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ADRC-based control strategies to alleviate SSR using STATCOM

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Abstract

Increasing prominence of series compensation into the power system has evidently enhanced the rise of subsynchronous resonance (SSR). Alleviation of SSR with two novel control designs for static synchronous compensator (STATCOM) is proposed in this paper. Since it is quite challenging to optimize proportional and integral (PI) controllers in a nonlinear framework, hence a nonlinear active disturbance rejection controller (ADRC)-based strategies are proposed. First control design is template-based ADRC (TADRC), and the second control design is synchronous ADRC (SADRC). To validate the effectiveness of control schemes, an IEEE second benchmark model is used. Furthermore, different analyses are demonstrated to study the phenomenon of SSR. Firstly, the state space model-based design is provided for eigenvalue analysis. Fast Fourier transform (FFT) analysis is also carried out to show the dominant mode of oscillations along with the frequency scan at various levels of compensation. Finally, trends in generator speed and other parameters are shown in the time domain analysis of the system. The analyses and measures to alleviate the oscillations proposed in this paper are eminently cogent.

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Abbreviations

\(\varDelta \) :

Small deviation when used as prefix

\(\delta \) :

Load angle in rad/s

\(\varDelta \delta \) :

Angle of twist of mass

\(\varDelta \omega \) :

Deviation in speed of mass in pu

\(\omega \) :

Rotor speed in pu

\(\omega _0\) :

Speed (rated) in electrical rad/s

\(\varPsi \) :

Flux linkage in pu

\(\tau \) :

Torques in turbine sections

’.’:

Differential operator

bb:

Infinite bus when subscript

cd:

Capacitive and d-axis when subscript

cq:

Capacitive and q-axis when subscript

D:

Coefficient of damping in pu torque/pu speed deviation

d:

d-axis when subscript

ds:

Damper winding on q-axis when subscript

dw:

Damper winding on d-axis when subscript

e,E:

Voltage at sending end in pu

EXM:

Excitation when subscript

F\(\tau \) :

Torques in fractions

fd:

Field winding when subscript

GM:

Generator when subscript

GXM:

Excitation and generator when subscript

HLM:

High pressure and low pressure when subscript

HPM:

High pressure turbine when subscript

i:

Current in pu

K:

Stiffness in pu torque/electrical rad

\(\hbox {K}_{\mathrm{GVNR}}\) :

Governor system gain constant

L:

Transmission line when subscript.

LGM:

Low pressure turbine and generator when subscript

LPM:

Low pressure turbine when subscript

M:

Constant of inertia in MW.\(s^2\)/rad

md:

Mutual and d-axis when subscript

mq:

Mutual and q-axis when subscript

\(\hbox {O}_{\mathrm{GVNR}}\) :

Opening of governor

\(\hbox {O}_{\mathrm{SRP}}\) :

Speed relay position

q:

q-axis when subscript

qw:

Damper winding on q-axis when subscript

r,R:

Resistance in pu

rw:

Armature winding when subscript

Rx:

Regulation by excitation system when subscript

t0:

Terminal base value when subscript

\(\hbox {T}_{\mathrm{A}}\) :

Excitation due to regulation time constant

\(\hbox {T}_{\mathrm{CHP}}\) :

Chamber time constant in front of HP turbine

\(\hbox {T}_{\mathrm{ex}}\) :

Excitation time constant due to field

\(\hbox {T}_{\mathrm{GVNR}}\) :

Governor opening time constant

\(\hbox {T}_{\mathrm{HLM}}\) :

HP and LP turbine connection time constant

\(\hbox {T}_{\mathrm{RPG}}\) :

Speed relay position time constant in governor

td:

Terminal and d-axis when subscript

tq:

Terminal and q-axis when subscript

V:

Voltage in pu

x,X:

Reactance in pu

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Authors and Affiliations

  1. Electrical Engineering Department, National Institute of Technology, Srinagar, J&K, India

    Viqar Yousuf & Aijaz Ahmad

Authors
  1. Viqar Yousuf
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  2. Aijaz Ahmad
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Correspondence to Viqar Yousuf.

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Appendix

Appendix

$$\begin{aligned} {[}L]= & {} \omega \begin{bmatrix} -X_{dxx} &{} 0 &{} X_{mdx} &{} X_{mdx} &{} 0 &{} 0\\ 0 &{} -X_{qxx} &{} 0 &{} 0 &{} X_{mqx} &{} X_{mqx}\\ X_{mdx} &{} 0 &{} X_{fd} &{} X_{mdx} &{} 0 &{} 0\\ -X_{mdx} &{} 0 &{} X_{mdx} &{} X_{dpw} &{} 0 &{} 0\\ 0 &{} -X_{mqx} &{} 0 &{} 0 &{} X_{qpw} &{} X_{mqx}\\ 0 &{} -X_{mqx} &{} 0 &{} 0 &{} X_{mqx} &{} X_{ds}\\ \end{bmatrix} \end{aligned}$$
(a1)
$$\begin{aligned} {[}Q]= & {} \begin{bmatrix} r_a &{} -X_{qxx} &{} 0 &{} 0 &{} X_{mqx} &{} X_{mqx}\\ X_{dxx} &{} r_{arw} &{} -X_{mdx} &{} -X_{mdx} &{} 0 &{} 0\\ 0 &{} 0 &{} -r_{fd} &{} 0 &{} 0 &{} 0\\ 0 &{} 0 &{} 0 &{} -r_{dpw} &{} 0 &{} 0\\ 0 &{} 0 &{} 0 &{} 0 &{} -r_{qpw} &{} 0\\ 0 &{} 0 &{} 0 &{} 0 &{} 0 &{} -r_{ds} \\ \end{bmatrix} \end{aligned}$$
(a2)
$$\begin{aligned} {[}R]= & {} \begin{bmatrix} \psi _{qx0} &{} 0 &{} 1 &{} 0 \\ 0 &{} \psi _{dx0} &{} 0 &{} 1\\ \frac{r_{fd}}{X_{mdx}} &{} 0 &{} 0 &{} 0\\ 0 &{} 0 &{} 0 &{} 0\\ 0 &{} 0 &{} 0 &{} 0\\ 0 &{} 0 &{} 0 &{} 0\\ \end{bmatrix} \end{aligned}$$
(a3)

All the system design parameters are provided in [19], and parameters of STATCOM are :

Capacitance = 1F

DC Link Voltage = 20 KV

Transformer Voltage Ratio = 20/500 KV

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Yousuf, V., Ahmad, A. ADRC-based control strategies to alleviate SSR using STATCOM. Electr Eng 103, 2303–2314 (2021). https://doi.org/10.1007/s00202-021-01233-5

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