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

phaseshifting 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)

T_{12}, T_{23}, T_{13}

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 ij}

tieline power increment among control area i and area j (p.u)

T

simulation time (s)
