The development of renewable energy is fundamental to accelerating the green and low-carbon transition scheme. Consequently, the issue of optimization capacity design of an integrated new power system has received considerable critical attention.

Recently, several types of renewable energy systems have been studied. Reference [1] designed an integrated charging station for photovoltaic (PV) and hydrogen storage. Reference [2] proposed a biogas-dominated energy hub that can supply heat, cooling, and electricity to users simultaneously. An energy storage system containing a flywheel and a lithium battery was proposed in [3], which can better help in the frequency modulation of wind farms. Reference [4] proposed a novel energy system, which consists of two sub-systems: the power generation sub-system includes an alkaline fuel cell, photovoltaic system, electrolysis tank, Stirling engine, and absorption chiller; the energy storage sub-system includes pumped-hydro-compressed air system. In [5], the authors proposed an industrial multi-energy scheduling framework consisting of PV, electric boilers, energy storage devices, energy trading platforms, and thermal energy storage. In [6], excess electricity would be converted to natural gas and generated revenue. Gas turbines also were adopted in a power-to-gas system, which can supply heat and electric power to the system [7]. In [8], a photovoltaic microgrid energy storage system was established to provide electricity to consumers. In [9], a hybrid energy storage system was established to supply energy by using electricity generated from wind turbines. A multi-energy coordination model was developed in [10], and the model includes three components: wind power generation, heat-gas coupling, and power to gas. As the technology of hydrogen production by electrolysis of water has matured and the price of related equipment has become more acceptable, more and more small-scale energy systems are considering the installation of electrolysis cell devices. Reference [11] proposed a comprehensive and tractable yet multi-energy microgrid model, including multiple sub-systems for power generation, natural gas, and hydrogen. Reference [12] proposed a microgrid model in the island mode through hydrogen fuel cells.

To make the above microgrid model more stable and reliable, the optimization of the microgrid is essential. In [13], the authors analyzed the impact of power cost and deficiency of power supply probability on the system and establish an objective function: the renewable factor. Then the objective function was solved by a hybrid Particle Swarm Optimization-Grey Wolf Optimizer (PSO-GWO). In [14], an improved particle swarm algorithm was proposed to optimize the operating cost of a grid-connected microgrid, and the results indicated eighteen percent less expensive compared to the traditional PSO. To improve the reliability of the microgrid, a nondominated sorting genetic algorithm (NSGA-II) was adopted to optimize the grid-connected microgrid model through two objective functions: average peak load (APL) and operating cost [15]. In [16], the authors designed three objective functions: the net present cost, the penalty cost of emission, and greenhouse gas emissions. Then the microgrid hybrid system is made to balance reliability and availability by the strength Pareto evolutionary algorithm (SPEA2). Reference [17] established three objective functions: initial investment cost, transaction cost, and load loss rate. Then the capacity allocation of the comprehensive energy system is optimate based on an improved NSGA-II to meet. Reference [18] established three objective functions: the integrated demand of a comprehensive energy system economic cost, renewable energy utilization, and energy supply reliability. Then an improved multiple objective particle swarm optimization (MOPSO) is adopted to reduce the impact of uncertainty on the multi-energy hub. Reference [19] established three objective functions: average annual cost, energy storage power deviation, and load peak-to-valley difference. Reference [20] presented a hybrid probabilistic optimization algorithm combining a discretization approach with MOPSO and NSGA-II to form a hybrid probabilistic optimization algorithm (HPOA) that can find the optimal location and size of an energy storage system with expected cost, voltage deviation, and expected carbon emissions as the objective function, fully taking into account the uncertainty of the wind farm output power. Reference [21] proposed a multi-level microgrid model consisting of energy demand schedulers, energy storage systems, and photovoltaic systems, as well as optimizes the above model level by level by using convex programming, game-theoretic framework, and genetic algorithms. Reference [22] proposed a new hybrid probabilistic optimization algorithm combining the advantages of probabilistic discretizing methods, multi-objective particle swarm optimization, and NSGA-II. Reference [23] established two objective functions: ESS investment cost and network power loss. Meanwhile, the improved simulated annealing PSO algorithm (ISAPSO) was proposed to solve the optimal capacity allocation problem. The results show that the above method can effectively reduce investment costs with a small power loss. In [24], PSO is used to minimize the combined cost of the electricity market, and it is reasonable and effective in a two-tier simulation model. The stochastic optimization approach is used in [25] to establish a tri-objective residential smart electrical distribution grid, and the model is solved using the epsilon-constraint method. Reference [26] established a smart energy hub system (SEHS) that includes multiple energy forms with electrical, thermal, wind, solar, and natural gas. The optimization of the system was performed using GAMS software to reduce operating costs and energy waste. Expansion of the above SEHS system to include a hydrogen storage component. The new model is optimized using the shuffled frog leaping algorithm (SFLA) to provide optimal decisions for the system thereby increasing flexibility [27]. The smart microgrid model developed in [28] considered demand-side management strategies. Reference [29] accomplished the optimization of techno-economic and socio-environmental indicators of the PV-wind-diesel generator-battery storage system using the HOMER PRO software. Reference [30] proposed a two-layer collaborative optimization method with the objective function of the upper layer objective function and the under layer objective function. The upper layer objective function includes the primary energy-saving rate (PESR), the annual cost-saving rate (ACSR), and the equivalent emission reduction rate (EERR). The upper layer objective function includes the primary energy rate (PER) and the annual ACSR. In [31], a wind-PV hybrid power system was developed then the levelized cost of energy and loss of power supply probability of the model were optimized using the multi-objective evolutionary algorithm for supplying energy. The optimization of the model was accomplished in [32] by using a predatory parasitic algorithm (PPA) to improve the system efficiency and reduce hydrogen consumption. In [33], a railroad power system was developed, and the possible investment cost was used as the objective function to optimize the proposed model using a genetic algorithm (GA).

For the sake of clarity, the proposed model is compared with the other studies reported in the literature in Table 1. Based on the previous studies, several multi-energy complementary modes have been established. However, a model of completely using clean energy to be the power generation units and simultaneously using hydrogen and batteries for energy storage has not been established. Furthermore, less research considers the influence of the community load. The model optimization results tend to be for the rated capacity or real-time power, with fewer relevant results for the optimum number of devices to work. Nevertheless, in the actual construction of energy storage systems, the number of devices is more instructive than the real-time power of the devices.

The contributions of this work can be summarized as follows:

The presented paper establishes a hydrogen system consisting of the electrolysis cell, hydrogen storage tank, and hydrogen fuel cell, and thus constructs a wind/PV/hydrogen storage power system for community energy supply. The power generation unit is completely composed of renewable energy, which avoids dependence on thermal power generation and greatly reduces carbon emissions.

The presented paper is organized as follows. Section 2 presents the mathematical model, objective function, and constraints of the wind/PV/hydrogen power system. Section 3 describes the basic theory of PSO and NSGA-II, and then proposes the hybrid algorithm that is used in the optimization capacity design. Section 4 analyses the optimization results of the proposed algorithm.

The presence of the battery and the hydrogen storage tank reduces the instability of the wind and PV power output, and the excess portion can be converted into hydrogen. If the system wants to increase revenue, the number of devices or the capacity of the devices should be increased. However, it inevitably leads to an increase in the economic cost, so the capacity of the individual units of the system need to be optimized. In order to solve for the optimal allocation of capacity, three objective functions are define, economic cost of the system, the rate of wind and photovoltaic power consumption, and the rate of load shortage. The first objective function f₁ is to minimize the economic cost of the system [44], which includes the investment cost of the system (C_ic), the operation and maintenance cost of the system (C_oc) and the replacement cost of the system (C_re). The function can be expressed as,

(13)minf1=Cic+Coc+Cre

(14)Cic=∑i=1Nkic,iPimaxηi(1+ηi)Lsf,i(1+ηi)Lsf,i−1where P_i^max is equipment capacity of PV, wind turbines, batteries, and electrolytic cells. N is the total amount of equipment. k_ic,i is the investment cost per unit of capacity. η_i is the inflation rate (taken as 5%). L_sf,i is the remaining useful life of the equipment [45].

The operation and maintenance costs can be expressed as [46],

(15)Coc=∑i=1N(koc,iFIXPimax+koc,iVAR∑t=124Pi,t)where P_i,t is the operation power of the i-th device. koc,iFIX and koc,iVAR are fixed and variable maintenance costs.

The replacement cost can be described as [47],

(16)Coc=∑i=1NPimaxβiTtiwhere β_i is the replacement cost. T is the expected operation time of the energy storage system (30 years). t_i is the useful life of the i-th device.

The second objective function f₂ is to maximize the power consumption rate of PV and wind. The system output is consumed by customers and the electrolysis cell, so increasing the hydrogen production of the electrolysis cell after satisfying the customers’ demand can achieve the purpose of improving the consumption rate. The function can be expressed as [48],

(17)maxf2=Pwind +Ppv−Pload −PBat Pwind +Ppv−Pload where P_wind is the power generated by wind turbines. P_pv is the power generated by PV. P_load is the customer power consumption. P_Bat is the battery power.

The third objective function f₃ is to minimize the loss of load probability. The loss of load probability related to the stable of the system. The objective function can be calculated as [49],

(18)minf3=∑i=124{Pload,i−[Ppv,i+Pwind,i+PBat,i+PFC,i]}∑i=124Pload,iwhere P_FC is the output of hydrogen fuel cells.

In order to better solve the proposed multi-objective planning problem and arrive at the optimal and realistic capacity optimization configuration, two constraints are applied, namely the power balance constraint and the equipment unit constraint [50]. The following formula for the power balance constraint can be derived from the principle of conservation of energy:

(19)Pwind +Ppv+PFC=Pload +PBat +Pele+Pabawhere P_ele is the output of the electrolytic tank. P_aba is the abandoned portion.

The unit constraints mainly restrict the output and capacity of devices, which can be described as,

(20)0<PBatin<Ppv+Pwind+Pload

(21)0<Pele<PBatout

(22)0<Pele<Ppv+Pwind+Pload

(23)0<ηtnH2<Qmax

(24)0<PFC<QmaxHHHVηFCwhere PBatin is the charging power of the battery. PBatout is the discharge power of the battery. Q_max is the maximum capacity of hydrogen storage tank. n_H2 is the hydrogen production of the electrolysis cells. η_t is the hydrogen storage efficiency [51]. The power constraint of the electrolytic cell is followed by Eq. (21) when the wind and photovoltaic power generation is small. On the contrary, the power constraint of the electrolytic cell is followed by Eq. (22).

NSGA-II introduces elite strategies, crowding comparison operators, and fast non-dominated sorting compared to the first generation of genetic algorithms. For non-dominated sorting, the calculation of the congestion distance is briefly described below: (1)

Non-dominant sorting

For each solution x in the population, two values need to be calculated: one is the domination number n_x, which means the number of solutions that dominate x; and the other is S_x, which means the set of solutions dominated by x. Since the dominance of a solution on the first non-dominated level is equal to 0, for each solution of n_x = 0, each member of the solution q is visited and its dominance is subtracted by 1. If the dominance of x is 0, it will be placed in a list Q, which therefore contains solutions belonging to the second non-dominated level. The process is then repeated for the solutions in this set until a third non-dominated hierarchy is found. The above process continues until all non-dominated layers have been found [52]. (2)

Calculation of congestion

First, the populations are sorted according to the order of each objective function value from smallest to largest. Next, for each objective function, the boundary solutions are assigned an infinite distance value and each intermediate solution is assigned a distance value that is equal to the absolute value of the difference between the two neighboring solutions. The process is repeated for the different objective functions, and the distance value of the congestion is the sum of the distances on each objective.

In the multi-objective optimization problems, the objective functions are contradictory to each other and cannot be optimal at the same time, so the final result is a Pareto-optimal set of solutions. In practical engineering, it is often necessary to select a solution from the Pareto-optimal set of solutions based on three indicators (the cost, the wind and PV power consumption rate, and the loss of load probability) as the model optimization result [53].

In order to give full play to the advantages of NSGA-Ⅱ, PSO is introduced to optimize the two hyperparameter (the crossover ratio and the probability of variation) of NSGA-Ⅱ. PSO is inspired by and modeled on the predatory behavior of birds. The search space of the optimization problem is analogous to the flight space of a bird, with each bird abstracted as a particle, and the optimal solution to the optimization problem is equivalent to the food source sought by the bird. PSO formulates simple behavioral rules for each particle that are similar to the movement of a bird, so that the movement of the whole swarm exhibits similar properties to those of a bird feeding, allowing complex optimization problems to be solved.

At each iteration, each particle will record the individual optimal position and the particle swarm will record the global optimal position. When these two optima are found, the velocity and position of the particles are updated using the following expressions [54]:(25)vij(t+1)=vij(t)+c1r1(t)[pij(t)−xij(t)]+c2r2(t)[pgj(t)−xij(t)]

(26)xij(t+1)=xij(t)+vij(t+1)where c₁ and c₂ are the learning factor. r₁ and r₂ are the random numbers between zero and one. v_ij is the velocity of particles. p_ij is the individual particle values. p_gj is the global optimal value. x_ij is the position of the particles.

The detailed process for finding the number of devices in the microgrid model using NSGA-II after hyperparameter optimization can be seen in Fig. 2, which can be summarized as:

Step 1: The number of devices is first optimized using a traditional NSGA-II.

Step 2: An evaluation scheme is established to assess the optimization results.

Step 3: Sensitivity analysis of the relevant hyperparameters is performed in NSGA-II.

Step 4: The relevant hyperparameters are optimized based on PSO.

Step 5: The Pareto optimal solution set obtained from the optimization is brought into the evaluation function to calculate the satisfaction of the various solutions, and finally the best solution is selected as the solution for the model to optimize the number of devices according to the satisfaction size.

In the presented paper, the construction of an evaluation function is used to calculate the satisfaction of each solution in the solution set. The comparison of satisfaction allows the superiority of solutions to be compared with each other, and serves as a criterion for optimizing the hyperparameters of the genetic algorithm by PSO. The expression for the evaluation function can be expressed as [55],

(27)F(x)=(1−ω(f1))+f2+(1−f3)3where ω(f₁) denotes the normalization of the value of the objective function one.