ANALYSIS OF SYNCHRONOUS MACHINES WITH BYPASSED COILS USING FEM-BASED MODELING SOFTWARE

Transcription

1 ANALYSIS OF SYNCHRONOUS MACHINES WITH BYPASSED COILS USING FEM-BASED MODELING SOFTWARE by Moshe Jeffrey Redmon i

2 A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Master of Science (Electrical Engineering). Golden, Colorado Date Signed: Moshe J. Redmon Signed: Dr. Pankaj Sen Thesis Advisor Golden, Colorado Date Signed: Randy Haupt Professor and Head Department of Electrical Engineering ii

3 ABSTRACT This thesis examines the viability of analyzing large synchronous machine performance with bypassed stator coils using modeling software. Defined operating points of an existing hydro-electric generator with bypassed coils are simulated using Finite Element Method (FEM)- based electromagnetic modeling software using a 2-D model of the generator consisting of the rotor and stator core, rotor poles, field winding, damper bars, and stator coils. Separate electrical circuits for the field winding, the damper winding, and the stator circuits are also defined to simplify the model. The resulting model is then used to simulate a machine at rated operating conditions without bypassed coils and then at various operating conditions with bypassed coils. The results for the model are further analyzed and compared to corresponding measured field data to assess the accuracy of the model. iii

4 TABLE OF CONTENTS ABSTRACT... iii LIST OF FIGURES... vi LIST OF TABLES... vii ACKNOWLEDGMENTS... ix NOMENCLATURE...x CHAPTER 1 INTRODUCTION Overview Motivation Performing Bypass Work on Synchronous Machines Scope of Problem...3 CHAPTER 2 GENERAL BACKGROUND Introduction Synchronous Machines Finite Element Analysis MagNet Circuit Window Solving in MagNet...12 CHAPTER 3 APPLICATION TO GLEN CANYON POWER PLANT Introduction Unit G2 Damage & Repair History Unit G2 Nameplate Data Field Measurements Diagnostic Measurement Process Resulting Data Unit G2 Model Model Inputs & Assumptions...28 iv

5 3.5.2 Model Inputs & Assumptions - Circuit Window Simulation Results Conclusion...42 CHAPTER 4 CONCLUSIONS & FUTURE WORK Conclusions Thesis Contribution Future Work...44 REFERENCES...46 APPENDIX MATLAB CODE USED TO CALCULATE RMS OF SIMULATED MACHINE VOLTAGES & CURRENTS...47 v

6 LIST OF FIGURES Figure 2.1 Synchronous Machine Diagram [7]... 6 Figure 2.2 Synchronous Machine Rotor Diagram Showing Damper Bars [7]... 6 Figure 2.3 Synchronous Machine Stator Diagram Showing Coil Locations [7]... 7 Figure 2.4 Glen Canyon Unit G2 Stator Core Slot... 7 Figure 2.5 Glen Canyon Unit Rotor... 8 Figure 2.6 Glen Canyon Unit Stator... 9 Figure 2.7 MagNet Mesh Grid Example Figure 2.8 MagNet Circuit Window [10] Figure 3.1 Glen Canyon Unit G2 Timeline [8] Figure 3.2 Glen Canyon Unit Nameplate Ratings Prior to 2002 Rewind [Ref] Figure 3.3 Glen Canyon Unit Nameplate Existing Ratings [Ref] Figure 3.4 Clamp CT Location on Machine Winding [Ref] Figure 3.5 Glen Canyon Unit G2 Neutral Bar Drawing with CT Locations [Ref] Figure 3.6 Glen Canyon Unit G2 Measured Operating Points Figure 3.7 Glen Canyon Unit G2 Synchronous Machine Model Figure 3.8 Coil Components Example [Ref] Figure 3.9 Glen Canyon Unit G2 Circuit Window - Field Winding Figure 3.10 Glen Canyon Unit G2 Circuit Window - Damper Winding [Ref] Figure 3.11 Glen Canyon Unit G2 Stator Winding Connections [Ref] Figure 3.12 Glen Canyon Unit G2 Circuit Window Stator Winding Including Load Imp vi

7 LIST OF TABLES Table 3.1 Glen Canyon Unit G2 Measured Field Current and Phase Currents Table 3.2 Glen Canyon Unit G2 Measured A-Phase Circuit Currents Table 3.3 Glen Canyon Unit G2 Measured B-Phase Circuit Currents Table 3.4 Glen Canyon Unit G2 Measured C-Phase Circuit Currents Table 3.5 Glen Canyon Unit G2 Measured A-Phase Per-Unit Circuit Currents Table 3.6 Glen Canyon Unit G2 Measured B-Phase Per-Unit Circuit Currents Table 3.7 Glen Canyon Unit G2 Measured C-Phase Per-Unit Circuit Currents Table 3.8 Glen Canyon Unit G2 General Information Table 3.9 Glen Canyon Unit G2 Physical Dimensions Table 3.10 Glen Canyon Unit G2 Solver Parameters Table 3.11 Unit G2 Model Simulation Results (Phase Voltages & Currents) Existing Table 3.12 Unit G2 Simulation Results (Phase Voltages & Currents) 23% Load, PF = Table 3.13 Unit G2 Simulation Results (Phase Voltages & Currents) 58% Load, PF = Table 3.14 Unit G2 Simulation Results (Phase Voltages & Currents) 75% Load, PF = Table 3.15 Unit G2 Simulation Results (Phase Voltages & Currents) 78% Load, PF = Table 3.16 Unit G2 Simulation Results (Phase Voltages & Currents) 74% Load, PF = Table 3.17 Unit G2 Simulation Results (Phase Voltages & Currents) 58% Load, PF = Table 3.18 Unit G2 Simulation Results (Parallel Circuit Currents) 23% Load, PF Table 3.19 Unit G2 Simulation Results (Parallel Circuit Currents) 58% Load, PF = Table 3.20 Unit G2 Simulation Results (Parallel Circuit Currents) 75% Load, PF Table 3.21 Unit G2 Simulation Results (Parallel Circuit Currents) 78% Load, PF Table 3.22 Unit G2 Simulation Results (Parallel Circuit Currents) 74% Load, PF vii

8 Table 3.23 Unit G2 Simulation Results (Parallel Circuit Currents) 75% Load, PF viii

9 ACKNOWLEDGEMENTS I would first like to thank my advisor, Dr. Pankaj K. Sen, for the guidance and support he provided to me while working towards my Master s degree. I would also like to thank Dr. Ravel Ammerman, for teaching the Power Systems Analysis and Analysis and Design of Advanced Energy Systems courses, which helped to solidify my understanding of power systems fundamentals. I would like to thank Shawn Patterson and James Zeiger for giving me the opportunity to work at the Bureau of Reclamation, as well sponsoring my education at the Colorado School of Mines over the last three years. I would finally like to thank my family for their love and financial support throughout this process, which enabled me to better pursue my degree. ix

10 NOMENCLATURE FEM E H μ ε Finite Element Method Electric Field Magnetic Field Magnetic Permeability Electric Permittivity x

11 CHAPTER 1 INTRODUCTION 1.1 Overview Damage to individual stator coils (which occurs more often in the older units running in excess of their operating life) within a synchronous machine can render the unit inoperable and lead to a significant loss in revenue for the unit s owner, as well as decrease the amount of generation available to the overall power grid. In order to mitigate these problems, the damaged unit can be temporarily repaired and operated at reduced loading until permanent repairs can be scheduled and performed. While the new operating limits of a unit were traditionally determined using a set of hand calculations outlined by sources including EPRI report EL-4983 [1], they could be more effectively determined using sophisticated numerical modeling software. The main objective of this thesis is to examine a more accurate method of determining the operating limits of synchronous machines with temporarily bypassed coils using finite element analysis software. Chapter two covers the topics relevant to modeling synchronous machines in Finite Element Method (FEM)-based software. Chapter three details a study performed on a temporarily repaired unit at the Glen Canyon (owned and operated by the Bureau of Reclamation, Department of the Interior) power plant, where a model of the unit was developed in the modeling software MagNet [10] and assessed for its accuracy. Chapter four concludes the thesis and covers future work to be performed. 1

12 1.2 Motivation Whenever a section of a unit s armature (stator) winding is damaged, the unit is taken out of service to prevent further damage to the unit or harm to plant personnel. This leaves the unit unavailable to provide energy to the grid to stabilize it in the event that more power is demanded than can be supplied, which could be caused by an unexpected outage at another power plant generating power. In the case of hydroelectric power plants, the loss of one unit at Glen Canyon would result in 165 MW of lost generation, while the loss of one unit at Grand Coulee (owned and operated by the Bureau of Reclamation) would result in up to 805 MW of lost generation. Such an outage would also lead to a significant loss of revenue for the affected power plant. For the Glen Canyon power plant, the average monthly net generation per hydro unit in 2014 was 19,116 MWh [4]. At an estimated cost of $30.00/MWh (or 3 /kwh), taking a unit offline at Glen Canyon could cost roughly $573, per month. Similarly, for the Grand Coulee power plant, the average monthly net generation for one of the largest units in 2014 was 215,170 MWh [5]. At the rate mentioned above, an outage of one of these units could cost roughly $6,455, per month. With these potential losses, it is not only imperative to bring the damaged unit back online as soon as possible, but also to accurately determine the new temporary operating limits of the unit in order to salvage as much generation as possible. 1.3 Performing Bypass Work on Synchronous Machines When stator winding coils in a synchronous machine are damaged, they can be electrically bypassed in procedures that allow the damaged unit to continue operating at reduced loading until permanent repairs can be made, or until the unit winding can be replaced. Additional undamaged coils can also be bypassed to create more balanced magnetic forces and 2

13 currents in the stator winding [1]. Alternatively, depending on the resulting current between parallel stator circuits and the overall current unbalance between phases, it may be more beneficial to electrically isolate the entire affected circuit(s) to prevent overloading the remaining undamaged ones. Ultimately, to determine which method of repair, if any, is most beneficial to the damaged unit, the operational limits of each potential resulting scenario should be examined. This, however, is the beyond the scope of this research. 1.4 Scope of Problem The performance of a unit with temporarily bypassed coils should to be determined prior to bringing it back online to avoid needlessly underutilizing or overloading the unit. This includes examining the circulating current in each parallel circuit of the stator winding to make sure the current limit of each isn t exceeded, which limits the maximum power generation. A more accurate assessment of this limit ensures a more reliable and cost effective operation of the unit in question. Therefore, the method of determining the operating limits of synchronous machines with temporarily bypassed coils using finite element analysis software needs to be examined to determine if it is a more viable alternative to traditional methods. 3

14 CHAPTER 2 GENERAL BACKGROUND 2.1 Introduction To develop a finite element method (FEM)-based numerical model of a synchronous machine, a general understanding of the principles relevant to the operation and design of synchronous machines, as well as an understanding of finite element analysis, is necessary. This chapter briefly covers each of these topics, and examines a specific FEM-based modeling software, MagNet, and its usefulness in modeling and analyzing synchronous machines. 2.2 Synchronous Machines A synchronous machine generates electrical power at a frequency equal to the frequency of the grid system that it is connected to, which in the United States is 60 Hz. In the rotating portion of the machine, called the rotor, magnetic flux produced by the DC field winding current flows from the rotor poles and interacts with the flux in the stationary part of the machine, called the stator, across an air gap while rotating. This allows for power transfer between the rotor and the stator, which can occur in either direction depending on whether the machine is a generator (turbine to the grid) or a motor (the grid to the pump). Synchronous machine operation can be explained based on two of Maxwell s equations (equations 2.1 and 2.2 below) describing electromagnetism, also called Ampere s law and Faraday s law. Ampere s law states that a magnetic flux can be induced either around a current 4

15 or a time-changing electric flux density [6]. Faraday s law states that a voltage can be induced counter to a time-changing magnetic flux. E = -μ H t (Faraday s Law) (2.1) H = J + ε E t (Ampere s Law) (2.2) Most of the large salient-pole synchronous machines have three different sets of windings: the field winding, the armature (or stator) winding, and the amortisseur (or damper) winding. The field winding carrying DC field current, located on the rotor poles, employs ampere s law to generate the DC flux through the entire winding. The amount of flux induced by this winding depends not only on the amount of current in the winding, but also on the number of turns, or number of times the winding is wrapped around each pole and of course, the reluctance of the magnetic circuit. The windings on each adjacent pole, which are all connected in series, are wrapped in alternating directions from pole to pole to ensure that the induced flux also flows between these poles. The armature winding (or stator winding) which is usually three-phase, located on the stator of the machine, interacts with the rotating DC flux from the rotor to induce three-phase voltages via Faraday s law. Three-phase currents in turn are flowing in these windings corresponding to the amount of power being generated or consumed by the machine. The amortisseur winding (or damper bars), located on each pole face of the rotor, is used to dampen any oscillations in the rotor due to a sudden change in power, which improves the machine s stability. Each of these bars are shorted together either on each pole or the entire rotor. Figure 2.1 shows an example of a synchronous machine, including the field and armature windings, Figure 2.2 shows an example of the damper bars located on the rotor pole faces, and Figure 2.3 shows an example of how the stator coils are fitted into the slots of the stator core. 5

16 Figure 2.4 shows a single stator core slot of a unit at Glen Canyon (taken from Reclamation drawings). Figure 2.1 Synchronous Machine Diagram [7] Figure 2.2 Synchronous Machine Rotor Diagram Showing Damper Bars [7] 6

17 Figure 2.3 Synchronous Machine Stator Diagram Showing Coil Locations [7] Figure 2.4 Glen Canyon Unit G2 Stator Core Slot 7

18 In larger synchronous machines, the stator coils are connected to each other in series and form multiple parallel circuits per phase, which allows the machine to generate significantly more current and thus more power for the same voltage level and coil current rating. These hydro units also have a large number of poles, which reduce the machine s operating speed and stator coil pitch, or the distance between the top half of a stator coil and the bottom half. The top half of a stator coil is the side of the coil which is slotted radially closest to the rotor (or center of the machine), and the bottom half is the side that is slotted radially farthest from the rotor. Figures 2.5 and 2.6, taken from Reclamation site visit pictures, provide an example of the actual rotor and stator of a large synchronous generator, respectively, at the Glen Canyon power plant. Figure 2.5 Glen Canyon Unit Rotor 8

19 Figure 2.6 Glen Canyon Unit Stator 2.3 Finite Element Analysis Finite Element Analysis (FEA) is a numerical tool used to approximate solutions to complex systems. To implement FEA, a physical model of the problem is first developed and then overlaid with a mesh grid that divides the model into smaller simpler geometric pieces (triangles, rectangles, etc.) which are called elements. Figure 2.7 shows an example of a mesh grid applied to a synchronous machine model that divides the model into various triangles. The resulting elements of the physical model have a set of approximated difference equations applied to them (i.e. based on Maxwell s equations). These equations are then solved iteratively (or using other techniques) for each element using either numerical linear algebra, which is preferable for steady state problems, or numerical integration, which is preferable for transient problems. At the end of this process, when the equations for all of the model s elements are solved for, a global set of equations are obtained that describe the solutions of the entire model. 9

20 Figure 2.7 MagNet Mesh Grid Example [10] The main issues with this or any numerical method involve the convergence of a given model s solution, the simulation time for the model, and the accuracy of the solution. It is essential that simulations performed on an FEM-based numerical model converge on a solution within a reasonable amount of time, and that the solution accurately describes or predicts the physical properties being analyzed in the model. When developing and analyzing FEM-based models, there is also a tradeoff between the model s complexity and its accuracy. If an FEMbased model is divided into more elements, it will take longer to obtain a solution, but the solution will be more accurate. On the flip side, a model with less elements can be solved more quickly, but the solution will not be as accurate. 10

21 2.3.0 MagNet [10] MagNet is a FEM-based analysis software, available commercially, which allows the examination of the electromagnetic fields resulting from a given physical model. It allows one to create or import a model whose components each have physical properties including the component s magnetic permeability, electric permittivity, and mass density. These properties can be manually specified in a custom material, or a pre-defined material can be applied from MagNet s material library. The software solves the given model by first applying a mesh grid that divides a given model into either triangular (2-D modeling) or tetrahedral (3-D modeling) elements. The resulting elements have Maxwell s equations applied to them, which are then solved using both the Newton Raphson and the Conjugate Gradient methods. Once a solution is obtained, MagNet uses the resulting data (electric and magnetic fields, current densities, etc.) to calculate other parameters for each element, including their forces, currents, and voltages. The solver can perform both steady state and transient simulations, which obtain solutions for multiple time increments instead of just one for steady state simulations Circuit Window For each component specifically defined as a coil, MagNet will take the solutions from Maxwell s equations and calculate the corresponding voltages across the coils and currents through the coils. To analyze the voltages and currents of coils modeled in MagNet, they can be modeled electrically in the software s circuit window, which allows various components that are connected to the coils but are external to the model. Figure 2.8 shows an example of the circuit window in MagNet. 11

22 Figure 2.8 MagNet Circuit Window Example [10] When a coil is defined in the main window, a corresponding electrical model is created in the circuit window. This model, which appears in a separate sub-window on the left (as shown in Figure 2.8), can be placed in the main window on the right and connected to resistors, inductors, capacitors, voltage or current sources, and other simple electrical components. This feature can be used to drastically reduce the complexity of the entire model while still allowing for a detailed examination of the electrical characteristics of the model s coils, which reduces the model s simulation time Solving in MagNet When solving a given model, Magnet uses two layers of numerical methods to improve the accuracy of the solution. The Conjugate Gradient method is the inner layer that performs the main calculation, and the Newton Raphson method is the outer layer that refines the solution. 12

23 The Conjugate Gradient Method iteratively solves Maxwell s equations for each element using equations shown below [9]. Once the residual vector r is within a specified tolerance (called the CG tolerance), the solution is obtained [10]. Ax = b (Linear Matrix System) (2.3) f(x) = x T Ax 2x T b (2.4) α n = p n T r n r n T Ar n (2.5) x n+1 = x n + α n p n (2.6) r n+1 = r n + α n Ap n (2.7) β n = p n T Ar n+1 p n T Ap n (2.8) p n+1 = r n+1 + β n p n (2.9) Where: x Solution Vector A Positive Definite Matrix (linearized) b Given Vector f(x) Quadratic Function (Minimized at x) x T Transposed Solution Vector p Direction Vector 13

24 r Residual Vector (Initially set to Ax - b) α Scalar Multiplier (for Incrementing x) β Scaling Multiplier (for Adjusting p) n Iteration Number Once the Conjugate Gradient method obtains a solution, the Newton Raphson method further refines the solution using equations shown below [11]. Similar to the Conjugate Gradient method, once the solution difference x comes within a specified tolerance, the solution is obtained. y n = y f(x n ) (2.10) x n = J n -1 y n (2.11) x n+1 = x n + x n (2.12) Where: x Solution Vector y Given Vector f(x) Given Function Vector J Jacobian Matrix n Iteration Number 14

25 CHAPTER 3 APPLICATION TO GLEN CANYON POWER PLANT 3.1 Introduction There are two hydro units at the Glen Canyon power plant which have had temporary bypass work performed on their stator windings after sustaining significant damage. While performing load tests on unit G2, the Bureau of Reclamation s (BOR) Diagnostics Team measured the parallel winding currents flowing in this unit at various operating points. A numerical model was recently developed in Finite Element Method (FEM) modeling software to represent the bypass work performed on the unit. With this model, the operating points measured by the Diagnostics Team were simulated, and the resulting currents calculated in the winding were compared to the corresponding field data to assess the model s accuracy. This chapter outlines the history of unit G2 at Glen Canyon power plant from when its winding sustained damaged to when the unit was rewound, details the measurement process and results, describes the inputs and assumptions used to create the numerical model, and shows the simulation results and compares them to the field measurements. 3.2 Unit G2 Damage & Repair History The stator winding of unit G2 sustained damage on December 1, 2001, as it was being manually brought online [2]. When water from cooling equipment located one floor above the unit leaked into the unit s air housing deck and into the machine, it caused a ground fault to 15

26 occur in the A-phase of the winding. This was detected by the unit s ground fault relay, which tripped the unit offline before the unit breaker was closed. During multiple visits to the plant, Reclamation s Diagnostics Team worked with plant personnel to assess G2 s electrical and physical condition and dried the stator winding by operating the unit into a bolted terminal short. They then located the two stator coils where the fault occurred and electrically isolated them by bypassing the entire parallel circuit that contained them. The unit was then successfully brought back online on February 20, 2002, and was subsequently operated at reduced capacity until the unit was rewound in November of that year. Figure 3.1 shows a timeline of the events described in this section. Figure 3.1 Glen Canyon Unit G2 Timeline [8] 3.3 Unit G2 Nameplate Data Before the unit was rewound in November 2002, G2 s winding was rated for 165 MVA at 13.8 kv and a lagging power factor of After it was rewound, the rating was increased to 16

27 174 MVA at the same voltage and power factor. Examples of the full nameplate ratings for each winding (taken from Reclamation site visit pictures) are shown in Figures 3.2 and 3.3 below. Figure 3.2 Glen Canyon Unit Nameplate Ratings Prior to 2002 Rewind Figure 3.3 Glen Canyon Unit Nameplate Existing Ratings 17

28 3.4 Field Measurements Prior to unit G2 s rewind, the Diagnostic Team recorded data on the unit s temporarily repaired winding to examine the effects of electrically bypassing an entire parallel circuit. The measurements consisted of the current flowing in each of the unit s parallel circuits (excluding the one that was electrically removed), as well as the total current flowing out of each phase of the machine Diagnostic Measurement Process The measurements on G2 s stator winding were recorded while the Diagnostics Team was performing an operating limit test. During the first part of this test, the maximum unit load at unity power factor was determined by incrementally increasing the amount of MW being generated by the unit and monitoring the resulting currents flowing in each parallel circuit [2]. The maximum load was reached when the maximum circuit current went above the rated current per circuit of the unit, which was 865A. In the second part of this test, the MW output of the unit was lowered to just below the maximum loading limit and the MVAR output was varied so that MVAR flowed into and out of the unit. This allowed the Diagnostics Team to evaluate the effects of MVAR loading on current flow in the winding. To measure the parallel circuit currents, clamp CTs were connected around each of the remaining 23 jumpers running between the neutral end of the stator circuits and the ring bus along the outside of the winding. An example of this (Also taken from Reclamation site visit pictures) is shown in Figure 3.4. The leads of these clamp CTs were then connected to a given burden board, which produced voltages corresponding to the current flowing into the board. These voltages were related to the input currents by a simple conversion factor determined by the 18

29 burden board. Once the output voltage was obtained, the circuit currents were calculated using the burden board and CT ratios. Figure 3.4 Clamp CT Location on Machine Winding Similarly, the line currents were measured by connecting transducers to the existing metering circuits for the units, which included CTs connected around the neutral bar of each phase of the stator winding. Figure 3.5, which is taken from electrical drawings for unit G2, shows the location of these CTs on the neutral bars. The conversion factor for the transducers and the metering CT ratios were used to calculate the line currents. 19

30 Figure 3.5 Glen Canyon Unit G2 Neutral Bar Drawing with CT Locations Resulting Data The measurements made on G2 by the Diagnostics Team were collected at six different operating points, as shown in Figure 3.6. For four of these points, no MVARs were generated or absorbed by the unit (unity power factor) while the maximum loading limit was being determined; for the other two points, MVARs were generated and absorbed by the unit at a MW loading just below the maximum limit previously determined. 20

31 Glen Canyon Unit 2 - Measured Operating Points 200 Stator Limit (Undamaged Unit) Stator Limit (Damaged Unit) Measured Operating Points Reactive Power (MVAR) Active Power (MW) Figure 3.6 Glen Canyon Unit G2 Measured Operating Points The following tables detail the resulting currents measured from G2. Table 3.1 shows the field and line currents measured for each operating point. Tables 3.2, 3.3, and 3.4 show the parallel circuit currents for phases A, B, and C, respectively, as well as the percentage of total line current each circuit generates. Note that there are no measurements for circuit A5, as this was the circuit electrically removed from G2 s winding. There are also no measurements for circuit B7, since the clamp CT placed on this circuit s jumper failed during testing. 21

32 Table 3.1 Glen Canyon Unit G2 Measured Field Current and Phase Currents Glen Canyon Unit 2 - Measured Field Current and Phase Currents MW MVAR If (A) Ia (A) Ib (A) Ic (A) Average Current (A) Table 3.2 Glen Canyon Unit G2 Measured A-Phase Circuit Currents Glen Canyon Unit 2 - Measured A-Phase Circuit Currents Unit Loading T4-26 T10-71 T4-116 T MW MVAR A1 (A) % of Ia A2 (A) % of Ia A3 (A) % of Ia A4 (A) % of Ia % % % % % % % % % % % % % % % % % % % % % % % % Unit Loading T4-206 T T4-296 T MW MVAR *A5 (A) % of Ia A6 (A) % of Ia A7 (A) % of Ia A8 (A) % of Ia N/A N/A % % % N/A N/A % % % N/A N/A % % % N/A N/A % % % N/A N/A % % % N/A N/A % % % *Circuit electrically removed 22

33 Table 3.3 Glen Canyon Unit G2 Measured B-Phase Circuit Currents Glen Canyon Unit G2 - Measured B-Phase Circuit Currents Unit Loading T5-40 T11-85 T5-130 T MW MVAR B1 (A) % of Ib B2 (A) % of Ib B3 (A) % of Ib B4 (A) % of Ib % % % % % % % % % % % % % % % % % % % % % % % % Unit Loading T5-220 T T5-310 T MW MVAR B5 (A) % of Ib B6 (A) % of Ib **B7(A) % of Ib B8 (A) % of Ib % % N/A N/A % % % N/A N/A % % % N/A N/A % % % N/A N/A % % % N/A N/A % % % N/A N/A % ** Clamp-on CT failed, no data recorded Table 3.4 Glen Canyon Unit G2 Measured C-Phase Circuit Currents Glen Canyon Unit G2 - Measured C-Phase Circuit Currents Unit Loading T6-51 T12-96 T6-141 T MW MVAR C1 (A) % of Ic C2 (A) % of Ic C3 (A) % of Ic C4 (A) % of Ic % % % % % % % % % % % % % % % % % % % % % % % % Unit Loading T6-231 T T6-321 T12-6 MW MVAR C5 (A) % of Ic C6 (A) % of Ic C7 (A) % of Ic C8 (A) % of Ic % % % % % % % % % % % % % % % % % % % % % % % % 23

34 Tables 3.5, 3.6, and 3.7 similarly show the parallel circuit currents for phases A, B, and C, respectively; they also include a comparison to the expected currents in an equivalent undamaged machine using a per-unit current calculation. This calculation is performed using equations 3.1 and 3.2, where V t represents the rated terminal voltage of the machine and # of circuits represents the number of parallel circuits per phase in the machine winding. I base = MW 2 + MVAR 2 3 V t (# of circuits) (3.1) I pu = I measured I base (3.2) Table 3.5 Glen Canyon Unit G2 Measured A-Phase Per-Unit Circuit Currents Glen Canyon Unit G2 - Measured A-Phase Per-Unit Circuit Currents Unit Loading T4-26 T10-71 T4-116 T MW MVAR Ibase (A) A1 (A) P.U. A2 (A) P.U. A3 (A) P.U. A4 (A) P.U Unit Loading T4-206 T T4-296 T MW MVAR Ibase (A) *A5 (A) P.U. A6 (A) P.U. A7 (A) P.U. A8 (A) P.U N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A * Circuit electrically removed 24

35 Table 3.6 Glen Canyon Unit G2 Measured B-Phase Per-Unit Circuit Currents Glen Canyon Unit G2 - Measured B-Phase Per-Unit Circuit Currents Unit Loading T5-40 T11-85 T5-130 T MW MVAR Ibase (A) B1 (A) P.U. B2 (A) P.U. B3 (A) P.U. B4 (A) P.U Unit Loading T5-220 T T5-310 T MW MVAR Ibase (A) B5 (A) P.U. B6 (A) P.U. **B7 (A) P.U. B8 (A) P.U N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A ** Clamp-on CT failed, no data recorded Table 3.7 Glen Canyon Unit G2 Measured C-Phase Per-Unit Circuit Currents Glen Canyon Unit G2 - Measured C-Phase Per-Unit Circuit Currents Unit Loading T6-51 T12-96 T6-141 T MW MVAR Ibase (A) C1 (A) P.U. C2 (A) P.U. C3 (A) P.U. C4 (A) P.U Unit Loading T6-231 T T6-321 T12-6 MW MVAR Ibase (A) C5 (A) P.U. C6 (A) P.U. C7 (A) P.U. C8 (A) P.U

36 The maximum load limit from the measurements shown above was determined to be 135 MVA, or roughly 82% of the rated operating limit for G2 prior to sustaining damage. Overall, this meant an 18% reduction in loading from the rated operating limit for G2. The reduction in loading recommended based on EPRI report EL-4983 [1] was only half of this (9%), which would have put the loading limit at 91% of the rated operating limit. From these measurements, the effect of removing an entire parallel circuit from G2 s stator winding can be seen. Since circuit A5 was removed, the magnetic flux from the rotor induced higher voltages (and thus higher currents) in the corresponding circuits B5 and C5. The highest parallel circuit current measured in G2 s stator winding at the maximum load limit was 850A in circuit C5, which is just below the rated current per circuit, 865A. As shown by Table 3.7, this value was 20% higher than what the current would have been in a similar undamaged winding. 3.5 Unit G2 Model A 2-D symmetrical model, shown in Figure 3.7, was created for unit 2 at Glen Canyon using the FEM-based software, MagNet [10]. This model was developed primarily using drawings and machine data provided by the U.S. Bureau of Reclamation (USBR), which included nameplate ratings, physical dimensions, and winding coil connections. The numerical model was used to run simulations of both the damaged winding from 2002 and the current undamaged winding, and the results were compared to the previously mentioned field data to assess the accuracy of the model. 26

37 Figure 3.7 Glen Canyon Unit G2 Synchronous Machine Model 27

38 3.5.1 Model Inputs & Assumptions The general information that was used to create the 2-D synchronous machine model in MagNet included information on the number of poles and stator coils, the number of turns per coil (rotor and stator coils), the stator coil pitch, the air gap thickness, and the depth of the core material (which was used to define the depth of the entire model). These inputs are listed in Table 3.8. Table 3.8 Glen Canyon Unit G2 General Information General Parameters Value Number of Poles 48 Number of Rotor Coil Turns (per pole) 33 Number of Stator Coils 360 Number of Stator Coil Turns (per coil) 3 Stator Coil Pitch 1 to 8 Air Gap Thickness (inches) 0.58 Model Depth (inches; based on core depth) 83.5 Number of Stator Circuits (per phase) 8 The physical dimensions used to develop the model for G2 were divided among those for the stator, those for the rotor, and those for the damper bars. Table 3.9 shows these dimensions, which were used to create the outlines for the rotor core, poles and coils, the stator core and coils, and the damper bars. Once the model outline was finished, each of the components was created using the model depth specified in Table 3.8. The damper bars, rotor coils, and stator coils were modeled as solid pieces (including insulation) using the pre-defined model material Copper: 101% IACS (ETP) from MagNet s material library. Both cores and all 48 poles were modeled with user defined materials. The magnetic permeability and loss data for these materials were referenced 28

39 from a similar CEATI study [3], whose report is titled Operation of Hydro Generators with Bypassed Stator Coils. The mass density for these materials was provided by USBR. Table 3.9 Glen Canyon Unit G2 Physical Dimensions Stator Parameters Value (inches) Stator Inner Radius 155 Stator Outer Radius Wedge Offset Wedge Length (radial) Wedge Width Stator Coil Length Stator Coil Width Rotor Parameters Value (inches) Core Inner Radius Core Outer Radius (w/out poles) Core + Poles Outer Radius Coil Length Coil Width Pole Length w/out Tooth 13 Tooth Inner Width Tooth Outer Width Pole Face Radius - Center Pole Face Radius - Side Damper Winding Parameters Value (inches) Damper Bar Diameter 0.75 Damper Bar Radius Pole Face Edge (Center) to Center Bar Pole Face Edge (Center) to 1 Bar out Pole Face Edge (Center) to 2 Bars Out Center Bar to 1 Bar out Center Bar to 2 Bars out

40 3.5.2 Model Inputs and Assumptions Circuit Window To model the coil connections for the field winding, stator winding, and damper bars, the coil components were grouped together and defined as coils which created corresponding electrical components for them in the circuit window. An example of this is shown in Figure 3.8. Figure 3.8 Coil Components Example (Taken from Unit G2 Model) Since the field winding was not altered during the bypass work, all 48 coils were grouped together to form a single component in the circuit window, which was connected to an independent current source that supplied the DC field current. This current was updated with the measured field currents from Table 3.1. The damper bar components in the circuit window were all shorted together on both ends, just like the actual damper bars on unit G2. The resulting field and damper windings are shown in Figures 3.9 and 3.10, respectively. 30

41 Figure 3.9 Glen Canyon Unit G2 Circuit Window - Field Winding Figure 3.10 Glen Canyon Unit G2 Circuit Window - Damper Winding 31

42 The stator coils for G2 are connected together in alternating groups of two and three coils in series going around the stator. Each stator circuit consists of six coil groups, or fifteen individual coils, and there are eight circuits paralleled together per phase (24 circuits total). Since the end windings were not modeled in the main window, they were modeled in the circuit window as a single resistor and inductor for each parallel circuit, which represented the total resistance and leakage reactance of all 15 coils per circuit lumped together. The values used for the end winding resistance and leakage reactance were referenced from the CEATI study mentioned in section To represent the loading of the unit, a simple three-phase impedance was connected to each phase of the stator winding. The value of this impedance was changed with loading, and was calculated using equations Figure 3.11 shows a portion of the Reclamation drawing referenced for the winding connections, and Figure 3.12 shows the resulting circuit of one phase (including the load impedance). To model the bypass work performed on G2, circuit A5 was disconnected from the rest of the A-phase circuit; the circuit removed is circled in Figure Z load = V t 2 MW 2 + MVAR 2 (3.3) R load = Z load *PF (3.4) L load = Z load 2 2 R load 120 π (3.5) C load = 120 π Z 2 2 load R load (3.6) Where: V t Terminal Voltage 32

43 Z load Load Impedance R load Load Resistance PF Power Factor L load Load Inductance (Lagging PF Load Only) C load Load Capacitance (Leading PF Load Only) Figure 3.11 Glen Canyon Unit G2 Stator Winding Connections 33

44 Figure 3.12 Glen Canyon Unit G2 Circuit Window Stator Winding Including Load Impedance 3.6 Simulation Results Using the model developed for Glen Canyon Unit G2, transient simulations were performed at seven different operating points: one at the rated conditions of the existing unit, and six at the operating points described in section The solver parameters used for these simulations are detailed in Table Table 3.10 Glen Canyon Unit G2 Solver Parameters Parameter Value Maximum Newton Iterations 50 Newton Tolerance 1% Polynomial Order 2 CG Tolerance 0.01% Transient Simulation Stop Time 450ms Transient Simulation Time Step 1ms 34

45 To assess the accuracy of the simulated voltages and currents, the simulation results were compared to the machine ratings and the field measurements in the following tables. Since MagNet produces time domain currents and voltages, the RMS of these values were calculated using MATLAB code (given in Appendix A). The simulated voltages were each expressed in kv and as a per unit value of the machine s rated phase voltage. For the phase and parallel circuit currents, the percentage difference between the simulated and measured currents were displayed below the simulated and measured values. The percentage difference for each simulated current was calculated using equation 3.7. Tables cover the phase voltages and line currents calculated for each simulation. Tables cover the parallel circuit currents calculated for each simulation. Margin of Error = ( I simulated I measured - 1)*100% (3.7) Table 3.11 Unit G2 Model Simulation Results (Phase Voltages & Currents) Existing Ratings Glen Canyon Undamaged Model - 100% Load, PF = 0.95 Lagging S (MVA) P (MW) Q (MVAR) 54.2 Terminal Voltage (kv) 13.8 Field Current (A) 1040 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical 35

46 Table 3.12 Unit G2 Simulation Results (Phase Voltages & Currents) 23% Load, PF = 1.0 Glen Canyon Unit 2-23% Load, PF = 1.0 (Unity; Modeled with leading PF due to small amount of MVAR absorbed) S (MVA) 39.4 P (MW) 39.4 Q (MVAR) -1.3 Terminal Voltage (kv) 13.8 Field Current (A) 466 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical Table 3.13 Unit G2 Simulation Results (Phase Voltages & Currents) 58% Load, PF = 1.0 Glen Canyon Unit 2-58% Load, PF = 1.0 (Unity) S (MVA) P (MW) Q (MVAR) 0.0 Terminal Voltage (kv) 13.8 Field Current (A) 580 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical 36

47 Table 3.14 Unit G2 Simulation Results (Phase Voltages & Currents) 75% Load, PF = 1.0 Glen Canyon Unit 2-75% Load, PF = 1.0 (Unity) S (MVA) P (MW) Q (MVAR) 0.0 Terminal Voltage (kv) 13.8 Field Current (A) 650 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical Table 3.15 Unit G2 Simulation Results (Phase Voltages & Currents) 78% Load, PF = 1.0 Glen Canyon Unit 2-78% Load, PF = 1.0 (Unity) S (MVA) P (MW) Q (MVAR) 0.0 Terminal Voltage (kv) 13.8 Field Current (A) 662 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical 37

48 Table 3.16 Unit G2 Simulation Results (Phase Voltages & Currents) 74% Load, PF = 0.97 Lag Glen Canyon Unit 2-74% Load, PF = 0.97 Lagging S (MVA) P (MW) Q (MVAR) 29.0 Terminal Voltage (kv) 13.8 Field Current (A) 772 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical Table 3.17 Unit G2 Simulation Results (Phase Voltages & Currents) 58% Load, PF = 0.97Lead Glen Canyon Unit 2-75% Load, PF = 0.97 Leading S (MVA) 130 P (MW) Q (MVAR) Terminal Voltage (kv) 13.8 Field Current (A) 500 Simulation Results Phase A B C Voltage Simulated Phase Voltage (kv) Per Unit Voltage (p.u.) Current Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical 38

49 Table 3.18 Unit G2 Simulation Results (Parallel Circuit Currents) 23% Load, PF 1.0 Glen Canyon Unit 2-23% Load, PF = 1.0 (Unity; Modeled with leading PF due to small amount of MVAR absorbed) A-Phase A1 A2 A3 A4 A5 A6 A7 A8 Simulated Current (A) Measured Current (A) Margin of Error (%) N/A B-Phase B1 B2 B3 B4 B5 B6 B7 B8 Simulated Current (A) Measured Current (A) N/A 202 Margin of Error (%) N/A C-Phase C1 C2 C3 C4 C5 C6 C7 C8 Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical Table 3.19 Unit G2 Simulation Results (Parallel Circuit Currents) 58% Load, PF = 1.0 Glen Canyon Unit 2-58% Load, PF = 1.0 (Unity) A-Phase A1 A2 A3 A4 A5 A6 A7 A8 Simulated Current (A) Measured Current (A) Margin of Error (%) N/A B-Phase B1 B2 B3 B4 B5 B6 B7 B8 Simulated Current (A) Measured Current (A) N/A 517 Margin of Error (%) N/A C-Phase C1 C2 C3 C4 C5 C6 C7 C8 Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical 39

50 Table 3.20 Unit G2 Simulation Results (Parallel Circuit Currents) 75% Load, PF 1.0 Glen Canyon Unit 2-75% Load, PF = 1.0 (Unity) A-Phase A1 A2 A3 A4 A5 A6 A7 A8 Simulated Current (A) Measured Current (A) Margin of Error (%) N/A B-Phase B1 B2 B3 B4 B5 B6 B7 B8 Simulated Current (A) Measured Current (A) N/A 667 Margin of Error (%) N/A C-Phase C1 C2 C3 C4 C5 C6 C7 C8 Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical Table 3.21 Unit G2 Simulation Results (Parallel Circuit Currents) 78% Load, PF 1.0 Glen Canyon Unit 2-78% Load, PF = 1.0 (Unity) A-Phase A1 A2 A3 A4 A5 A6 A7 A8 Simulated Current (A) Measured Current (A) Margin of Error (%) N/A B-Phase B1 B2 B3 B4 B5 B6 B7 B8 Simulated Current (A) Measured Current (A) N/A 696 Margin of Error (%) N/A C-Phase C1 C2 C3 C4 C5 C6 C7 C8 Simulated Current (A) Measured Current (A) Margin of Error (%) *All results are rms, symmetrical 40