactive power Q r is given in (3.5) and (3.6), respectively. The transferred complex power is expressed by (3.7). [ ] R P r = (V s cos(δ s δ r ) V r ) R 2 +X 2 +V X ssin(δ s δ r ) R 2 +X 2 V r (3.5) [ ] X Q r = (V s cos(δ s δ r ) V r ) R 2 +X 2 V R ssin(δ s δ r ) R 2 +X 2 V r (3.6) 27

42 where ϕ = arctan( Qr P r ). S = P r +jq r (3.7) P max = Q rr X V s 2 R 2X 2 + Z V s V 2 s 4Q r X 2X 2 (3.8) Q max = P rx R V s 2 X 2R 2 + Z V s V 2 s 4P r R 2R 2 (3.9) S max = V s 2 [ Z (Xsinϕ+Rsinϕ)] 2(Xcosϕ Rsinϕ) 2 (3.10) { Pmax P r VSI = min P max, Q max Q r Q max, S max S S max } (3.11) The maximum transferable active power, maximum transferable reactive power and maximum transferable complex power are expressed by (3.8)-(3.10), respectively. Equation (3.11) is the formula to calculate voltage stability index (VSI) proposed by [27]. The smaller the value of VSI, the more vulnerable the system is to collapse. So when VSI reaches to zero, the system becomes unstable. In this study, we compared both methods, VCPI (1) and VSI of voltage stability calculation. In the rest of the chapter, we will use VCPI instead of VCPI(1) which is considered to represent voltage collapse when it is equal to 1.0. For comparison purpose, we have modified (3.11) to (3.12) so that the VSI index yield similar values as VCPI. { Pr Q r VSI = max,, P max Q max S S max } (3.12) This means transmission lines with higher VSI value is close to its instability point which is the concept similar to VCPI Voltage Stability Boundary in P-Q Plane Glavic et al. [35] proposed a method to draw a voltage stability boundary in P-Q plane which provides a visual illustration of the system stability condition. Fig. 3.2 shows such voltage stability boundary of a transmission line which is produced based on an assumption of explicit parabolic relationship between active and reactive power as stated by (3.13). Q t = ap 2 t +bp t +c (3.13) The coefficients a, b, c are determined by points A, B and C in P-Q plane shown in Fig The coordinates of these points are defined as follows in the P-Q plane. 28

43 Figure 3.2: Voltage stability boundary in a P-Q Plane A : (0,Q t max), B : (Pmax,0), t C : (S max cosθ,s max sinθ) By using these three points we can find the values of a,b and c which can be used to draw the boundary line represented by parabolic equation (3.13). The significance of this voltage stability boundary in P-Q plane is that, any time the operating point touches the stability boundary or goes beyond the boundary, it indicates voltage instability situation. So the closer the operating point to the boundary, the more closer the system is to instability. For visualization of voltage instability margin, it is very useful in control center operation Temperature Impact on Voltage Stability The electrical resistance of bare stranded conductor varies with frequency, average current density, and temperature [38]. The resistance at different temperature can be calculated using equation (3.14)[39]. R 2 = R 1 [1+α 1 (T 2 T 1 )] (3.14) Where R 1 = Resistance at temperature T 1 R 2 = Resistance at temperature T 2 29

44 α 1 = Temperature coefficient of resistance at temperature T 1. There are some studies available in literature regarding temperature impact on transmission line models and state estimation accuracy [40] [41]. In this study, we simulated how temperature impacts on voltage stability of the power system. 3.4 Simulation Setup A real time digital simulation (RTDS ) model of IEEE 39 Bus [37] has been prepared to compare voltage stability indices. Both active & reactive power load have been increased by 1% at a 10s interval to simulate voltage instability condition. The generators governors, exciters and other components were modeled based on the dynamic data of the test system. Fig.3.3 shows the run time view of the simulation model with PMU locations shown by arrows. The placement of PMUs are chosen so that power system have full observability. Our study (chapter-4) showed that to have full observability of IEEE 39 Bus power system, at least 13 PMUs are required. PMUs are being connected at those 13 Bus locations. Also additional PMUs are being connected at buses at the opposite side of the transmission line to have real-time impedance measurement. All the simulations are performed in real-time and VCPI, VSI and stability boundaries are calculated using streaming PMU measurement data. Real time ranking of the transmission lines using VCPI and VSI method are also done and compared the ranking with each other. All the algorithms are implemented in MATLAB scripting environment and these are interfaced with RSCAD through scripting. RTDS streamed all PMU measurements in real-time which are stored in a text file by scripting in RSCAD run time environment. A MATLAB program reads the text file in real-time and calculates VCPI, VSI and voltage stability boundaries at every 0.1 sec. 3.5 Simulation Results and Analysis To study the voltage stability, the load increment started 20s after the initiation of simulation so that all the generators can reach to steady state by then Voltage Stability Indices Results As mentioned earlier, we simulated voltage instability situation by increasing the load. Two cases studies are designed for the simulation. In case-1, an infinite source, representing grid is 30

45 Figure 3.3: Run-time view of the IEEE 39 Bus system in single line diagram connected at Bus 39 and in case-2 it is replaced by a generator model. Fig. 3.4 depicts the voltage profile of few buses with respect to load change for case-1 (only a few results are shown). It can be seen that initially, the changes in voltages were very slow with the change of load. When load increased to more than 135%, the voltages started to fall rapidly. But the system did not collapse until the load reached to around 147%. After the load reaches to 147%, the whole system collapsed and almost all buses showed voltage instability simultaneously. Fig. 3.5 shows the output power of few selected generators during the simulation period. It is clear that as the load demand increases, infinite source representing the grid has supported the additional required power. Other generators generated steady power within their limit. But during the collapse point, all generators including infinite source went out of synchronization. On the other hand, reactive power generation was increasing according to the reactive load demand until all generators became unstable. Fig

46 1.2 Voltage Vs. Load 1 Voltage (p.u.) Load % V2 V4 V9 V16 V28 Figure 3.4: Voltage at each bus (case-1) shows how VSI and VCPI indicated stability situation. For case-1, where an infinite source is present in the network, it can be observed that both voltage stability indicators increases gradually with the increase of load. The rate of change of VSI and VCPI increased significantly after 135% load. Both indices identified line 2t1 (line connecting bus 2 and 1) and 1t39 as the weakest line whose value reached to 1 indicating that they reached to their maximum power transfer limit. One thing we can notice that although for both transmission lines, VSI and VCPI reached 1.00, the whole system did not collapsed. The whole system collapsed when VSI for line 16t19 and 25t26 reached to If we analyze the network structure from Fig.3.3, we can see that, even though line 2t1 and 1t39 reached their maximum power transfer limit, power from generators PG30 and PG39 were able to transfer through other lines to the system. On the other hand, when line 16t19 reached to its maximum power transfer limit, it actually limited power transfer from two large generators, PG33 and PG34 to the system. There were no alternate lines to transfer additional power from these generators to the system, as a result the whole system collapsed. We found that for case-2 where no infinite source is connected at bus 39, the whole system collapsed simultaneously when VSI and VCPI for line 16t19 reached 1.00 at 122% load. In this case, the system collapsed at 122% 32

47 Generators active power output (P) Generators Reactive power output (Q) MW Mvar Load % Load% PinfSource PG30 PG32 QinfSource QG30 QG32 PG36 PG38 QG36 QG38 Figure 3.5: Active power & reactive power of generators (case-1) load when line 16t19 reached its maximum power transfer limit, and both VCPI and VSI reaching to the value of We found that in this case, VSI & VCPI for line 2t1 and 1t39 did not reached to 1 but they ranked as 2nd and 3rd weakest line, respectively. From these findings, we can conclude that these two indicators, VCPI and VSI can identify voltage collapse point accurately and they can be a good situational awareness tool for control centers in wide area monitoring system (WAMS). They also provide real time ranking of lines indicating their vulnerability to voltage instability. Fig. 3.8 illustrates the differences between the two stability indices, VSI and VCPI values at 140% load i.e. at stable state just before the system collapses. It can be seen that both indices gave similar values for all lines. And both indices identified same lines as top two vulnerable lines before the system collapsed. However there are differences for other lines as VSI considers all three power types; on the other hand VCPI considers only active power. Such an example is shown in Fig. 3.9 where we found that VSI for line 2t1 reached to 1.00 before VCPI (top chart). From bottom chart 33

48 VSI vs. VCPI (case-1) VSI2t1 VSI16t19 VSI1t VSI39t9 Value VSI25t26 VCPI2t VCPI16t19 VCPI1t39 VCPI39t9 VCPI25t26 Load % Figure 3.6: VSI and VCPI for selected 5 transmission lines (case-1) of Fig. 3.9 we can see that, although before instability occurs, active power P was dominating the VSI, but during instability, reactive power based VSI became the highest. So VSI index reached to 1 before VCPI as it also consider reactive power based index. The reason VSI reaches to 1.00 earlier than VCPI is it does not consider line capacitance which provides limited reactive support Results of Voltage Stability Boundary in the P-Q Plane Voltage stability condition of a system can also be depicted by drawing voltage stability boundary in P-Q plane. Fig shows voltage stability boundary for transmission line 2t1 (left), 1t39 (middle) and 16t19 (right) at three different loading conditions. Dotted line is during 100% load (initial condition), dash-dotted line is during 135% load (stable condition) and continuous line is during 147% load (during system collapse). These parabolic lines are voltage stability boundaries which are drawn according to the formula mentioned earlier. The pointed dots are operating points at respective load conditions. The x-axis is representing P and y-axis is representing Q. We can ob- 34

49 VSI vs. VCPI (case-2) VSI2t1 VSI16t VSI1t VSI39t9 Value VSI25t26 VCPI2t VCPI16t19 VCPI1t39 VCPI39t9 VCPI25t26 Load % Figure 3.7: VSI and VCPI for selected 5 transmission lines (case-2) serve that as load is increasing the boundaries are shrinking and the operating point is getting closer to the boundary. During normal condition, the operating points (triangular and square points) are inside the voltage stability boundaries represented by dotted and dash-dotted lines. But after the system collapses at load 147%, the voltage stability boundary indicated by continuous line shrank significantly and operating point indicated by circular point overlapped with the continuous lined boundary for line 2t1 and went outside for line 1t39 and 16t19. So by using this tool, it is also possible to visualize voltage stability condition of the system Analysis of Results From these results, we can observe that voltage indices(vsi, VCPI) and voltage stability boundary in P-Q plane can effectively represent voltage instability condition of the network. However, each method has their own pros and cons in terms of effectiveness as described below: 35

50 Figure 3.8: line ranking comparison by VSI and VCPI (at 140% load, case-1) ❼ Between the two indices VSI and VCPI, we found VSI consider maximum power transfer capacity of all three types of power i.e. P, Q and S where as VCPI used only real power to derive the index. although it has derived four separate indices. ❼ For case-1, VSI and VCPI reached to 1.00 (for two transmission lines) earlier than the whole system collapsed. But for case-2 when VSI and VCPI reached to 1.00 for one transmission line whole system collapsed simultaneously. We found in both cases, VCPI and VSI identified same lines as the weakest. So VSI and VCPI can be used for weakest line ranking. ❼ VSI indicates voltage collapse earlier because it does not consider the shunt capacitance. VCPI considers shunt capacitance which provides limited reactive support and therefore, it shows voltage collapse at slightly later time. On the other hand, voltage stability boundary in P-Q plane has the real-time visualization of the maximum transferable P, Q and S and current operating point. So as the system approaches to collapse point, we can observe that the boundaries shrink toward operating point and also which part (P or Q) is shrinking the most can be easily identifiable. So this voltage stability visualization has more meaningful information for the control center. However we found the trajectory of the operating points and boundary is different for different lines (Fig. 3.11). So the visualization of the trajectory andtheoperatingpointforeachlinemayclutterthescreen. Forthat, byscreeningtheweakest line through VSI or VCPI, the stability boundary of that particular weak transmission line can be monitored. 36

51 Index Value VSI VCPI Load % Value S/S max Q/Q max P/P max Load % Figure 3.9: VSI and VCPI comparsion at line 2t1: Top Plot : VSI vs. VCPI; Bottom plot: Ratio comparison of P,Q,S to see which type of power got limited Results of Temperature Impact Study on Voltage Stability To observe how change in line resistance due to change in temperature affect voltage stability indices, we assumed resistances are given for ambient temperature of 20 C. To analyze variation in worst case we calculated line resistance at 75 C using equation (3.11) and used these updated line resistances in real time simulation model. Fig shows VSI value comparison for line 16t19 and 1t39 respectively. We can see that during low loading condition, the differences in VSI values for these two temperatures are very minimal. But at high loading condition when transmission lines are approaching toward their maximum power transfer capacity, the differences in VSI values are more significant. It is also noticeable that for line 16t19 the difference is more significant than line 1t39 and this is due to longer length of the line 16t19, having higher resistance value. It is also noticeable that the VSI value reached to maximum value earlier during temperature 75 C. We observed that at 75 C, voltage instability occurs at 146% loading condition whereas at 20 C, voltage 37

52 Q t1 x P x 10 8 Q t39 x P x 10 8 Q 16t19 x P x 10 8 Figure 3.10: Voltage Stability Boundary of line 2t1, 1t39 & 16t19 4 #10 8 2t # t39 Q 2 Q #10 8 P P #10 8 Figure 3.11: Operating point trajectory in P-Q plane for varying loading, Left chart: line 2t1; Right chart: line 1t39 instability occurs at 147% loading condition. That means at higher temperature, transmission lines reach their maximum transferable capacity earlier, resulting into earlier instability. 38

53 VSI Value for line 16t19 : at 20 C vs. 75 C VSI Value for line 1t39 : at 20 C vs. 75 C VSI16t19_20C VSI16t19_75C VSI1t39_20C VSI1t39_75C VSI Value 0.6 VSI Value Load % Load % Figure 3.12: VSI value comparison (20 C vs. 75 C) 3.6 Discussion By using PMU data we have studied the effectiveness of voltage stability index (VSI), voltage collapse proximity indicator (VCPI) and voltage stability boundary in P-Q plane for voltage stability contingency analysis and identified each tools advantages and limitations. Both VCPI and VSI indices properly identify weak lines and warns upcoming voltage instability ahead of time. Voltage stability boundary in P-Q plane is very effective for visualization in the control center as it provides comprehensive information for the operator. When the system approaches to instability, the boundary starts shrinking and the operating point moves toward the boundary. The stability boundary also indicates whether the collapse point is approaching due to whether P or Q is approaching the limit. Considering all these facts, it is reasonable to conclude that using both types of tools, simultaneously, a better picture of voltage stability situation can be assessed in the control center. VSI can be used for real-time weakest line ranking, and voltage stability boundary can be 39

54 used for real-time visualization of current voltage stability condition. So in our real-time voltage stability monitoring tool, we used VSI and voltage stability boundary for real-time visualization. A version of this chapter has been submitted to 47 th NAPS 2015 (October) conference (Accepted): Md Kamrul Hasan Pulok, M. Omar Faruque, Utilization of PMU data to evaluate the effectiveness of voltage stability boundary and indices. 40

55 CHAPTER 4 ALGORITHM FOR OPTIMAL PMU PLACEMENT One of the primary requirements of smart grid is gathering power system s state information through very fast digital communication. PMU devices provide the foundation of gathering very fast metered data as it can provide time synchronized sub-second phasor measurement data of the system. PMU devices can measure phase and sequence values of voltage and current at critical intersecting locations, normally in substations of a power grid. The PMU monitored buses are preselected through various studies to make the the power system network under study to be fully or optimally observable. Since PMU devices are expensive, an algorithm is required so that the whole system is observable by using minimum number of PMUs. In this study, a new algorithm is developed to identify minimum number of PMU requirements for the power system network to be fully observable. The proposed algorithm is explained in this chapter along with the comparative performance analysis. 4.1 Introduction The prerequisite of good state estimation is that the system must be fully observable from the available measurements. If the network is observable through optimally placed PMUs, a linear state estimator provides system states in a single iteration. The main objective of the optimal PMU placement is to determine the minimal number of PMUs to be installed at strategic locations so that the entire power system becomes completely observable for state estimation. Higher cost of PMU has prompted the necessity of identifying the optimal locations for PMUs for complete system observability. It is neither economically feasible nor necessary to install PMUs at all the substations in a power system. Numerous research publications [44]-[55] have proposed different mathematical and heuristic methods to address the issue of optimal PMU placement. Some of them are like simulated annealing method [44], Tabu search meta heuristic method [45], Integer Linear Programming (ILP) based methods [46] [50], Genetic algorithm based methods [51] [53], Particle Swarm Optimization (PSO) based methods [54] [55], topological observability based method [56] 41

56 etc. In this study, a new algorithm has been developed to solve optimal PMU placement problem for power system network. A dedicated graphical user interface has also been developed for implementing the algorithm. The performance of the proposed algorithm has been compared with others [55] and it is found that it can compute faster than the other algorithms. 4.2 Network Observability Analysis A bus is said to be observable if both voltage and current flows across a given bus are known. Therefore, a given power network is said to be fully observable if all of it s buses are observable through direct or indirect measurements. There are two methods to evaluate system observability: a) Numerical observability and b) Topological observability. A system is said to be numerically observable if design matrix H is well conditioned and is of full rank. Topological observability is based on graph theory approach where system is represented by non-oriented graph. A power system can be considered as topologically observable if at least one spanning measurement tree is of full rank [55]. Based on the fundamental laws of branch current and node voltage in circuit theory, several rules are applied to analyze the network to ensure that the network is fully observable. Following rules are used to estimate the observability of each bus. Rule 1: If a PMU is installed at bus 1, it s voltage phasor and current phasor of all incident branches are directly measured. Here bus 1 is directly observable. Rule 2: If voltage phasor and current phasor of an incident branch at bus 1 is known, then voltage phasor at bus 2 (connected to bus 1) can be calculated, thus making the bus 2 as indirectly observable. Rule 3: For known voltage phasors at both ends of a branch, current phasor of this branch can be calculated. For an example, referring Fig. 4.1, if we place a PMU at bus 2, the voltage at bus 2 and current flow through line 8 can be measured (rule 1). Thus bus 2 is directly observable. Bus 8 is indirectly observable as its voltage can be calculated using bus 2 voltage and line 8 current flow (rule 2). Similarly if a PMU is placed at bus 4, then the three connected buses 1, 5 and 9 will also be observable (rule 2). Using rule 3, current flows through line 5 can be calculated. And placing a PMU at bus 6 make the incident buses 3, 5 and 7 observable (rule 2). Using rule 3 current flow 42

57 1 4 Line 2 5 G Line 1 9 Line 3 Line Line 7 G G Line 5 Line 6 2 Line Line 9 Figure 4.1: 9-Bus test system through line 9 can be calculated. Thus having only 3 PMUs for this 9 Bus system, the whole system becomes fully observable (either by direct measurement or indirect measurement). But to identify PMU locations (in this case 2, 4, 6), solution of mathematical optimization is needed which is explained in the next section. 4.3 Proposed Algorithm to Identify Optimum PMU Locations PMU placement identification is a mathematical optimization problem. The objective of PMU placement problem is to find minimum number of bus locations so that the whole system becomes fully observable. The basic formulation can be found in literature [56]. Equation (4.1) is used to optimize the problem for N-Bus system. The constraint for the optimization problem is defined as (4.2). N minimize w i x i (4.1) i=1 [O] [b] (4.2) o 1 a 11 a a 1N x 1 o 2 a 21 a a 2N x 2 [O] = [A][X]. = (4.3) o N a N1 a N2... a NN x N 43

58 where x i are the elements of matrix [X] which has N 1 elements. It is a binary decision variable vector for PMU placement, whose elements are defined as (4.4), w i is the PMU installation cost at i th bus, [O] is the observability constraint vector function which is N 1 matrix and it s elements are nonzero if the corresponding individual bus are observable and zero if it is non-observable. The matrix [O] is obtained from the multiplication of matrix [A] and [X]. [A] is the binary connectivity matrix having N N size and it represents the bus connectivity information of the power system network. The elements of matrix [A] is defined as (4.5) and [b] is an unit vector of size N 1 as shown in (4.6). { 1 if PMU is placed at i th bus x i =,for i = 1,..,N (4.4) 0 otherwise 1 if m = n a m,n = 1 if bus m is connected to bus n (4.5) 0 otherwise 1 1 [b] =. (4.6). 1 In this study, w i is assumed unity, thus the optimal PMU placement problem is represented by (4.7) and the constraint is defined as (4.8). N minimize x i (4.7) i=1 o 1 1 o 2 1 [O] [b].... o N 1 To solve this mathematical optimization problem, a new algorithm has been developed. The optimum placement of PMUs are identified in two stages. The first stage is named as addition stage as in this stage, PMUs are added one by one so that the network becomes fully observable. The flow chart of this stage is shown in Fig The second stage is reduction stage as PMUs are reduced one by one maintaining the full observability of the network. The flow chart of this stage is shown in Fig (4.8) 44

59 Start Load Bus information (From Bus and To bus) information Initialize PMU placement binary matrix as X = 0 and Unity Matrix B =1 Caculate connectivity matrix (A) Initialize a variable as newt=a loop i < Bus Number? Yes Identify Bus with maximum connection loop n < Bus Number? Yes No Set newt(n,i) =0 n=n+1 No Set X(I,1) = 1 Is A*X >= B? Yes result = X No i = i+1 End Figure 4.2: Addition stage of proposed PMU placement optimization algorithm 45

60 variables from addition stage: result, X Initialize "PMU_required_matrix" as blank matrix and "valency" = [BusID X sum(a)' A*X] loop n <= Bus Number? Yes No busid = n; X(busID,1) = 1 loop i <= Bus Number? Yes Is X(i,1)==1? Yes store Unique rows from "PMU_required_matrix" to "UniquePMUMatrix" Checking Observability No Is min(a*x) > 0 No Is i==busid? Yes X(i,1)=1 X(i,1)=0 "MinimumPMUMatrix" = 1st row of "UniquePMUMatrix" Update X matrix (1 or 0) according to "MinimumPMUMatrix" No No Yes Identify location of PMUs by finding '1' in X matrix result = X X(i,1) = 1 Update "PMU_required_matrix" i = i+1 n = n+1 End Figure 4.3: Reduction stage of proposed PMU placement optimization algorithm 46

61 4.4 Developed GUI Tool The PMU placement optimization algorithm is implemented in MATLAB environment. A dedicated graphical user interface (GUI) has also been developed to identify the optimum locations of the PMUs as shown in Fig The input of this tool is a csv file containing the bus connectivity information of the power system under study. The csv file should contain two columns, first column contains the From Bus information and second column contains the To Bus information. Once the csv file is loaded, the Get PMU Buses button will run the algorithm and identify the optimum PMU bus locations. One of the useful features of this GUI tool is that Figure 4.4: GUI developed for optimum PMU placement identifier tool it will not only provide minimum number of required PMU bus information but also provide alternative PMU bus locations maintaining same minimum number of PMUs. For instance, the location of the PMUs for IEEE 39 Bus test system were identified by using the developed tool and it provides total 5 possible options as shown in Table 4.1. It can be seen from the table that, for 47

62 all options minimum number of required PMUs are 13. But the number of observable branches are different. The option which have most number of observable branches will provide redundant measurements which will help in good state estimation. On the other hand, it needs more C.T. transformers resulting into higher cost. So this feature of the tool is helpful in case when PMU locations are needed for least observable branches resulting into less required C.T. transformers. Table 4.1: PMU Placement Results for IEEE 39 Bus Option No. Min. Req. PMU Observable Branches Candidate Bus IDs for PMU Installation ,6,9,10,13,14,17,19,20,22,23, 25, ,6,9,13,14,17,19,20,22,23,25, 29, ,6,9,13,14,17,20,22,23,25,29, 32, ,6,9,13,14,17,22,23,25,29,32, 33, ,6,9,13,14,17,22,23,29,32,33, 34, PMU Placement Optimization Result The developed PMU placement optimization tool has been tested with many different IEEE test bus systems. For comparison purpose, placement results for four test systems are shown in Table 4.2. The comparison is performed with the method described in [55] which uses improved particle swarm optimization method. Since for same network, different combination of PMU placements are possible at the same minimum number of PMUs, there are differences at the PMU bus locations. However, it can be observed from the table that for all test systems, the minimum number of PMUs are same. Fig. 4.5 shows the computational time comparison between the two algorithms. It can be seen that the proposed algorithm is very fast in comparison to other methods. For instance, the BPSO (Binary Particle Swarm Optimization) method needs 658sec to get the results for IEEE 57 bus system, IBPSO (Improved Binary Particle Swarm Optimization) needs around 48

63 Table 4.2: Comparison of PMU placements for IEEE test systems Minimum Number of PMUs Optimum Locations Proposed Method IPSO Method Proposed Method IPSO Method IEEE 24 Bus 7 7 2,3,8,10,16, 21,23 IEEE 30 Bus ,5,6,9,10,12, 18,24,25,27 IEEE 39 Bus ,6,9,10,13, 14,17,19,20, 22,23,25,29 IEEE 57 Bus ,6,9,15,19, 22,25,27,29, 32,36,38,39, 41,47,50,53 1,2,8,11,15, 17,23 1,2,6,10,11,12, 19,23,25,27 2,6,9,10,13, 14,17,19,20, 22,23,29,37 1,4,6,13,19, 22,25,26,29, 32,36,39,41, 45,47,51,54 350sec, whereas the proposed algorithm needs only 0.567sec. That means the proposed algorithm is very fast to calculate the results which is very useful when calculating for very large power system. The developed tool ran in a normal laptop computer having Intel Core2Duo processor and 3GB RAM. The time required for BPSO and IBPSO are collected from [55]. Table 4.3: Computational time comparison with [55] 4.6 Discussion The main objective of this research is to develop a real-time voltage stability monitoring tool and analyze it s performance with real-time digital simulation of a power system. For this, IEEE 39 Bus power system is considered as the test system and a real-time simulation model has been built in Real-time Digital Simulator (RTDS ). To identify the location of PMU buses, the developed GUI of PMU Placement identifier has been used. As can be seen from Table 4.1 that we can have 49

64 five possible combinations to install PMUs. The option that provides highest observable branches (52) is chosen so that it offers redundancy in measurements which will help in good state estimation. Fig. 4.5 illustrates the locations of PMU installation with red circles. The PMU Bus IDs are 2, 6, 9, 10, 13, 14, 17, 19, 20, 22, 23, 25 and G G G G G G G G G G Figure 4.5: PMU locations of IEEE 39 Bus System A version of this chapter has been submitted to 47 th NAPS 2015 (October) conference (Accepted): Md Kamrul Hasan Pulok, M. Omar Faruque, Real-time Dynamic State Estimation Using Synchrophasor Data. 50

65 CHAPTER 5 REAL-TIME DYNAMIC STATE ESTIMATION Real-time dynamic state estimation is one of the important tools for modern control center operation in this smart grid era. Efficient and accurate dynamic state estimation is essential for a reliable operation of power system. Synchrophasor technology or PMU devices provide the technological advantage to perform efficient and accurate dynamic real-time state estimation. In this study, a real-time dynamic state estimation tool with graphical user interface (GUI) has been developed in MATLAB environment. Performance testing are performed by using real-time digital simulation of IEEE 39 Bus test system. The algorithm to perform real-time dynamic state estimation is explained in this chapter along with the comprehensive simulation results. 5.1 Introduction The process of estimating a value for an unknown system state variable based on the available measurements is known as State Estimation (SE). Since having measurements at every node of the system is not economically efficient, state estimator is being widely used to estimate the value of state variables which do not have measurement device. This is as an indispensable tool for on-line monitoring, analysis and control of power systems. Traditionally, entire power system measurements are obtained through Remote Terminal Unit (RTU) of Supervisory Control and Data Acquisition (SCADA) systems which have both analog and logical measurements. Logical measurements are used in topology processor to determine the system configuration. State estimator uses a set of analog measurements such as bus voltage magnitude, line current flows, real and reactive power flows etc. for estimating the unknown variables. Fig. 5.1 depicts the functional block diagram of SCADA system. There are many methods to perform SE. Two very good review papers are available on power system state estimation techniques [57] [58]. The computational procedure involved in SCADA based SE is an optimization function which can be first order or second order of the derivative [58]. The classical weighted least square method [59], the iteratively re-weighted least square 51

66 Figure 5.1: SCADA System State Estimation block diagram [61] method [60] are the first order methods. The second order method involves the evaluation of the Lagrangian Hessian matrix [58]. The methods mentioned above are static state estimators (SSE). In the dynamic state estimation (DSE), the system states are continuously monitored at the regular intervals. The Kalman filter, Leapfrog algorithm, non-linear observer technique and invariant imbedding method are also used to estimate the system states dynamically [58]. In SCADA based SE, the inclusion of power measurements makes the problem of state estimation highly non-linear, leading to iterative procedure. Therefore it is extremely time consuming and challenging for real-time implementation. With the advent of synchrophasor (PMU) technology, direct measurement of system states (voltage magnitude and phase angle) are possible with high precision synchronized manner which provides the facility to calculate real-time state estimation of the system. This method overcomes the drawbacks of SCADA based SE. Since PMU directly provides system state measurements, a non-iterative procedure like Linear State Estimation (LSE) can be used for estimating the states. With exclusive PMU measurements, the state estimation are done using LSE method. In this study, real-time state estimation of the IEEE 39 Bus test system are performed using PMU measurements. The output of real-time state estimation is bus voltage magnitude and phase 52

67 angles which is further utilized to monitor real-time voltage stability of the whole system. 5.2 Theoretical Background To have real-time state estimation, exclusive PMU measurements are required. Since PMUs can measure bus voltage magnitude and phase angle directly, the state estimation of other buses can be done linearly. This is called linear state estimation. However to perform state estimation with minimum error, PMU placement is very important in the sense that the network needs to be fully observable. It is also a normal practice to have redundant measurements so that if network topology changes due to fault or circuit breaker events, the redundant measurements can provide full observability. In this section, linear state estimation techniques considering positive sequence PMU measurements are presented Basic Principle of Linear State Estimation Phadke and Thorp [62] presented the formulation of the linear state estimation problem with the π-line model. Fig. 5.2 represents a π-line model of a transmission line neglecting the parallel conductance. Let s consider a transmission line connecting two buses i and j as shown in Fig 5.2. The line current I ij is positive in the direction flowing from bus i to bus j and line current I ji is negative in the direction flowing from bus j to bus i. The equations to calculate I ij and I ji are given by (5.1) and (5.3) respectively. (5.1) and (5.3) can be rewritten as (5.2) and (5.4) respectively from which we can relate current flows with state variables of this π-line model in matrix form shown in (5.5). Iij Vi Il y ij V j I ji Bus i Ii0 I j 0 y y i0 j 0 Bus j Figure 5.2: Transmission π-line model for calculating line flows I ij = I l +I i0 = y ij (V i V j )+y i0 V i (5.1) 53

68 I ij = (y ij +y i0 )V i y ij V j (5.2) I ji = I l +I j0 = y ij (V j V i )+y j0 V j (5.3) I ji = y ij V i +(y ij +y j0 )V j (5.4) [ ] Iij I ji = [ yij +y i0 y ij y ij y ij +y j0 ][ ] Vi V j (5.5) Now if this π-line model have PMU devices connected at both bus, then each PMU device will have voltage measurement of the connected bus and current flows through that bus. So having this information, matrix shown in (5.6) can be obtained which can also be represented as (5.7). V i 1 0 [ ] V j I ij = 0 1 Vi y ij +y i0 y ij V j I ji y ij y ij +y j0 [ ] z = [ ] II [ ] x M [ ] [ ][ ] ] where, M = Y A + [Y s (5.6) (5.7) (5.8) z = measurement matrix II = voltage measurement bus incidence matrix M = system characteristics matrix x = state variable matrix Y = series admittance matrix A = current measurement bus incidence matrix Y s = shunt admittance matrix It can be observed that the measurement matrix z is a vertical concatenation of the set of voltage and current phasor measurements, respectively. The system state matrix x is then related to the set of measurements by a vertical concatenation of the voltage measurement-bus incidence matrix II and a system matrix M composed of the series and shunt admittance matrices and the current measurement-bus incidence matrix. Rules to build the component of the matrix (5.7) is explained in the Methodology section. 54

69 5.2.2 Solution to the Linear State Estimation The derived state equation shown in previous subsection is a set of complex linear equations. The equation (5.7) can be written as (5.9) from which (5.10) and (5.11) can be derived. Equation (5.11) is the final equation which will be solved to get the state variables. Here [H] represents system topology matrix and [z] represents measurement matrix. Once the system topology matrix and measurement matrix are calculated, the states can be determined using only one mathematical operation. This allows us the calculation of the system state with exactly one iteration for every new set of measurements unlike traditional non-linear techniques which require an unknown number of iterations for each new state. [ ] [ ][ ] [ ] z = B x,where B = [ ] II M (5.9) [ ] [ ] 1 [ ] x = B z (5.10) [ ] [ x = (B T B) 1 B T][ ] z = [H][z] (5.11) 5.3 Methodology Formulating Matrices In this section, the rules to formulate matrices related to system topology matrix are explained. These matrices are 1) Current measurement-bus incidence matrix, 2) Voltage measurement-bus incidence matrix, 3) Series admittance matrix and 4) Shunt admittance Matrix. To illustrate the the process, a fictitious 4 bus system is considered and related matrices are formed for this system. The one line diagram of this system is shown in Fig It is found (by using the PMU placement identifier) that installing one PMU at bus 2 will make the whole system fully observable. So by installing a PMU at bus 2, line current flows through line 1, 3 and 4 are directly measurable by the PMU. Bus voltage is only measurable at bus 2. So in this example, total bus of the system is 4, the number of PMU is 1, the number of available current measurements are 3 and number of voltage measurement is 1. Considering this topology of the system, the algorithm to populate matrices are explained in the next subsections. 55

70 Bus 1 Bus 2 Bus 4 I 1 Line1 I 2 V 1 I 3 Line4 Line2 PMU Line3 Bus 3 Line Number Series Admittance Shunt Admittance Line 1 y 12 y 20 Line 2 y 13 y 10 Line 3 y 23 y 30 Line 4 y 24 Y 40 Figure 5.3: One-line diagram of a fictitious 4 bus system Forming current measurement-bus incidence matrix. The current measurement-bus incidence matrix represents the location of the available line current measurements in the network. The size of the matrix is determined based on the number of bus (b) of the system and the number of available current measurements (m) by PMU. The size of the matrix is m b. Following rules are used to formulate this matrix. 1. Rows of this matrix represents the serial number of current measurement. 2. Columns of this matrix represents the bus number. 3. If current measurement I k corresponding to row k, goes outward from the bus b n (corresponding to column n), then the matrix element (k,n) will be If current measurement I k corresponding to row k, goes inward of bus b n (corresponding to column n), then the matrix element (k,n) will be All other elements of this matrix will be zero. 56

71 In simplified language the rule is, for each current measurement, the bus from which the current is flowing outward, it s corresponding column will be 1. And the bus toward which the current is flowing, the corresponding column will be -1. By following these rules the current measurement-bus incidence matrix for this 4-bus system will be as (5.12). [ ] A = (5.12) Forming voltage measurement-bus incidence matrix. The voltage measurement-bus incidence matrix represents the location of the available voltage measurements in the network. The size of the matrix is determined based on the number of available voltage measurements (m) by PMU and the number of bus (b)of the system. The size of the matrix is m b. Following rules are used to formulate this matrix. 1. Rows of this matrix represents the serial number of voltage measurement. 2. Columns of this matrix represents the bus number. 3. If voltage measurement V k (corresponding to row k) is present at the bus b n (corresponding to column n), then the matrix element (k,n) will be All other elements of this matrix will be zero. In simplified language the rule is, for each voltage measurement, the bus at which voltage measurement present, it s corresponding column will be 1. By following these rules the voltage measurement-bus incidence matrix for this 4-bus system will be as (5.13). Since this system has only one PMU which measures voltage at bus 2, the size of the matrix is 1 4. [ ] [ ] II = (5.13) Forming series admittance matrix. This matrix elements are built by using the admittances of the lines which have current measurements by PMUs. It is a diagonal matrix with m m size. Here m represents the number of current measurements. Following rules are used to formulate this matrix. 1. For current measurement I n, the (n,n) matrix element is the series admittance of the line being measured. 57

72 2. All other elements of this matrix are zero. By following these rules, the Series Admittance matrix for this 4-bus system will be as (5.14). [ ] Y = y y y 24 (5.14) Forming shunt admittance matrix. This matrix elements are built by using the shunt admittances of the lines which have current measurements by PMUs. It is a diagonal matrix with m b size. Here m represents the number of current measurements and b represents the number of bus. Following rules are used to formulate this matrix. 1. If the current measurement I k is flowing out of the bus b n, then matrix element (k,n) is the shunt admittance of the line. 2. All other elements of this matrix are zero. By following these rules, the Shunt Admittance matrix for this 4-bus system will be as (5.15) Simulation Model and Test Setup ] 0 y 20 0 [Y s = 0 y 30 0 (5.15) 0 y 40 0 Fig. 5.4 illustrates the block diagram of the simulation setup. As mentioned earlier, the realtime power system model of IEEE 39 Bus test system was developed and run on Real Time Digital Simulator (RTDS ). Fig. 5.5 shows the one line diagram of the power system. The model used 2 racks of RTDS and the simulation ran at 50µs time-step resolution. The locations of the PMUs for the IEEE 39 Bus were identified by using the developed tool named PMU Placement Identifier. The tool shows many options for PMU placement at the same minimum number of required PMUs (as shown in Table 4.1). This study uses the option which have highest number of observable branches as it provides redundant measurements helping in good state estimation. For real-time PMU model simulation, RTDS has GTNET card along with GPS. The related PMU configurations for voltage and current measurements are shown in Table 5.1 and 5.2, respectively. In this study, P-class PMU model was used with data streaming rate of 10Hz. Then PMU devices measure phasors and stream the measurements using IEEE C protocol. The streaming phasor 58

73 measurements are then sent over the Internet using TCP protocol. A Phasor Data Concentrator (PDC) is used to receive the incoming time series phasor measurement data and store in a database server in real-time. Open source software named OpenPDC [16] has been used as PDC front end software which uses Microsoft SQL server 2012 as back end database server. MATLAB scripting has been used to develop the real-time state estimation tool. The developed tool fetches phasor measurements from SQL server in real-time and performs post processing and state estimation. The flow chart of the real-time state estimation tool is shown in Fig Communication System Internet TCP Protocol RTDS Power system Model Representing Remote Power System PMU measurements Phasor data streaming using IEEE C Protocol Phasor Data Concentrator (OpenPDC) Representing Control Center Microsoft SQL server 2012 Dynamic State Estimation Figure 5.4: Block diagram of simulation and test setup for the SE tool 5.4 Results In this study, a real-time state estimator tool has been developed that has three major functions. The task of the first function is to update network topology matrix. To obtain this matrix, it reads two input csv files: 1) Impedance table and 2) Measurement table. The impedance table contains the value of R, X and B for each transmission lines and transformers connected between buses. The measurement table contains the information related to PMU monitored bus and related lines. Based on these two tables, voltage measurement bus incidence matrix ([II]), current measurement bus incidence matrix ([A]), series admittance matrix ([Y]) and shunt admittance matrix ([Ys]) are calculated. Using these four matrices, topology matrix [H] is obtained. The second function of the 59

74 G 30 G G G G G G G G G Figure 5.5: One line diagram of IEEE 39 Bus system tool is to update real-time measurement matrix [z]. To update this matrix, this tool communicates with SQL server and fetches latest time-frame data and process measurement matrix [z] (Fig. 5.6). The third function of the tool is to perform state estimation using (5.11) and to visualize the results. It is found that the developed state estimation tool is very fast to calculate the states. The incoming rate of new phasor measurements from PMU devices are one measurement at each 100ms. And the average processing time of the state estimation tool is only 50ms. The algorithm is developed in such a way that, if the tool falls behind the timing, it will not miss any measurement, as the tool buffers latest three time-frame measurements. Fig. 5.7 illustrates the state estimation error distribution for the IEEE 39 bus test system. It can be observed that for only 7 bus the SE error is between 2% and 5%. For 29 bus, the SE error is below 0.5% which is very good. 60

75 RTDS Real-time Power System model run in 50usec time-setp Collection of Phasor measurements (V&I) by installed PMU Devices using C protocol Streaming of Phasor measurements using TCP protocol over the Internet at 10Hz sampling rate OpenPDC Receive the streaming Phasor measurements incoming over the Internet Process the measurements to store as time-series measurement SQL Server Store the Phasor measurements in a database table named "Time Series Measurements" Hard Disk (SQL Database server) State Estimation Tool Input "Impedance table" and "Measurement table" Calculate Network topology matrix [H] Perform State estimation Send query to SQL server to retrieve latest 3 time-frame measurement data Visualization Generate measurement matrix [z] Buffer database storing 3 time-frame measurements Yes All PMU data available? new time frame? Yes No Storing measurements Historic database storing previous 1000 time-frame measurements Figure 5.6: Flow chart of real-time state estimation process 5.5 Discussion In this chapter, a detailed explanation of the developed real-time state estimation tool has been provided. It is found that the developed state estimator with GUI can work in real-time and it can visualize state estimated voltages dynamically. In the next chapters, the usage of state estimated voltages in voltage stability analysis are explained. 61

76 Table 5.1: PMU configurations for voltage measurements Figure 5.7: State estimation error distribution 62

77 Table 5.2: PMU configurations for current measurements 63

78 A version of this chapter has been submitted to 47 th NAPS 2015 (October) conference (Accepted): Md Kamrul Hasan Pulok, M. Omar Faruque, Real-time Dynamic State Estimation Using Synchrophasor Data. 64

79 CHAPTER 6 REAL-TIME VOLTAGE STABILITY MONITORING TOOL 6.1 Introduction To visualize the voltage stability condition of the system a graphical user interface (GUI) is developed. The name of the GUI tool is given as Voltage Stability Monitoring (VSM) tool. Fig. 6.1 illustrates the functional block diagram and process flow of the developed VSM tool. Real-time digital simulation model of IEEE 39 bus run and streams PMU measurements over the Internet using IEEE C protocol. The phasor data concentrator- OpenPDC receives the streaming PMU measurements and store them in Microsoft SQL server The VSM tool then retrieve Communication System Internet TCP Protocol RTDS Power system Model Representing Remote Power System PMU measurements Phasor data streaming using IEEE C Protocol Phasor Data Concentrator (OpenPDC) VSM Tool VSI Calculation and Visualization Representing Control Center Microsoft SQL server 2012 Dynamic State Estimation Figure 6.1: Functional block diagram and process flow of VSM tool phasor measurements, process the measurements and perform state estimation. Then the estimated voltages are used to calculate voltage stability index (VSI) and voltage stability boundary for every 65

80 transmission lines. Real-time ranking of the lines based on VSI are also performed by the VSM tool. Then all the results and information are visualized in a graphical user interface. 6.2 Features of the Developed Tool The most challenging part of the developed VSM tool is to retrieve PMU measurements from Microsoft SQL server, run the state estimation, perform VSI calculations and finally visualize the information in real-time. To fulfill this objective the whole software is optimally organized and coded. The GUI is developed using MATLAB GUIDE toolbox. All the related codes are given in the appendix section of this thesis. Fig. 6.2 depicts the disconnected mode home screen of the VSM tool. The numbered labels identifies the elements of the GUI as follows: Figure 6.2: Home screen of voltage stability monitoring tool : Disconnected mode 66

81 1. Initialize Button: To reset the historical data and refresh the VSM tool. 2. Connect Button: To Connect/Disconnect with the SQL server. 3. Show One-line Diagram: To show the one-line diagram of IEEE 39 Bus system and visualize VSI index on the transmission lines in real-time. 4. Exit Button: To close the VSM tool. 5. Bus ID Selection List Box: To select BUS ID to visualize it s voltage trend. 6. Line Number Selection List Box: To select Line number to visualize it s VSI trend. 7. Timing Info: To show time required to process latest measurements. It is useful to understand how fast the VSM tool is running. 8. Voltage Table: This table shows the state estimated magnitude and phase of every buses in a tabular format. 9. VSI Table: This table shows the VSI of every lines in a tabular format. The table is continuously updated with the latest VSI ranking which is sorted from weakest line to strongest line. This table also shows the active and reactive power flow through each line. 10. State Estimated Voltage Bar Chart: This bar chart visualizes latest estimated voltage magnitudes of every bus. 11. VSI Bar Chart: This bar chart visualizes latest estimated VSI of every transmission lines. 12. Voltage Trend Line Chart: To visualize voltage trend comparing every bus. 13. VSI Trend Line Chart: To visualize VSI trend comparing every transmission lines. 14. Phase Angle Difference Bar Chart: To visualize phase angle differences of every bus in reference to bus Voltage Stability Boundary: To visualize weakest line s voltage stability boundary in P-Q plane. 16. Connection Status Indicator: Green line indicating Connected status, and red line indicating Disconnected status. There is a good feature added in this GUI, which is by right clicking any chart will give the option to enlarge the chart to full screen with full control. 67

82 Figure 6.3: Home screen of voltage stability monitoring tool : Connected mode 6.3 Simulation Results Extensive simulations are performed using real-time digital simulation of IEEE 39 Bus system and the performance of the VSM tool is evaluated. Fig. 6.3 shows the home screen of VSM tool in connected mode. Fig. 6.4 illustrates the one-line diagram view of the IEEE 39 Bus system inside VSM tool which visualizes the VSI information of transmission lines. It is found from the simulation that to calculate all the algorithms and finally to visualize the charts, the VSM tool requires on an average around 0.12s. As mentioned earlier, the PMU measurements are streaming at the rate of 10Hz sampling rate. That means at every 0.1s, a new set of measurements are available. So the VSM tool lags behind the PMU measurement timing by around 0.02s. To ensure that no measurements are missing, the VSM tool retrieves latest 3 set of measurements and put in 68

83 Figure 6.4: One-line Diagram view of voltage stability monitoring tool a buffer and maintains a historical database. Thus according to the algorithm, the VSM tool can lag behind the PMU measurements up to 0.3s without missing any measurements. However this timing is adjustable by adjusting the size of the buffer. It is found that at the current settings the VSM tool can visualize all information in near real-time with great accuracy. It should be noted that the simulation is performed at the computer which run both PDC server (OpenPDC and SQL server) and VSM tool. So the performance of the VSM tool s timing can be enhanced by providing a dedicated PC for the VSM tool. 69

84 CHAPTER 7 CONCLUSION AND FUTURE WORK 7.1 Key Contributions of This Thesis The objective of this thesis was to develop real-time voltage stability monitoring tool which can be utilized for control center operation. And the motivation of this research is to use available advanced technologies for the advancement of power system with the goal of achieving smart grid. With this motivation, there are multiple accomplishment of this research. Key contributions are highlighted as follows: 1. Proposed a new algorithm to identify optimum number of PMU requirements along with their locations in the power system transmission network. It is found that the developed algorithm is computationally very fast and efficient. 2. Developed a dedicated Graphical User Interface (GUI) with *.exe file for Optimal PMU Placement Identifier tool which can be used in other research. 3. A phasor data concentrator (PDC) is setup in the CAPS laboratory which can be further used for other research related to real-time PMU applications. The PDC works with the combination of OpenPDC and Microsoft SQL server Developed a real-time dynamic state estimation tool using Synchrophasor technology which can be utilized in other research related to Synchrophasor technology. 5. In this research, developed a real-time voltage stability monitoring (VSM) tool with graphical visualization. Control centers can easily monitor the systems condition by using this tool and can take precautionary actions if needed. The software architecture is modular which gives the easier flexibility to add any future algorithms or tools to be integrated with the existing GUI. 7.2 Future Work As mentioned earlier, the objective of this research is to explore available advanced technologies and apply them in the development of power system. Thus this study explored the applications of 70

85 Synchrophasor (PMU) technology and used it for real-time dynamic state estimation and finally visualize voltage stability margin of power system transmission network. The developed GUI tool in this study can visualize various information in charts in real-time. The GUI tool is developed according to modular architecture. So new function can be built and integrated easily with the current GUI in MATLAB environment. In addition, the PDC server setup in the CAPS laboratory can be used in many real-time simulation projects which require usage of PMU. For future functions and features of this tool, various real-time applications of PMU can be explored and implemented. Fo instance, future research can be done on real-time Power oscillation monitoring, Wide area frequency monitoring, Power swing detection and protection, Load shedding under Remedial Action Schemes (RAS), Automatic Generator Shedding, Detection of power system inter-area oscillations etc. 7.3 Conclusion In the literature there are many studies already available in the field of Synchrophasor technology, state estimation and voltage stability analysis. But most of the studies are at theoretical level and most of their applications found limited to static and quasi static level. Traditional SCADA measurements and control center operation are based on system snapshots whose time range can be from 2s to 10s. This study explored the available technologies and made a way to utilize those technologies for real-time application. The real-time information of the system can be utilized in many contingency analysis like voltage stability analysis. Having real-time voltage stability contingency information of the system can help the control center to avoid unwanted system blackout. To develop real-time voltage stability monitoring tool, this study utilizes PMU measurements collected from optimal PMU locations. The streaming phasor measurements are stored in Microsoft SQL server using OpenPDC. A real-time dynamic state estimator tool has been developed in this study to estimate magnitude and phase of voltage of unmonitored buses. Thus the tool provides voltage measurement of whole system in real-time which is further utilized to perform real-time voltage stability analysis. The voltage stability monitoring tool calculate voltage stability index (VSI) of each line and performs real-time ranking, sorting from weakest line to strongest line and visualize the results in one-line diagram. Also it visualizes the trend of the VSI index, bus voltages and phase angle differences. This tool calculates the voltage stability boundary in P-Q plane and visualize 71

86 the boundary for weakest three lines. Successful simulation and testing are performed using this tool achieving the research objective. 72

87 APPENDIX A CONFIGURATION OF OPEN-PDC In the developed simulation model, real time phasor measurements will continuously stream over the Internet from PMU devices. So a real-time time-series phasor data storage system is needed which will receive those phasor data in real-time and store in a database system. This whole system is called Phasor Data Concentrator or PDC. There is an open source PDC software available which is called Open PDC [16]. In this study OpenPDC has been setup in CAPS laboratory which stores phasor data in Microsoft SQL database server in real-time. In this appendix, the procedures need to be followed to configure this PDC server is provided. A.1 Installation of OpenPDC The OpenPDC software is freely download-able from [16]. During the installation, certain procedures need to be followed. This software runs in windows platform and can be used with Microsoft SQL Server, MySQL, Microsoft Access, Oracle or SQLite system as database server. During the installation, we need to select the database system in which all the measurements will store. In that step, we need to select ADO: archives measurements to any ADO data source (e.g., OSI-PI via ODBC) (Fig. A.1). We selected this because for real-time usage it is most efficient and fast. ADO stands for ActiveX Data Objects and developed by Microsoft. We could have use CSV: archives measurements to a CSV file, but it has following limitations: 1. OpenPDC needs comparatively long time to write data in CSV file, thus it loses synchronization of data between receiving of phasors and writing to CSV. This results into putting a limit in number of PMUs to be configured if we want real-time operation. For case where real-time operation do not need, the csv file can be used. 2. In CSV file Time stamps are in UNIX epoch format [64]. Thus further processing required in MATLAB or other post processing software for which delay may occur. 3. The CSV file become very large easily and reading data by MATLAB or other software need long time. Thus real-time characteristics will not me there. So we used ADO database system 73

88 Figure A.1: Database type selection during the installation of OpenPDC as primary database or phasor measurement archiver which is very fast, efficient to store data and reliable. After finishing the installation, the OpenPDC need to be configured so that we can view stored phasor measurement data in Microsoft SQL server management studio by SQL query. If we do not configure this step, still data will be stored but may not be viewable in SQL server by query. So for this configuration, we need to browse by selecting menu Outputs Manage Historian Instances. Then we need to select Add New and put field values as shown in the Fig.(A.2). In the connection string field we need to put the field values as shown in Fig. A.3. After putting all values we have to click Initialize button to initialize the historian database in SQL server. More details about creating above script can be found in discussion section of OpenPDC website [65]. 74

89 Figure A.2: Configuration of Historian instances Figure A.3: Connection String 75

90 A.2 Configuring PMU Devices in OpenPDC OpenPDC can connect with remote PMU devices which are using IEEE C protocol and streaming data over the Internet. In our IEEE 39 Bus Real-Time Digital Simulation(RTDS) model, 13 PMUs are placed at different preselected locations which are streaming 52 phasor data in realtime using IEEE C protocol over the Internet. Among 52 phasors, 13 are positive sequence voltage phasors and 39 are positive sequence current phasors. To configure a PMU device in OpenPDC, we need four information of each PMU device which are used in RTDS model: 1. IP address of the PMU 2. Port number 3. Device ID 4. Device Protocol like IEEE C OpenPDC supports other 11 PMU streaming standards along with IEEE C as shown in Fig. A.4. We can use Input Device Wizard button in OpenPDC home screen by which we can Figure A.4: The names of the PMU streaming standards supported by OpenPDC configure a PMU in three steps. Fig. A.5 illustrates the step 1 of PMU connection configuration window. In this step we put device IP address, port number in following format in connection string text box: 76

91 transportprotocol=tcp;server= ; port=4711; interface= ; islistener=false Figure A.5: PMU connection configuration window of OpenPDC (step-1) In this above code snippet, we need to put IP address and port number according to their respective PMU IP address and port number. Next we need to put respective device ID in Device ID Code input text box. Then we select Device protocol as IEEE C from the drop down list. Fig. A.6 shows the step-2 of the configuration process. Before proceeding this step, we have to make sure that the PMU devices are currently running in the simulation model and streaming phasor data. After confirmation, we need to click Request Configuration button which will try to connect with the PMU device using IP address and device ID given in the previous step and will retrieve required phasor channel configuration information. In the third step we can modify the phasor names if we want to. We kept as it suggest and press Finish button. After finishing the 77

92 Figure A.6: PMU connection configuration window of OpenPDC (step-2) step-3 we should have a configured PMU device in OpenPDC. To verify the status of the PMU, we will select Graph Measurements button from home screen of OpenPDC. This will show a window depicted in Fig. A.7. It is a graphical real-time measurement window of OpenPDC where selected phasor data under PMU device are visualized. In the figure, voltage magnitude of PMU1 2T1 is shown, however other data such as voltage angle, current magnitude, current angle, and frequency data can also be selected. If PMU devices are working indicated by green circle, then the OpenPDC will store phasor data in SQL server in real-time. In next section, the process of configuring SQL server and using SQL server for getting stored raw phasor measurement data are explained. 78

93 Figure A.7: List of PMU measurements for Graphical Real-time visualization 79

94 APPENDIX B CONFIGURATION OF MICROSOFT SQL SERVER 2012 DATABASE Microsoft SQL Server Express database engine and Management Studio are available for free from the Microsoft Download Center. If Visual Studio is installed, SQL Server Express may have been installed during the Visual Studio installation. We can also download and install SQL Server Express and Management Studio together. The link to the current SQL Server 2012 Express downloads is given in [66]. Fig. B.1 is showing the server connection authentication window of Microsoft SQL Server Management Studio. Since we are using local server, we will select default server, whatever it appears in the server name. Authentication should be selected as Windows Authentication. Now we should be able to connect to the local SQL server. After connecting to the SQL server, we will see that there is a database named openpdc under which several Tables are present as shown in Fig. B.2. All these tables are related to storing data of configuration parameters of OpenPDC. Initially we will not find any table where time series phasor measurements are stored. To be able to view those measurement data, we have to create a table. The important thing is that we have to be consistent with the naming of the SQL server table and its column name with the OpenPDC Historian instances configuration. As previously shown in Fig. A.2, we wrote the script as shown in Fig. A.3 in the Connection string text box. If we look into the last two line, we can observe that it has the table and related column name in which OpenPDC will store data in SQL server. Therefore, in SQL server, we need to create a table with same table name and column names so that SQL server can store phasor measurement data. For this we need to run a New Query and execute the script-1 (Fig. B.4) in the code section as shown in Fig. B.3 : After this procedure, OpenPDC will store phasor measurement data in SQL server tabular format. If the PMU devices are streaming measurement data, then OpenPDC will write those phasor measurements in real-time in the table named TimeSeriesMeasurement of SQL server. To view latest 1000 phasor measurements in SQL server, we can execute the script- 2 as shown in Fig. B.5. If we look into the data returned by the SQL query (Fig. B.6), we 80

95 Figure B.1: Connect to Server window of Microsoft SQL Server Management Studio will find that Timestamp column have the time info in millisecond range. Values column showing measurements in decimal format. But SignalID is very long and in unreadable format. Whenever we configure a new PMU device in OpenPDC, it assigns a unique SignalID for each measurement which is quite long and unreadable for human eyes. However there is also a more easily readable ID created by OpenPDC called PointID for each phasor measurement. This information along with other information are stored in dbo.measurement table as shown in Fig. B.7. We found that for each PMU device, OpenPDC stores 40 distinct measurements as shown in Fig. B.8. Also we noticed that, magnitude and angles have separate IDs and stores in different rows. In our simulation, we have 13 voltage measurements, 39 current measurements, each have one magnitude measurements and one angle measurements. So we will have total ((13+39) x2) 81

96 Figure B.2: Home screen of Microsoft SQL Server Management Studio = 104 unique measurements for each time frame. Since we currently do not need other statistical measurements, only need voltage and current measurements, we need to create a separate table which will have the voltage and current PointIDs we need for post processing. We named this table as RequiredMeasurements and created by executing script-3 as shown in Fig. B.9. We have to be sure that we run this script only once and after executing, we need to refresh the database to see if the new table appeared in the left side. If not appeared, we have to disconnect the SQL server and connect to the server again. Next, we need to execute script-4 as shown in Fig. B.10 to populate the previously created RequiredMeasurements table. This query will filter only voltage magnitude, voltage angle, current magnitude and current angle by their related PointID, DeviceID, SignalID, PointTag & description of each PMU device. We can run this query whenever we want to run and whenever we configure a new PMU device. Fig. B.11 shows the partial view of the results after executing the script-4. Now we have a table in SQL server which stores all 82

97 Figure B.3: Executing a new query to create a table named TimeSeriesMeasurement Figure B.4: Script-1: To create a table named TimeSeriesMeasurement the signal IDs of voltage and current measurements of all PMUs configured in OpenPDC. There may be case where additional PMUs are configured in OpenPDC and not all PMU measurements are required in post processing. Like in our case, we need only 13 voltage phasors and 39 current phasors for state estimation which will be processed by MATLAB tool. So we created a table as 83

98 Figure B.5: Script-2: for Selecting Latest 1000 Rows from TimeSeriesMeasurement table Figure B.6: Retrieval result of Latest 1000 measurement in SQL server shown in Fig. B.1 in excel and identified the input element of Z matrix which will be used in our state estimation. Then for each elements, we identified PointID related to the magnitude and angle s Point Tag by running script-4 or from the contents of dbo.requiredmeasurements table. From the Z Matrix (Fig. B.1), we identified required PointIDs and wrote in following 84

99 Figure B.7: Contents of dbo.measurement Table in SQL server Table B.1: The formation of zmatrix with PMU PointIDs format in a text file: 54, 55, 56, 57, 96, 97, 136, 137, 176, 177, 214, 215, 216, 217, 256, 257, 296, 297, 336, 337, 374, 375, 376, 377, 416, 417, 454, 455, 456, 457, 496, 497, 536, 537, 574, 575, 576, 577, 616, 617, 656, 657, 694, 695, 696, 697, 736, 737, 776, 777, 814, 815, 816, 817, 856, 857, 896, 897, 934, 935, 936, 937, 976, 977, 1016, 1017, 1054, 1055, 1056, 1057, 1096, 85

100 Figure B.8: Types of measurement data stored for each PMU device (example for PMU6 14T13) Figure B.9: Script-3: for creating RequiredMeasurements table 86

101 Figure B.10: Script-4: for populating data in RequiredMeasurements table Figure B.11: The contents of dbo.requiredmeasurements Table 1097, 1134, 1135, 1136, 1137, 1176, 1177, 1216, 1217, 1254, 1255, 1256, 1257, 1296, 1297, 1336, 1337, 1374, 1375, 1376, 1377, 1416, 1417, 1456, 1457, 1494, 1495, 1496, 1497, 1536, 1537, 1576, 1577 Then we need to execute Script-5 (Fig. B.12) in SQL server to create a table named Z Matrix which will store only the phasor measurements that will be used in Z Matrix for state estimation. After the execution of script-5 once, we need to execute script-6. The script-6 is to update the Z Matrix table. Before executing this query, we have to modify the query according to our phasor measurement requirement. We need to put the previously collected PointIDs inside the first 87

102 Figure B.12: Script 5: for creating Z Matrix table bracket of PointID IN(). So based on these Point IDs Z Matrix table will be updated. Fig. Figure B.13: Script-6: for Updating the Z Matrix Table B.14 is showing the contents of the Z Matrix table after the execution of script-6. The difference between Z Matrix table and RequiredMeasurements table is that, RequiredMeasurements holds voltage and current measurements of all PMU devices configured in OpenPDC. Z Matrix table holds only the voltage and current measurements of selected PMU devices. These are done so that we don t have to execute long and repetitive query from MATLAB to the SQL server. Since we will use real-time data transfer from SQL server to MATLAB, these predefined tables in SQL server will reduce the execution timing of each query from MATLAB. Thus interfacing between 88

103 MATLAB and SQL server will be very fast and efficient. So after all these step, we have completed the interfacing between OpenPDC and SQL server; also made ready our SQL server database for easier interfacing with MATLAB. Next appendix explains the procedure of interfacing MATLAB with SQL server. Figure B.14: Partial view of the contents of Z Matrix Table 89

104 APPENDIX C INTERFACING MATLAB WITH SQL SERVER DATABASE C.1 Setting up the Real-time Interface The MATLAB has Database Toolbox in APPs section which can be used for exchanging data between relational databases and MATLAB. We can use SQL commands in MATLAB script to import and export data. The toolbox supports ODBC-compliant and JDBC-compliant databases such as Microsoft SQL server, MySQL, Oracle, Sybase and Informix. In the documentation of the MATLAB website, a good tutorial is given, explaining the procedure of using Database toolbox for importing data form database server and exporting data back to the database server [67]. It should be noted that MATLAB version 2013b and later are only supported the following configurations we used in our study. In our study, we used MATLAB 2014b. In the first step, we need to configure a driver and a data source. In our simulation model, we used ODBC driver. A Data Source Name (DSN) is the logical name that is used by Open Database Connectivity (ODBC) to refer to the drive and other information that is required to access data. This name is used to connect to an ODBC data source, such as a Microsoft SQL Server database. Fig. C.1 shows the compatibility requirement among the operating system, database, ODBC driver and MATLAB 32 bit and 64 bit versions. The grey boxes represents 64 bit version and white boxes represent 32 bit version. According to the Fig. C.1, the bitness (32-bit or 64-bit) of MATLAB, ODBC driver and the database must match. Otherwise MATLAB displays an error. In our study, we used 64 bit version of MATLAB, ODBC driver, SQL Server Database and Windows operating system. To check the bit version of each software, following method can be followed: MATLAB: It is possible to check from startup splash screen or Help about menu or by typing following command: computer( arch ) Operating System: Control Panel\All Control Panel Items\System ODBC Driver: If OS is 32 bit, installed ODBC driver will be 32 bit. If OS is 64bit, both 32bit and 64bit 90

105 Figure C.1: Compatibility requirement of MATLAB database toolbox [67] ODBC driver is installed. SQL Server: Run SELECT command in query in SQL Server. After version checkup and meeting the compatibility requirement, we have to set up a data source. In MATLAB, we can set up a new ODBC data source by using Database explorer app. Followings are the step by step procedure which are also available in [67]: 1. We need to open Database Explorer by clicking the Apps tab on the MATLAB Tool strip. Then, select Database Explorer from the Database Connectivity and Reporting section in the apps gallery. Alternatively, we can enter dexplore at the command line. If no data sources are set up, a message box opens. We have to click OK to close it. Otherwise, the Connect to a Data Source dialog box opens. We have to click Cancel to close this dialog box. 2. Then we have to click the Database Explorer tab, and then select New ODBC (Fig. C.2). It will open ODBC Data Source Administrator dialog box (Fig. C.3). This can also 91

106 be opened from windows control panel: Control Panel\Administrative Tools\Data Sources (ODBC). 3. Then we need to click the System DSN tab and then click Add. When setting up an ODBC data source, we can use a User DSN or System DSN. A User DSN is specific to the user on a machine. Any data sources a user defines under User DSN are seen only by that specific user. Conversely, a System DSN is not specific to the user on a machine. Any data sources a user defines under System DSN on a machine can be seen by any user who logs into that machine. The ability to set up a User DSN or System DSN might depend on the database and ODBC driver we are using. 4. A list of installed ODBC drivers appears in the Create New Data Source dialog box (Fig. C.4). We need to select SQL Server Native Client 11.0 and then nedd to click Finish. 5. After Finishing the create new data source selection, it will pop up a new dialog box named Microsoft SQL Server DSN Configuration (Fig. C.5). 6. Inthisdialogbox, Fig. C.5, wewillenteranappropriatenameforourdatasource. Weusethis name to establish a connection to our SQL server database and it can be any arbitrary related name. In our study, we entered OpenPDC as the data source name in the Name field. Then we entered Open PDC PMU Data Storage as the description in the Description field. Then in the Server field, we need to select the database server for this data source to be used. It can be local SQL EXPRESS server or other networked SQL server. In our case we used local SQL server, meaning SQL server in the same PC of the ODBC driver, and in our case it is: CAPS-RM230-05\SQLEXPRESS. We need to consult our database administrator for the name of our database server. Then we need to click Next for next step. 7. In the step 2, Fig. C.6, we will select With Integrated Windows authentication to connect to Microsoft SQL Server. If we want we can also use specific user ID and password which needs to be log in SQL server. 8. In the step 3, Fig. C.7, we need to select the specific database of the SQL server in which we want to connect. Because in SQL server, there are other databases excluding openpdc database, this dialog box will fetch available databases in SQL server and will show in a drop down list box. We need to select our required specific database. In our study, we will select openpdc as the default database. And also, we will make sure that, the Application intent is selected as READWRITE. 9. In the step 4, Fig. C.8, a summary window will appear showing all the configurations we set up for the new ODBC Microsoft SQL server. It will also have a button to Test Data Source. By clicking this we will get a test results. This test result should be successfully completed to be able to import data from SQL server database to MATLAB. 92

107 10. Now our ODBC data source is set up. To connect to the SQL server database, we can use MATLAB GUI of Database Explorer or use command prompt. Figure C.2: Creating New Data source using MATLAB Database explorer Figure C.3: ODBC Data Source Administrator dialog box 93

108 Figure C.4: Create a New Data Source dialog box C.2 Importing Data Using MATLAB Database Explorer GUI Initially after the ODBC data source setup, it is suitable to use Database Explorer GUI to test the interface between MATLAB and Microsoft SQL Server. As shown in Fig. C.9, we need to go Database Explorer app from APPS section of MATLAB. Then click Connect menu which will bring a dialog box showing available data sources. We will find that our data source name will appear in the drop down list which we configured in previous section of new ODBC data source configuration. In our study, we configured data source name as openpdc, and so it appeared in the drop down list. Since we used windows integrated login to the SQL server, we will leave the user name and password as blank, and click Connect button. Now it will connect to the openpdc database of SQL server and show all tables in the Database Explorer window of MATLAB. It should be noted that some error message like [Microsoft] [ODBC Driver Manager] Invalid string or buffer length may appear as shown in Fig. C.10. This error may come if we use earlier MATLAB version like 2013a or MATLAB Also it may appear if bit version(32/64-bit) is not compatible. 94

109 Figure C.5: Microsoft SQL Server DSN Configuration, step 1 Or in 2014b, we found this message appear when we try to connect with Database server as soon as MATLAB starts. So we need to give MATLAB 2014b some time to initialize all its tool set for further operation. After successful connection setup with SQL server, we can select any table and column to view its contents as shown in Fig. C.11. This figure is showing the contents of Z Matrix table as we selected in the left side. It is noticeable that the GUI is showing only 25 rows among 104 rows. This can be controlled by preferences of the Database explorer. This number is just to set up Data preview. When we import data in MATLAB workspace, all 104 rows will appear. Now, to import the selected values of the table and columns, we have to select data type of the variable which will appear in MATLAB workspace. MATLAB can import these tabular data in various formats like, Cell Array, Numeric, Structure, Table and Dataset. For our study, Cell Array is suitable and adequate. So we will select Cell Array. Then if we select Import it will import the selected data in MATLAB workspace and the name of the variable will appear as untitled as shown in Fig. C.12. If we want to modify title of the variable, we can do it in Data explorer GUI, Data preview section. It is noticeable that, the cell array size is 104 5, that means all the rows of the Z Matrix table are imported in the MATLAB workspace. 95

110 Figure C.6: Microsoft SQL Server DSN Configuration, step 2 C.3 Importing Data Using MATLAB Command and Scripting Importing Data using MATLAB command prompt or scripting is easier. We can use following code to connect to the openpdc database of SQL server. The last two part are kept blank with in the inverted comma since we are using windows integrated user login. If we used specific user log in, then we have to write user name and password in the command. conn = database.odbcconnection( openpdc,, ); Now there is a way to generate an automatic script of importing data to MATLAB Workspace by using Database explorer GUI. In the drop down menu of Import of Database Explorer GUI, we need to click Generate Script. It will generate a script which can be later modified according to our need and save in a *.m file. Fig. C.13 illustrates the auto generated script by Database explorer for the data import operation performed in using Database explorer GUI described in previous section. We can then modify the code according to our need which is described in next appendices. 96

111 Figure C.7: Microsoft SQL Server DSN Configuration, step 3 Figure C.8: Microsoft SQL Server DSN Configuration, step 4 97

112 Figure C.9: Connecting to SQL server using MATLAB Database explorer GUI Figure C.10: Common connection failure error message 98

113 Figure C.11: After successful connection with SQL server, all tables and selected table values are appeared in Database explorer 99

114 Figure C.12: Matlab Cell Array variable in Workspace after Data Import 100

115 Figure C.13: Auto generated script by Database explorer GUI 101

116 APPENDIX D MATLAB CODE OF OPTIMAL PMU PLACEMENT ALGORITHM D.1 Graphical User Interface (GUI) Design A dedicated, feature rich graphical user interface has been developed for Optimal PMU placement identifier tool. The GUI is built using GUIDE tool of MATLAB. Fig. D.1 illustrates the GUIDE design of the optimal PMU placement identifier tool. Fig. D.2 illustrates the complete Figure D.1: GUIDE design of the optimal PMU placement identifier tool GUI of PMU placement identifier tool. This tool has following features: ❼ It can load BUS information data in csv file format. 102