Dynamic load model and its incorporation in MATLAB based Voltage Stability Toolbox

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1 Dynamic load model and its incorporation in MATLAB based Voltage Stability Toolbox Sujit Lande, Prof.S.P.Ghanegaonkar, Dr. N. Gopalakrishnan, Dr.V.N.Pande Department of Electrical Engineering College Of Engineering Pune Shivajinagar, Pune, INDIA. Abstract Economical system expansion strategies and reliable system operation, requires comprehensive system simulation studies. For this various simulation tools are available, which use static load models. This paper deals with the impact of load modelling on the validity of power system studies mainly concentrating on voltage stability. VST toolbox of MATLAB is a powerful tool and is convenient to use. This is used for load flow, small signal stability, transient stability and voltage stability analysis. Presently static load model is considered for all these analysis. However static load models are not accurate enough for capturing the dynamics of network. So inclusion of dynamic load model instead of static load model in the VST for various analysis is presented in this paper. For determining the dynamic load parameters, measurement based approach is preferred due to its numerous advantages over the component based approach. Sweden based measurement data with large disturbance voltage variations is used for determination of dynamic load model parameters. In place of static load model, dynamic load model is included in the VST. Voltage stability analysis is carried out on standard IEEE 14 system with VST including static load model and dynamic load model. Voltage collapse points on PV curve of test system in both the cases are compared under various conditions with different dynamic load parameters. The paper presents a methodology of implementation of dynamic load modelling in voltage stability toolbox for large disturbance voltage stability studies. Keywords Voltage Stability, Power System Simulation Toolbox, Measurement based dynamic Load Modelling approach. 1 INTRODUCTION There is rapid increase in the electric energy demand worldwide. In order to fulfil the energy demand, it is necessary to operate energy systems in the most effective way. Therefore the determination of accurate transfer limits of power will pay an important roll in maintaining a secure, stable and economic operation of power system. The more efficient use of transmission network has already led to a situation in which many power systems are operated more often and longer close to voltage stability limits [1]-[2]. Voltage stability is a subset of overall power system stability. Voltage stability is a wide range of phenomena. It is convenient to use a simulation tool to analyse voltage stability problems. In education and research, Matlab based voltage stability toolboxes provides common platform to analyse the voltage stability with static load models [3]-[4]. Since dynamic load models are more accurate in capturing the dynamics of network compared to static load models. More accurate voltage stability of power system can be achieved by incorporation of dynamic load models in place of static load models. In operation planning, the use of inaccurate load model may yield optimistically stable operating scenarios, whereas actual operation under those scenarios may result in catastrophic blackouts. Therefore, dynamic load models are needed to predict the accurate voltage stability [5]-[7]. This paper addresses one important component in the study of voltage stability and voltage collapse, namely dynamic load models. This paper discusses the nonlinear dynamic load model development as a set of mathematical equations and determination of load parameters. Methodology to calculate the dynamic load model parameters based on measurement based approach in large disturbance voltage stability studies is described. The structure of paper is as follows. Section 2 discusses basic concept of voltage stability. Section 3 reviews the available power system simulation toolboxes. Section 4 and 5 gives brief idea about general load modelling and developing the dynamic load models which are to be incorporated in toolboxes. Section shows the simulation results with IEEE 14 system. Section 7 and 8 discusses the conclusion and Future work in this research area. 2 VOLTAGE STABILITY ANALYSIS Voltage stability is the ability of a power system to maintain steady acceptable voltage at all buses in the system under normal operating conditions and after being subjected to a disturbance [2]. Voltage instability is the absence of voltage stability & results in progressive voltage decrease/ increase. A system enters a state of voltage instability due to disturbance, load demand, uncontrolled drop in voltage. Conditions for Voltage instability are as follows: 1. The bus magnitude voltage decrease when reactive power injection at the same bus 1

2 increased. In the other words, An V-Q sensitivity is negative for at least one bus. 2. Progressive drop in bus voltage beyond the acceptable limit. P-V curves (and Q-V curves) are more general method of assessing the voltage stability. The P-V curve method is also used for large meshed network where P is the total load in area and V is the voltage at a critical or representative bus. Voltage stability is concerned with load areas & load characteristics. Determination of large disturbance voltage stability requires examination of dynamic performance of the system over a period of time. Study period of interest may extend from few seconds to tens of minute. 3 POWER SYSTEM TOOLBOXES Simulation tools for power system stability analysis can be divided into two classes commercial programs and customized toolboxes developed for education and research. Various commercial programs, are available in the market. These programs provide detailed component/system models and computationally efficient algorithms for the analysis. [3]-[4] However, they are not suitable for educational and research purposes since they usually do not allow modification or addition of new component models and algorithms. For education and research purposes, flexibility and ability of easy prototyping are often more crucial aspects than computational efficiency. In the area of power systems, a MATLAB [8] software package has become one of the most popular scientific programming languages for research and teaching applications. 3.1 Toolboxes for power system analysis: Several Matlab-based programs are available in power system simulation, modelling and analysis, such as Power System Toolbox (PST), Electromagnetic Transients Program in Matlab (MatEMTP), Power Analysis Toolbox (PAT), Educational Simulation Tool (EST), Sim Power Systems (SPS) and Matlab Power System Simulation Package (MatPower). Table 1 gives a comparison of the currently available Matlab-based tools for power system analysis and VST. The features illustrated in the table are: load flow (LF), voltage stability analysis (VSA), small-signal stability analysis (SSA), time-domain (TD) simulation, electromagnetic transients (EMT), and graphical-user interface (GUI). As the table clearly indicates, the VSA function included in VST is a great advantage over other Matlab-based packages for power system analysis. Table VST Toolbox: VST was designed to analyze bifurcation and voltage stability problems in electric power systems. VST combines symbolic and numeric computations with a graphical menu-driven interface based on Matlab and its extended symbolic toolbox. The main features and application modules of VST can be summarized as follows. use of Matlab s visualization capability to create GUI and visualize output data; use of stand-alone MEX-files to generate classical power system model equations; use of symbolic toolbox to generate Jacobian and second order derivative matrices; load flow calculations: standard NR and convergent NRS methods; Voltage stability analysis: identification of local static and dynamic bifurcation points, such as SN, Hopf, and SI bifurcations; small-signal stability analysis; dynamic (time-domain) simulations. 4 LOAD MODELING In recent years, the interest in load modelling has been continuously increasing, and power system load has become a new area for researching into power systems stability. Inaccurate load modelling could lead to a power system operation towards actual system collapse. Several studies [], [7] have shown the critical effect of load representation in voltage stability studies and therefore the need of finding more accurate load models than the traditionally used ones. The load model is one of the most important elements in power system simulation and control. The majority of power system loads respond dynamically to voltage disturbances & such contribute to the overall system dynamics. Power system load model can be considered as a set of mathematical equations that describe the relationship between the real & reactive power, voltage & frequency at a given bus bar in a system Load Classes & load composition: The load class data is often grouped in industrial, residential, commercial and agricultural load data. The industrial load is mainly related to industrial processes, and most of the load corresponds to industrial motors, up to 95%. Heavy industries may include electric 2

3 heating processes such as soldering. The residential load includes most of the devices related to housing habits, but also a big percent of electric heating and air conditioner units during winter and summer respectively. The commercial load corresponds to air conditioner units and a large percent of discharge lighting, and agricultural load to induction motors for driving pumps. The composition of the load is strongly dependent on the time of day, month and season, but also on weather. Load composition of a particular area is characterized by the load class data, the composition of each one of the classes, and the characteristics of each single load component. 4.2 Different Load Models: Load models are traditionally classified in two broad categories, static load models and dynamic load models [9]-[10]. Common types of load models are mentioned below: Standard Load Model: Standard load model comprises of constant current, constant power and constant impedance models. These models are represented by relationship of voltage and power. Constant Impedance [ Power α V 2 ] Constant Current [ Power α V ] Constant Power Exponential Load Model Equations given below express the power dependence with the voltage, as an exponential function. P = Po.(V/Vo) np Q = Qo.(V/Vo) nq P & Q are Load Active & reactive power respectively. Po & Qo are active & reactive power consumption at rated voltage Vo. For the special case, where np or nq are equal to 0, 1 and 2, the load model will represent a constant power, constant current or constant impedance model respectively. Polynomial Load Model Equations in a polynomial model represent the sum of three categories. It is a static load model that represents power relationship to voltage magnitude as a polynomial equation, usually in the following form: P = Po [ a p.(v/)vo) 2 + b p (V/Vo) + c p ] Q = Qo [ a q.(v/)vo) 2 + b q (V/Vo) + c q ] Vo, Po and Qo are the s at the initial conditions of the system for the study, and the coefficients a p,b p, c p,a q, b q,c q are the parameters of the load model. Frequency Based Load Model It is a static load model that includes the frequency dependence. This is usually represented by multiplying either exponential or polynomial load model by a factor of following form: (1+ A (f fo) ) f = Frequency of bus voltage fo = Rated frequency of bus voltage A = Frequency sensitivity parameter of model Induction Motor Load Model For modelling the induction motor, most stability programs include the dynamic model based on equivalent circuit as mentioned below. Fig. 1 Induction motor steady state equivalent circuit Rs, Rr, Xs and Xr are the stator and rotor resistances and reactances respectively. Xm is the magnetizing reactance, and s is the motor slip. The stator flux dynamics are normally neglected in stability analysis, and the rotor flux in long-term analysis. Dynamic Load model: When the traditional static load models are not sufficient to represent the behaviour of the load, the alternative dynamic load models are necessary [11]. D.Karlsson & Hill proposed the aggregate load model which includes the aggregate effect of numerous load devices such as lighting, heating and motors plus some levels of transformer tap changing [12]. Tp. (dpr/dt) +Pr = Po.(V/Vo) αs - Po.(V/Vo) αt Pd = Pr + Po.(V/Vo) αt (1) Pr = Active Power recovery Tp = Active load recovery time constant Pd =Total active power consumption αs = Steady state active load voltage dependence αt = Transient active load voltage dependence V = Supply voltage Vo = Prefault / Pre disturbance voltage Similarly dynamic Reactive power model can be given by Tq. (dqr/dt) +Qr = Qo.(V/Vo) βs - Qo.(V/Vo) βt Qd = Qr + Qo.(V/Vo) βt (2) Qr = Reactive Power recovery Tq = Reactive load recovery time constant Qd =Total Reactive power consumption βs = Steady state reactive load voltage dependence βt = Transient reactive load voltage dependence 3

4 5 IMPLEMENTATION OF DYNAMIC LOAD MODELS: In [13], [14] Navarro, described the measurement based approach and steps to include the dynamic load model. Implementing the dynamic load model in the VST toolbox involves following main steps: Measurement/Estimation of the Load data Detection of voltage variation Load Parameter identification Voltage Stability Analysis using dynamic load model 5.1 Measurement/Estimation of the Load data The parameters of the dynamic load models can be determined either by using a measurement-based approach, by carrying field measurements and observing the load response as a result of alterations in the system, or by using a component-based approach I. Component based approach: The component based approach builds up the model of the composition of loads & corresponding specific models of main components. The difficulty of this approach for a large utility is a collection of statistics information of load components. The component-based approach builds up the load model from information on dynamic behaviours of all the individual components and load components (load composition data + load mixture data) of a particular load bus. For a large utility the surveys of load components are very difficult tasks. II. Measurement based approach: In this the dynamic variation of aggregate load is recorded during a disturbance. The recording device installed at the load bus & load model is further determined either on-line or off line. The measurement-based approach involves placing sensors at various load buses to determine model structures and model parameters. In this prior knowledge of the actual load composition is not needed. This approach has the advantage of direct measurement of actual load behaviours. It is simple as compared to component based approach & possible to track seasonal variations in load. However accuracy of final results depends on measurement kit accuracy. This approach requires large data handling. 5.2 Detection of Voltage Variation: Voltage step variations are of special interest due to their relation with daily normal and abnormal operation at a substation, i.e. connection and disconnection of capacitors and tap changer operations. To encounter the load dynamics different test are carried out. Field measurement with continuous acquisition of data from normal operation Field measurement with variation of capacitor banks and tap changers Field measurement involves data collection of real power (P), reactive power (Q) & voltage (V) at various buses. For data collection measurement setup is required with software for data acquisition and waveform analysis. 5.3 Determination of Dynamic Load Model Parameters:[14] The method of determining the dynamic load parameter involves mathematical simplification of equation (1) and (2). It also involves calculation of dynamic load parameters i.e. Tp, αs, αt, Tq, βs, βt from the measured data for various seasons throughout the year. Dynamic load model parameters proposed from study of Swedish power system are used in the analysis. The details of case study on Swedish power system are included in [13]. The ranges of dynamic load parameters proposed from the Sweden study are given in Table 2 as follows:- Table 2 Dynamic load parameter Range Transient active load voltage dependence (αt) 1.2 to2.23 Transient reactive load voltage dependence (βt) 0.7 to 1.35 Steady state active load voltage dependence (αs) 0.3 to 1.2 Steady state reactive load voltage dependence (βs) 0.3 to 1.5 Active load recovery time constant (Tp) 80 to 200 sec Reactive load recovery time constant (Tq) 78 to 21 sec 5.4 Voltage Stability analysis using dynamic load model: Final calculation involves measurement of total active & reactive power demand Pd and Qd respectively. Then use these s for defining the dynamic load models in voltage stability toolbox. For simulation different cases are prepared with and without synchronous condenser effects and with different s of loads. The test system is studied with VST toolbox for following conditions. A] Static load with synchronous B] Geometric mean Dynamic load with synchronous C] Pmax- Qmin Dynamic load with synchronous D] Static load without synchronous E] Geometric mean Dynamic load without synchronous F] Pmax- Qmin Dynamic load without synchronous Comparison of Static and dynamic load model s: Final comparison is made between the static load and dynamic load s. Table 3 shows the comparison of the static load and variation of dynamic load at various buses on IEEE 14 bus system. 4

5 Table 3 Comparison of Static load s with dynamic load s on test system No. Static load Active Load Dema nd Reacti ve Load Dema nd Active load demand Min (Pmin.) Max. (Pmax) Dynamic load G. M. (PG.M.) Min (Qmin) Reactive load demand Max. (Qmax) G. M. (QG.M) Fig. 7 B] G.M. dynamic load with Syn.Cond SIMULATION RESULTS: After calculation of the dynamic load model s for equivalent static load s; the same load model parameters are entered in the VST toolbox for voltage stability analysis with six different cases. The P-V curves are drawn with details of nose point x and y coordinates. Here, curves are drawn with Voltage (V) in p.u. and incremental change in active power demand alpha(α). The results are shown on sample bus of test system. The P-V curves are shown with synchronous condenser. Fig. A] Static load with synchronous : Fig. 8 C] Pmax-Qmin dynamic load with Syn. Cond. In Fig. to 8 nose point coordinates are shown on P- V curve for various conditions. Value Y denotes the voltage at nose point in p.u. and X denotes the alpha ( i.e incremental change in active power loading) at that bus. Based on s of X and Y obtained from voltage stability simulation final table is prepared; which shows voltage in p.u. and active power loading at that bus at nose point or collapse point. The comparison of voltage (in p.u.) & maximum power loading (in MW) for various simulation cases is shown in Table 4. Table 4 Comparison of nose point for six simulation cases Study Nose point s [A] [B] [C] [D] [E] [F] details no.14 no.13 no.10 no.9 no. Voltage (p.u.) Power (MW) Voltage (p.u.) Power (MW) Voltage (p.u.) Power (MW) Voltage (p.u.) Power (MW) Voltage (p.u.) Power (MW) Voltage (p.u.) Power (MW)

6 Powered by TCPDF ( The nose point in case [B], Geometric Mean Dynamic load model is further than the static load model. Voltage dependence in GM load model is observed to be more compared to static model. In case [C], Pmax- Qmin load, stability improves. 7 CONCLUSION: This paper has presented an approach to improve the voltage stability toolbox by incorporating dynamic load models. This will improve the accuracy of predicting voltage stability analysis and will be useful to researchers in the power system and allied areas. Various power system toolboxes available in market are classified into commercial and Matlab based toolboxes. Matlab based toolboxes are compared from voltage stability point of view. Matlab based VST toolbox features which is used for simulation is explained in brief. Measurement based approach can be used for dynamic load modeling with powerful and accurate instrumentation setup. The method of determining dynamic load parameters from measurement of voltage, current, active and reactive power is described. Matlab simulink based exponential dynamic load model is developed. On test system, maximum power that can be transferred from system to load has been investigated with different load characteristics under various system operating conditions. Simulation study employing the dynamic load model shows that, with dynamic load model nose point or collapse point shifts further away on right hand side direction. Voltage collapse of system without synchronous condensers occurs earlier even for lesser load conditions compared to system with synchronous condensers. I. Future Work: The measurement data is taken from case study of Swedish power system. In future work, similar measurements can be carried out to develop the dynamic load model suitable for Indian power system which will consider the different load composition as well as different operating conditions considering the seasonal variations in load. Simulation results show that voltage stability have improved with dynamic load model. This work uses the methodology of P-V curve for determining the voltage collapse in the system. This work can be examined more thoroughly by a dynamic simulation of a practical system. For this purpose, necessary programes for dynamic modeling and simulation needs to be developed. 3] J. H. Chow and K. W. Cheung,.A Toolbox for Power System Dynamics and Control Engineering Education and Research,. IEEE Trans. Power Syst., vol. 7, no. 4, pp , Nov ] C. D. Vournas, E. G. Potamianakis, C. Moors, and T. Van Cutsem,.An Educational Simulation Tool for Power System Control and Stability,. IEEE Trans. Power Syst., vol. 19, no. 1, pp , Feb ] M.K.Pal, Voltage stability conditions considering load characteristics, IEEE Trans. on Power Sys., Vol.7 no.1, Feb. 1992, pp ] K. Morison, H.hamadani, L.Wnag, Practical Issues in load modeling for Voltage stability Studies, IEEE Trans. Power Sys.,Feb ] W. Xu, Y. Mansour. Voltage Stability using generic dynamic load models, IEEE Trans. Power sys., Vol. 9, no.1, Feb ] Saffet Ayasun,Chika Nwankpa and Harry Kwatny Voltage Stability Toolbox for Power system Education & Research IEEE Trans. on Power Sys. Edu.,vol.49,no.4,Nov ] IEEE Task Force on Load Representation for Dynamic Performance, Load representation for dynamic performance analysis, IEEE Trans. on Power sys, Vol.8, no.2, pp , May ] IEEE Task Force on Load Representation for Dynamic Performance, Bibliography on Load models for power flow and dynamic performance simulation, IEEE Trans. on Power sys, Vol. 10, No.1, pp , Feb ] D.J.Hill, Nonlinear dynamic load models with recovery for voltage stability studies,ieee Trans. Power Sys.,Vol.8,No.1,Feb ] D. Karlsson, D.J.Hill, Modelling and identification of nonlinear dynamic loads in power systems,ieee Trans. Power sys.,vol. 9, no.1, Feb ] I.R.Navarro, Estimation of time-varying dynamic load parameters during normal operation, Ph.d. Thesis, Lund University, Sweden ] I. R. Navarro, O. Samuelsson and S. Lindahl. Automatic Determination of Parameters in Dynamic Load Models from Normal Operation Data. Submitted and accepted for Panel session on load modeling at IEEE Power Engg. Society meeting in July 2003, Toronto. 15] VST toolbox files from Drexel university website: 1] EPRI Website: REFERENCES 1] Taylor C. W., Power System Voltage Stability, McGraw-Hill, New York, USA, ] Kundur P., Power System stability and control, McGraw-Hill, New York, USA, 1994.