Table 7 Nominal parameters of the system: system frequency f = 60 Hz, Tgi = 0.08 s, Tti = 0.3 s; Tri = 10 s; Kri = 0.5; Kpi = 120 Hz/pu MW; Tpi = 20 s; T12 = 0.086 pu MW/rad; Hi = s; Di = 8.33X10–3 pu MW/Hz; βi = 0.425 pu MW/Hz; Ri = 2.4 pu Hz/MW; loading = 50%; TSSSC = 0.03 s; KSSSC = 0.1802; Kφ = 1.5 rad/Hz; TPS = 0.1 s; TTCSC = 0.015 s; TIPFC = 0.01 s

i

Control area number i (1,2,3)

m, n

Grasshopper index

X_m

location of m^th Grasshopper

S_m

correlation

G_m

gravitational strength on the m^th Grasshopper

A_m

wind abeyance

C

Coefficient of the comfort zone

K_SSSC

SSSC gain

T_SSC

SSSC time constant

T_TCPS

TCPS time constant

K_φ

TCPS gain

∆φ

phase-shifting angle

T_TCSC

TCSC time constant

T_IPFC

IPFC time constant

H_i

inertia constant of control area i (s)

∆P_Li

load increments in (p.u)

∆P_gi

generation increments in (p.u)

D_i

∆P_Li /∆f_i (pu/Hz)

T₁₂, T₂₃, T₁₃

synchronizing factors

R_i

speed regulation factor of control area i (Hz/pu MW)

T_gi

the time constant of reheat governor control area i (s)

K_ri

reheat coefficient of control area i

T_ri

Reheat time constant of area i (s)

T_ti

the turbine time constant of control area i (s)

B_i

frequency bias constant of area i

T_pi

2H_i/ f * D_i

K_pi

1/D_i (Hz/pu)

K_Pi

proportional gain of PI, PID, PIDF, and PIDF plus (1 + PI) controller in the control area i

K_Ii

integral gain of integral, PI, PID, PIDF and PIDF plus (1 + PI) controller in control area i

K_Di

derivative gain of PID, PIDF, and PIDF plus (1 + PI) controller in the control area i

K_PPi

the proportional gain of (1 + PI) controller in the control area i

N_i

filter coefficient of PIDF & PDF controller in control area i

D(s)

estimated derivative term = s/ 1 + Ns

βi

control area frequency response characteristics of area I (AFRC) = D_i + 1/R_i

∆fi

frequency incremental of control area i (Hz)

∆P_gi

Generation increments of control area i (p.u)

∆P_{tie i-j}

tie-line power increment among control area i and area j (p.u)

T

simulation time (s)