Page 359 - Decision Making Applications in Modern Power Systems

Heuristic methods for the evaluation of environmental impacts Chapter | 12 321

where d i ; e i ; and f i are the coefficients of emission characteristics for each
generating unit.

12.3.1.3 Load dispatch restrictions considering emissions
In this section, a number of restrictions are considered:
An equal restriction of active power balance generated
The following equation is the power balance constraint [72,73]:
n
X D L
P i 2 P 2 P 5 0 ð12:19Þ
i51
D
where P i is the output power of each i generator, P is the load demand,
L
and P are transmission losses.
In other words, the total power generation has to meet the total
L
D
demand, P , and the loss of active power transmission lines, P :
n
X D L
P i 5 P 1 P ð12:20Þ
i51
The calculation of power losses involves the solution of the load flow
problem, which has equal restrictions on active and reactive power in
each bar as follows [74]:
n
X
L
P 5 B i P 2 ð12:21Þ
i
i51
To model the transmission loss, each function generator loss through
the derivatives of formula Kron coefficients for loss is set to output.
M
N N X
L
X X
P 5 P Gi B ij P Gj 1 B 0i P Gi 1 B 00 ð12:22Þ
i51 j51 i51
where B ij ; B 0i ; andB 00 are the power loss coefficient in the transmission
line. A reasonable accuracy can be obtained when the actual operating
conditions are close to the base case where the coefficients B were
obtained [75].
An inequality constraint in terms of generation capacity
For stable operation, the active power generated by each generator is
limited by the upper and lower limits. These restrictions in the generation
limits are expressed by
P min;i # P i # P max;i ð12:23Þ
where P i is the output power of the generator, i; P min;i is the minimum
power of the generator, i, and P max;i is the maximum generator power.
An inequality constraint in terms of fuel supply