An Action Dependent Heuristic Dynamic Programming-controlled Superconducting Magnetic Energy Storage for Transient Stability Augmentation

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Physics Procedia 65 ( 2015 ) 286 – 290 Available online at www.sciencedirect.com

Peer-review under responsibility of the ISS 2014 Program Committee doi: 10.1016/j.phpro.2015.05.153

ScienceDirect

27th International Symposium on Superconductivity, ISS 2014

An Action Dependent Heuristic Dynamic Programming-Controlled

Superconducting Magnetic Energy Storage for Transient Stability

Augmentation

Xinpu Wang

1

_{, JunYang}

*,1

_{, Xiaodong Zhang}

2

_{, Xiaopeng Yu}

2

(1_{School of Electrical Engineering, Wuhan University, Wuhan 430072, Hubei Province, China;}2_{State Grid Henan Electric Power Company,}

Zhengzhou 450052, Henan Province, China) E-mail address:[email protected]

Abstract

To enhance the stability of power system, the active power and reactive power can be absorbed from or released to Superconducting magnetic energy storage (SMES) unit according to system power requirements. This paper proposes a control strategy based on action dependent heuristic dynamic programing (ADHDP) which can control SMES to improve the stability of electric power system with on-line learning ability. Based on back propagation (BP) neural network, ADHDP approximates the optimal control solution of nonlinear system through iteration step by step. This on-line learning ability improves its performance by learning from its own mistakes through reinforcement signal from external environment, so that it can adjust the neural network weights according to the back propagation error to achieve optimal control performance. To investigate the effectiveness of the proposed control strategy, simulation tests are carried out in Matlab/Simulink. And a conventional Proportional-Integral (PI) controlled method is used to compare the performance of ADHDP. Simulation results show that the proposed controller demonstrates superior damping performance on power system oscillation caused by three-phase fault and wind power fluctuation over the PI controller.

Peer-review under responsibility of the ISS 2014 Program Committee.

Keywords: action dependent heuristicdynamicprograming (ADHDP)㧧superconducting magnetic energy storage (SMES)㧧Transient Stability

1. Introduction

According to the increasing concerns of energy crisis, renewable energy, such as wind power and solar power, will be widely applied in the electric power system in the future. Because of the intermittency and fluctuation of renewable energy integrating into the smart grid, it will have a significant impact on the stabilization of the power system.

Energy storage device should play an important role in transient stability augmentation of power system for its ability of exchanging power according to system requirements. With the rapid development of electric power system and superconducting technology, superconducting magnetic energy storage (SMES) unit is more likely to be applied in practice. Furthermore, SMES systems can be used in diurnal load demand leveling, frequency control, automatic generation control etc[1]_{. By controlling the fire angle of source voltage converters (SVC) in the SMES unit, SMES} supplies or receives energy to maintain the stabilization of power system during the disturbance period.

* Corresponding author. Tel.: +86-27-68776346; fax: +86-27-68772047.

E-mail address: [email protected]

Peer-review under responsibility of the ISS 2014 Program Committee Provided by Elsevier - Publisher Connector

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This paper proposes an intelligence control method called action dependent heuristic dynamic programing (ADHDP) to design the controller for enhancing the stability of power system. ADHDP is model-free and it can learn from its own mistakes. Based on back propagation (BP) neural network, it can automatic adjust its parameters to achieve optimal control performance. A Proportional-Integral (PI) controlled method is used to compare the performance of ADHDP. A doubly fed induction generator wind turbine is used in the Matlab/Simulink to demonstrate the validity of the proposed method.

2. The Model of SMES

Fig.1 shows the proposed SMES unit which consists of a three-phase six-bridge arm converter and a superconducting coil. The capacitor in parallel with the converter is used to keep the voltage of the DC side to be a constant. A DC chopper in this model is used to charge or discharge the superconducting coil. Firstly the superconducting coil disconnects with the converter when the voltage of the DC side reaches the set value. Then the coil is charged to the predefined value and remains unchanged. After the SMES ends its charge behavior, it is ready to absorb or release power when fault occurs in the system.

'&OLQN FDSDFLWRU %\SDVV VZLWFK 60(6 FRLO < WUDQVI RUPHU 7KUHH SKDVH$& ˄IURP JHQHUDWRU WHUPLQDO EXV˅ 9ROWDJHVRXUFH FRQYHUWHUXVLQJ *72 '&'& FKRSSHU XVLQJ *72

Fig.1. Basic configuration of SMES system

3. The Design of ADHDP Controller

Fig.2 shows the designed SMES controller based on the on-line learning ADHDP. X is the measured system state vector P(t), Q(t), their one time delayed values P(t-1), Q(t-1) and two time delayed values P(t-2), Q(t-2), and u is the

control signal presented the power reference value (P_r,Q_r).E is the fundamental voltage of the converter at the

installation point , J is the cost/reward function of the Bellman equation in dynamic programming, and r is the reinforcement signal which can be obtained from the external environment.

'),* f 3 3UHI 4UHI 4 1_[( ₎ 1₍₂ _{) ]} 3 3 sm ab a bc a bc b sm bc ab a ab bc b P u i u i u i Q u u i u u i ' 2 2 ' 2 2 i i sd ref sq ref d sd sq sq ref sd ref q sd sq E P E Q E E E P E Q E E 3, 3, ,QQHU ORRS FRQWURO DEFGT Esd Esq % 0HDVXUHPHQWV [ W 3 4 [ W $FWLRQ QHWZRUN &ULWLF QHWZRUN J X W - W - W U W 7 7 sa E E_sbEsc 60(6

Fig.2. The schematic diagram of ADHDP controlled SMES

ADHDP consists of two main parts: an action network and a critic network. These two parts are implemented by neural networks for their universal approximation capabilities, and the back-propagation learning algorithm is used in the design of the ADHDP controller.

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3.1 The critic network

The objective of the ADHDP controller is to obtain the optimal control signal to dampen the power oscillation of power system. Therefore, the reinforcement signal can be designed as follows.

2 ' [1 0.5 0.5 ] ( ) ( ) * * ( ) ° ® °¯ Q diag r t x t Q x t (1)

The critic network is trained to approximate the function J by minimizing the error function which is presented as follows. ( ) ( ) r( 1) J ( 1) c e k J k k J k (2) 2 1 ( ) 2 c c E e k (3)

The updating weight in the critic network is a gradient descent method which can be calculated as follows.

W (c k 1) W ( )c k 'W ( )c k (4) c c ( ) ( ) ( ) W ( ) ( ) ( ) ( ) _{( )} ( ) c c c c c E k E k J k k l k l k W k _{J k} W k ª º ª w º _« w w _» ' _« _» « » w w ¬ ¼ _¬ _w _¼ (5)

Wherel_cis the learning rate of the critic network and W_c is the weight vector in the critic network.

3.2 The action network

The action network is trained to get the optimal control signal offered to the system to obtain stable state in the next time interval. The weights in the action network are adjusted by minimizing the following error functions.

( ) ( ) a e k J k (6) 2 1 ( ) 2 a a E e k (7)

The updating rule of the weight for the action network is a gradient descent method given as follows.

W (a k 1) W ( )a k 'W ( )a k (8) ( ) ( ) ( 1) ( ) W ( ) ( ) ( ) ( ) ₍ ₁₎ ( ) ( ) a a a a a a a E k E k J k u k k l k l k W k _{J k} u k W k ª º ª w º _« w w w _» ' «_w » _« _w _w _» ¬ ¼ _¬ _w _¼ (9)

Wherelais the learning rate of the action network and Wais the weight vector in the action network.

4. Simulation and Discussion

To investigate the performance of the proposed ADHDP controller, simulations are carried out in matlab/Simulink for the model shown in Fig.3. This single machine infinite bus (SMIB) power system which contains six wind power generators with the capacity of 9MW is used in this paper. Table 1 shows the major parameters of SMES and the wind power system.

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Table 1.Major parameters of SMES and power system

SMES DFIG

Coil Inductance value 10H capacity 9MW Capacitor capacitance value 0.01f

Stator [Rs, Lls] (pu) [0.023 0.18] Rotor[Rr’, Llr’] (pu) [0.016 0.16] H(s) 0.685 G SMES Pr

∞

id iq vt iLd iLq XT _X L vs PeQe XDT isd isq Psm Qsm vsm Qr PL QL K(3)

Fig.3. The SMIB power system Fig.4. The wind speed

The wind speed is shown in Fig.4, and the rated speed is 15 meters per second. To compare the performance of the proposed ADHDP controller, two cases considering the wind power fluctuation and the fault disturbance are analyzed in Fig.5.

Fig.5 (a) shows the power oscillation caused by wind power fluctuation be dampened by SMES, and the performance of the proposed ADHDP controller is better than the PI controller. In Fig.5 (b), SMES with ADADP controller dampens the power oscillation caused by both three-phase fault and wind power fluctuation more quickly than SMES with PI controller. Fig.6 (a) shows the output active power of the ADHDP controlled SMES and PI controlled SMES on condition of unstable wind power, and Fig.6 (b) shows the same waveforms considering both three-phase fault and wind power fluctuation. From the simulation results, we can draw a conclusion that the power fluctuation can be most effective suppressed by the proposed ADHDP controller, so it can greatly improve the stability of the power system.

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Fig.5 (a) The active power of the transmission line in stable state considering wind power fluctuation (b) The active power of the transmission line in fault state considering wind power fluctuation

0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20 Time (sec) W ind S peed (m/s ) 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 14x 10 6 Time (sec) Output P o w e r Of T rans m is s ion Li ne (W ) PI control SMES ADHDP control SMES without SMES 0 1 2 3 4 5 6 7 8 9 10 -2 0 2 4 6 8 10 12 14 16 18x 10 6 Time ˄sec˅ output pow er of trans m is s ion l ine ˄ W ˅ without SMES ADHDP control SMES PI control SMES

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Fig.6 (a) The output active power of the SMES in stable state considering wind power fluctuation (b) The output active power of the SMES in fault state considering wind power fluctuation

5. Conclusion

By exchanging active power and reactive power with power grid through suitable controller, SMES can enhance the stability of power system. This paper proposes an intelligence control method called ADHDP to design the controller for improving the stability of power grid. To verify the performance of the proposed ADHDP controller, two cases considering the wind power fluctuation and the fault disturbance are investigated. Also, a PI controller is designed for comparable analysis. From the simulation results above, the following conclusions can be drawn.

(1)SMES is an effective measure for stabilizing the active power in the transmission line during wind power fluctuation.

(2)Comparing to the PI controlled SMES, SMES with the proposed ADHDP controller has better performance on dampening power oscillation caused by three-phase fault and wind power fluctuation according to its ability of learning on-line.

Reference

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[4]Y. Tang, H. He, J. Wen, Comparative study between HDP and PSS on DFIG damping control, in: Computational Intelligence Applications In Smart Grid (CIASG), 2013 IEEE Symposium on, 2013, pp. 59–65. doi:10.1109/CIASG.2013.6611499.

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0 1 2 3 4 5 6 7 8 9 10 -4 -3 -2 -1 0 1 2 3 4 5 6x 10 6 Time (sec) Out put ac ti v e pow er of S M E S (W )

ADHDP controlled SMES PI controlled SMES 0 1 2 3 4 5 6 7 8 9 10 -3 -2 -1 0 1 2 3 4 5 6x 10 6 Time˄sec˅ Out put ac ti v e pow er of S M E S (W )

ADHDP controlled SMES