Direct-start of the Flexible Power Conditioner with Back-to-back Converters Huang Daocheng1, Zhao Yang2, Zou Xudong1, Liu Xinmin1, Cao Fengxiang1, Kang Yong1, Cheng Shijie1 1

College of Electrical and Electronic Engineering, Huazhong University of Science and Technology Wuhan 430074, Hubei Province, China 2

College of Electrical and Electronic Engineering, Hubei University of Technology,

Wuhan 430068, Hubei Province, China FPC DFIM based on vector control. On the supply side of back-to-back converters, the voltage control mode is employed; while on the rotor side, the speed control mode is utilized. By limit of control variables, the control system could largely diminish the start impulsion to the equipment and power system, restraint the power flowed between the power system and the equipment, and keep a constant large torque to shorten the start time. Detailed theoretical analysis of the direct-start control strategy proves that this strategy could meet most system requirements during the start process. And experiment Keywords-Flexible power conditioner, doubly-fed induction results of a small capacity system verify it.

Abstract-The multi-functional flexible power conditioner (FPC), which can be considered as a doubly-fed induction machine (DFIM) with a flywheel, is a new kind of Flexible AC Transmission Systems (FACTS) equipment. It can regulate active power rapidly to enhance power system stability and forestall many power system faults. For the special needs of the start process of FPC, a novel direct-start control strategy, which includes some treatments to the speed control system of the rotor-side of back-to-back converters, is proposed in this paper. Detailed analysis of this strategy and experimental result show that it can effectively avoid the start impulsion to the equipment and power system and restraint the power flowed between them. machine, direct-start, back-to-back converters, speed control mode

I. INTRODUCTION Flexible power conditioner (FPC), which can enhance the stability of power system, is one of the novel FACTS equipments. It makes use of an advanced synchronous condenser with a flywheel, which is controlled by a vector technology based on an AC excitation system. This is made up of back-to-back SVPWM converters. Incorporating the functions of the synchronous condenser and flywheel energy storage, the FPC can perform multi-functions including energy storage, active and reactive power regulation in power system. With such characters, it can considerably stabilize the power system and forestall those faults of power system when the imbalance of active and reactive power happens. This method is called active stabilization [1, 2]. The FPC, showed in Figure 1, is made up of a doubly-fed induction machine (DFIM), a flywheel, back-to-back converters for AC excitation and the microchip controller. The FPC DFIM can be considered as a doubly-fed induction generator without prime mover or a doubly-fed induction motor without mechanical load, thus it can be started when a little electromagnetic torque, which overcomes the friction, is addressed. This start process, in which the FPC DFIM is started from the static only by AC excitation without any device switching, is called direct-start. Recently, many papers have been published which discuss the quasi-synchronizing paralleling of the doubly-fed induction generator [3]. However, most of them give little information on the direct-start of the doubly-fed induction machine. This paper presents a novel direct-start control strategy of

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Figure 1. Flexible Power Conditioner.

II. CONTROL STRATEGY OF SUPPLY-SIDE CONVERTER The aim of the supply-side converter is to keep the DC-link voltage constant regardless of the magnitude and direction of the rotor power. A vector-control method is used, with a synchronously rotating d-q reference frame oriented along the grid voltage vector position, enabling independent control of the active and reactive power flowing between the grid and the supply-side converter. The converter is current regulated, with the d-axis current used to regulate the DC-link voltage and the q-axis current component used to regulate the reactive power [4]. Figure 2 shows the schematic of the supply-side converter. The mathematical model of the supply-side converter is showed below:

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­vd ° ® vq ° ¯

 Lpid  Rid  Z1 Liq  ud  Lpiq  Riq  Z1 Lid  uq C ˜ pU dc idc  iL

(1)

with the d-axis oriented along the stator flux position. The generator conversion is used in the stator side of FPC DFIM [7], and the motor conversion, which is on the contrary, is used in the rotor side. All these conversions are power invariance coordinate conversions. The mathematical model of the FPC DFIM is given below: Flux linkage equation:

Figure 2. Supply-side Converter of Back-to-back Converters

With R being the resistance, L is the inductance, u is the grid voltage, v is the input voltage of converter, p is the derivative operator, Ȧ1 is the synchronous electrical angular velocity, d and q indicate the direct and quadrature axis components of the reference frame, and Udc is the DC-link voltage. And the power equation is given as:

­ P ud id  uq iq ud id U dc iL ® ¯ Q uq id  ud iq ud iq

(2)

 Ls ids  L0idr

­ < ds °< ° qs ® ° < dr °¯ < qr

Voltage equation:

 Ls iqs  L0iqr  L0ids  Lr idr

(3)

 L0iqs  Lr iqr

­uds  Rs ids  p< ds  Z1< qs °u ° qs  Rs iqs  p< qs  Z1< ds ® ° udr Rr idr  p< dr  Z2 < qr °¯ uqr Rr iqr  p< qr  Z2 < dr

(4)

Electromagnetic torque equation:

Equation (1), (2) construct the voltage control system of the supply-side converter, as shown in Figure 3. In this system, 3s/2s represents the conversion from the abc reference frame to the Į-ȕ reference frame, 2r/2s, 2s/2r represent the mutual conversion between the d-q reference frame and the Į-ȕ reference frame, K/P represents the calculation process of the magnitude and angle of the input vector. III. CONTROL STRATEGY OF FPC DFIM The modeling of FPC DFIM can be referred to the DFIM’s [4-6]. A synchronously rotating d-q reference frame is used

Tem

(5)

Rotor motion equation:

Tem

1 np

( D  Jp )Zr

(6)

Stator-side power equation:

­ Ps uds ids  uqs iqs ® ¯Qs uqs ids  uds iqs

Figure 3. Voltage control system of the supply-side converter.

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n p L0 (iqs idr  ids iqr )

(7)

With R being the resistance, L is the inductance, u is the voltage, Ȍ is the flux linkage, D is the viscous friction coefficient, np is the number of pole pairs, J is the moment of inertia, Ȧr is the rotor electrical angular velocity, p is the derivative operator, The subscripts d and q indicate the direct and quadrature axis components of the reference frame and s and r indicate stator and rotor quantities, respectively. All quantities above are functions of time. In order to simplify the model above, it is assumed that (a). neglecting the influence of the stator flux linkage's transient state and orienting the d-axis of the synchronous frame to the direction of the stator flux vector. (b). omitting the stator resistance Rs. Equation (7) and (4) can be written as: ­ P | U L0 i s sm qr °° Ls  (8) ® L i U Z  dr sm 1 0 °Q | U sm °¯ s Z1 Ls

­udr ( Rr  V Lr p )idr  Z2V L r iqr ° udr1  'udr ° ° (9) L0 ® °uqr ( Rr  V Lr p )iqr  Z2V L r idr  Z2 L < sm s ° °¯ ˙uqr1  'uqr  'u

With ı=1-Lo2/LsLr being leakage reactance factor, Ȧ1 is the stator electrical angular velocity, Ȧ2 is the slip electrical angular velocity, ǻudr and ǻuqr are the decoupled compensations, udr1 and uqr1 are the decoupled elements, ǻu is the feed-forward element. And equation (3) can be deduced to:

Tem |

L0 U sm Ls Z1

n p iqr

(10)

Equation (4), (6), (7), (8) and (10) form the speed control system of FPC DFIM, which is showed on Figure 4. șs is the electrical angle of stator flux, șr is the electrical angle of rotor position, șslip is the slip electrical angle, U*rm is the reference magnitude of rotor voltage and ș*r is the reference angle of rotor voltage. Based on equation (8) and (9), another control system, the power control system, can be constructed as well. IV. START STRATEGEIES OF FPC DFIM Treated as a generator, the FPC DFIM need an assistant motor and a quasi-synchronization device to start. Nevertheless, these will significantly increase the cost and complexity of the whole system.

Figure 4. Speed control system of the rotor-side converter.

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There are two kinds of start strategies for the FPC DFIM, when treated as a motor. The first is called serial rotor resistance start. The other is the direct-start strategy using back-to-back SVPWM converters connecting the rotor windings and the grid. The first strategy is commonly used in frequency conversion start [8]. Nevertheless, the weight and size of the entire device are increased due to the extra resistor or reactor. Furthermore, the mode switch is complicated, and the cost of the entire control system is also increased. The back-to-back converters can generate AC voltage of a wide frequency range including the power system frequency. Thus it can directly start the FPC DFIM. As mentioned above, there are two modes of direct-start strategy, which are based on power control mode and speed control mode. The detailed analysis about power control mode is mentioned in document [8]. And the speed control mode is discussed below. V. DIRECT-START OF FPC DFIM Four key problems need to be considered during the direct-start process of FPC DFIM. The first problem is how to keep the DC-link voltage of back-to-back converters stable. The second is how to reduce the impulse current when the AC excitation is cut in the rotor windings. Thirdly, the active power transferred between the FPC and the power system during the start process should be restrained. The last is how to increase the electromagnetic torque to shorten the time of start. If the DC-link voltage of back-to-back converters is unstable, the AC voltage generated from the back-to-back converters is also unstable. When the DC-link voltage is small enough that the needed AC voltage can not be generated. This situation would make the FPC DFIM out of control. Before the start of the FPC DFIM, the stator is connected to the grid. At this moment when the FPC DFIM is static, the FPC DFIM can be treated as a transformer. Thus, the frequency and phase of the rotor EMF (electromotive force) is the same as the grid, while the ratio of its amplitude and the grid’s is the same as that of stator and rotor. Only when the difference between the voltage of the rotor-side of back-to-back converters and the rotor EMF is little, the rotor-side of back-to-back converters could be connected to the rotor windings, or else, a large impulse current, which can damage the machine and the back-to-back converters, may be generated. The main function of FPC is to absorb and release the active power to stabilize the power system. If the FPC sucks a lot of active power during the start process, the stability of the power system will be weakened. To avoid the results mentioned above, some actions should be taken on the control system of FPC DFIM. The DC-link voltage is offered by the supply-side of back-to-back converters. The supply-side converter is current regulated, with the d-axis current component used to regulate the DC-link voltage and the q-axis current component used to regulate the reactive power [4].

The power control mode in the rotor-side of back-to-back converters can well control the active and reactive power transferred between the power system and the FPC DFIM. However, it can not maintain the machine at a constant speed. Thereby, if the power control mode is employed, the switch to speed mode is necessary. Nevertheless, the speed control mode has not that problem, and following discussion will show the speed mode also can control the power well during the start progress. In the speed mode, the q-axis current is used to regulate the speed, and the d-axis current is used to regulate the reactive power. Using speed control mode, several treatments are needed for solving these key problems mentioned before. The speed control system of FPC DFIM is in Figure 4. To diminish the impulse current, two restraint treatments are used. The first is to restrain the input error of each controller. The next is to restrain the reference magnitude of rotor voltage U*rm. The relationship of the stator voltage and rotor voltage is showed below:

U rm

Z1  Zr

s ˜ k ˜ U sm

Z1

˜ k ˜ U sm

(11)

With s being the slip, Urm is the amplitude of rotor voltage, k is the turn ratio of the FPC DFIM when the rotor is static. Before the start, Ȧr=0, s=1, from the equation (11), Urm=kUsm can be deduced. During the start, Ȧr rises, and s drops, so does Urm. Only when the speed of the FPC DFIM is larger than the twice of synchronous speed or the speed inverses, Urm can be larger than kUsm, but this situation can not happen during the FPC operation progress. Thereby, when the grid voltage is stable, the maximum of Urm is kUsm, which can be set as the limit of U*rm. At the same time, the rotor currents and speed are all zero. Thus, following equation can be deduced from equation (9):

­udr ° ® °uqr ¯

0

Z1

L0 Ls

< sm

'u

(12)

The feed-forward element ǻu now plays a dominant role. When the rotor-side of the back-to-back converters is cut in the rotor windings, the feedbacks of speed and rotor currents are near zero, so the input errors of the speed controller and current controller are the all limit values which are very small. The sums of the output of current controller, which are also small quantities, so the value of U*rm is a little less than its limit. Therefore, the error between the two voltages of the rotor-side of back-to-back converters and the rotor is so little that nearly no impulse current generates. And phase locking is needed to keep the phases of the two voltages alike. There is also a treatment restraining the power transferred between the grid and the FPC DFIM and to maintain a large electromagnetic torque. It is to confine the output of each controller. After the cut-in moment, the real speed of FPC DFIM is

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much less than the Ȧ*r, so the output of speed controller is a limit value until the end of start, that is, the speed loop is like an open loop. Then, the rotor current quickly rises until it near the output of the speed loop (iqr*). Because of the constant output of the speed loop, iqr would not change until the end of the start. From the equation (10), the electromagnetic torque Tem, which are proportional to iqr, are also constant. At this time, the output of speed controller (iqr*) is the maximum, so the electromagnetic torque is also the maximum. From the equation (10), the active power Ps, which are proportional to iqr, are also constant, that is, it is confined. When the speed is near the demand, the input error of speed controller is smaller than the limit, so the output of it would be it no longer. Now the speed loop plays a major role to keep the speed stable. The theoretical analysis demonstrates that the speed control mode is an ideal direct-start mode, which needs not any switching strategy. Only some limit treatments could fulfill the system requirements. And the following experimental system of a small capacity proves it.

Figure 5. DC-link voltage and phase current of grid of the supply-side converter.

VI. EXPERIMENTAL RESULTS An experimental system, showed in Figure. 1, is constructed for testing this control strategy. The supply-side converter is connected to the grid by a transformer. The ratio of this transformer is 380V/110V, and the capacity is 2500VA. A TMS320F240 DSP-based digital control platform is designed and employed for implementing the proposed control strategy. The supply-side converter employed the control strategy mentioned at the section two, and the rotor-side converter uses the one proposed in section 5. The demand DC-link voltage is 400V, the demand speed is 1700r/min, and the demand reactive power is -1500var. Parameters of the FPC DFIM are given in the Appendix. The system is started in the following manner. Initially, the supply-side converter is started to form and stable the DC-link voltage. Then, the rotor-side of converters cuts in at the moment of 4s. During the whole start process, the DC-link voltage is kept well, and the fluctuation of this voltage is no more than 4V, as showed in Figure 5. At the point of 4s, the cut-in time, the rotor voltages have no sudden change in Figure 7, thus the rotor currents have little impulsion in Figure 6. The speed of FPC rises linearly, which can be noticed in Figure 6, 7 and 9. That means the sum of the electromagnetic torque and the friction is nearly constant, while the friction is small. Thus, the electromagnetic torque can be considered as stable, which is proportional to iqr, as shown in equation (10). The FPC’s stator-side power is also proportional to iqr, which is shown in Figure 8 and 9. In Figure 6, 7 and 9, the speed of FPC DFIM smoothly become stable without any overshoot at the end of the start process.

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Figure 6. Speed of FPC and the phase current of rotor.

Figure 7. Speed of FPC and the line voltage of rotor.

rated speed nN=1420r/min stator voltage UsN=380V rotor voltage UrN=260V synchronous speed n=1500r/min the moment of inertia J=0.3kgm2 stator self-inductance Ls=0.286H rotor self-inductance Lr=0.286H mutual inductance L0=0.270H stator resistance Rs=2.8ȍ rotor resistance Rr=2.52ȍ the number of pole pairs 2 REFERENCES [1] [2]

Figure 8. Q-axis and D-axis components of rotor currents.

[3]

[4]

[5]

[6] [7]

[8]

Figure 9. Speed of FPC and the FPC’s stator-side Power.

VII. CONCLUSION This paper investigates a new direct-start strategy for FPC with back-to-back converters, which includes some treatments to PI controllers based on the speed control system of the rotor-side of back-to-back converters. Detailed theoretical analysis of this method shows that it can effectively avoid the start impulsion to the equipment and power system, and maintain a constant large torque to shorten the time of the start. A small capacity experimental system verifies the theoretical analysis. Thereby, the conditions for a large capacity experimental system are prepared. ACKNOWLEDGMENT The authors gratefully acknowledge the support provided by Special Fund of the National Basic Research Program of China (No. 2004CB217906) and National Natural Science Foundation of China (No. 50507006). APPENDIX The machine parameters that have been used are given below. rated power PN=2.2kW

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Wen Jinyu, Li Gang, Cheng Shijie, al. A multi-functional flexible power conditioner for power system stabilities enhancement. Proceedings of the CSEE, 2005, 25(25): 6-11. Cheng Shijie, Wen Jinyu, Sun Haishun. Application of power energy storage techniques in the modern power system. Electrotechnical Application, 2005, 24(4): 1-8. Guofeng Yuan, Jianyun Chai, Yongdong Li., “Vector control and synchronization of doubly fed induction wind generator system” Power Electronics and Motion Control Conference, 2004. IPEMC 2004. The 4th International, Volume 2, 14-16 Aug. 2004 Page(s):886 - 890 Vol.2 R. Pena, J. C. Clare, G. M. Asher. Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proc. -Electr. Power. Appl, 1996, 143(3): 231~241 Mohamed, M.B, Jemli, M., Gossa, M, Jemli, K.. Doubly fed induction generator (DFIG) in wind turbine modeling and power flow control. Industrial Technology, 2004. IEEE ICIT '04. 2004 IEEE International Conference on Volume 2, 8-10 Dec. 2004 Page(s):580 - 584 Yang Hao, Wen Jinyu, Li Gang, et al. Investigation on operation characteristics of multi-functional flexible power conditioner. Proceedings of the CSEE, 2006, 26(2): 19-24 Morren, J, de Haan, S.W.H. Ridethrough of wind turbines with doubly-fed induction generator during a voltage dip. Energy Conversion, IEEE Transactions on Volume 20, Issue 2, June 2005 Page(s):435 441 Li Gang, Wen Jinyu, Cheng Shijie, et al. Investigation on start and cut-in of the multi-function flexible power conditioners. Automation of Electric Power Systems, 2006, 30(3): 17-22.