Application of ICA for Controller Parameter Tuning of HVDC Current Modulation Control

(1)

1

Application of ICA for Controller Parameter Tuning of HVDC Current Modulation Control

R. Gholizadeh R. S. Najafi R. A. Ajami Electrical Engineering Department, Faculty of Engineering,

Azarbaijan University of Tarbiat Moallem Tabriz, Iran

Keywords: Imperialist Competitive Algorithm (ICA), Supplementary Controller, HVDC, Low Frequency Oscillations

Abstract

In this paper design of HVDC current modulation controller for damping of electromechanical oscillations in a two-area test system is investigated. The selection of controller parameters is converted to an optimization problem with the multiobjective function which is solved by imperialist competitive algorithm (ICA). ICA is a new evolutionary algorithm that has a strong capability in finding the most optimistic results. The effectiveness and validity of the proposed controller on damping low frequency oscillations is tested through eigenvalue analysis and time domain simulation under two different disturbances which are applied simultaneously to the test system. The simulation results show that the tuned ICA based HVDC supplementary controller has an excellent capability in damping low frequency oscillations and enhances greatly the dynamic stability of the power system.

1. Introduction

Large-scale interconnected power systems are very often incorporated with HVDC transmission links due to their ability to link asynchronous areas and also because of the advantages during long distance transmission [1]. Over the last decades, the usage of HVDC links’ supplementary controller has been proved to be a good option in damping low frequency oscillations. Therefore its design and impact on the power systems need to be thoroughly studied.

Several works have been reported in the literature regarding HVDC supplementary controller design [1]-[5]. The design of power modulation controller in [1] is based on advanced nonlinear robust adaptive control theory and its controller parameters have been tuned using genetic algorithm (GA) and ordinal optimization. In [2] the parameters of the HVDC modulator were optimized with an inherent non-linear optimization module of NETOMAC. The H

∞

method of the robust

11-E-PSS-1128

(2)

Application of ICA for Controller Parameter Tuning of HVDC Current Modulation Control

26^th International Power System Conference

2 control was used to design the controller in which damping of the system is satisfied by additional constraints on the closed-loop pole location [3]. Although using the robust control methods, power system uncertainties are directly introduced to the synthesis, but in general resulting controller will be very large owning to the large model order of power systems, therefore making its computational and economical implementation difficult.

Authors in [4, 5] have used the signals obtained from phasor measurement units (PMU) in order to find the oscillation modes i.e. using methods like FFT and prony analysis. Some evolutionary algorithms, like bacterial foraging algorithm (BFA) and memetic algorithm with population management (MAPM) have been used to optimize the HVDC supplementary controller parameters [4, 13]. However in [5] classical control method has been used to find the controller parameters which is often proved not to be robust to different operating conditions. Remote signals which are being obtained using PMUs have also been proved to be good inputs for the HVDC supplementary controllers [3]-[6].

In this paper imperialist competitive algorithm which is a recently developed evolutionary algorithm. ICA has been proved to have better results than GA in [7] and some of its features in comparison with PSO have been highlighted in [8]. It is used here in order to tune the HVDC current modulation controller parameters. For this purpose a detailed 2-area test system with an HVDC link is used. The controller is designed using eigenvalue method and the effectiveness of the controller is shown with eigenvalue analysis as well as a time domain simulation under two different disturbances which are applied to the test system simultaneously.

2. ICA Technique

Imperialist Competitive Algorithm is a new evolutionary optimization method which is inspired by imperialistic competition [7]. It

starts with an initial population which is called country and is divided into two types, i.e. colonies and imperialists, which together form empires. Each country includes predefined number of variables reflecting its characteristics e.g. culture, language, and religion.

One of the main parts of this algorithm which forms its formation is imperialistic competition among empires. Weak empires collapse and powerful ones take possession of their colonies, during this competition.

Imperialistic competition converges to a state in which there exists only one empire and colonies have the same cost function value as the imperialist [7].

The pseudo code of Imperialist competitive algorithm is as follows [7]:

1) Select some random points on the function and initialize the empires.

2) Move the colonies toward their relevant imperialist (Assimilation).

3) Randomly change the position of some colonies (Revolution).

4) If there is a colony in an empire which has lower cost than the imperialist, exchange the positions of that colony and the imperialist.

5) Unite the similar empires.

6) Compute the total cost of all empires.

7) Pick the weakest colony (colonies) from the weakest empires and give it (them) to one of the empires (Imperialistic competition).

8) Eliminate the powerless empires.

9) If stop conditions satisfied, stop, if not go to 2.

Fig. 1. Motion of colonies toward their relevant imperialist [7]

(3)

3 Initial empires are created dividing all colonies among imperialists. Through a policy which is called assimilation, these colonies start moving toward their relevant imperialist. Figure 1 shows the movement of a colony towards the imperialist. In this movement, θ and x are random numbers with uniform distribution as illustrated in (1) and d is the distance between colony and the imperialist [7].

) , ( ),

, 0

(       

 U d U

x (1)

Where, β and γ are parameters which randomly modify the area that colonies search around the imperialist. In ICA, revolution causes a country to suddenly change its socio- political characteristics. That is, the colony randomly changes its position in the socio- political axis, instead of being assimilated by an imperialist. In this way exploration is increased and early convergence of countries to local minimums is prevented. The total power of an empire depends on both the power of the imperialist country and the power of its colonies which is shown in (2) [7].

T.C.n = Cost (imperialistn) + ζica mean{Cost

(colonies of empiren)}

(2)

In this paper, ICA is applied to search for the optimal parameters of the HVDC supplementary controller.

3. Description of Case Study System

In this paper, a two-area, four-machine system is used as a test case, as shown in figure 2. In this figure, L

4

and L

14

are loads. All the generators are modeled in detail. And the simplified excitation system models are included. It is assumed that the generators are not equipped with power system stabilizers (PSS) in order to study damping capability of the HVDC current modulation.

Fig. 2. Two-area test system equipped with an HVDC link [9]

The HVDC link works in normal conditions in which the rectifier is in constant current control and the inverter is in constant extinction angle control. The parameters of the test system come from [9]. The compensation capacity of the shunt capacitor in both bus 3 and bus 15 are 600Mvar. Under normal condition, the exchange power between the two areas is 400MW from area 1 to area 2 and the HVDC link transmits 100MW.

5. Simulation Results

In order to design the ICA based supplementary controller and verify its effectiveness, an eigenvalue analysis as well as a time domain simulation has been carried out using toolboxes provided in [9-10].

5.1. ICA Implementation

The ICA has been applied to search for the optimal parameters setting of the supplementary controller so that the objective function is optimized. In this study, the values of σ

0

and ξ

0

are taken as -0.5 and 0.1, respectively. In order to acquire better performance, number of countries, number of initial imperialist, number of decades, assimilation coefficient (β), assimilation angle coefficient (γ), and ζ

ica

are chosen as 30, 6, 1200, 2, 0.4 and 0.2, respectively.

The final values of the optimized parameters with the objective function are given in Table I and T

W

and T

R

are taken as 10 and 0.03 respectively. Figure 5 shows the cost versus iteration illustration of the ICA technique.

From the figure, the minimum value for the

objective function becomes equal to 1.2680.

(4)

4

Fig. 4. Flowchart of the implemented ICA technique

Fig. 5. Convergence illustration of ICA

Table I.

Optimal parameters of the proposed controller

K T

1

T

2

4.7285 1.5000 0.8925 5.2. Eigenvalue Analysis

The system eigenvalues with and without the supplementary controller are given in Table II. It is clear that system without the controller has a mode with positive eigenvalue which it shows that the overall system is unstable.

However, the system with the proposed controller is stable and its damping capability is hopefully increased.

0 400 800 1200

1.2 1.5 2 2.3

Iteration

Cost

(5)

5

Table II.

The three modes with the lowest damping Without Controller With Controller Eigenvalue ζ (%) Eigenvalue ζ (%) 0.0525±j4.0457 -1.30 -

0.6109±j7.2675 8.38 -0.6284±j7.2483 8.64 -

0.7878±j7.1746 10.91 -0.7522±j7.3207 10.22 -

0.3467±j1.9705 17.33

5.3. Time Domain Simulation

To assess the effectiveness of the proposed controller, a 0.01 p.u. increase in generator G

12

exciter input reference and a 0.1 p.u.

increase in generator G

2

mechanical input torque disturbances are considered.

The system responses with and without the controller in the presence of two simultaneous disturbances are given in figures 6.a-c, in which the response of Δθ

3-13

, Δω

12

, and ΔP

e2

are shown respectively. It is clear that the system without controller is unstable, whereas the proposed controller dramatically stabilizes the system.

6. Conclusion

The imperialist competitive algorithm has been successfully applied to the design of HVDC modulation controller. The design problem of the controller parameters tuning is converted into a multiobjective optimization problem which was solved by an ICA technique. A detailed two-area test system was used to study application of an HVDC modulation controller in a power network subjected to simultaneous disturbances. The voltage phase angle difference between two areas, which were obtained using PMUs, was applied as the input signal to the supplementary controller. The eigenvalue analysis and time domain simulation results showed the effectiveness of the designed HVDC current modulation controller in successfully damping the electromechanical oscillation.

Fig. 6. Dynamic response of system to the simultaneous disturbances: (a) Δθ3-13, (b) Δω12, and

(c) ΔPe2; solid (with controller) dash-dotted (without controller)

Acknowledgements

This research has been supported by Azarbaijan University of Tarbiat Moallem.

0 15 30

-0.5 0 0.5

Bus angle deviation difference (rad)

Time (s)

(a)

0 15 30

-0.01 0 0.01

Speed deviation (p.u.)

Time (s)

(b)

0 15 30

0 0.1 0.2

Power deviation (p.u.)

Time (s)

(c)

(6)

6 References

[1] K.K.Y. Poon, Z. Lan, H. Zhu, Y. Ni,

“Application of a Coordinated Optimization Algorithm for Controller Parameter Tuning of HVDC Power Modulation Control”, presented at IEEE Power Engineering Society General meeting, Tampa, FL, 2007.

[2] H. Liu, Z. Xu, L. Jin, “Coordination and Optimization of Small Signal Modulators in Multi-infeed HVDC Systems”, in Transmission and Distribution Conference and Exposition, 2003 IEEE PES, Vol.1, September 2003, pp. 35-40.

[3] Y. Chang, H. Chen, F. Zhang, “Design of Multi-objective Robust HVDC Supplementary Controller Based on Global Signal”, in Power Systems Conference and Exposition, PSCE '06.

2006 IEEE PES, Atlanta, GA, pp. 2146- 2151.

[4] C. Li, M. Watanabe, Y. Mitani, “HVDC Controller Design for Damping of Inter- area Oscillation Using Synchronized Phasor Measurements and Bacteria Foraging Algorithm”, presented at the International Conference on Electrical Engineering, 2009.

[5] Y. Huang, Z. Xu, “HVDC Supplementary Controller Based on Synchronized Phasor Measurement Units”, in Power Systems Conference and Exposition, 2004. IEEE PES, Vol.2, pp. 668-672.

[6] I. Kamwa, J. Beland, G. Trudel, R.

Grondin, C. Lafond, D. McNabb, “Wide- area Monitoring and Control at Hydro- Quebec: Past, Present and Future”, presented at IEEE Power Engineering Society General meeting, Montreal Que., 2006.

[7] E. Atashpaz-Gargari, C. Lucas,

“Imperialist Competitive Algorithm: An Algorithm for Optimization Inspired by Imperialistic Competition”, in IEEE Congress on Evolutionary Computation, Singapore, September 2007, pp. 4661 – 4667.

[8] A. Kaveh, S. Talatahari, “Optimum design of skeletal structures using imperialist

competitive algorithm”, Computers and Structures, Vol. 88, 2010, p.p. 1220–1229.

[9] J. H. Chow and K. W. Cheung, A toolbox for power system dynamics and control engineering education and research, IEEE Transaction on Power Systems, 7(4), November 1992, pp. 1559–1564.

[10] G. Rogers, Power System Oscillations, New York: Kluwer, 2000.

[11] P. Kundur, Power System Stability and Control, New York: McGraw-Hill Inc., 1994, p. 1151.

[12] H. Shayeghi, H.A. Shayanfar, S.

Jalilzadeh, A. Safari, “A PSO Based Unified Power Flow Controller for Damping of Power System Oscillations”, Energy Conversion and Management, Vol. 50(Issue 10), October 2009, pp.