Medium Voltage DC Testbed: Generator System GS-1
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1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Medium Voltage DC Testbed: Generator System GS-1 Michelle Bash and Ricky R. Chan Abstract In this paper, a description of the generation system GS-1 which is part of the medium voltage dc (MVDC) testbed is set forth. This paper describes the control strategy as well as three mathematical models of GS-1. These models vary in the level of detail, from the non-linear average value model (AVM) to the highly detailed model that incorporates a brushless exciter machine model. Index Terms synchronous machine, medium voltage, brushless exciter G I. OVERVIEW OF GS-1 ENERATION system 1 (GS-1) includes a dynamometer for a prime mover (PM-1), a synchronous generator (SG-1), a brushless exciter, a voltage regulator (VR-1), a linecommutated rectifier, and an output low-pass filter as depicted in Fig. 1. Herein, the prime mover is considered as an ideal commanded source with a commanded speed of 1800 rpm. More realistic prime mover behavior, such as a turbine emulator, may be included for future work. The synchronous machine is a 4-pole wound-rotor synchronous machine rated for 59 kw at 1800 rpm. A brushless excitation unit is utilized to control the system so as to achieve 750 V dc. The ac components out of the synchronous machine are passed through a rectifier to obtain dc. A double pole LC-filter is included to reduce the high frequency ripple from propagating into the distribution bus. Note that in Fig. 1, the equivalent series resistances (ESR) of the capacitors C dc1 and C dc2 are not depicted in Fig. 1 for brevity. However, it is considered in the models and denoted by r Cdc1 and r Cdc2, respectively. The passive components of GS-1 are listed in Table I. Currently, a diode rectifier is used in place of the controlled thyristor-based rectifier. As a result, the diodes will conduct when they become forward biased, which occurs as soon as the prime mover is operational. It is desired, for future work, that a thyristor-based rectifier will be utilized in order to provide fault protection. TABLE I. GS-1 PASSIVE COMPONENT PARAMETERS Parameter Value Description L dc1 5.0 mh DC link inductor inductance r Ldc Ω DC link inductor ESR Ldc2 2.5 mh DC link inductor inductance rldc Ω DC link inductor ESR Cdc1 2.3 mf DC link capacitor capacitance rcdc Ω DC link capacitor ESR C dc2 2.8 mf DC link capacitor capacitance r Cdc Ω DC link capacitor ESR rpcdc2 4 kω DC link capacitor parallel resistance II. CONTROL OF GS-1 The one-line diagram of the control is depicted in Fig. 2. Therein, v dc denotes the reference (or commanded) dc voltage, vˆ dc denotes the low-pass filtered dc bus voltage with filter time constant τ fv, and î dc denotes the low-pass filtered inductor current with filter time constant τ fi. The reference dc voltage is slew-rate limited to prevent excessive capacitor inrush currents on startup. Short circuit protection is also included by sharply reducing the voltage command when the current exceeds a certain threshold. The droop term, k, allows multiple generators to share the load. Voltage regulation utilizes a PI control with anti wind-up. The proportional and integral gains of the PI control are denoted as k pv and k iv respectively. The output of the control is the commanded field current into the brushless exciter, control parameters are listed in Table II. III. DETAILED WAVEFORM MODEL i fde d. The In the highly detailed model, the synchronous machine model and the brushless exciter model are obtained from [1]- [2]. In particular, the synchronous machine model employs a transfer function model as opposed to the equivalent circuit model commonly found in the literature. The prime mover, as mentioned previously, is modeled as a constant speed. In this work, the commanded speed is 1800 rpm. The control is described in Section II.
2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 Fig. 1. Generation Source GS-1. Fig. 2. GS-1 Control. The rectifier model utilized in the highly detailed model is a three-phase diode rectifier with line commutation. A thyristor- a similar based rectifier model is set forth in [3]. However, model can be utilized when a diode rectifier is considered. IV. SIMPLIFIED WAVEFORM MODEL The simplified waveform model of GS-1 replaces the highly detailed synchronous machine model with the model set forth in [3]. However, the models depicted in [3] require lumped circuit machine parameters, such as the q- and d-axis damper bar resistances and leakage inductances, which are not available in [1]. By fitting the frequency response of the q- and d-axis transfer functions expressed in terms of machine parameters to the transfer functions in [1], the values of resistance and inductance can be obtained. The frequency response curve fit for the q-axis and d-axis transfer functions are shown in Figs. 3 and 4, respectively. It was sufficient to represent the machine with one damper bar in the q-axis and one damper bar in the d-axis. The machine parameters are given in the Table III.
3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 TABLE II. GS-1 CONTROL PARAMETERS Parameter Value Description i fde, max 3.0 A Brushless exciter maximum field current i sc 92 A Short circuit current protection i thr 84 A Threshold current τ slr 1.0 ms Slew rate limit time constant kd 0.59 Ω Droop term kpv 7.5 ma/v Proportional gain k iv 10 ma/v-s Integral gain τ fv ms Bus voltage filter time constant τ fi ms Inductor current filter time constant p vdc,max 500 V/s Maximum dc voltage rate of increase Fig. 3: Frequency response of the q-axis transfer function. TABLE III. SYNCHRONOUS MACHINE PARAMETERS Parameters Value Description L mq 8.75 mh q-axis magnetizing inductance L md mh d-axis magnetizing inductance r s Ω Stator winding resistance l ls 0.97 mh Stator winding leakage inductance l lkd 4.2 mh d-axis damper winding leakage inductance rkd Ω d-axis damper winding resistance llfd 0.1 mh d-axis field winding leakage inductance rfd Ω d-axis field winding leakage resistance l lkq mh q-axis damper winding leakage inductance rkq Ω q-axis damper winding resistance N s / N fd Stator winding to field winding ratio P 4 Number of poles ( k i v + v ) 1 = (1) τ pv fd r fde fd fd, offset vfd The reduced order exciter parameters are listed in Table IV. These parameters are obtained by applying step changes in the commanded field current i fde to the brushless exciter model and observing the behavior of the field voltage v fd. The remaining components of the simplified waveform model including the prime mover, the exciter control, and the rectifier are the same as for the detailed waveform model. TABLE IV. REDUCED ORDER EXCITER PARAMETERS Parameters Value Description τ vfd 1.0 ms Integration time constant k r 15 Ω Proportional gain v fd, offset 2.0 V Field voltage offset Fig. 4: Frequency response of the d-axis transfer function. The simplified waveform model is also different from the detailed waveform model in that it replaces the brushless exciter model with a transfer function between the commanded field exciter current i fde and the field voltage of the synchronous machine expressed as v fd. The simplified exciter model is V. AVERAGE VALUE MODEL (AVM) In the non-linear average value model (AVM), the prime mover model is the same as the highly detailed and the detailed model. The brushless exciter is modeled the same as for the detailed model using the transfer function in (1). The synchronous machine model utilized is a reduced order model which neglects the machine dynamics in the stator. The model is presented in the chapter on reduced-order machine equations in [3], and it again requires the machine parameters given in Table III. Lastly, the average value model of the rectifier is set forth in [4].
4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 VI. SIMULATION STUDIES Simulation results are now presented. For the following studies, GS-1 provides power to a constant power load whose load varies as a function of time. In particular, the scenario shown in Table V, which includes both step load increases and a step load decrease, is considered. TABLE V. SIMULATION SCENARIO Event Time Enable GS s 5 kw Load 3.0 s 10 kw Load 3.5 s 15 kw Load 4.0 s 20 kw Load 4.5 s 10 kw Load 5.0 s Fig. 6. Detailed waveform simulation dc current. Figs. 5-7 depict the bus voltage, inductor current, and the phase current, respectively, of the detailed waveform models. Figs depict the results obtained using the simplified waveform models. In particular, Fig. 8 depicts the bus voltage, Fig. 9 depicts the dc inductor current, and Fig. 10 depicts the phase current of the synchronous machine. Lastly, Figs depict the results obtained using the non-linear average value model. In particular, Fig. 11 depicts the bus voltage, Fig. 12 depicts the dc inductor current, and Fig. 13 depicts the fundamental component of the ac current. Fig. 7. Detailed waveform simulation synchronous machine phase current. Fig. 5. Detailed waveform simulation bus voltage. Fig. 8. Simplified waveform simulation bus voltage.
5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 Fig. 9. Simplified waveform simulation dc current. Fig. 12. AVM simulation dc current. Fig. 10. Simplified waveform simulation synchronous machine phase current. Fig. 13. AVM simulation fundamental component of ac current. From these figures, the results obtained from the detailed waveform model, the simplified waveform model, and the non-linear average value model are consistent. Fig. 11. AVM simulation bus voltage. REFERENCES [1] D. C. Aliprantis, S. D. Sudhoff, and B. T. Kuhn, A Synchronous Machine Model with Saturation and Arbitrary Rotor Network Representation,.IEEE Trans. Energy Convers., vol. 20, no. 3, pp , Sep [2] D. C. Aliprantis, S. D. Sudhoff, and B. T. Kuhn, A Brushless Exciter Model Incorporating Multiple Rectifier Modes and Preisach s Hysteresis Theory,.IEEE Trans. Energy Convers., vol. 21, no. 1, pp , Mar [3] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, 2 nd. ed, New York: John Wiley and Sons/IEEE Press, [4] S. D. Sudhoff, K.A. Corzine, H.J. Hegner, and D.E. Delisle, Transient and Dynamic Average-Value Modeling of Synchronous Machine Fed Load-Commutated Converters IEEE Trans. Energy Conv., vol. 11, no. 3, Sept. 1996, pp Michelle Bash received a B.S. in electrical engineering from Ohio Northern University in 2006 and an M.S. in electrical engineering from Purdue University in She is currently working towards a Ph.D. degree in electrical engineering at Purdue University. Her interests include electric machines, power electronics, and machine design.
6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 Ricky R. Chan received a B.S. and M.S. degrees in electrical engineering from Purdue University, West Lafayette, IN, in 2003 and 2005, respectively, where he is currently pursuing the Ph.D. degree in electrical engineering. His research interests include power electronic converters, power system, and population based optimization techniques.
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