A hybrid crossover multi-agent multi-objective evolutionary algorithm and its application in microgrid operation optimization

Abstract

The power generation industry needs to adopt renewable energy so as to reduce the utilization of fossil energy and pollution emission. In renewable energy power generation, microgrid operation optimization needs to consider multiple objectives such as economy and environmental protection, which is a multi-objective optimization problem. Aiming at the multi-objective optimization problem, based on the Pareto optimal concept, a hybrid crossover multi-agent multi-objective evolutionary algorithm is proposed and applied to the multi-objective optimization problem of microgrid systems, in which the economical cost and environmental protection are considered. The simulation results under three operating conditions show that compared with the classical NSGA-â…¡ algorithm, the proposed algorithm can obtain higher quality Pareto optimal solution in a shorter time. The efficiency of the proposed algorithm in this problem is higher than that of the classical NSGA-â…¡ algorithm. It can provide a higher quality solution for the optimal operation of a microgrid.

Keywords

Microgrid operation optimization multi agent system multi-objective optimization pareto optimal solution

1. Introduction

According to the statistics of the International Energy Agency (IEA), the global energy related carbon dioxide emissions in 2019 were the same as those in 2018 (about 330 $\times$ 10 ${}^{8}$ t) [1]. Fossil fuel utilization is the main factor of increased CO ${}_{2}$ emissions. The power industry is the largest carbon emission industry, accounting for 38% of the total emission. Therefore, developing renewable energy in the power industry, realizing energy transformation, reducing fossil energy consumption and building a green low-carbon energy system are important measures to reduce CO ${}_{2}$ emissions and bring about global carbon neutrality [2].

Microgrids are a key technology for applying clean and renewable energy [3]. It is a small power generation and distribution system composed of a variety of renewable energy, energy storage system and energy conversion devices. Normally, a typical microgrid system includes wind power, photovoltaic, fuel cell,diesel generator, battery, which can increase reliability of microgrid, and other power generation equipment [4]. It is important to coordinate the resources with daily management, so as to obtain the benefit from microgrid [5].

When solving the multi-objective problem of microgrid operation optimization, there are two types of methods: one is to convert the multi-objective problem into a single objective problem, such as weight method. In reference [7], considering the economic and environmental factors, a multi-objective optimal model of microgrid is constructed. Based on the fuzzy optimization theory, the maximum fuzzy satisfaction method is used to convert the nonlinear multi-objective optimization problem into a single objective optimization problem. Combined with the Tabu search idea, the PSO algorithm is improved to solve the multi-objective optimization problem Reference [8] designed a fuzzy adaptive particle swarm optimization algorithm, which converts the multi-objective microgrid operation optimization problem considering economic and environmental objectives into a single objective optimization problem by weight method In reference [9], aiming at the economic operation cost and environmental pollution cost of microgrid, NSGA-II algorithm and PSO algorithm are combined and a new method NSGA-IIPSO optimization algorithm is proposed, which can obtain a higher dominant solution set when solving the multi-objective optimization problem Reference [10] takes the total operation and maintenance cost and total CO ${}_{2}$ emission of distributed integrated energy microgrid containing cold, heat, electricity and gas as the goal in one operation cycle, and uses the weight method to solve it, so as to take into account the requirements of economy and carbon emission In reference [11], the objectives of economic cost, pollutant emission and carbon emission of the microgrid containing electric vehicles are integrated into a single objective optimization problem by weight method, and then solved by artificial bee colony and particle swarm optimization algorithm In reference [12], the economic cost, pollutant emission and constraint regulation are cleverly integrated into a single objective problem through the weight method and then solved by the single objective intelligent algorithm Reference [13] converts pollutant discharge into pollution treatment cost, thus, the pollution treatment cost become a part of the operation cost. By this treatment, a multi-objective optimization problem is transformed into single objective optimization problem and it is finally solved by a single objective optimal algorithm

Another method is to use a hybrid intelligent algorithm based on Pareto optimization. Reference [14] designed a multi-objective particle swarm optimization method and applied it to a microgrid system containing micro turbine, wind turbine, solar cell, battery and diesel generator, considering the operation economy and pollution emission In reference [15], MOEA and dynamic multiconstraints handling strategy were combined to solve the multi-objective optimization problem, which includes the economic operation and the pollutant emission in the microgrid operation Reference [16] proposed a non dominated genetic algorithm based on coevolution theory and Beetle antenna, and applied it on economic and environmental multi-objective optimization for a microgrid system integrating cold, heat and electricity Considering the most practical constraints and the variable loads reference [17] used NSGA-II and PSO algorithm to minimize two objectives, including emissions and cost in combined heat and power microgrid simultaneously, and compared the simulation results.

In a word, for the microgrid optimal operation problem considering multiple objectives, the solution set of the problem can be obtained in one operation by using the Pareto optimal swarm intelligence method, which is more efficient than the weight method. In the process of algorithm design, generally speaking, the solution quality of hybrid intelligent method is a good choice. In addition, agents in the multi-agent system (MAS) can act individually and cooperatively, and search in different regions at the same time, so as to obtain a solution set with better distribution and higher quality [18, 19]. Therefore, this paper combines multi-agent technology with evolutionary strategy, designs agent exponential crossover and orthogonal crossover cooperation operators, agent neighborhood optimization operators, agent mutation operators, etc., and proposes a hybrid crossover multi-agent multi-objective evolutionary algorithm (HCMAMOEA). The algorithm is applied to the multi-objective optimization problem of microgrid considering economic operation and pollutant emission, which contains micro turbine, fuel cell, photovoltaic, wind turbine, and energy storage equipment. The simulation results show that the algorithm in this work can obtain the Pareto optimal solution better than the classical NSGA? algorithm in a short time, so as to provide guidance for the optimal operation of microgrid.

2. Objective functions of microgrid operation

The grid connected microgrid system in this paper includes micro turbine (MT), photovoltaic power (PV), fuel cell (FC), battery (BAT) and wind turbine (WT) [8, 14]. Various micro sources are connected to the power transmission bus and connected to the external power grid, so they can also interact with the external power grid. The structure is shown below in Fig. 1.

Figure 1.

Microgrid system structure.

2.1 Objective functions

The multi-objective optimization problem of microgrid operation includes two objective functions, the operation cost objective and the microgrid pollutant emission objective [8, 9, 14].

Objective 1: Operating cost objective can be described as below:

$\displaystyle F_{1}=f_{1}+f_{2}+f_{3}$ (1) $\displaystyle f_{1}=\sum_{t=1}^{24}\sum_{i=1}^{n}{P_{i}(t)C_{i}}(t)$ (2) $\displaystyle f_{2}=\sum_{t=1}^{24}\sum_{i=1}^{n}\textit{SS}_{i}(R_{i}(t)-R_{i% }(t-1))$ (3) $\displaystyle f_{3}=\sum_{t=1}^{24}P_{b}(t)C_{b}(t)-\sum_{t=1}^{24}{P_{s}(t)C_% {s}(t)}$ (4)

Where, $f_{1}$ is the operation cost, $P_{i}(t)$ is the output of the $i$ -th equipment in time $t$ , $C_{i}(t)$ is the operation cost of the equipment in time $t$ , and $n$ is the number of equipment; $f_{2}$ is the start-up and shutdown cost, SS ${}_{i}$ is the start-up and shutdown cost of the $i$ -th equipment, and $R_{i}$ ( $t)$ , $R_{i}$ ( $t-1$ ) is the current time and last time operation state of the $i$ -th equipment; $f_{3}$ is the cost of purchasing and selling electricity with external power network. This cost consists of two parts: electricity purchase expenses and electricity sales expenses, in which $P_{b}(t)$ is the electricity purchase power at time $t$ , $C_{b}$ ( $T$ ) is the electricity purchase price at time $t$ , Ps ( $t$ ) is the electricity sales Power at time $t$ , and Cs ( $t$ ) is the electricity sales price at time $t$ .

Objective 2: The pollution emission objective can be described as below:

$\displaystyle F_{2}=\sum_{t=1}^{24}\sum_{i=1}^{n}{P_{i}}(t)E_{i}+\sum_{t=1}^{2% 4}P(t)E$ (5)

In the above formula, $P_{i}$ ( $t)$ is the power of the $i$ -th micro source at time $t$ , $E_{i}$ is the pollutant generated by the unit power of the i-th micro source, $P$ ( $t)$ is the interactive power between the microgrid and the external power grid at time $t$ , and $E$ is the pollutant corresponding to the unit power of the external power grid.

2.2 Constraints

(1) Balance constrain

$\displaystyle P_{\textit{load}}(t)=\sum_{i=1}^{n}{P_{i}(t)+P(t)}$ (6)

Where $P_{\textit{load}}(t)$ is the load demand at time $t$ , $P_{i}$ ( $t$ ) is the output at time t of the $i$ -th micro source, and $P(t)$ is the power interaction between microgrid and external power grid.

(2) Upper and lower bound constraints

$\displaystyle P_{i\min}\leqslant P_{i}(t)\leqslant P_{i\max}$ (7) $\displaystyle P_{ex\min}\leqslant P(t)\leqslant P_{ex\max}$ (8)

Where $P_{i}(t)$ is the output of the i-th micro source at time $t$ , $P_{\textit{imax}}$ is the upper limit of the output of the $i$ -th micro source, $P_{\textit{imin}}$ is the lower limit of the output of the $i$ -th micro source, $P$ ( $t$ ) is the power interaction between the microgrid and the external power grid at time $t$ , $P_{\textit{exmax}}$ is the upper limit of the power interaction between the microgrid and the external power grid, and $P_{\textit{exmin}}$ is the lower limit of the power interaction between the microgrid and the external power grid.

(3) Battery charge discharge rate limit [8, 14]

$\displaystyle 0\leqslant P_{\textit{ch/dch rate}}\leqslant P_{\textit{ch/dch}\max}$ (9)

Where, $P_{\textit{ch/dch rate}}$ is the charge and discharge rate of the battery, and $P_{\textit{ch/dch}\max}$ is the maximum charge and discharge rate of the battery.

3. Hybrid crossover multi-agent multi-objective evolutionary algorithm

Multi-agent system is a collection of multiple single agents. The system cooperates to complete the problem to be solved by coordinating the behavior of a group of agents. For the multi-agent system in this work, in order to reduce the amount of calculation, a lattice with 3 $\times$ 3 structure is adopted as shown in Fig. 2 [20]. In the agent system, each agent completes the solution of the optimization problem by interacting with other agents in the grid.

Figure 2.

Structure diagram of a multi-agent system.

In this work, multi-agent technology and evolutionary strategy are combined, multi-agent crossover operator, multi-agent neighborhood optimization operator, multi-agent self-learning operator, multi-agent mutation operator, and archive set optimization operator are designed respectively, and finally a hybrid crossover multi-agent multi-objective evolution algorithm (HCMAMOEA) is proposed.

For the multi-agent crossover operator, it can act on any two individuals in the agent architecture, while for the multi-agent neighborhood optimization operator and self-learning operator, it only acts on the individuals connected by solid lines.

3.1 Hybrid crossover operator

Hybrid crossover combines conventional crossover and orthogonal crossover, so as to give full play to the respective characteristics of the two crossover methods. From this strategy, the search area is expanded and the optimal solutions are obtained. The strategy of combining orthogonal crossover and conventional crossover is as follows.

Let the multi-agent crossover operator act on the individual $L_{i}=(l_{i,1},l_{i,2},\ldots,L_{i,n})$ and $L_{j}=(l_{j,1},l_{j,2},\ldots,L_{j,n})$ .

(1) Implement the general crossover strategy on $L_{i}$ and $L_{j}$ as below [21]:

$\displaystyle\textit{newL}_{a}=\left({1-\alpha}\right)L_{i}+\beta L_{j}$ (10) $\displaystyle\textit{newL}_{b}=\left({1-\beta}\right)L_{i}+\alpha L_{j}$ (11)

Where, $\alpha$ , $\beta$ are a random number evenly distributed in the (0, 1) interval. If a variable in the new individual newL ${}_{a}$ and newL ${}_{b}$ exceeds the upper and lower limits of the variable interval, the upper and lower limits are taken.

(2) The orthogonal crossover strategy is implemented for newL ${}_{a}$ and newL ${}_{b}$ [22, 23].

Upper and lower limit of the k-th variable defined by $\textit{newL}_{a}$ and $\textit{newL}_{b}$ can be determined as follow:

$\displaystyle\left[{\min l_{k},\max l_{k}}\right]=\left[{\min(\textit{newl}_{a% ,k},\textit{newl}_{b,k}),\max(\textit{newl}_{a,k},\textit{newl}_{b,k})}\right]$ (12)

Where $k=1,2,\ldots,n$ .

The upper and lower limits [min $l_{k}$ , max $l_{k}$ ] can be divided into Q levels, namely $x_{k,1}$ , $x_{k,2}$ , $\ldots$ , $x_{k,Q}$ , which can be shown as follows:

$\displaystyle x_{k,v}=\left\{\begin{array}[]{ll}\min(\textit{newl}_{a,k},% \textit{newl}_{b,k})&{v=1}\\ \min(\textit{newl}_{a,k},\textit{newl}_{b,k})+(v-1)\frac{\left|\textit{newl}_{% a,k}-\textit{newl}_{b,k}\right|}{Q-1}\\ \max(\textit{newl}_{a,k},\textit{newl}_{b,k})&{v=Q}\\ \end{array}\right.\ \ 2\leqslant v\leqslant Q-1$ (13)

Randomly generate $m$ integers, $a_{1}$ , $a_{2}$ , $\ldots$ , $a_{m}$ ( $1<a_{1}<a_{2}<\ldots<a_{m}<n)$ , thereby generating $m+1$ factors for the independent variable vector, each of which can be described as follows:

$\displaystyle\left\{\begin{array}[]{l}y_{1}=(x_{1},x_{2},\ldots,x_{a1})\\ y_{2}=(x_{a1+1},x_{a1+2},\ldots,x_{a2})\\ \ldots\\ y_{m+1}=(x_{am},x_{am+1},\ldots,x_{n})\\ \end{array}\right.$ (14)

$Q$ levels for the $i$ -th factor can be expressed as follows:

$\displaystyle\left\{\begin{array}[]{l}y_{i1}=(x_{a_{i-1}+1,1},x_{a_{i-1}+2,1},% \ldots,x_{ai,1})\\ y_{i2}=(x_{a_{i-1}+1,2},x_{a_{i-1}+2,2},\ldots,x_{ai,2})\\ \ldots\\ y_{iQ}=(x_{a_{i-1}+1,Q},x_{a_{i-1}+2,Q},\ldots,x_{ai,Q})\\ \end{array}\right.$ (15)

An orthogonal table $L_{Q}^{2}$ ( $Q^{m+1})$ was established to produce $Q^{2}$ progeny individuals.

In this work, the orthogonal table $L_{9}(3^{4})$ is selected, which is shown in Table 1.

Table 1

$L_{9}(3^{4})$ orthogonal table

Sequence	Factors
	A	B	C	D
1	1	1	1	1
2	1	2	2	2
3	1	3	3	3
4	2	1	2	2
5	2	2	3	1
6	2	3	1	2
7	3	1	3	2
8	3	2	1	3
9	3	3	2	1

(3) Through conventional crossover and orthogonal crossover, the individuals with the highest dominance level are selected and added to the external archive set. Two of them were randomly selected to replace the original agent.

3.2 Neighborhood optimal selection operator

Compare the dominance of the individuals in the neighborhood of the agent $L_{i}$ , and find out Max_Neighbor( $L_{i}$ ), which indicates the individual with the highest dominance level. Max_Neighbor( $L_{i}$ ) is then added to the external archive set.

3.3 Multi-agent self-learning operator

Impose Cauchy random number perturbation on Max_Neighbor( $L_{i}$ ) and $L_{i}$ with a certain probability.

Take $L_{i}$ as an example, where $l_{i,k}$ is the $k$ -th variable of $L_{i}$ , and $C_{k}$ is the $k$ -th Cauchy random number.

$\displaystyle\textit{newl}_{i,k}=\left\{\begin{array}[]{ll}\overline{x_{i,k}}&% {l_{i,k}+C_{k}>\overline{x_{i,k}}}\\ \underline{x_{i,k}}&{l_{i,k}+C_{k}<\underline{x_{i,k}}}\\ l_{i,k}+C_{k}&\text{otherwise}\end{array}\right.$ (16)

Cauchy random number perturbation can be applied to Max_Neighbor( $L_{i}$ ) in the same way, and the generated new individual is compared with other individuals in the archive set to update.

3.4 Multi-agent mutation operator

In order to further improve the quality of solutions, the mutation operation is implemented on the variables of agents with the probability $P_{m}$ . This implementation process is described below [24].

$\displaystyle l_{{}_{i,k}}^{\textit{mutated}}=\left\{{\begin{array}[]{ll}% \overline{x}_{i,k}&{l_{i,k}+\alpha*\beta>\overline{x}_{i,k}}\\ \underline{x}_{i,k}&{l_{i,k}+\alpha*\beta<\underline{x}_{i,k}}\\ l_{i,k}+\alpha*\beta&\text{otherwise}\end{array}}\right.$ (17)

$\displaystyle\alpha=0.5*(\overline{x}-\underline{x})*\textit{sign}(U(0,1)-0.5)$ (18)

$\displaystyle\beta=\sum\limits_{i=0}^{n}{2^{-i}*\delta}$ (19)

$\displaystyle\delta=\left\{\begin{array}[]{ll}0&{p>1/n}\\ 1&p<1/n\\ \end{array}\right.$ (20)

Where, $l_{i,k}$ is the original variable, $l_{i,k}^{\textit{mutated}}$ is the variable after mutation. $p$ is a random number in the range(0,1), $\alpha$ is the perturbation variable, $\beta$ is the sum of all the values selected in the set $X=(2^{-0}$ , 2 ${}^{-1}$ , $\ldots$ , 2 ${}^{-m})$ with probability 1/ $n$ , n is the number of variables.

3.5 Archive set optimization operator

Since the archive sets are the individuals with the highest level of dominance, there is no dominance relationship between them. By calculating the crowding distance of individuals in the archive set [25], individuals with large crowding distance are selected and performed Cauchy random perturbation, so as to make the individuals in the archive set have higher approximation and better distribution.

3.6 Steps of HCMAMOEA

The steps of HCMAMOEA designed in this paper are as follows:

Step 1
Randomly generate 9 individuals on the 3 $\times$ 3 grid;
Step 2
If the number of iterations Gen is an integer multiple of genset, randomly select two individuals and implement the multi-agent crossover operator including conventional crossover and orthogonal crossover, compare the generated new individuals with the individuals in the archive set respectively, and retain the solution with the highest dominance level;
Step 3
Implement multi-agent neighborhood optimization operator for individuals on the grid, select the individuals with the highest dominance level and compare them with the individuals in the archive set, and update the archive set;
Step 4
Implement the multi-agent self-learning operator on the individual on the grid;
Step 5
Implement multi-agent mutation operator for individuals on grid;
Step 6
Calculate the crowding distance for the individuals in the archive set, select the part with the largest crowding distance, perform Cauchy random number perturbation, calculate the objective function value for the newly generated individuals, compare it with the original individuals in the archive set, update the archive set, and return to Step 2;
Step 7
If the number of iterations Gen is equal to the maximum number of iterations, output the individual in the archive set and end the operation.

The overall algorithm flow chart is shown in Fig. 3.

Figure 3.
Flow chart of HCMAMOEA.

4. Simulation

In this microgrid system, there are three working modes: the first is the basic mode, the second is the maximum renewable energy output mode, and the third is the unrestricted power interaction mode, which is between microgrid and external power grid [8, 14]. In the first mode, the output of each micro source is adjusted by optimizing the two conflicting objective functions of economic cost and pollutant emission; In the second mode, photovoltaic and wind turbines work at the maximum power allowed by natural conditions, and the Pareto optimal solutions of the two objective functions of pollutant emission and economic cost are obtained by adjusting the output of other micro sources; In the third mode, the power interaction between microgrid and external power grid is no longer limited.

Table 2
Operation cost and pollution emission of micro sources

Type	Running cost(Ect)	Start up/ shut down cost(Ect)	Pmin (KW)	Pmax (KW)	CO ${}_{2}$ Emission (Kg/MWh)	SO ${}_{2}$ Emission (Kg/MWh)	NO ${}_{x}$ Emission (Kg/MWh)
MT	0.475	0.960	6	30	720	0.0036	0.1
1 FC	0.294	1.65	3	30	460	0.003	0.0075
1 BAT	0.380	0	$-$ 30	30	10	0.0002	0.001
1 WT	1.073	0	0	15	0	0	0
1 PV	2.584	0	0	25	0	0	0
1 Ext grid	–	0	$-$ 30	30	950	0.5	2.1

Table 3

The Maximum allowable operating power of WT and PV under current day conditions

Hour	WT (KW)	PV (KW)	Hour	WT (KW)	PV (KW)
1	1.785	0	13	3.915	23.90
2	1.785	0	14	2.370	21.05
3	1.785	0	15	1.785	7.875
4	1.785	0	16	1.305	4.225
5	1.785	0	17	1.785	0.550
6	0.915	0	18	1.785	0
7	1.785	0	19	1.302	0
8	1.305	0.2	20	1.785	0
9	1.785	3.75	21	1.3005	0
10	3.090	7.525	22	1.3005	0
11	8.775	10.45	23	0.915	0
12	10.41	11.95	24	0.615	0

The start-up and shutdown cost, operation cost, and pollutant emission of micro sources are shown in Table 2, and the maximum allowable operating power of photovoltaic and wind power is shown in Table 3 [8, 14].

The purchase and sale price are shown in Table 2, and the load demand is shown in Fig. 4.

Table 4

Daily peak to valley electricity price

Price (Ect)	Peak 15:00 $\sim$ 21:00	Valley 24:00 $\sim$ 7:00	Normal 7:00 $\sim$ 15:00 21:00 $\sim$ 24:00
Supply	2.3	0.45	0.85
Sell	0.9	0.15	0.45

Figure 4.

Hourly power demand in a day.

This optimization problem includes different working modes, and the optimization variables include the actual output and operation and stop states of the equipments. In order to improve computational efficiency, the operation and stop states of the equipment are determined by the output of the equipment.

The simulation environment consists of hardware and software, the hardware is Intel (R) core (TM) i5-6300hq CPU, 8G memory, and the software is MATLAB 7.1.

4.1 Working mode 1

In the first working mode, the hourly output of each micro source is reasonably optimized to minimize the cost and pollutant emission of the micro grid system as much as possible. In this mode, since the gas turbine and fuel cell have startup and shutdown costs, the startup and shutdown of gas turbine and fuel cell are determined according to the load distribution of gas turbine and fuel cell in each iteration. In the shutdown states, the load that does not meet the startup conditions shall be preferentially distributed to wind power, photovoltaic and other clean energy [26], in the order of wind, solar energy, storage battery and external power grid. Under this working mode, there are 24 * 5 independent variables, which respectively correspond to the output of 5 micro sources per hour in a day. The load demand subtracts the sum of the output of the first five micro sources, so as to determine the output of another source, from which the balance constrain is satisfied. The number of iterations of hybrid crossover multi-agent multi-objective evolutionary algorithm is 3000, the crossover operator acts once every 80 generations

In reference [27], several classical multi-objective evolutionary algorithms are compared. For 2-objective problems, NSGA-II algorithm can obtain higher quality solution sets in a short time. Therefore, the NSGA-II algorithm is selected for comparative research. The number of iterations of the NSGA-â…¡alogrithm is 600, the population size is 100 The results are shown in Fig. 4.

Figure 5.

The pareto solutions obtained by HCMAMOEA and NSGA-II under the working mode 1.

Under this working condition, the running time of HCMAMOEA is 43 s and that of the NSGA-II alogrithm is 71 s. It can be seen from the results that HCMAMOEA can obtain a solution set better than the classical NSGA-II algorithm in a short time.

The compromise solution is calculated by the formula below [28].

$\displaystyle\mu_{f_{i}}=\left\{{\begin{array}[]{ll}1&{f_{i}\leqslant f_{i}^{% \min}}\\ \frac{f_{i}^{\max}-f_{i}}{f_{i}^{\max}-f_{i}^{\min}}&{f_{i}^{\min}<f_{i}<f_{i}% ^{\max}}\\ 0&{f_{i}\geqslant f_{i}^{\max}}\\ \end{array}}\right.$ (21) $\displaystyle\mu^{k}=\frac{\sum\limits_{i=1}^{N}{\mu_{f_{i}}^{k}}}{\sum\limits% _{k=1}^{M}{\sum\limits_{i=1}^{N}{\mu_{f_{i}}^{k}}}}$ (22)

Let the individual with the maximum value in Eq. (22) be the optimal compromise solution, where: $f_{i}^{\max}$ is the maximum value of the $i$ -th goal, $f_{i}^{\text{min}}$ is the minimum value of the $i$ th goal, N is the number of goals, and $M$ is the number of individuals in the Pareto solution set.

Table 5 shows the output of each micro source in every hour corresponding to the optimal compromise solution under working mode 1, in which the economic cost is 646.7871Ect and the pollution emission is 438.8846 kg.

Table 5

Output of each micro source per hour corresponding to the optimal compromise solution under mode 1

TIME/hour	MT (KW)		FC (KW)		BAT (KW)		WT (KW)		PV (KW)		GRID (KW)		MT STATUS	FC STATUS
1	0		0		30		$-$ 11	.9263	0		29	.92627	0	0
2	0		25	.36214	29	.83499	0	.017334	0		$-$ 1	.21447	0	1
3	0		0		29	.95104	$-$ 13	.8375	0		29	.88642	0	0
4	0		29	.41737	30		1	.769173	0		$-$ 6	.18655	0	1
5	0		30		29	.76871	1	.785	0		$-$ 1	.55371	0	1
6	0		29	.00451	29	.8624	0	.271992	0		$-$ 0	.1389	0	1
7	15	.41115	30		29	.92055	0	.914981	0		$-$ 2	.24668	1	1
8	30		30		30		1	.305	0	.2	$-$ 20	.505	1	1
9	29	.70797	30		30		0	.106696	3	.648866	$-$ 13	.4635	1	1
10	29	.37714	30		30		3	.09	7	.419098	$-$ 23	.8862	1	1
11	29	.65188	30		29	.80654	0	.653543	3	.299964	$-$ 19	.4119	1	1
12	28	.07878	30		30		0		11	.37922	$-$ 29	.458	1	1
13	29	.26027	30		29	.52188	0	.20999	17	.00786	$-$ 30	1	1
14	23	.17781	30		30		0	.473476	16	.31638	$-$ 23	.9677	1	1
15	28	.52408	30		30		0	.313892	7	.670421	$-$ 16	.5084	1	1
16	30		30		30		1	.305	4	.225	$-$ 11	.53	1	1
17	29	.94426	30		30		1	.759162	0	.548068	$-$ 11	.2515	1	1
18	30		30		29	.91897	1	.785	0		$-$ 1	.70397	1	1
19	30		30		30		1	.302	0		$-$ 5	.302	1	1
20	29	.93771	30		30		1	.785	0		$-$ 0	.72271	1	1
21	30		30		30		1	.3005	0		$-$ 9	.3005	1	1
22	30		30		30		1	.3005	0		$-$ 16	.3005	1	1
23	29	.85044	30		30		0	.860978	0		$-$ 29	.7114	1	1
24	22	.45059	30		28	.93441	0	.615	0		$-$ 30	1	1

4.2 Working mode 2

Under this working condition, because the outputs of wind power and photovoltaic are in the maximum allowed power mode, only the output of gas turbine, fuel cell , battery, and external power grid need to be considered every hour. The sum of the current load demand minus the output of five micro sources is used as the output of the external power grid. If the output currently allocated to the gas turbine or fuel cell is lower than the minimum operating load, stop the gas turbine or fuel cell and allocate the output to the battery and external power grid. Under the current working mode, the number of actual equipment output variables is set to 24 * 3, the number of iterations of HCMAMOEA is set to 7000, the crossover operator acts once every 80 generations, the number of iterations of the NSGA-II algorithm is set to 600, and the population size is set to 100. The results are shown in Fig. 6.

Figure 6.

The Pareto solutions obtained by HCMAMOEA and NSGA-II under the working mode 2.

Compared with NSGA-II algorithm, it can be seen from the simulation results that some solutions obtained by HCMAMOEA are dominant and the other is non dominant.

The solution time of HCMAMOEA is 52 s and that of the NSGA-II is 72 s. On the whole, in this working mode, this algorithm is slightly better than the classical algorithm.

Table 6 shows the output of each micro source in every hour corresponding to the optimal compromise solution under working mode 2, in which the economic cost is 786.1415Ect and the pollution emission is 339.6266 kg.

Table 6

Output of each micro source per hour corresponding to the optimal compromise solution under mode 2

TIME/hour	MT (KW)		FC (KW)		BAT (KW)		WT (KW)		PV (KW)		GRID (KW)		MT STATUS	FC STATUS
1	0		29	.70873	30		1	.785	0		$-$ 13	.4937	0	1
2	0		29	.77023	30		1	.785	0		$-$ 7	.55523	0	1
3	0		30		30		1	.785	0		$-$ 15	.785	0	1
4	0		29	.71598	29	.05121	1	.785	0		$-$ 5	.5522	0	1
5	0		30		29	.7348	1	.785	0		$-$ 1	.5198	0	1
6	0		30		30		0	.915	0		$-$ 1	.915	0	1
7	19	.02397	29	.09267	30		1	.785	0		$-$ 5	.90164	1	1
8	30		29	.01312	30		1	.305	0	.2	$-$ 19	.5181	1	1
9	30		29	.98915	30		1	.785	3	.75	$-$ 15	.5241	1	1
10	29	.9	29	.23887	30		3	.09	7	.525	$-$ 23	.7539	1	1
11	24	.75847	29	.97921	30		8	.775	10	.45	$-$ 29	.9627	1	1
12	17	.50941	29	.85762	30		10	.41	11	.95	$-$ 29	.727	1	1
13	17	.78382	29	.35638	30		3	.915	23	.9	$-$ 28	.9552	1	1
14	15	.29314	28	.77502	29	.86052	2	.37	21	.05	$-$ 21	.3487	1	1
15	29	.62134	29	.92193	30		1	.785	7	.875	$-$ 19	.2033	1	1
16	30		30		30		1	.305	4	.225	$-$ 11	.53	1	1
17	30		30		30		1	.785	0	.55	$-$ 11	.335	1	1
18	29	.96743	30		29	.99371	1	.785	0		$-$ 1	.74614	1	1
19	30		30		30		1	.302	0		$-$ 5	.302	1	1
20	30		30		30		1	.785	0		$-$ 0	.785	1	1
21	29	.99891	30		30		1	.3005	0		$-$ 9	.29941	1	1
22	29	.99039	30		30		1	.3005	0		$-$ 16	.2909	1	1
23	29	.8673	30		29	.46418	0	.915	0		$-$ 29	.2465	1	0
24	21	.14019	30		29	.95909	0	.615	0		$-$ 29	.7143	1	1

4.3 Working mode 3

Under working mode 3, the power interaction between the microgrid and the external power grid is no longer limited. Therefore, the power exchanged between the microgrid and the external power grid is determined by subtracting the total output of the five micro sources from the load demand of the current time. Under this condition, if the load currently allocated to the gas turbine or fuel cell is lower than the minimum starting load, it will shut down and regenerate other equipment loads, and the sum of load demand minus other equipment loads will be used as the interactive power of microgrid and external power grid. Under the current working condition, the number of actual equipment output variables is set to 24 * 5, the number of iterations of HCMAMOEA is set to 3000, the crossover operator acts once every 80 generations, the number of iterations of the NSGA-â…¡ algorithm is set to 600, and the population size is set to 100. The results are shown in Fig. 7.

Under this working mode, the calculation time of HCMAMOEA algorithm is 31 s, while that of the NSGA-II algorithm is 173 s.

It can be seen from Fig. 7, the Pareto optimal solution of the problem obtained by HCMAMOEA algorithm is much better than the solution obtained by the NSGA-II algorithm.

Table 7 shows the output of each micro source in every hour corresponding to the optimal compromise solution under working mode 2, in which the economic cost is 682.3919Ect and the pollution emission is 420.9909 kg.

Table 7
Output of each micro source per hour corresponding to the optimal compromise solution under mode 3

TIME/hour	MT (KW)		PAFC (KW)		BAT (KW)		WT (KW)		PV (KW)		GRID (KW)		MT STATUS	FC STATUS
1	12	.971	28	.66073	27	.7596	0	.291901	0		$-$ 21	.6832	1	1
2	10	.53324	28	.4326	29	.8625	1	.682256	0		$-$ 16	.5106	1	1
3	29	.19893	23	.42693	29	.46477	0	.00773	0		$-$ 36	.0984	1	1
4	0		24	.98659	27	.94599	0	.083822	0		1	.983601	0	1
5	12	.2143	29	.21738	28	.52432	0	.081411	0		$-$ 10	.0374	1	1
6	17	.7603	25	.08043	29	.85768	0	.915	0		$-$ 14	.6134	1	1
7	20	.30844	29	.15447	26	.65396	0	.062762	0		$-$ 2	.17963	1	1
8	29	.30468	29	.49656	28	.99766	0	.034634	0	.053318	$-$ 16	.8868	1	1
9	26	.0328	27	.35251	30		0	.016427	0	.062933	$-$ 3	.46468	1	1
10	28	.4568	30		29	.69596	0	.116351	0	.013319	$-$ 12	.2824	1	1
11	29	.63668	30		29	.72839	0	.345154	5	.984458	$-$ 21	.6947	1	1
12	30		29	.37977	30		0		3	.299639	$-$ 22	.6794	1	1
13	30		30		29	.4044	0	.527357	13	.88987	$-$ 27	.8216	1	1
14	29	.83808	29	.54774	28	.95137	0	.126776	16	.95094	$-$ 29	.4149	1	1
15	29	.59845	30		28	.91625	0	.165448	7	.86538	$-$ 16	.5455	1	1
16	30		29	.33887	30		0	.000949	4	.008046	$-$ 9	.34787	1	1
17	29	.05677	28	.92559	29	.46232	0	.06505	0	.199745	$-$ 6	.70947	1	1
18	30		28	.92783	30		1	.201796	0		$-$ 0	.12963	1	1
19	30		30		29	.69197	0	.062724	0		$-$ 3	.75469	1	1
20	29	.94056	29	.81469	30		1	.460133	0		$-$ 0	.21538	1	1
21	30		30		30		0		0		$-$ 8		1	1
22	29	.36834	29	.91456	29	.62338	0	.784663	0		$-$ 14	.6909	1	1
23	30		26	.24301	29	.84687	0	.673666	0		$-$ 25	.7635	1	1
24	23	.49056	30		29	.21008	0	.223662	0		$-$ 30	.9243	1	1

Figure 7.

The pareto solutions obtained by HCMAMOEA and NSGA-II under the working mode 3.

From the optimal compromise solution of the results obtained under the three working modes, it can be seen that under working mode 2, the pollutant emission is the least, where the wind power and PV are working in maximum power mode. However, due to the operation cost of the two micro sources, the operation cost of the optimal compromise solution is the highest under the three working conditions. The optimal compromise solutions obtained under conditions 1 and 2 are relatively close, the operating cost of condition 1 is slightly lower than that of condition 3, and the pollutant emission is slightly higher than that of condition 3. The total electricity sales to the external power grid under the optimal compromise solution of working mode 1 is about 244 kwh, while the electricity sales to the external power grid under the optimal compromise solution of working mode 3 is about 349 KWH. Because the electricity sales price is lower than the micro source operating cost as a whole, Thus, the operation cost of condition 3 is slightly higher than that of working mode 1, and the pollution emission is lower than that of working mode 1.

Table 8

Pareto optimal compromise solutions of different working modes

Working mode	Economic cost (Ect)	Pollution emission (kg)
1	646.7871	438.8846
2	786.1415	339.6266
3	682.3919	420.9909

5. Conclusions

Aiming at the multi-objective optimization problem of microgrid operation, a hybrid cross multi-agent multi-objective evolutionary algorithm is designed and applied to the multi-objective optimization problem. Then this algorithm is compared with the classical multi-objective evolutionary algorithm NSGA-II. The conclusions are as follows:

Using the grid structure of an agent system, the orthogonal crossover method is combined with conventional crossover, the multi-agent hybrid crossover operator is designed, and a hybrid crossover multi-agent multi-objective evolutionary algorithm is proposed.

The algorithm is applied to the multi-objective optimization problem of microgrid operation, and the results are better than the classical NSGA-II algorithm. Especially under conditions 1 and 3, the results obtained in a short time are obviously dominant compared with NSGA-II algorithm. The reason focuses on two aspects. One is the application of multi-agent structure in the algorithm designing. The structure has remarkable features, such as autonomy, distribution, coordination, etc. By the above characteristics, it is conducive to the design algorithm to find a higher quality solution set.

The other reason is the application of hybrid strategy. In this algorithm, evolutionary strategy and multi-agent framework are mixed. The hybrid strategy mixes the advantages of different algorithms and give full play to their respective strengths, so that the high-quality solution of the problem can be found effictively.

The optimal compromise solution of HCMAMOEA under three working modes is analyzed, and the results are consistent with the actual operating conditions.

Footnotes

Acknowledgments

This work was supported by the scientific research fund of Nanjing Institute of Technology (Grant No. YKJ201610).

Conflict of interest

The authors declare no conflict of interest.

Author contributions

Liheng Liu and Dongliang Zhang conceived and designed the experiments; Liheng Liu performed the simulation; Liheng Liu, Jinping Wang and Jin Yan analyzed the data; Liheng Liu wrote the paper.

References

IEA. Global CO

{}_{2}

emissions in 2019. https://www.iea.org/articles/global-co2-emissions-in-2019.

Zou

Xiong

Xue

Zheng

Wang

. The role of new energy in carbon Neutral. Petroleum Exploration and Development. 2021; 48: 411-420.

Gao

Wang

Han

Xie

Peng

. A review of optimization of microgrid operation. Energies. 2021; 14: 1-39.

Dawoud

Lin

OKba

. Hybrid renewable microgrid optimization techniques: A review. Renewable and Sustainable Energy Reviews. 2018; 82: 2039-2052.

Nilgun

Ayca

Damla

Ugur

Ali

Eren

Tugrul

Ozden

. Resource management optimization for a smart microgrid. Journal of Renewable and Sustainable Energy. 2019; 11: 1-12.

Jithendranath

Debapriya

. Scenario-based multi-objective optimization with loadability in islanded microgrids considering load and renewable generation uncertainties. IET Renewable Power Generation. 2019; 13: 785-800.

Zhao

Cui

Fan

. Multi-objective coordination optimization of multi-microgrid considering economic and environmental benefits. Renewable Energy Resources. 2019; 37: 372-378.

Amjad

Alireza

Taher

. Multi-operation management of a typical micro-grids using Particle swarm optimization: A comparative study. Renewable and Sustainable Energy Reviews. 2012; 16: 1268-1281.

Zhao

Wang

Fan

Wang

. Multi-objective optimization operation model of microgrid based on NSGA-II-PSO algorithm. Journal of Power Supply (Accepted).

10.

Geng

Yang

Gao

Chen

Liu

Chen

. Optimal Operation of distributed integrated energy microgrid with CCHP considering energy storage. Electric Power Engineering Technology. 2021; 40: 25-32.

11.

Habib

HUR

Subramaniam

Waqar

Farhan

Kotb

Wang

. Energy Cost Optimization of Hybrid Renewables Based V2G Microgrid Considering Multi Objective Function by Using Artificial Bee Colony Optimization. IEEE Access. 2020; 8: 62076-62039.

12.

Yang

Sun

Wang

. Multi-Objective Optimization Scheduling Considering the Operation Performance of Islanded Microgrid. IEEE Access. 2020; 8: 83405-83413.

13.

Jiang

Ning

. Multi-objective optimal dispatch of microgrid with large-scale electric vehicles. IEEE Access. 2019; 7: 145880-145888.

14.

Aghajani

Ghadimi

. Multi-objective energy management in a micro-grid. Energy Reports. 2018; 4: 218-225.

15.

Xia

. A dynamic multi-constraints handling strategy for multi-objective energy management of microgrid based on MOEA. IEEE Access. 2019; 7: 138732-138744.

16.

Tan

Chen

. Stochastic multi-objective optimized dispatch of combined cooling, Heating, and power microgrids based on hybrid evolutionary optimization algorithm. IEEE Access. 2019; 7: 176218-176232.

17.

Mehrabadi

Sathiakumar

. Multi-Objective Optimization of Combined Heat and Power Industrial Microgrid. Journal of Solar Energy Engineering. 2020; 142: 1-8.

18.

Lopes Silva

De Souza

Freitas Souza

De Franca Filho

. Hybrid metaheuristics and multi-agent systems for solving optimization problems: A review of frameworks and a comparative analysis. Applied Soft Computing. 2018; 71: 433-459.

19.

Mohamed

Walid

. Adaptive multi-objective reinforcement learning with hybrid exploration for traffic signal control based on cooperative multi-agent framework. Journal of Engineering Applications of Artificial Intelligence. 2014; 29: 134-151.

20.

Pan

Jiao

Liu

. A Multi-agent Social Evolutionary Algorithm for SAT problem. Chinese Journal of Computers. 2014; 37: 2011-2020.

21.

Han

. Modern Engineering Cybernetic, China Electric Power Press: Beijing, China, 2017; pp. 201-210.

22.

Chen

Zhong

Wang

. Bat algorithm with the cooperation of orthogonal crossover and exponential crossover. Journal of Nanjing University (Natural Sciences). 2015; 51: 731-740.

23.

Jiang

Cai

Wang

. Hybrid Orthogonal Genetic Algorithm for Global Optimization. Computer Engineering. 2009; 35: 204-209.

24.

Lei

Zhang

. Matlab genetic algorithm toolbox and its application , Xidian University Press: Xi’an, China, 2014, pp. 72-73.

25.

Deb

Pratab

Agarwal

Meyarivan

. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. Evolutionary Computation. 2002; 6: 182197.

26.

Chen

. Predictive control and optimal operation, China Machine Press: Beijing, China, 2020; pp. 237-244.

27.

Zheng

. Multi objective evolutionary algorithm and its application, Science Press: Beijing, China, 2007, pp. 51-60.

28.

Chen

Tai

Gao

Zhu

. Expansing planning of Renewable Energy Power System Considering Flexibility and Economy. Journal of Shanghai Jiao Tong University. 2021; 55: 791-801.

A hybrid crossover multi-agent multi-objective evolutionary algorithm and its application in microgrid operation optimization

Abstract

Keywords

1. Introduction

2. Objective functions of microgrid operation

3.3 Multi-agent self-learning operator

3.6 Steps of HCMAMOEA

Table 2 Operation cost and pollution emission of micro sources

Table 7 Output of each micro source per hour corresponding to the optimal compromise solution under mode 3

Footnotes

Acknowledgments

Conflict of interest

Author contributions

References

Table 2
Operation cost and pollution emission of micro sources

Table 7
Output of each micro source per hour corresponding to the optimal compromise solution under mode 3