A Fast Market Competition Approach to Power System Unit Commitment Using Expert Systems - Intelligent Computing for Sustainable Energy and Environment - page 448

N unit
i =1 P i min ≤ P t D

(23)

N unit
i =1 P i max ≥ P t D + P R

(24)

N unit

i =1 P i min > P t D , assign offline status “0” to online unit
with the highest cost until constraint (23) is satisfied.
ER5 (Insufficient capacity rule):For

ER4 (Excess capacity rule): For

∑

N unit

i =1 P i max < P t D + P R , assign online status “1”
to online unit with the lowest cost until constraint (24) is satisfied.

∑

Minimum Up/Down Time Constraints. For the minimum up/down time constraints
during the THMCA process, ER3 is applied the same as pre-scheduling.

Ramp Rate Constraints. Combining the ramp rate limit inequalities (8) and (9) with
the generation limit inequality (5) yields the generation limits and the ramp rate limits
of unit in hour as (25), which can be determined in the THMCA process.
ER6 (Ramp rate rule):

max( P i min , P t − 1 min( P i max , P t − 1 P i ≤ + DR i ) ≤ + UR i ) (25)

i i

5 Simulation Studies

The proposed THMCA using expert system was tested on a popular power system with
Num = 10, 20, 50 and 100 generating units. The required data for ten generating units
is the same in [10]. For power system with 20 generating units, the data of the ten units
was duplicated and the total load demand was multiplied by two. For the problem with
more units, the data was scaled appropriately.
The optimal THMCA parameters for ten generating units which were chosen after
several runs are given as N holding = 10, N sub = 200, ω = 2. For power system

with more units, the same parameters were utilized, except for N holding and N sub

τ = 0 . 2,

which

(45 ◦ , 90 ◦ ),which
adjusts the deviation from the original direction. These values were found suitable to
produce good solutions in terms of the processing time and the quality of the solutions.
From the results of 10 simulation runs, it is found that the optimal solution can be ob-
tained after 8-th to 10-th market competition interactions. Fig.1 shows the convergence
of the iteration for the 10-unit power system. This indeed verifies the high convergence
rate of the algorithm.
For the comparison purpose among the THMCA and other optimization methods, all
the simulation experiments used the same basic parameter settings.
Table 2 lists the solution of UC for 10-unit system obtained by THMCA using ES,
THMCA without ES, the shuffled frog leaping algorithm (SFLA) [10], BF [9], GA [6],
hybrid quantum clone evolutionary algorithm (HQCE) [8], and quantum inspired PSO
(Q-PSO) [7]. It is obvious that THMCA using ES has satisfactory results in comparison
with other methods, especially for the execution time.

increase correspondingly. Another parameter to be selected is θ ∈