Optimal allocation of microgrid using a differential multi-agent multi-objective evolution algorithm

Compared with traditional fossil energy, renewable and clean energy such as wind energy and solar energy are safe, pollution-free, widely distributed and conducive to small-scale decentralised utilisation [1]. With the growth of these clean and renewable energies, distributed generation has created a steadily increasing amount of research interest. To improve security, stability and power quality, it is an effective way to exert the efficiency of distributed generation system in the form of a microgrid [2].

A microgrid is an automatic and stand-alone system, which can realise self-control, safeguard and administration. From the macroscopic view, a microgrid can be seen as a ‘virtual’ power supply source or a load in the network. The optimal configuration of a microgrid is one of the key issues to ensure the economic and reliable operation of the microgrid. It is generally necessary to consider the following aspects: economic indicator, self-power supply capacity indicator and environmental protection indicator in the microgrid allocation optimisation problem. The economic indicator mainly reflects the economy of microgrid operation, such as the construction of distributed generation, operation and maintenance costs, replacement costs and fuel costs [3]. The load power shortage rate indicator refers to the power supply performance of the microgrid, which reflects the ability of the microgrid to meet the load requirements of the microgrid in an independent state. Environmental protection indicator refers to the environmental benefits of microgrid operation. Through environmental protection indicators, the advantages of the environmental protection benefits of the microgrid can be measured. In addition, targets such as power loss minimisation and voltage profile improvement are also considered. Therefore, the optimal configuration of the microgrid is a multi-objective optimisation problem.

In the optimisation of capacity allocation, the economic requirement can be considered separately according to specific needs [4, 5]. In this situation, the allocation problem is a single objective optimisation problem. However, in most cases, multiple objectives should be considered. When optimising multiple objective functions, multiple objectives can be integrated according to certain weights and then solved by the single-objective optimisation method [6]. A multi-objective optimisation algorithm based on Pareto optimal solution can also be used to solve the problem [7]. In this process, the Pareto solution set of the problem to be optimised can be obtained by a single run. Compared with the weight method, the latter can get the solution set more comprehensively and efficiently. In fact, the weight method takes only a small part in solving multi-objective optimisation problems, and the rest employ the Pareto front method.

In the process of solving the multi-objective capacity allocation problem, many algorithms have been designed and applied. Compared with the basic intelligent algorithm, a hybrid intelligent algorithm has many outstanding advantages in solution quality, problem processing scale and convergence speed, and therefore it may be more suitable for solving such problems [8,9,10]. Meanwhile, the utility of agents for solving problems has aroused much concern these years. The concept of agents and their generation, which constructs a multi-agent system (MAS) and allows different search spaces to be explored simultaneously, thereby achieving solutions with more diversity and high quality [11].

In view of the advantages of hybrid intelligent algorithms and the multi-agent approaches, approaches with multi-agent technology are a good choice in the process of hybridisation [9]. In this study, a differential multi-agent multi-objective evolutionary algorithm (DMAMOEA) was designed by combining differential evolution strategy and multi-agent technology, which is used to solve the capacity optimisation problem of the microgrid including wind turbine, photovoltaic equipment and battery storage, considering the two objectives of economy and load outage rate.

Comparing the results with the classical multi-objective evolutionary algorithm – Non-dominated Sorting Genetic Algorithm II (NSGA-II), the quality of the final solution set and solution time of the designed algorithm is better than that of the classical algorithm. Subsequently, some representative solution in the solution set is analysed and the effectiveness of microgrid implementation is also illustrated.

In this work, the optimal allocation model of microgrid capacity includes three kinds of equipment: photo-voltaic power production facility, wind power production facility and storage battery. The output models of the three kinds of equipment are as follows.

In the actual micro-grid operation process, it is necessary to consider not only the economics of the microgrid but also power supply reliability and environmental protection. In this work, the economy and power supply reliability are considered in the multi-objective planning and design of the microgrid, which is a two-objective optimisation problem. The optimised independent variables are the number of photovoltaic power generation equipment N_pv, the number of wind turbines N_wind, and the number of energy storage batteries N_battery.

Multi-agent search strategy has attracted much concern for its promising computational model in optimisation problems in these years. The agent can be seen as a physical or abstract entity, which has the perception, interaction and problem-solving ability [17]. Multiple agents compose the MAS. The MAS has remarkable features, such as autonomy, distribution, coordination, etc. By virtue of self-organisation ability, learning ability and reasoning ability, the multi-agent search strategy for optimisation problems achieved good results.

In this section, a DMAMOEA for a multi-objective microgrid allocation optimal problem is proposed based on the concept of the Pareto method. In this algorithm, several operators for a multi-objective problem are designed, such as neighbourhood Pareto preferred operator, neighbourhood differential evolution operator, mutation operator, etc. By these operators, the agents in MAS interact with each other and produce feasible solutions for the multi-objective microgrid allocation problem. The non-dominated solutions produced in each generation are kept in the archive set. To guarantee the uniformity of the archive set, the solutions with larger crowding distances are further optimised. The simulation results demonstrated the effectiveness of DMAMOEA.

4.1

The structure of MAS for multi-objective optimisation

In the structure of MAS, each agent stands for a feasible solution, which is a real-valued vector. All the agents are fixed on a squared network. The structure of the network is shown in Fig. 1. Each agent can only interact with the agent's neighbourhood.

Fig. 1

The neighbourhood of Agent L_ij can be depicted as follows: (18) Local Env Lij={Li′j,Lij′,Li″,Lij″} {\rm{Local}}\;{\rm{Env}}\;{L_{ij}} = \{ {L_{i'j}},{L_{ij'}},{L_{i''}},{L_{ij''}}\} where i′=|i−1i≠1Ni=1|, i″=|i+1i≠N1i=N|, j′=|j−1j≠1Nj=1|, j″=|j+1j≠N1j=N| i' = \left| {\matrix{ {i - 1} & {i \ne 1} \cr N & {i = 1} \cr} } \right|,\;\;i'' = \left| {\matrix{ {i + 1} & {i \ne N} \cr 1 & {i = N} \cr} } \right|,\;\;j' = \left| {\matrix{ {j - 1} & {j \ne 1} \cr N & {j = 1} \cr} } \right|,\;\;j'' = \left| {\matrix{ {j + 1} & {j \ne N} \cr 1 & {j = N} \cr} } \right| For example, the neighbourhood of L₂₂ can be depicted as:

Local Env L₂₂ = {L₁₂,L₂₁,L₃₂,L₂₃}

4.3

Distributed maintenance strategy

To maintain the distribution of the solution in the archive set, crowding distance is introduced to estimate the crowding degree of the solutions, as shown in Fig. 2. Taking the i-th point in the archive set as an example, the crowding distance is the average side length of a cuboid, which is composed of points near the i-th. The variables of solutions with the larger crowding distance in the set plus Gaussian perturbation and new solutions are produced. This process can be described in the equation below. In this equation, l_i is the variable in the solutions, and e_i’ is the variable in the new solutions. The new solutions are then compared to the solution in the set. The dominated solutions are eliminated and the dominating ones are kept. By this operation, the distribution of the solutions is more uniform. (25) ei={x¯ li+N(0,σ2)>x¯x_li+N(0,σ2)<x_li+N(0,σ2)otherwise {e_i} = \left\{ {\matrix{ {\bar x} & {\;\;{l_i} + N(0,{\sigma ^2}) > \bar x} \cr {\underline x } & {{l_i} + N(0,{\sigma ^2}) < \underline x } \cr {{l_i} + N(0,{\sigma ^2})} & {otherwise} \cr} } \right.

Fig. 2

4.4

Procedure of DMAMOEA

The procedure of DMAMOEA can be summarised as follows:

Step 1: Let t=0 and generate the population randomly, Q (t)= {X₁^t, X₂^t, . . . , X_n^t}, where X_i^t represents the ith individual and n is the number of individuals;

Step 2: Distribute all the individuals on a n×n \sqrt n \times \sqrt n lattice;

Step 3: If the iteration number reaches the set value (t = maxgen), terminate the procedure and output the archive set P_best;

Step 4: Implement the neighbourhood Pareto preferred operator on the agents on the lattice sequentially, and the best solution maxL_ij in the local environment of L_ij is compared with solutions in the archive set. In this process, the solutions dominated by maxL_ij will be eliminated from P_best, and maxL_ij will be added to P_best if it is not dominated by any solution.

Step 5: Implement the neighbourhood differential evolution operator on each agent;

Step 6: Implement the mutation operator on Q(t) with probability P_m, and generate a new population Q(t+1);

Step 7: Calculate the crowding distance of all the solutions in P_best, further optimise the solutions with a larger crowding distance. If the number of solutions in P_best exceeds the size (num_of_solutions > size_of _set), then the solutions will be sorted by the crowding distance, and the solutions with the largest crowding distance are kept in P_best.

If the iteration number is less than the set value, go back to Step 3.

This procedure is shown in Fig. 3.

Fig. 3

Take a certain year in a certain region as an example, its power consumption load, wind speed, sunlight intensity and the price of electricity are shown in Figs 4–7.

Fig. 4

Fig. 5

Fig. 6

Fig. 7

The capacity of the fan is 30 kW, the capacity of the photovoltaic equipment is 1 kW, and the single battery capacity is 50 kW h. The value of initially installing cost, operating and maintaining cost, the replacement cost of each item of equipment is shown in Table 1. The upper and lower limit of battery power is 0.3 and 0.8, and the default initial power is 0.5. The interactive power consumption with the grid is 10% of the maximum power consumption in the period.

Compared with other multi-objective optimisation algorithms, the NSGA-II algorithm has some advantages in solution efficiency and result division [18]. Therefore, the classical NSGA-II algorithm and the algorithm proposed in this article are used to optimise the problem.

In this study, the running CPU is Core i5-6300 CPU, the memory is 8 Gb, and MATLAB software is also used. In terms of parameter setting, the DMAMOEA is set to 16 agents, the archive set scale is 200 and the number of iterations is 100; the population number of NSGA-II is 200, and the number of iterations is 70. The simulation result is shown in Fig. 8.

Fig. 8

As can be seen from Fig. 8, the results of the two algorithms coincide. To evaluate the approximation degree of the results of the two algorithms to the real Pareto optimal solution, generation distance is used to evaluate the results of the two algorithms. The equation of generation distance is described as follows [18]: (26) GD(P,P*)=∑y∈Pminx∈P′dis(x,y)2|P| GD(P,{P^*}) = {{\sqrt {\sum\nolimits_{y \in P} \mathop {\min }\nolimits_{x \in P'} dis{{(x,y)}^2}} } \over {|P|}} Where, P is the solutions obtained by the proposed algorithm and P* is the ideal solution set.

In this study, the ideal solution set is represented by the non-dominated solution set of the two solution sets obtained by the two algorithms. Generation distance is the average value of the sum of the minimum distance of each solution in the solution set and the solution in the ideal solution set. The smaller the value is, the better the result is. Fig. 9 is a column comparison diagram of generation distance obtained by DMAMOEA and NSGA-II running 10 times respectively. In terms of the operation time, DMAMOEA takes an average of 52 s, while NSGA-II takes about 66 s. Therefore, the DMAMOEA is superior to the traditional NSGA-II in terms of operation time and the approximation of the final solution set.

Fig. 9

Table 2 shows some representative results of DMAMOEA algorithm. Taking Solution 1 as an example, using the Environmental Benefit Analysis Method [7], the representative results are obtained and the results are shown in Table 3.

From Tables 1 and 2, the following conclusions can be drawn: (1)

In terms of Solution 1 and Solution 2, there is some difference in the number of micro sources. Between the two solutions, the number of wind turbines and batteries in Solution 1 is more than that in Solution 2, while the photovoltaic equipment is less than that in Solution 2. Therefore, although the investment increases, the dependence of microgrids on the external network is reduced.

In this article, a DMAMOEA was proposed to optimise the two objectives allocation of microgrid system with photovoltaic, wind power and battery. The two optimisation objectives are the economy index which including investment, maintenance and replacement of the micro sources and the rate of load power shortage index which reflects the degree of dependence on the external power grid. At the end of the article, the optimisation results of this proposed algorithm are compared with the classic algorithm NSGA-II, and the following conclusions are reached: (1)

A DMAMOEA is designed by combining differential evolution strategy and multi-agent technology.