Shatha S. Abdulla Al-Kubragyi
| Inaam Ibrahim Ali*
© 2025 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
OPEN ACCESS
Unit commitment (UC) is the most important optimization task for power system operation. It is categorized as a large combinatorial, nonlinear, high-dimensional, mixed-integer optimization problem to schedule the best generation units during each distinct operating period to meet the demands of the system load and spinning reserve capacity. This study proposed a new hybrid paradigm by combining the Moth Flame Optimizer algorithm and particle swarm optimization (MPO-PSO) to determine the optimal solution to the unit commitment problem. The approach logically combines the ideas of MFO and PSO to overcome their shortcomings and improve their ability to search globally the MFO-PSO approach is better able to handle challenging, confined and unknown search space problems. Additionally, it is a simple methodology and requires a limited number of parameters. The MFO-PSO approach is evaluated against other evolutionary heuristic algorithms such as (EE, M-FA, PSO, AMFA, PSO-GWO, MPSO-EO, and MFO) on 26 bus-test system to manage the UC problem. It is evident from the statistical results, that the proposed algorithm can offer competitive and highly promising results. Regarding cost improvement and execution time the outcomes show that the suggested hybrid approach performs better than certain other heuristic algorithms and original MFO. The influence of the MFO-PSO approach on the accuracy and convergence rate for dealing the UC issue is shown by the simulation results section. It can be observed from the obtained results that, in comparison to the original MFO technique, the algorithm demonstrated improved accuracy, fast convergence, and good performance. Because of these details, the estimation showed increased accuracy and convergence. The interesting thing to note of it is that the PSO is added to improve the MFO's accuracy, which is already rather high. Furthermore, the study also shows the algorithm's efficacy in resolving difficult issues with constrained and unknown search spaces.
moth flam algorithm, particle swarm optimization, unit commitment (UC)
In the modern energy system technology, the greatest interesting and a challenging aspect of the power system process is deciding the prober electrical generating units should operate at each time in order to meet a fluctuating electricity demand [1]. These estimations and actions cover under the subject of the unit commitment (UC). Unit commitment is the issue of identifying the ideal set of power production units in service for a daily to weekly time in order to accomplish a specific goal subject to a wide range of operating restrictions. The committed units must meet the system's predicted demand and spinning reserve requirement at the lowest possible operating cost [2]. Thus, the UC problem is highly challenging because of its intrinsic high-dimensionality, non-convexity, discreteness, and non-linearity. The initial solution needs to meet the constraints on the start-up and shut-down of the scheduled units during each planning period, as well as the requirements for system capacity and unit generation limit. The final solution must locate the best scheduling of the generation units during each distinct operating period to meet the demands of the system load and spinning reserve capacity [2, 3].
Numerous approaches had been presented to address the UC topic. Some of classical methodologies such as dynamic programming (DP) [4], Lagrangian relaxation (LR) [5], Tabu Search and Interior Point Optimization [6] introduced to find a satisfactory solution or near optimum solution of the UC problem However, these methods necessitate a significant amount of work to establish inference rules for vast systems with an excessive number of units and a wide range of limitations. As a result, a long execution time is required. Recently, simulated annealing (SA) and genetic algorithms (GA) which simulate natural processes were being used more often to solve optimization problems in scientific and engineering fields. The UC problem was managed effectively by using adaptive SA method but the hill-climbing inspection is quick and it only chooses the best solution due to the sub-optimization search [7]. The implementation of GA to resolve the unit commitment issue had been covered [8]. The GA achieved a good solution in UC problem along with the constraints. However, GA requires a number of steps for resolving the unit commitment issue, for achieving satisfactory response and an accuracy solution, the fitness function, parameter coding, and genetic operations such as mutation, convergence, and crossover criteria were chosen based on the characteristics of the UC situation.
With the advancement in evolutionary heuristic algorithms some literatures had used evolutionary-based metaheuristic optimization algorithms to study the UC problem. In general, “shuffled frog leaping algorithm (SFLA) [9], artificial bee colony (ABC) [10], bat-inspired algorithm (BA) [11], gray wolf optimization (GWO) [12], firefly approach [13] and particle swarm optimization (PSO) [14]” build algorithmic logic from everyday occurrences in the natural world. These approaches can be effectively solving multi-objectives nonlinear optimization problems with continuous and discrete variables, doesn't require useless computation time in addition, effective in exploiting the solutions. However, the algorithms face challenges such as the method's exploitation of the possible solution is unacceptable and the global optimal solution becomes less efficient and requires more computing time if the parameters are not set correctly. Ananthan et al. [14, 15] proposed PSO algorithm based on the UC problem. PSO is initialized by particles which is represented the set of possible solutions. The evolutionary process has few adjustable factors and is very simple. “Combinatorial, multimodal, multi-objective, and nonlinear problems” could all be solved with it successfully. Nevertheless, this algorithm has limitations including parameters adjusting, the selection of a proper swarm size and penalty functions that depend on the problem. Later, to increase the level of performance, several hybrid algorithms had been used in the literature to tackle the UC problem. Rastgou and Bahramara [16] proposed an adjusted firefly method to deal the unit commitment issue more effectively. SA method was combined with “Modified Sub-gradient Method (MSG)” [17]. A hybrid PSO-GWO approach for the unit commitment problem was presented [18, 19]. Moreover, a hybrid method known as MPSO-EO [20] proposed that combines the modified particle swarm optimization (MPSO) with the equilibrium optimizer (EO).
In the course of time, the Moth Flame Optimization (MFO) technique is a recently offered as intelligence technique [21]. The MFO approach was applied to solve the UC issue [22]. It is characterized by a minimal number of parameters and a straightforward construct. Furthermore, MFO is simple to use, reliable, and effective. However, although MFO can find the global optimal solution in some cases with less computational values, it finds a difficult to find the optimal solution in some extremely difficult optimization cases. On the other hand, despite PSO has comparatively fast response level, PSO's early convergence to the near-optimal and inefficiency in exploring the whole search space are its main drawbacks. So, Yang et al. [23] suggested combining MFO and PSO to improve the search for diversification in extremely difficult optimization subjects. As it is pointed out, Shaikh et al. [24] suggest a hybrid approach integrating MFO with PSO (MFOPSO) to improve MFO efficiency for calculating transmission line parameters optimally.
This study proposed the hybrid MFO-PSO algorithm to determine the optimal solution of unit commitment problem as efficiently as possible. It is compared with a various optimization technique to address the UC problem and assess the accuracy of the proposed approach.
The paper's main contributions summarize as follows:
1. The motivation of this study, suggest a new approach with inspiration from nature for resolving the UC difficulty and to compete with other existing techniques to solve another power system issues.
2. Compared to other established methods, MFO-PSO approach is better able to handle challenging confined and unknown search space problems. Additionally, it is simple methodology and requires a limited number of parameters. Thus, MFO-PSO has been used to address a real complex power system issue.
3. As far as the authors are aware. The MFO-PSO approach which was motivated by the nocturnal navigation strategy of moths around light sources has never before been applied to the UC problem.
The remainder of the work is divided as below: Section 2 presents the formulation of the unit commitment problem. Then, the MFO-PSO approach is detailed in Section 3 in addition to a thorough explanation of the steps involved the using MFO-PSO approach to resolve the UC task. The outcomes and numerical results of the simulation provides in Section 4. The final section of the paper is concluded in Section 5.
The main focus of unit commitment is the generating unit’s ON and OFF states at various internal times. It also needs to maintain estimated load levels and spinning reserve requirements while satisfying all generating unit constraints. Additionally, optimal power flow is used to reduce fuel consumption [25]. Therefore, when combined, the unit commitment and optimal power flow study provide a cost-saving methodology for power generating units [8].
The target function of UC is to minimize the total cost over a period of time, considering the costs associated with operating, starting and shutting down each unit under the related constraints as stated mathematically in Eq. (1) [3, 16]:
F(Pti,Uti)=∑Tt=1∑Ni=1[Fi(Pti)+SCti(1−Ut−1i)]Uti+∑Tt=1∑Ni=1SDti×(1−Uti)Ut−1i (1)
where, Fi(Pti) represents the fuel cost of the i-th number of generators units at the t of hours, and it can be stated mathematically as:
Fi(Pti)=αii(Pti)2+βiPti+γi (2)
where, αii,βi and γi are the fuel cost constant of the i-th unit. T is time, N is the total number of generators, Pti represents output power of i-th unit at time t,Uti is status of unit i at hour t(ON=1,OFF=0).
SCti represents the startup cost of i-th unit at hour t, and is defined with following mathematical formula:
SCti={HScost if Ti, down ≤Tti,off≤Tdown i+Tcold iCScost if Tti,off≥Tdown i+Tcold i} (3)
SDti represents the shutdown cost of i-th unit at hour t, which it is assigned as a constant value for every generator unit.
Subject to the following system constraints:
System power balance:
The load demand must be met by the total power produced in each time [22].
∑Ni=1UtiPti=Ptd (4)
Ptd : Power loading on the system at hour t.
Units capacity limitation:
It's important to satisfy the minimum and maximum power limitations of units.
Pimin (5)
P_i^{\min }, P_i^{{Max }}: the lower and upper output power limits of i-th unit.
Minimum up/down time limitations:
The operating unit needs to be on for a specific amount of time. It's called minimum up time during this period. However, there is a minimum amount of time that must pass after a unit is de-committed before it can be recommitted. This period is called the time of minimum downtime. These limitations can be shown as [10]:
T_i^{o n} \geq M U T_i (6)
T_i^{ {off }} \geq M D T_i (7)
T_i^{o n} : Minimum time that the unit i-th has been online constantly.
T_i^{ {off }} : Minimum time that the unit i-th has been unavailable (offline)
M U T_i and M D T_i: The minimum up/down time of the i-th unit.
UC solution is not convex issue because it involves structure binary variables. These variables make solving the UC extremely challenging and problematic. The coupling constraint for the UC problem is load balance. The unit coupling constraints are designed so that, in the event that the coupling constraints are satisfied, the behavior of one unit influences that of other units.
Moth-flame optimization: MFO is based on the moth's nocturnal transverse navigation strategy around light sources by maintaining a constant angle with the sky. The moth population acts as the candidate search solutions flying throughout the area using the specified strategy. Whereas, the flame population displays the best locations for the moths that have been found thus far. Moths are capable of flying in multi-dimensions or hyper-dimensional space by manipulating their position vectors. The proposed algorithm ensures convergence, and it is simple to use, reliable, and effective [23, 24].
With N moths in a D-dimensional search area, at the k-th iteration, assume M_i^{k} and F_j^k represent the location of the i-th moth and the j-th flame consequently. Later, a flame updates each moth's position using a mathematical model that is created using the equation:
M_i^{k+1}=D_i^k * e^{b v} * \cos (2 \pi v)+F_j^k (8)
where, v is a vector consisting of D random values uniformly distributed on [-1, 1], the factor b is predetermined which determines the form of the logarithmic spiral, and D_i^k refers to the distance of the i-th moth from the j-th flame, which has the following definition:
D_i^k=\left|F_j^k-M_i^k\right| (9)
The population size of moths is predetermined, whereas the number of the flame population is adaptively determined based on the search iteration, which is computed using the following formula:
flame\_no ^k={round}\left(N-k * \frac{N-1}{K M a x}\right) (10)
where, KMax is the upper limit of search iterations. The number of flames appears to gradually decrease, and only in the last stages of iterations, the moths adjust their location in relation to the best flame.
The moths that have been sorted based on their fitness value form the flame population in the initial iteration. The optimal moth in the first location of the flame population will be designated and the remaining moths will be arranged similarly. Subsequently, the flame population will comprise the better flame\_no ^k individuals chosen from the set of the previous iteration’s flame population and the current iteration's moth population [23].
Particle swarm optimization: The process of the PSO algorithm consists of a random collection of particles in a certain trajectory traveling in the direction of the best solution. Particles are driven depending on their former best location, their neighboring locations, and the best position among total particles. Each particle moves towards the optimal solution based on its previous best position given by p_{-}best, position of other particles and the optimum solution attained out of all the other particles given by g_best. let v_i^k and x_i^k are the velocity and position, respectively [15, 24]. Typically, the adjusted values for the location and velocity of the i-th particle are determined by analyzing Eqs. (11) and (12).
v_i^{k+1}=\omega * v_i^k+c_1 r_1\left(p_{-}best_i^k-x_i^k\right)+c_2 r_2\left(g_{-}\right.best\left.^k-x_i^k\right) (11)
x_i^{k+1}=x_i^k+v_i^{k+1} (12)
Proposed hybrid MFO-PSO: Early convergence is a general disadvantage for both MFO and PSO. The PSO iteration results in the search center of the total swarm convergent to one point, the best global location, and a negligible decrease in the particle's speed as it leaves local optima in the next iterations. The situation in MFO is noticeably worse. since the search center index has adjusted to one at last iterations of the program [23].
To deal the premature convergence point and enhance their capacity for global search, a hybrid algorithm logically incorporates the ideas of the MFO position-adjusting process of moths about a flame and the PSO local attractor. To ensure that the PSO algorithm converges, that every particle must be close to its local attractor Q_i^k [26]. The local attractor is known as below:
Q_i^k=\emptyset * p_{-}best_i^k+(1-\emptyset) * g_{-}best^k (13)
where, \emptyset is "a vector with uniformly distributed multi-dimension random numbers on [0, 1]". In this approach assume there are no defined pbest and gbest in MFO, the flame with the same sequence number for every moth is considered the pbest, and the best flame in the flame population is considered the gbest in our approach [23, 24]. This leads to the following modification of each moth's position update equation:
M_i^{k+1}=D_i^k * e^{b v} * \cos (2 \pi v)+Q_i^k (14)
Hence, the distance is computed by following formula:
D_i^k=\left|Q_i^k-M_i^k\right| (15)
Figure 1. Flowchart of the proposed HMFOPSO
Figure 1 displays the flowchart for the suggested MFO-PSO approach for solving UC problem.
To evaluate the proposed MPO-PSO approach, ten units and a 24-hour period are considered as the bench-test system. Table 1 displays the generators input data for the system [22]. The daily load demand of this case study is shown in Figure 2, which shows that the maximum system's demand is at the 11th and 12th hours, and its minimum system's demand is at the first hour. Table 2 lists the parameters setting for MFO-PSO, MFO, and PSO that are utilized in this issue. The setting parameters of the suggested hybrid MFO-PSO algorithm and original MFO method are identical. The suggested MFO-PSO algorithm's parameters for the simulation analysis are the same as those of the MFO method with population size of 20 and maximum number of iterations is 100. The commitment and generation schedule optimization results are displayed in Tables 3 and 4, respectively. Each line shows the unit's output power. The total cost is displayed in the final row of Table 4. Because the methods used in the simulation analysis are stochastic optimization approaches, the algorithm is executed with 20 trials using different search agents (random initial population) over a 24-hour period to assess the robustness of the MFO-PSO approach for solving unit commitment problem. The MFO-PSO algorithm’s outcomes for the unit's output power for varied load demands are shown in Tables 4 and 5. From the Table 5, it evident that the values of the cost function and execution time that MFO-PSO obtained are outperform or close to the MFO, PSO, and other algorithms. It demonstrates the MFO-PSO algorithm's robustness in handling unit commitment problems. Table 5 shows the outcomes of using 7 various approaches on the 10-unit test system and compares them with the findings of the proposed method (MPO-PSO) for cost and implementation time. For the aforementioned 10-unit system, the obtained cost is 553552$. It is clear from Table 5 that the hierarchical proposed approach outperforms some other heuristic algorithms like (EE [3], M-FA [13], PSO [15], AMFA [16], PSO-GWO [18], MPSO-EO [20], and MFO [22]) in terms of reported cost improvement and execution time. Figure 3 depicts the convergence characteristics of fuel cost comparison of 10 generating unit test system according to the number of iterations. A comparison is made between the original MFO and the proposed method (MPO-PSO) performance. It is obvious that MFO-PSO has superior convergence than MFO.
Table 1. The input figures of ten generating unit system [22]
|
Unit |
γ ($/h) |
β ($/MWh) |
α ($/MW2h) |
Pimax (MW) |
Pimin (MW) |
HScost ($) |
CScost ($) |
MUTi (h) |
MDTi (h) |
Ti Cold (h) |
Initial State (h) |
|
P1 |
1000 |
16.19 |
0.00048 |
455 |
150 |
4500 |
9000 |
8 |
8 |
5 |
8 |
|
P2 |
970 |
17.26 |
0.00031 |
455 |
150 |
5000 |
10000 |
8 |
8 |
5 |
8 |
|
P3 |
700 |
16.6 |
0.002 |
130 |
20 |
550 |
1100 |
5 |
5 |
4 |
-5 |
|
P4 |
680 |
16.5 |
0.00211 |
130 |
20 |
560 |
1120 |
5 |
5 |
4 |
-5 |
|
P5 |
450 |
19.7 |
0.00398 |
162 |
25 |
900 |
1800 |
6 |
6 |
4 |
-6 |
|
P6 |
370 |
22.26 |
0.00712 |
80 |
20 |
170 |
340 |
3 |
3 |
2 |
-3 |
|
P7 |
480 |
27.74 |
0.00079 |
85 |
25 |
260 |
520 |
3 |
3 |
2 |
-3 |
|
P8 |
660 |
25.92 |
0.00413 |
55 |
10 |
30 |
60 |
1 |
1 |
0 |
-1 |
|
P9 |
665 |
27.27 |
0.00222 |
55 |
10 |
30 |
60 |
1 |
1 |
0 |
-1 |
|
P10 |
670 |
27.79 |
0.00173 |
55 |
10 |
30 |
60 |
1 |
1 |
0 |
-1 |
Figure 2. Load demand pattern for 24 h for 10-unit system
Table 2. The parameters setting for MFO-PSO, MFO, and PSO
|
Parameters of PSO |
|
|
inertia weight \omega |
0.85 |
|
c1 and c2 |
2 |
|
random values of numbers r1 and r2 |
0, 1 |
|
Parameters of MFO |
|
|
v is a vector consisting of random values |
[-1, 1] |
|
factor b |
1 |
Table 3. Commitment schedule for ten generating unit system using proposed method (HMFOPSO)
|
Hour |
Generation Schedule for 10 Generating Unit System |
|||||||||
|
S1 |
S2 |
S3 |
S4 |
S5 |
S6 |
S7 |
S8 |
S9 |
S10 |
|
|
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
2 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
3 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
4 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
|
5 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
|
6 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
7 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
8 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
9 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
|
10 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
|
11 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
|
12 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
|
13 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
|
14 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
|
15 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
16 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
17 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
18 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
19 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
|
20 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
|
21 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
|
22 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
|
23 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
|
24 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Table 4. Generation schedule for 10 generating unit system using proposed method (HMFOPSO)
|
Hour |
Generation Schedule for 10 Generating Unit System |
PD |
|||||||||
|
S1 |
S2 |
S3 |
S4 |
S5 |
S6 |
S7 |
S8 |
S9 |
S10 |
||
|
1 |
455 |
245 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
700 |
|
2 |
455 |
295 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
750 |
|
3 |
455 |
395 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
850 |
|
4 |
455 |
455 |
0 |
0 |
40 |
0 |
0 |
0 |
0 |
0 |
950 |
|
5 |
455 |
455 |
0 |
0 |
90 |
0 |
0 |
0 |
0 |
0 |
1000 |
|
6 |
455 |
455 |
0 |
130 |
60 |
0 |
0 |
0 |
0 |
0 |
1100 |
|
7 |
455 |
410.071 |
130 |
130 |
25 |
0 |
0 |
0 |
0 |
0 |
1150 |
|
8 |
455 |
455 |
130 |
130 |
29.999 |
0 |
0 |
0 |
0 |
0 |
1200 |
|
9 |
455 |
455 |
130 |
130 |
110 |
20 |
0 |
0 |
0 |
0 |
1300 |
|
10 |
455 |
455 |
130 |
130 |
162 |
43 |
25 |
0 |
0 |
0 |
1400 |
|
11 |
455 |
455 |
130 |
130 |
162 |
80 |
25 |
13 |
0 |
0 |
1450 |
|
12 |
455 |
455 |
130 |
130 |
162 |
80 |
25 |
53 |
10 |
|
1500 |
|
13 |
455 |
455 |
130 |
130 |
162 |
43 |
25 |
0 |
0 |
0 |
1400 |
|
14 |
455 |
455 |
130 |
130 |
110 |
20 |
0 |
0 |
0 |
0 |
1300 |
|
15 |
455 |
455 |
130 |
130 |
30 |
0 |
0 |
0 |
0 |
0 |
1200 |
|
16 |
455 |
310 |
130 |
130 |
25 |
0 |
0 |
0 |
0 |
0 |
1050 |
|
17 |
455 |
260 |
130 |
130 |
25 |
0 |
0 |
0 |
0 |
0 |
1000 |
|
18 |
455 |
360 |
130 |
130 |
25 |
0 |
0 |
0 |
0 |
0 |
1100 |
|
19 |
455 |
455 |
130 |
130 |
30 |
0 |
0 |
0 |
0 |
0 |
1200 |
|
20 |
455 |
455 |
130 |
130 |
162 |
43 |
25 |
0 |
0 |
0 |
1400 |
|
21 |
455 |
455 |
0 |
130 |
162 |
73 |
25 |
0 |
0 |
0 |
1300 |
|
22 |
455 |
455 |
0 |
0 |
145 |
20 |
25 |
0 |
0 |
0 |
1100 |
|
23 |
455 |
425.001 |
0 |
0 |
0 |
20 |
0 |
0 |
0 |
0 |
900 |
|
24 |
455 |
345 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
800 |
|
Total cost |
553552$ |
||||||||||
Table 5. Overall cost ($) and implementation time (s.) comparison of various methods
|
Method |
Overall Cost ($) |
Implementation Time (s.) |
|
EE [3] |
563978.9812 |
---- |
|
M-FA [13] |
557873 |
0.117938 |
|
PSO [15] |
567330.56 |
---- |
|
AMFA [16] |
563865 |
2.62 |
|
PSO-GWO [18] |
565210 |
---- |
|
MPSO-EO [20] |
563977.0122 |
---- |
|
MFO [22] |
564810 |
20.4563 |
|
HMFOPSO (proposed) |
553552 |
0.135 |
Figure 3. The convergence characteristic of fuel cost
Unit commitment plays a vital role in optimization tasks for power system operation to meet their system level requirements of power quality and demand response capability. It attempts to reschedule the generation units at a specific time in order to achieve an overall reduction in generation costs subject to a wide range of operating restrictions. To resolve the unit commitment issue and to superior of the sub-optimal operation of existing algorithms, a hierarchical hybrid approach by combining the Moth Flame Optimizer algorithm and particle swarm optimization (MPO-PSO) has been presented in this paper. The hierarchical approach plans the generating units for each hour in order to achieve the feasible states while meeting given constraints. It is tested on a benchmark system (10-unit case study), and the estimated cost is 553552 $. A comparison is made between the efficacy of the suggested algorithms and several other evolutionary algorithms. Comparison results confirm that the MFO-PSO approach is better able to handle challenging confined and unknown search space problems. Additionally, it is simple methodology and requires a limited number of parameters. Thus, MFO-PSO has been used to address a real complex power system issue.
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