Coordinated Control of EPT and Generator Excitation ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008

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Coordinated Control of EPT and Generator Excitation System for Multidouble-Circuit Transmission-Lines System Dan Wang, Member, IEEE, Chengxiong Mao, Member, IEEE, and Jiming Lu

Abstract—A new optimal coordinated control strategy between an electronic power transformer (EPT) and generator excitation is proposed to improve power system dynamic performance and stability. The studied system is based on a single-machine multidouble-circuit transmission-lines (SMTL) system. In the SMTL system, the generator is connected to an infinite bus through a conventional power transformer with a double-circuit transmission line, and to another infinite bus with an EPT with a doublecircuit transmission line. The mathematical model of the SMTL system is established, and the proposed optimal coordinated control strategy is upon linear optimal control theory. Numerical simulations were carried out for the SMTL system, and the simulation results showed that the proposed control strategy has good dynamical performance for a variety of disturbances, and can improve the system damping and voltage performance effectively. Index Terms—Electronic power transformer (EPT), generator excitation, optimal control, power-electronic transformer (PET), transformer.

NOMENCLATURE AVR EPT FACTS LOEC PSS SMIB SMTL VSC VSC–HVDC

Automatic voltage regulator. Electronic power transformer. Flexible ac transmission system. Linear optimal excitation control/controller. Power system stabilizer. Single-machine infinite bus. Single-machine multidouble-circuit transmission lines. Voltage-source converter. VSC-based HVDC. I. INTRODUCTION

A

N ELECTRONIC power transformer (EPT), also called a power-electronic transformer (PET), is a novel transmission and transformation device based on power electronics, which can be applied in transmission or distribution power systems. A significant advantage of EPT is that the magnitude and phase angle of voltages in both the primary side and the secondary side of EPT can be controlled in real time through power-

Manuscript received August 29, 2006; revised December 14, 2006. This work was supported in part by the Program for New Century Excellent Talents in University and in part by the Excellent Young Teachers Program of MOE, R.O.C. Paper no. TPWRD-00500-2006. The authors are with the Department of Electrical Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. Digital Object Identifier 10.1109/TPWRD.2007.905552

electronic converters to achieve flexible regulation of the current and power. So EPT can be regarded as a power transformer with the functions of flexible ac transmission systems (FACTS) or distribution flexible ac transmission system (DFACTS) device. In fact, EPT is a multifunctional flexible transmission and distribution systems device. It not only can realize power-flow control, voltage control, static and transient stability improvement, oscillation damping when it is applied to transmission systems, but when used in distribution systems, it also can solve the power-quality (PQ) problems, such as voltage sags, voltage swells, overvoltages, undervoltages, voltage fluctuations, voltage unbalance, and harmonics. Since the active and reactive power of EPT can be regulated independently, it has the great potential to optimize reactive power flow in transmission or distribution systems. Another characteristic of EPT is that the voltage level and frequency are able to change simultaneously. This means that EPT can offer the custom power supply with a particular voltage level and particular frequency without additional power transformers and frequency conversion equipment. So compared with conventional FACTS or DFACTS devices, EPT has more powerful functions. Compared with the voltage-source converter–HVDC (VSC–HVDC), EPT only has a high-frequency transformer to realize a voltage level change. As the size of transformer is inversely proportional to its work frequency, the size of the high-frequency transformer will be much smaller than that of the power-frequency transformer. EPT not only has an ac bus, but it also has two different voltage-level dc buses. So it can be more easily used to connect the different types of distributed generation sources and energy storage devices than VSC–HVDC. In recent years, EPT has attracted much attention from both academy and industry. A lot of literature has studied its work mechanisms and topology design [1]–[10]. And the applications of EPT to a power system have also been studied [8]–[15]. But most of these application studies on EPT mainly focused on its applications to the distribution system. And less attention was paid in the areas of the applications of the EPT to the transmission system. In [13], EPT was located at the midpoint of the long transmission lines and controlled as a voltage source to improve the dynamic characteristics of the transmission system. References [14] and [15] discussed the control methods of EPT to improve the single-machine infinite bus system (SMIB) stability. In [15], the optimal-coordinated EPT and generator excitation control was designed for SMIB. And simulation results showed that the

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Fig. 1. System model with EPT. (a) Structure of the system. (b) Structure of the EPT. (c) Simplified basic diagram of the EPT.

Fig. 2. Coordinated controller of EPT and the generator excitation system.

optimal coordinated control have very good performance for a generator–EPT unit. However, for the actual power system, the single-machine (or equivalent) multidouble-circuit transmission lines (SMTL) system is more common than the SMIB system because more huge scale generators were put into operation [16]. And the interaction between transmission systems can be studied in the SMTL system. So the performance of EPT and the coordination between EPT and the conventional transformer can be deeply verified in an SMTL system. The application of EPT to an SMTL system with a conventional power transformer power system is discussed, a new kind of optimal performance index is proposed for the coordinated EPT and a generator excitation control strategy, and a new optimal coordinated control law is obtained in this paper. In the studied SMTL system, the generator is connected to an infinite bus through a conventional power transformer with a double-circuit transmission line (line 1), and to another infinite bus by an EPT with a double-circuit transmission line (line 2).

Fig. 3. System with a coordinated controller response to a 5% generator reference voltage step change.

II. SYSTEM OVERVIEW The SMTL power system with EPT is shown in Fig. 1(a). It consists of a generator, a conventional power transformer, an

EPT, and two double-circuit transmission lines. The configuration of an EPT is shown in Fig. 1(b). As can be seen, the EPT

WANG et al.: COORDINATED CONTROL OF EPT AND GENERATOR EXCITATION SYSTEM

consists of a front-end voltage-source converter (VSC), two H-bridge converters, a high-frequency transformer, a back-end VSC, and two filter inductors. The two H-bridge converters and high-frequency transformer constitute a high-frequency modulating–demodulating block only for voltage transformation and isolation. The transient of this block is so fast compared with that of the external power system that it can be omitted in the stability or oscillation damping analysis [17]. Therefore, the reasonable simplified equivalent model can be described in Fig. 1(c). The excitation system provides field current for the synchronous generator including power, regulating, control, and protective elements. The synchronous generator terminal voltage or reactive power can be regulated by a changing field current which is realized by the excitation controller. In the modern power system, an automatic voltage regulator with a power system stabilizer (AVR+PSS) and a linear optimal excitation controller (LOEC) are the two most popular excitation controllers in China. In this paper, a coordinated excitation control with EPT control is designed on the basis of linear optimal control theory. The detail is given in the following sections. and are the equivalent inductances of the In Fig. 1, is the conventional transformer and line 1, respectively. and are the filter equivalent inductance of line 2, inductances, and is the dc capacitance. and are the and output active and reactive power of the generator. are the input active and reactive power of EPT, whereas and are the output active and reactive power of EPT. and are the ac voltage of the VSCs in the primary and the and are the output secondary sides of EPT, respectively. voltages of conventional transformer and EPT, respectively. is the generator terminal voltage. and are the voltages and refer to the of infinite buses 1 and 2, respectively. amplitude-modulation index and phase angle of the control signal of each VSC, respectively, and is the transformation ratio of the high-frequency transformer.

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Fig. 4. Conventional SMTL response to a 5% generator reference voltage step change.

Ignoring the loss of EPT and the harmonics, the active power and the current of the dc bus can be given by (4)–(7)

(4) (5)

III. OPTIMAL COORDINATED CONTROL DESIGN For the dynamics of the system shown in Fig. 1, the following differential equations and algebraic equations are satisfied:

(1) (6) (7) (2) Linearizing state (1)–(7), we can obtain

(3) (8) where coefficients in (2) and (3) are defined in Appendix A.

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Fig. 5. System with the coordinated controller response to the opening and closing of one of the transmission lines in line 1.

where

, the

where

(9) (10)

, and elements of matrices and are given in Appendix A. is not easy to be measured, is replaced by , Since as shown in (13) at the bottom of the page. Linearizing (13) (14)

(11) Substituting (9)–(11) into (8), the state variable equations of the power system installed with EPT can be obtained

Let relation between

, and then we can get the and

(12)

(13)


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Here, transformation matrices and can be acquired from appearing in state (14). In order to avoid the differential of equations, a new state vector is introduced (15) and then (16) , . where According to the linear optimal control theory, the performance index is defined (17) where and are the weighting matrices. Minimizing the performance index of (17) will guarantee the and . In fact, we hope to guaroptimal performance of and . So the perforantee the optimal performance of mance index is redefined (18) Substituting (15) into (18), as shown in (19) at the bottom of the page, where and are the equivalent weighting matrices. Minimizing , the optimal control law can be obtained as [18] (20) and (21) is the solution of the Riccati equation

(22) Substituting (14) into (19), yields

where

Fig. 6. Conventional SMTL response to the opening and closing of one of the transmission lines in line 1.

The coordinated controller of EPT and the generator excitation system is shown in Fig. 2. IV. NUMERICAL SIMULATIONS To demonstrate the effectiveness of the proposed control strategy, numerical simulations are carried out based on the system in Fig. 2. The system parameters and operation conditions are given in Appendix A. For comparison, an SMTL system with only two conventional transformers (defined as conventional SMTL) is also simulated. Here, the generator is equipped with an AVR+PSS controller. The configuration and parameters of the conventional SMTL are given in Appendix B.

(23)

A. 5% Generator Reference Voltage Step Change

(24)

The reference voltage suddenly changes from 1.0 p.u. to 1.05 p.u. The results are shown in Figs. 3 and 4. Compared with the conventional SMTL with only AVR+PSS, it can clearly be

is the optimal feedback gain.

(19)

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Fig. 7. System with a coordinated controller response to the three-phase-to-ground fault in line 1.

observed that the oscillation magnitude of the generator is very small and the voltage reaches its steady value in a short period in the SMTL system with a coordinated controller. The results shown in Fig. 3 also imply that EPT and generator excitation can coordinate under a small disturbance.

B. Opening and Closing of One of the Double-Circuit Transmission Lines in Line 1 One of the double-circuit transmission lines in line 1 opens suddenly and then closes after 3.5 s. The simulation results are shown in Figs. 5 and 6. The responses of the power angle and generator terminal voltage in the SMTL system with a coordinated controller have smaller amplitudes and less duration than those in a conventional SMTL with AVR+PSS. The reason is that EPT has very fast regulating capability to absorb the “surplus” active power from line 1 in time, so the generator suffer only a very small disturbance, which can be calmed down easily by the excitation controller.

C. Three-Phase to Ground Fault in Line 1 A three-phase-to-ground fault occurs at 0.5 s and is cleared after 100 ms in line 1. The responses are shown in Figs. 7 and 8. Compared with AVR+PSS for the conventional SMTL system, it can be seen that the optimal coordinated controller can provide very strong and very fast damping and guarantee very good voltage performance. The simulation results shown in Fig. 7 also indicate that EPT and generator excitation can coordinate under a large disturbance.

D. Opening and Closing of One of the Double-Circuit Transmission Lines in Line 2 One of the double-circuit transmission lines in line 2 is opened suddenly and then closed after 3.5 s. The responses are shown in Figs. 9 and 10. It can be seen from the figures that the proposed coordinated controller is more effective than AVR+PSS. Comparing the curves in Fig. 9 and in Fig. 5, it is


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Fig. 8. Conventional SMTL response to a three-phase-to-ground fault in line 1.

obvious that the transient responses in Fig. 9 are much larger than those in Fig. 3. The reason is: When the disturbance occurs in line 1, the EPT can rapidly regulate the active power of the system; but when the disturbance occurs in line 2, the regulation ability of EPT is limited just during the disturbance, and the conventional power transformer has no active power regulation ability. Anyway, the regulation ability of the EPT is restored just after the disturbance, so the coordinated controller of the EPT and excitation can still provide strong damping against the oscillations. E. Three-Phase-to-Ground Fault in Line 2 A three-phase-to-ground fault occurs at 0.5 s and is cleared after 100 ms in line 2. The responses are shown in Figs. 11 and 12. As can be seen, the optimal coordinated control can provide much stronger damping than AVR+PSS under a large disturbance. V. CONCLUSION Based on a single-machine multidouble-circuit transmissionlines power system, a new optimal coordinated controller of EPT and excitation is proposed. The simulation results show that EPT can be coordinated with a generator excitation system, and the proposed controller can improve the performance of the power system under small and large disturbances. APPENDIX A COEFFICIENTS, ELEMENTS, AND PARAMETERS Fig. 9. System with a coordinated controller response to the opening and closing of one of the transmission lines in line 2.

Coefficients of (2)–(3) , , ,

, ,

,

, ,

,

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Fig. 10. Conventional SMTL response to the opening and closing of one of the transmission lines in line 2.

Nonzero elements of matrix , , ,

,

, , ,

, ,

,

Nonzero elements of matrix , , , ,

, ,

, ,

Generator and system parameters in per unit , , , , , , , , The initial operation point: , , ,

,

, ,

,

.

APPENDIX B CONVENTIONAL SMTL SYSTEM CONFIGURATION AND PARAMETERS The conventional SMTL system configuration is shown in Fig. 13. The initial operation point Fig. 11. System with a coordinated controller response to a three-phase-toground fault in line 2.


Fig. 12. Conventional SMTL response to a three-phase-to-ground fault in line 2.

Fig. 13. Conventional SMTL system configuration.

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[8] E. R. Ronan, S. D. Sudhoff, S. F. Glover, and D. L. Galloway, “A power electronic-based distribution transformer,” IEEE Trans. Power Del., vol. 17, no. 2, pp. 537–543, Apr. 2002. [9] C. Mao, S. Fan, D. Wang, H. Fang, and Y. Huang, “Theory of power electronic transformer and its applications (part I),” High Voltage Eng., vol. 29, no. 10, pp. 4–6, 2003. [10] C. Mao, S. Fan, Y. Huang, and J. Lu, “Theory of power electronic transformer and its applications (part II),” High Voltage Eng., vol. 29, no. 12, pp. 1–3, 2003. [11] M. D. Manjrekar, R. Kieferndorf, and G. Venkataramanan, “Power electronic transformers for utility applications,” in Proc. IEEE Ind. Appl. Soc. Annu. Meeting, 2000, vol. 4, pp. 2496–2502. [12] M. Marchesoni, R. Novaro, and S. Savio, “AC locomotive conversion systems without heavy transformers: Is it a practicable solution?,” in Proc. IEEE Int. Symp. Ind. Electron., 2002, vol. 4, pp. 1172–1177. [13] J. Cao et al., “Improving power system dynamic characteristics with power electronic transformer,” Elect. Power Autom. Equip., vol. 25, no. 4, pp. 65–68, 2005. [14] Y. Huang et al., “Study on control strategy for power electronic transformer in power system,” Relay, vol. 32, no. 6, pp. 35–39, 2004. [15] S. Fan, C. Mao, and L. Chen, “Optimal coordinated PET and generator excitation control for power systems,” Int. J. Elect. Power Energy Syst., vol. 28, no. 3, pp. 158–165, 2006. [16] W. Xizai, Power Engineering. Wuhan, China: Huahzhong Univ. Sci. Technol. Press, 2004, pp. 29–38. [17] Y.-X. Ni and S.-S. Chen, Theory and Analysis of Dynamic Electric Power System. Beijing, China: Tsinghua Univ. Press, 2002, pp. 97–103, 106-109. [18] J. Doyle, in Advances in Multivariable Control, Minneapolis, MN, Oct. 8–10, 1984, Lecture Notes at ONR/Honeywell Workshop.

Dan Wang (M’07) was born in Jiangxi, China, in 1977. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology (HUST), Hubei, China, in 1999, 2002, and 2006, respectively. He is currently conducting postdoctoral research at HUST. His interest is the application of high-power electronic technology to power systems and excitation control of synchronous generators.

AVR+PSS

REFERENCES [1] H. Wrede, V. Staudt, and A. Steimel, “Design of an electronic power transformer,” in Proc. IEEE/IES 28th Annu. Conf., 2002, pp. 1380–1385. [2] J. L. Brooks, “Solid state transformer concept development,” in Naval Mat. Command. Port Hueneme, CA: Civil Eng. Laboratory, Naval Construction Battalion Ctr., 1980. [3] K. Harada, F. Anan, K. Yamasaki, M. Jinno, Y. Kawata, T. Nkashima, K. Murata, and H. Sakamoto, “Intelligent transformer,” in Proc. IEEE Power Eng. Soc. Conf., 1996, pp. 1337–1341. [4] Proof of the Principle of the Solid-State Transformer the AC/AC Switch Mode Regulator EPRI TR-105067, Res. Project 8001-13, Final Rep., 1995. [5] M. Kang, P. N. Enjeti, and I. J. Pitel, “Analysis and design of electronic transformers for electric power distribution system,” IEEE Trans. Power Electron., vol. 14, no. 6, pp. 1133–1141, Nov. 1999. [6] C. Mao, J. Lu, S. Fan, and H. Fang, “Power electronic transformer,” China Patent ZL 02 1 39030.4, 2002. [7] J. Cheng, C. Mao, S. Fan, and D. Wang, “Principle of electronic power transformer and its simulation study,” Electr. Power Autom. Equip., vol. 24, no. 12, pp. 23–25, 2004.

Chengxiong Mao (M’93) was born in Hubei, China, in 1964. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology (HUST), Hubei, in 1984, 1987, and 1991, respectively. He was a Visiting Scholar with the University of Calgary, Calgary, AB, Canada, from 1989 to 1990 and at Queen’s University of Belfast, Belfast, U.K., from 1994 to 1995, respectively. He conducted research at the Technische Universitaet Berlin, Berlin, Germany, from 1996 to 1997 under the support of the Humboldt Foundation. Currently, he is a Professor at HUST. His fields of interest are power system operation and control, excitation control of the synchronous generator, and applications of high-power electronic technology to power systems.

Jiming Lu was born in Jiangsu, China, in 1956. He received the B.S. degree from Shanghai Jiaotong University, Shanghai, China, and the M.S. degree from Huazhong University of Science and Technology (HUST), Hubei, China. Currently, he is a Professor with HUST. His research is focused on excitation control based on microcomputers.