ISSN: 1693-6930
TELKOMNIKA Vol. 10, No. 2, June 2012 : 199 – 210
202 The equation of the total objective function using into account the Economic Power
Dispatch ED objective function; active power transmission losses
loss
P
; and the sum of the normalized violations of voltages
Vi
F
is as follow:
ED l loss
V V
f F
P F
ω ω
= +
+ 6
where
lim max
min 1
PQ
N V
PQj PQj
PQj PQj
j
F V
V V
V
=
= −
− ∑
l
ω
and
V
ω
constants are related to line loss and voltage deviation. These constants were found as a result of trials.
2.1.2. Types of Equality Constraints
While minimising the objective function, it is necessary to make sure that the generation still supplies the load demands plus losses in transmission lines. The equality constraints are
the power flow equations describing bus injected active and reactive may be defined as follows:
1
cos sin
nb i
i i
i j
ij ij
ij ij
j
P Pg
Pd V V
g b
q q
=
= -
= +
å
7
1
sin cos
nb i
i i
i j
ij ij
ij ij
j
Q Qg
Qd V V
g b
q q
=
= -
= -
å
8 where
i
P g ,
i
Q g are the active and reactive power generation at bus i;
i
P d ,
i
Q d are the real and reactive power demands at bus i;
i
V ,
j
V
, the voltage magnitude at bus i,j, respectively;
ij
q
is the admittance angle,
ij
b
and
ij
g are the real and imaginary part of the admittance and nb is the total number of buses. The equality constraints are satisfied by running Newton-Raphson
algorithm. 2.1.3. Types of Inequality Constraints
The inequality constraints of the OPF reflect the limits on physical devices in the power system as well as the limits created to ensure system security. The most usual types of
inequality constraints are upper bus voltage limits at generations and load buses, lower bus voltage limits at load buses, var. limits at generation buses, maximum active power limits
corresponding to lower limits at some generators, maximum line loading limits and limits on transformer tap setting. The inequality constraints on the problem variables considered include:
1 upper and lower bounds on the active generations at generator buses Pg
i min
≤
Pg
i
≤
Pg
i max
, i= 1, ng, 2 upper and lower bounds on the reactive power generations at generator buses
Qg
i min
≤
Qg
i
≤
Qg
i max
, i = 1, ng, 3 upper and lower bounds on reactive power injection at buses with VAR compensation Qc
i min
≤
Qc
i
≤
Qc
i max
, i=1, nc, 4 Upper and lower bounds on the voltage magnitude at the all buses. V
i min
≤
V
i
≤
V
i max
, i=1, nb, 5 upper and lower bounds on the bus voltage phase angles
θιµιν≤ θι ≤ θιµαξ , i = 1, nb; and 6 for secure operation, the transmission
line loading Sl is restricted by its upper limit as:S
li
≤
S
li max
, i = 1, nl, where S
li
, S
li max
are stand for the power of transmission line and limit of transfer capacity of transmission line and nl is the
number of transmission lines. The constraints on the state variables can be taken into consideration by adding penalty
function to the objective function.
2.1.4. Application of FACTS in Electric Power System
