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A Framework for \(H_{2} /H_\infty\) Synthesis in Damping Power Network Oscillations with STATCOM

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Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

The escalating in load demand prioritized the incorporation of additional renewable energy generation plants to the existing grid. In parallel, the necessity of reactive power balance and damping characteristics has advised the incorporation of flexible AC transmission system controllers to the existing power network. Hereby, the modern power system has been driven towards the much more composite system which in turn necessitates a healthy controller technique. The objective of this paper is to contribute recommendations to incorporate robust controller technique in the field of the electrical power system. Detailed design considerations for the \(H\infty\) controller design of a modern power network have been specified, and the same has been demonstrated with mathematical modelling of power network with static synchronous compensator (STATCOM) connected in the middle of the transmission line and in a multi-machine power system. To comment on the suitability of the controller design, a deep stability analysis has been presented and compared with the traditional power system stabilizer, power system stabilizer optimized using particle swarm optimization with time-varying acceleration coefficients algorithm and whale optimization algorithm under adverse system operating conditions. The proposed controller framework has been presented by considering the case studies of single machine infinite bus system, two-machine system model and the benchmark two-area four-generator multi-machine systems connected with STATCOM. The controller performance analysis has been verified by considering eigenvalues analysis, singular value analysis and dynamic response of system states during perturbations for the first two case studies, and system analysis under faulty condition has been investigated for the multi-machine system.

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Abbreviations

FACTS:

Flexible AC transmission system

\(H_{2} /H\infty\) :

Hardy space techniques

STATCOM:

Static synchronous compensator

PSS:

Power system stabilizer

SMIB:

Single machine infinite bus system

VSC:

Voltage source converter

LHS S-Plane:

Left-hand side of S-plane

\(E_{{{\text{q}}1}}^{{\prime }} ,E_{{{\text{q}}2}}^{{\prime }}\) :

Internal voltage of the generator 1, 2

E fd1 , E fd1 :

Field voltage of the generator 1, 2

\(x_{{{\text{d}}1}}^{{\prime }} , \, x_{{{\text{d}}2}}^{{\prime }}\) :

Direct axis transient reactance of the generator 1, 2

x d1 , x d2 :

Direct axis steady-state reactance of generator 1, 2

xq1, xq2 :

Quadrature axis steady-state reactance of generator 1, 2

m e :

Amplitude modulation ratio of STATCOM

δ e :

Phase angle of STATCOM

ω :

Fundamental frequency

c dc :

DC link capacitor

v dc :

Voltage across the DC link capacitor

i dc :

Current through the DC link capacitor

δ :

Torque angle/power angle

V t :

Terminal voltage of the generator

x te :

Transmission line reactance before STATCOM

x bv :

Transmission line reactance next STATCOM

\(T_{{{\text{d}}01}}^{\prime} , \, T_{{{\text{d}}02}}^{\prime}\) :

Field time constant for generator 1, 2

T A1 , T A2 :

Time constant of voltage regulator for generator 1, 2

KA1, KA2 :

Gain of voltage regulator for generator 1, 2

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Dhanbad, Jharkhand, India

    Ramesh Devarapalli & Biplab Bhattacharyya

Authors
  1. Ramesh Devarapalli
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  2. Biplab Bhattacharyya
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Corresponding author

Correspondence to Ramesh Devarapalli.

Appendix

Appendix

1.1 Power system parameters

  • SMIB system with STACOM:

  • SATCOM parameters:

  • Cdc =  1.0 pu; Vdc =  1 pu; me =  0.7; xe = 0.15 pu

  • Synchronous Generator parameters:

  • X1d =  0.3; x1q =  0.6; M  =  6.0; D  =  0; xd = 1;

  • Other parameters:

  • Ka =  50; Ta =  0.01

  • Hardy Space Weighing functions:

  • W1 = []; W2 =  1 * 10−5; W3 = []

  • Two-area system with STATCOM:

  • M1  =  M2  = 6.0; D1 = D2 = 0;

  • Vt1 = 1.0; Vt2 = 0.89;

  • Ka1 = Ka2 = 50; Ta1 = Ta2 = 0.01; Td011 = Td012 = 6.3;

  • xe = 0.15; x1L = 0.3; x2L = 0.3;

  • Load parameters:

  • Pe1 = Pe2 = 0.8; Qe1 = Qe2 = 0.2;

  • Hardy Space Weighing functions:

  • W1 = 0.2e−10 * (0.05 * s + 1)/(50 * s + 1); W2 = 1e−4; W3 = 0.2e−13 * (0.05 * s + 1)/(50 * s + 1);

  • Two-area four-generator system with STATCOM:

  • Xd = 1.8; Xq = 1.7; Xl = 0.2; \(X_{d}^{\prime}\) = 0.3; \(X_{d}^{\prime}\) = 0.55; \(X_{d}^{\prime\prime}\) = 0.25; \(X_{\rm q}^{\prime\prime}\) = 0.25; Ra = 0.0025; \(T_{d0}^{\prime }\) = 8; \(T_{q0}^{\prime }\) = 0.4; \(T_{d0}^{\prime \prime}\) = 0.03; \(T_{q0}^{\prime\prime}\) = 0.05; H = 6.5 (for G1, G2); H = 6.175 (for G3, G4); KD = 0

  • Base values: 100 MVA, 230 kV

  • Transmission line parameters:

  • r = 0.0001 pu/km; xL = 0.001 pu/km; bC = 0.00175 pu/km

  • Optimization Algorithm Parameters:

PSO-TVAC:

Swarm size = 20

Max_iteration = 100

wmin = 0.4

wmax = 0.9

 

c1i = 2.5

c1f = 0.2

c2i = 0.2

c2f = 2.5

WOA:

SearchAgents_no = 30

Max_iteration = 100

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Devarapalli, R., Bhattacharyya, B. A Framework for \(H_{2} /H_\infty\) Synthesis in Damping Power Network Oscillations with STATCOM. Iran J Sci Technol Trans Electr Eng 44, 927–948 (2020). https://doi.org/10.1007/s40998-019-00278-4

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  • DOI: https://doi.org/10.1007/s40998-019-00278-4

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