Study on Economic Dispatch of the Combined Cooling Heating and Power Microgrid Based on Improved Sparrow Search Algorithm

Abstract

The reasonable and efficient use of the abundant biomass resources in rural areas has not been realized. Therefore, the concept of a combined cooling, heating, and power (CCHP) microgrid system, considering biomass pyrolysis and gasification, has been developed by researchers. A biomass gasification device can fully use biomass resources and can play a role in absorbing wind energy. Meanwhile, in order to minimize the operating cost of each micropower supply unit, as well as the environmental pollution costs, researchers have also established an optimal scheduling model for CCHP microgrids, which uses the sparrow search algorithm. In this paper, we have improved upon the traditional sparrow algorithm to solve the problems of its uneven population distribution, poor global search ability, and the risk of falling into local optima, through the development of the random walk sparrow search algorithm (RSSA). First, a sinusoidal chaotic map is used to generate the early-generation sparrow population with a uniform distribution in space. Second, in this study we add a sharing factor to the discoverer’s optimization process to enhance information sharing and the global research capability among individuals in this field. Finally, a random walk strategy is used to form new participants to improve the algorithm’s skill in locally searching for optimal locations. Taking the CCHP microgrid with grid-connected action as a case study, we concluded that compared with the optimization outcomes of the SSA, the total costs incurred by RSSA in summer and winter were reduced by 2.2% and 3.1%, respectively. Compared with the optimization findings for the chaotic SSA algorithm, the total costs incurred using the RSSA algorithm under typical summer and winter days were reduced by 0.14% and 0.13%, respectively. The productiveness of the RSSA algorithm for solving the CCHP microgrid economic dispatch issues has thus been verified.

1. Introduction

With increasingly serious problems such as the energy crisis, air pollution, and the greenhouse effect, the comprehensive utilization of clean energy and other forms of energy has drawn extensive attention from scholars in China and abroad [1]. Among these forms of energy, biomass energy is the only renewable resource that can directly produce clean energy such as gas and liquid on a large scale. It has the characteristics of a wide resource distribution, little environmental pollution, and a sufficient raw material supply [2,3]. According to statistics, crop straw amounts to 650 million tons per year, equivalent to 4.6 billion tons of standard coal, indicating that biomass energy resources contain colossal energy [4]. The development and utilization of biomass energy can help lessen greenhouse gas emissions and environmental pollution and achieve low-carbon growth [5]. A cooling, heating, and power cogeneration system can be implemented to realize the cascade utilization of power and recover the waste heat generated from refrigeration and heating, while generating electricity. Therefore, the cogeneration system is a necessary part of the distributed energy system [6]. Cooling, heating, and power cogeneration involving biomass gasification is also an efficient, clean, and energy-saving utilization method of renewable energy. On the basis of these considerations, the CCHP micro-grid system based on biomass gasification syngas came into being.

At present, research on the CCHP microgrid has mainly aimed to identify the optimal combination of apparatuses and the optimal export level of each kit, as well as the capacity of the power storage apparatus, the improvement of the optimization algorithm, and the operation of the microgrid in association with economic and environmental protection. Luo Ping established a cogeneration microgrid with various renewable energies, gas turbines, and other equipment. Taking the lowest system operating expense and the pollutant control cost as the optimal scheduling goals, the improved multi-objective particle swarm optimization (MPSO) algorithm was applied to improve the microgrid [7]. Considering the rate of utilization of renewable energy, economic benefits, and energy conservation and emissions reductions, Yang G established a variety of cold, heat, and power cogeneration systems with multiple coordinated energy supplies and utilized the improved particle swarm optimization algorithm (PSO) to improve the solution [8]. Wu Xuanru built a day-ahead scheduling pattern for the CCHP integrated energy system. Still, this model of the CCHP system did not consider electricity sales to the large grid, which was not conducive to the consumption of excessive renewable energy and the economy of microgrid operation [9]. Xiong Yan established a coordinated optimization model of CCHP for renewable energy and energy storage in complementary power generation, using different scheduling strategies to account for additional rates and seasonal differences in electricity and natural gas. However, that paper only considered economic benefits, not considering environmental effects [10]. Li G developed a blended CCHP system with solar and geothermal power, which accounted for carbon dioxide emissions in the objective function and analyzed the impact of FEL and FTL action tactics on the economy and ecological protection of the CCHP system [11]. Yang Zhipeng proposed a CCHP microgrid operation model with energy storage and heat pumps. The example analysis showed that heat pumps can efficiently improve energy efficiency and energy storage devices can reduce the peak–valley differences of loads in a microgrid and substantially reduce the operating costs of the microgrid. However, the author did not consider the capacity allocation of heat pumps and energy storage equipment [12]. In a study of the optimal economic scheduling of a CCHP microgrid, the response of the user demand side was considered, and microgrid loads were classified into non-controllable, shiftable, and controllable comfort-based loads and controllable energy-based loads for optimal scheduling, which enabled to authors to effectively improve the economy of microgrid operation [13,14]. A study of traditional CCHP microgrids found that, although some progress has been made in the economic dispatch of thermoelectricity and wind power consumption, the following defects remain in the economic dispatch. Through proper dispatching, excess wind power has been absorbed, but the benefits brought about by wind power consumption have not been quantified. In the scheduling cycle, some studies have only considered the economic benefits of the system, ignoring the environmental effects. A series of PSO algorithms are often adapted to resolve optimization problems, but when working out higher-dimensional issues, it is easy to become confined to local optimizations. Most of the existing CCHP systems use natural gas as fuel. Still, natural gas is a form of non-renewable energy, for which it is difficult to highlight the energy conservation characteristics and the emissions reductions in distributed systems. Biomass is a form of renewable energy, so some scholars have begun to consider biomass gas produced by biomass pyrolysis and gasification as a primary energy source for CCHP systems, which is also in line with the general trend of the coordinated development of the energy environment. Wei Dajun designed a small-scale biomass biogas internal combustion electric generator that combined cooling, heating, and electrical systems. With the gas cogeneration system as a reference, the biogas system has demonstrated significant benefits in terms of energy savings [15]. Paria M established a CCHP system with biogas as the primary energy source. The system’s full cost rate and biogas production were the target functions. Through their analysis, they concluded that the system efficiently realized the cascade usage of energy [16]. Bai Zhang proposed a novel power generation system on the basis of solar-driven biomass gasification. The system converted solar energy into stable chemical energy through thermodynamic performance analysis and improved the purity of biomass gasification syngas [17]. Zhang Dong established a mathematical model of a thermoelectric system based on biogas, taking five typical new rural buildings as an example. The system’s annual load supply/demand energy balance was calculated and analyzed day by day. The results showed that the integrated system improved the primary energy utilization rate and the energy savings rate [18]. Wang J J proposed a CCHP system considering biomass-air gasification and analyzed its energy and exergy performance under different environmental conditions and system parameters [19]. Mao T integrated biomass gasification CCHP systems with heat exchangers. The cost distribution and influencing factors of biomass gasification cogeneration system products were evaluated by means of the exergy economic method. The variation law of the unit electricity cost with the biomass cost and operation time was obtained [20]. Guo Wei conducted in-depth research on rural small-scale CHP systems and used the GW-PSO algorithm to optimize the system, involving the combustion of biomass pyrolysis gas for power generation and heating, but the cogeneration system did not consider the cooling mode [21]. In the above studies, if the biomass gasification unit is used to absorb wind energy in the scheduling, the economic and environmental conservation of the system may be improved.

In the optimization process, the swarm intelligence optimization algorithm can continuously use its group behavior to conduct a comprehensive search with strong parallelism and stability. In addition, the algorithm uses local and global search strategies to solve the optimization problem, which has good searchability. Therefore, many scholars have applied it to the CCHP microgrid optimal scheduling problem and achieved good results. B. Tan combines the idea of co-evolution theory and the beetle antenna search algorithm into the non-dominated sorting genetic algorithm (NSGA) to form a hybrid evolutionary optimization algorithm to resolve the CCHP microgrid optimization issue and diminish the raw material consumption and operation expenses of the microgrid [22]. In order to diminish the microgrid’s operating costs and CO₂ emissions, X. Yang created a CCHP microgrid model considering multi-objective optimization, using the maximum fuzzy satisfaction method to simplify the multi-objective issue into a single-objective point, and then the water cycle algorithm (WCA) to optimize the single-objective problem [23]. Y. Wang adopted a mixed rolling-horizon and PSO to allocate system scheduling factors, which promoted the CCHP system’s optimal operation and dramatically reduced the scheduling time and cost [24]. To reduce the energy cost for residential areas, H. U. R. Habib uses an artificial bee colony algorithm (ABC) to solve the optimal scheduling problem in a cogeneration system [25]. In addition, recent scientific research on energy management has shown that, compared with the traditional solution method, the Harris Hawk algorithm (HHO) [26] and the water cycle algorithm (WCA) [27] have superior performance and high accuracy in solving this problem. The sparrow search algorithm (SSA) [28] is a novel swarm intellect algorithm, suggested in 2020. Contrasted with conventional intelligent optimization algorithms such as PSO [29], the whale optimization algorithm (WOA) [30], the gray wolf optimization algorithm (GWO) [31], and ABC [32], the sparrow search algorithm is superior due to its uncomplicated construction, fewer optimization parameters, robust local search skills, rapid convergence speed, and ease of implementation. It is widely used in solving the optimization of engineering problems. Li Yali’s experimental findings indicate that the sparrow search algorithm has higher convergence precision and stability than other swarm intelligence algorithms [33]. Through various function tests, Song Liqin observed that the sparrow search algorithm (SSA) performed better than traditional algorithms such as the PSO algorithm and the WOA algorithm in optimization accuracy and speed [34]. However, it still has defects, including diminished population variety, the ease of falling into the regional optimal, and unstable search results when the traditional SSA algorithm is used to solve complex engineering optimization problems. Therefore, scholars have successively proposed a series of improvement measures to overcome the above shortcomings and improve the algorithm’s performance. J. Dong proposed a niche multi-objective SSA algorithm, introduced Lévy flight interference tactics to upgrade the capability of the SSA algorithm to skip away from the regional optimal, and used the algorithm to optimize the distributed power capacity configuration [35]. W. Song utilized a chaotic tent map to initialize people and adjusted the population using a nonlinear decreasing weight, a mutation strategy, and a chaotic search method to improve the population quality and expand the search range, thus enhancing the aptitude of the algorithm to skip away from the regional optimal [36]. G. Liu introduced an improved SSA into the UAV path-planning problem and used the global and local probe and development capabilities of the algorithm to enhance the speed and precision of path planning [37]. C. Ouyang proposed an LLSSA algorithm and used this algorithm to optimize the path planning of three-dimensional UAVs and successfully obtain a safe and low-cost path [38]. J. Yuan constructed an improved SSA algorithm predicated on the barycenter reverse-learning mechanism, learning coefficient, and mutation operator and used it to optimize the distributed maximum power point tracking (DMPPT) problem [39]. C. Zhang used the chaotic sparrow algorithm to optimize the SCN, selected using random parameters, to ensure the CSSA-SCN model’s reversion precision. Meanwhile, compared with other algorithms to optimize the SCN, CSSA-SCN demonstrated better performance [40]. Y. Zhu proposed an adaptive sparrow search algorithm, which was used to improve the recognition variables of a polymer electrolyte fuel cell (PEMFC) stack, effectively diminishing the voltage inaccuracy level of the battery and enhancing the power transformation productiveness [41]. Some scholars have applied improved SSA to problems such as fault diagnosis [42], brain tumor detection [43], and the parameter optimization of machine learning algorithms [44] and have achieved good results. No research has been carried out using the sparrow algorithm to solve the CCHP microgrid optimal scheduling problem.

To solve the above problems, in this study we first combined biomass energy with the traditional CCHP system and designed an economic dispatch model of the CCHP microgrid predicated on improved biomass gasification. Secondly, considering the constraints of the cooling, heating, and power load and the output of each piece of equipment, the microgrid’s running costs and environmental governance costs were taken as the optimization goal function, and an improved sparrow search algorithm (RSSA) was used to solve the problem. Finally, in summer and winter, in two typical daily operation environments, the optimization results of the RSSA algorithm, the chaotic sparrow algorithm (CSSA), the traditional sparrow algorithm, and the particle swarm algorithm were compared to demonstrate the validity and practicability of the RSSA algorithm. By analyzing the simulation findings, we observed that the model can efficaciously boost the application rate of sustainable energy and the economic benefits of the CCHP microgrid. The results showed that this model of an improved biological gasification CCHP microgrid could ensure the economy of the system, while consuming excess wind energy and reducing pollution gas emissions.

In this study, based on reading a large number of related writings on CCHP microgrids, and considering the influence of an improved biomass gasification device on a microgrid, an optimal scheduling model for CCHP microgrid was established with the minimum operating cost and environmental pollution cost of each micro-power supply as the optimization objectives, and the improved sparrow algorithm was used to solve the problem. The main research contents of this paper are as follows: in Section 2 we introduce the framework of the new CCHP microgrid model. In Section 3 we construct the economic optimal scheduling model of the CCHP microgrid. In Section 4, an improved sparrow algorithm is proposed, and function tests and comparative experiments prove the validity of the improved algorithm. In addition, in Section 5, the RSSA algorithm is applied to the optimal solution of the microgrid economic dispatch model. In Section 6, the shortcomings and future research prospects are summarized.

2. Mathematical Model of CCHP Microgrid

2.1. Model Overview

In this paper, the cold and hot electric microgrid model shown in Figure 1 is established, mainly including cold, hot, and electric loads. Gas turbines, fans, photovoltaic cells, power storage equipment, and large power grids bear the electrical load; gas boilers, waste heat boilers, and electric heating take the heat load; and the absorption refrigerator and electric refrigerator carry the cooling burden. In this paper, we add an electric heating device to the traditional biomass gasification process. The biomass gasification device designed in this paper is composed of a gasification furnace and an electric heating device. The electric heating device has two substantive functions. On the one hand, it provides an external heat source for the biomass gasifier to replace the oxidation combustion reaction in the conventional biomass gasification process, reduce the combustion consumption of biomass, and reduce the release of plentiful CO₂ in the combustion process of the biomass to improve the chemical energy and purity of the gasification gas. On the other hand, the electric heating device absorbs excess wind power and converts the extra wind power into chemical energy for storage. The gas storage tank is used to store biomass gasification gas.

2.2. Biomass Gasification Unit Model

The biomass gasification device converts electrical energy into chemical energy and stores it through gasified synthesis gas. The combination of an electric heating device and a gasification reactor is collectively referred to as a biomass gasification device for this analysis. The electric heater consumes electricity to provide the required temperature conditions for biomass gasification to produce combustible gas. Equation (1) represents the gas flow rate generated by the gasification equipment.

$$F_{gas,t}={\phi }_{gas}{P}_{gas,t}/LHV$$

(1)

where LHV = 17.4 × 10⁶ J/m³.

For the mathematical models of the leading equipment (gas turbine, gas boiler, waste heat boiler, absorption chillers, etc.) involved in the CCHP microgrid studied in this article, refer to the models established in [22,45]. We do not describe these models here.

3. Optimal Scheduling Model of CCHP Microgrid

This section introduces the optimization objectives and constraints of the CCHP microgrid.

3.1. Objective Function

To minimize economic costs under the condition of satisfying the user’s cooling, heating, and power load demands and the constraints of the micro-source characteristics, the optimization variables of the optimal scheduling problem of the combined cooling, heating, and power supply microgrid studied in this section are the output of the gas turbine, the gas boiler, hot boiler, wind power, photovoltaic, absorption chiller, electric refrigeration and electric heating at each timepoint in 24 h. The objective function of the optimal scheduling model of the CCHP microgrid established in this section consists of two parts: the operation cost and the environmental cost of the microgrid. Under the operational constraints of each micro-source and micro-grid, the system’s objective function is minimized by reasonably arranging the micro-source output.

3.1.1. Operation Costs of the Microgrid

The operating costs of all equipment in the CCHP system can be expressed as follows.

$$\min C_E=\left(f_{wp}+f_{ex}+f_{om}+f_{cg}-f_{pc}\right)$$

(2)

where $f_{wp}$ is the cost of wind power, photovoltaic, and gas storage tanks; $f_{ex}$ is the electricity purchase and sale cost; $f_{om}$ is maintenance cost; $f_{cg}$ is biomass gasification cost; and $f_{pc}$ is the penalty cost of wind curtailment and power curtailment reduced by biomass gasification technology.

1. Wind power, photovoltaic, and gas storage tank costs

The cost of wind power, photovoltaic, and gas storage tanks in the CCHP microgrid are represented as follows.

$$f_{wp}={\displaystyle \sum _{t=1}^T\sum _{k=1}^N}\alpha P_{WT,k,t}\Delta t+{\displaystyle \sum _{t=1}^T\sum _{k=1}^N}\beta P_{PV,k,t}\Delta t+{\displaystyle \sum _{t=1}^T\sum _{k=1}^N}({\gamma }_{in}{Q}_{g,t}^{in}+{\gamma }_{out}{Q}_{g,t}^{out})\Delta t$$

(3)

2. Electricity purchase and sale costs of the microgrid

The cost of the microgrid in purchasing and selling electricity from the large grid is expressed as follows.

$$f_{ex}=\frac{1}{2}\left(C_{buy,t}+C_{sell,t}\right)P_{ex,t}+\frac{1}{2}\left(C_{buy,t}-C_{sell,t}\right)\left|P_{ex,t}\right|$$

(4)

3. Equipment maintenance costs

The equipment maintenance cost of each micro-source is

$$f_{om}={\displaystyle \sum _{t=1}^T\sum _{k=1}^N}{C}_{om,k}\left(P_k\left(t\right)\right)\Delta t$$

(5)

$$\begin{array}{ll}{C}_{om,k}\left(P_k\left(t\right)\right)=& P_{MT,k,t}{C}_{MT\_om}+P_{WT,k,t}{C}_{WT\_om}+P_{PV,k,t}{C}_{PV\_om}+Q_{GB,k,t}{C}_{GB\_om}\\ & +Q_{AC,out}{C}_{AC\_om}+Q_{WH,k,t}{C}_{WH\_om}+Q_{ec}{C}_{ec\_om}+Q_{eh}{C}_{eh\_om}\end{array}$$

(6)

4. Biomass gasification cost

The cost of biomass gasification in the CCHP microgrid is expressed as follows.

$$f_{cg}={\displaystyle \sum }_{k=1}^N{C}_{gas}{F}_{gas,k,t}$$

(7)

5. The penalty cost of wind curtailment and power curtailment

This factor refers to the penalty cost of wind curtailment and power curtailment reduced by biomass gasification technology.

$$f_{pc}={\displaystyle \sum }_{t=1}^T\lambda P_{gas,k,t}\mathsf{\Delta }t$$

(8)

3.1.2. Environmental Cost

This refers to the environmental cost of polluting gases produced by gas turbines, large power grids, and gas boilers.

$$\min C_F={\displaystyle \sum _{t=1}^T}\left[{\displaystyle \sum _{n=1}^3}\left(W_{MT,n}{P}_{MT}+W_{g,n}{P}_g+W_{GB,n}{P}_{GB}\right)·C_n\right]$$

(9)

3.1.3. The CCHP Microgrid Operation Total Cost

Considering our objectives of minimizing the operating and environmental costs of the CCHP microgrid, in this study we used the weight coefficient method to weigh the operational and environmental costs. A multi-objective functional optimization purpose function, considering economic and environmental protection, was established as follows.

$$C_Z={\omega }_1{C}_E+{\omega }_2{C}_F$$

(10)

where Equation (10) means the total cost of CCHP microgrid operation. ${\omega }_1$ and ${\omega }_2$ are the weight coefficients of each target, and the size of the weight coefficient reflects the focus and preference of the target.

3.2. Constraint Conditions

3.2.1. Power Balance Conditions

The power balance conditions of the CCHP microgrid mainly include three aspects: electrical balance, thermal balance, and cold balance.

$$P_{MT}\left(t\right)+P_{WT}\left(t\right)+P_{PV}\left(t\right)+P_{buy}\left(t\right)=P_{load}\left(t\right)+P_{gas}\left(t\right)+P_{sell}\left(t\right)$$

(11)

$$Q_{MT}\left(t\right)+Q_{GB}\left(t\right)+Q_{eh}\left(t\right)=Q_{h,load}\left(t\right)$$

(12)

$$Q_{AC}\left(t\right)+Q_{ec}\left(t\right)=Q_{c,load}\left(t\right)$$

(13)

where Equation (11) indicates the electrical equilibrium condition. Equation (12) represents the heat equilibrium condition. Equation (13) expresses the cold equilibrium conditions.

3.2.2. Constraints Related to the Large Power Grid

To make the energy interaction between the microgrid and large power grid more stable, the microgrid sets the power limit of interaction with the power grid.

$$0\le P_{buy}\left(t\right)\le {\overline{P}}_{buy}{F}_{in}\left(t\right)$$

(14)

$$0\le P_{sell}\left(t\right)\le {\overline{P}}_{sell}{F}_{out}\left(t\right)$$

(15)

$$F_{in}\left(t\right)+F_{out}\left(t\right)\le 1$$

(16)

where $F_{in}$ and $F_{out}$ represent the purchasing and selling of electricity, respectively. Equation (16) indicates that electricity purchases and sales cannot be carried out simultaneously.

3.2.3. Output Constraints of Energy Conversion Equipment

The constraints of energy conversion devices mainly refer to their output constraints in each period.

$$0\le P_{gas,t}\le P_{gasn}$$

(17)

$$P_{WT,min}\le P_{WT,k,t}\le P_{WT,max}$$

(18)

$$P_{PV,min}\le P_{PV,k,t}\le P_{PV,max}$$

(19)

$$P_{MT,min}\le P_{MT}\le P_{MT,max}$$

(20)

$$Q_{GB,min}\le Q_{GB,t}\le Q_{GB,max}$$

(21)

$$Q_{WH,min}\le P_{MT,k,t}{\gamma }_{MT}{\eta }_{h{r}_{wh}}\le Q_{WH,max}$$

(22)

$$Q_{AC,min}\le Q_{AC,t}\le Q_{AC,max}$$

(23)

$$Q_{ec,min}\le Q_{ec}\le Q_{ec,max}$$

(24)

$$Q_{eh,min}\le Q_{eh}\le Q_{eh,max}$$

(25)

where Equation (17) expresses the limitations on the input power of the gasification equipment. Equations (18)–(25) specify the maximum output power of each micro-source.

3.2.4. Energy Storage Equipment Constraints

To ensure that the energy storage equipment plays a better role in the operation of the microgrid, the sets the power constraint of energy storage equipment.

$$S_g^{min}\le S_{g,t}\le S_g^{max}$$

(26)

$$0\le Q_{g,t}^{in}\le Q_{g,max}^{in}{C}_c\left(t\right)$$

(27)

$$0\le Q_{g,t}^{out}\le Q_{g,max}^{out}{C}_d\left(t\right)$$

(28)

$$C_c\left(t\right)+C_d\left(t\right)\le 1$$

(29)

where $C_c\left(t\right)$ and $C_d\left(t\right)$ are charge-discharge gas signs. Equation (29) indicates that gas storage and discharge cannot be carried out simultaneously.

Gas storage equipment, as a buffer device for combustible gas, does not produce flammable gas, so the ultimate scheduling cycle should meet the same amount of energy storage constraints:

$$S_{g,1}=S_{g,0}$$

(30)

Equations (31) and (32) represent the storage device constraint:

$$P_{es,min}\le P_{es,t}\le P_{es,max}$$

(31)

$$S_{es}^{min}\le S_{es}\le S_{es}^{max}$$

(32)

In order to book a specific adjustment margin in the next scheduling cycle so that the energy storage equipment can meet the microgrid’s needs at the beginning of the following scheduling cycle, one restores the electric batteries after a process of operation to the original charge, with the following constraints:

$$S_{e,1}=S_{e,0}$$

(33)

4. Improved Sparrow Search Algorithm

The SSA algorithm is mainly a swarm intelligence optimization algorithm founded on the performance of sparrows foraging for food and escaping from predators. Xue Jiankai proposed the algorithm in 2020. The advantages of this algorithm are a robust optimization ability, a fast convergence speed, and superior precision in its solutions. Therefore, we use the sparrow algorithm to settle the CCHP microgrid optimal operation issues.

4.1. Original Sparrow Search Algorithm

The algorithm simulates a sparrow hunt and overlays the recognition and beginning warning mechanisms based on the discoverer-follower model. In SSA, we select individuals with better fitness as discoverers, others as participants, and a certain proportion of guarders are equipped to provide the follow-up of dangerous locations. Equations (34) and (35) represent the position updating equation of the explorer and the participant, respectively.

$$X_{i,j}^{t+1}=\left\{\begin{array}{cc}{X}_{i,j}·\exp \left(-\frac{i}{\alpha ·ite{r}_{max}}\right),& R_2<ST\\ X_{i,j}+Q·L,& else\end{array}\right.$$

(34)

where $\alpha \in \left(0,1\right]$ is a random number, and $R_2\left(R_2\in \left[0,1\right]\right)$ and $ST\left(ST\in \left[0.5,1\right]\right)$ are a warning value and a security value, respectively. Q is a casual number, subject to a normal distribution. L denotes a matrix of $1\times d$, where each element in the matrix is one.

$$X_{i,j}^{t+1}=\left\{\begin{array}{cc}Q·\exp \left(\frac{X_{worst}-X_{i,j}^t}{i^2}\right),& i>\frac{n}{2}\\ X_P^{t+1}+\left|X_{i,j}-X_P^{t+1}\right|·A^{+}·L,& else\end{array}\right.$$

(35)

where $A$ indicates a matrix of $1\times d$, and each element is randomly assigned as 1 or −1, and $A^{+}={\left(A{A}^T\right)}^{-1}$.

Guarders are stochastically generated in the crowd, generally accounting for 10% to 20% of the total number. Equation (36) is the position updating formula of the guarders.

$$X_{i,j}^{t+1}=\left\{\begin{array}{cc}{X}_{best}^t+\beta ·\left|X_{i,j}^t-X_{best}^t\right|,& f_i>f_g\\ X_{i,j}^t+K·\left(\frac{\left|X_{i,j}^t-X_{worst}^t\right|}{\left(f_i-f_{\omega }\right)+\epsilon }\right),& else\end{array}\right.$$

(36)

where $\beta$ is a stochastic number conforming to the standard normal distribution, $K$ is a uniform random number of [−1,1], and $\epsilon$ is a small number to prevent the denominator from being zero. $f_g$ and $f_{\omega }$ are the current global superior and inferior fitness values, separately.

The traditional sparrow algorithm has excellent exploration performance when the optimal solution is close to the origin. However, when the optimal solution is distant from the origin, its searching performance degrades rapidly. Meanwhile, the traditional sparrow search algorithm converges to the current optimal solution by jumping directly to the vicinity of the optimal solution, resulting in the fact that it is easy for the sparrow algorithm to fall into the regional optimal, and its global search capacity is poor. On this basis, we improved SSA and formed the random walk sparrow algorithm (RSSA).

4.2. Improved Sparrow Search Algorithm

Population initialization has a significant influence on the operation speed of the algorithm. The quality of initialization determines the rate of the algorithm. Therefore, in this study we utilize sinusoidal chaos to initialize the population. Secondly, to settle the problem of the algorithm readily dropping into optimal regional solutions in the search process for the sparrow population, in this paper we add a sharing factor into the iterative process of the discoverer’s location so that the discoverer can exchange information with the neighborhood individual to better search for the optimal site. Finally, the random walk strategy is used to form new individuals, improving the algorithm’s local search aptitude in the optimal position.

4.2.1. Sinusoidal Chaos Initialization Population

Chaotic motion is ergodic, random, and regular. According to its laws, chaotic motion can travel through all states without repetition within a specific range. Therefore, in this paper we use chaotic variables to optimize the search, which is undoubtedly superior to the random search approach, so chaos is often used to optimize the search problem. The authors in [46] showed that, compared with the optimization algorithms improved by chaotic mapping such as the logistic and circle approaches, the improved algorithm based on sinusoidal chaos exhibited a better optimization performance. Therefore, in this study we used sinusoidal chaos to initialize the SSA algorithm’s population.

Peitfen H proposed sinusoidal mapping in 1992, and Equation (37) is its expression.

$$x_{k+1}=a{x}_k^{2}sin \pi x_k$$

(37)

where $a=2.3$ and $x\in \left[0,1\right].$

At the initial point $x_0=0.7$, Figure 2 shows the distribution of 200 iterations using sinusoidal mapping. It can be seen that, similarly to stochastic initialization, the number produced by sinusoidal mapping is distributed between (0, 1), but its spatial distribution is more uniform. Using chaos instead of randomness to generate the initial population can make the people more evenly distributed in the search space, significantly improving the algorithm’s operation speed.

4.2.2. Shared Factor

The discoverers in SSA are accountable for finding abundant food sources throughout the population and supplying foraging regions and orientations for all participants; hence, the process of finding food sources is essential. Therefore, according to the improved method of the artificial bee colony developed by Wang Hui [47], we add a shared factor to the search process so that the discoverer can exchange information on the neighborhood individuals, improve the global search ability, and better search for areas with rich food.

The improved discoverer location update formula in SSA is expressed as in Equation (38).

$$X_{i,j}^{t+1}=\left\{\begin{array}{cc}{X}_{i,j}+\alpha ·\gamma ·\left(X_{i,j}-X_{k,j}\right),& R_2<ST\\ X_{i,j}+Q·L,& else\end{array}\right.$$

(38)

where $k\in \left\{\left.1,2,\cdots ,n\right\},\right.j\in \left\{\left.1,2,\cdots ,d\right\}\right., \mathrm{and} k\ne j$. $\alpha$ is the information-sharing factor and $\gamma$ is a random number between (−1, 1).

To realize the dynamic adjustment of information sharing between discoverers and domain individuals and to boost the sparrow algorithm’s constriction velocity and global searchability, the sharing factor should increase with the increase in the number of iterations. Meanwhile, we should reduce information sharing at the initial search stage to avoid sparrows flying over optimal solutions, and enhance information sharing in the late search to strengthen the global optimization performance of the discoverer.

Therefore, the information-sharing factor changes nonlinearly with the number of iterations and is expressed as shown in Equation (39).

$$\alpha =\left(1-\delta \right){\alpha }_{final}$$

(39)

$$\delta =1-{\left({\alpha }_{init}/{\alpha }_{final}\right)}^{\frac{1}{t}}$$

(40)

where $t$ is the current iteration number and ${\alpha }_{final}$ and ${\alpha }_{init}$ are constants.

4.2.3. Random Walk Strategy

In solving the optimization problem, the participant will converge to the current optimal solution position under the guidance of the discoverer. However, instead of moving toward the optimal solution, as in the PSO algorithm, the individuals in the SSA algorithm converge to the current optimal solution by jumping directly to the vicinity of the optimal solution. As a result, the SSA algorithm is accessible to the regional optimum, and its global exploration ability is poor. To solve the above problems, in this paper we add the random walk tactic to the position updating mode of the participant; that is, the participant randomly walks around the current optimal solution to improve its searchability. At the start of the iteration, the bounds of this random walk are huge, which is conducive to enhancing global searchability. After many iterations, the bounds of the walk become smaller, which improves the algorithm’s local search capacity for the optimal position.

Equation (41) is the mathematical expression of the random walking process.

$$X\left(t\right)=\left[0,cussum\left(2r\left(t_1\right)-1\right),\cdots ,cussum\left(2r\left(t_n\right)-1\right)\right]$$

(41)

where $X\left(t\right)$ is the random walking step set, $cussum$ is the cumulative calculation sum, and $t$ is the step counts of a random walk. $r\left(t\right)$ is a stochastic function, defined as in Equation (42).

$$r\left(t\right)=\left\{\begin{array}{ll}1,& rand>0.5\\ 0,& rand\le 0.5\end{array}\right.$$

(42)

Due to the limitation of the allowable range, Equation (41) cannot be used directly to update the location of the sparrow. In order to guarantee that sparrows walk randomly within the allowed range, Equation (41) needs to be normalized.

$$X_i^t=\frac{\left(X_i^t-a_i\right)\ast \left(d_i^t-c_i^t\right)}{\left(b_i-a_i\right)}+c_{i}t$$

(43)

Equation (44) is the location updating formula for participants in the improved sparrow algorithm.

$$X_{i,j}^{t+1}=\left\{\begin{array}{cc}Q·\exp \left(\frac{X_{worst}-X_{i,j}^t}{i^2}\right),& i>\frac{n}{2}\\ RandomWalk\left(X_p\right),& else\end{array}\right.$$

(44)

where $RandomWalk\left(X_p\right)$ means that the participants walk randomly around the optimal global position.

Figure 3 presents a flowchart of the simplified process of RSSA.

4.3. Algorithm Performance Test

4.3.1. Experimental Setting

To corroborate the validity of the proposed RSSA algorithm, six benchmark functions were tested and compared using PSO, GWO, WOA, ABC, SSA, CSSA [48], and the improved random walk sparrow search algorithm (RSSA). To make the comparative test experiment fairer, for the parameter settings of each algorithm, we referred to the corresponding references. The parameter settings for each algorithm are shown in

Table 1. Algorithm parameter settings.

Algorithm	Parameter Setting
PSO	$c_1=c_2=2,\omega =1$
GWO	Decline from 2 to 0
WOA	Linear decrease from 2 to 0, b = 1
ABC	L = round (0.6 × dim × N), a = 1
SSA	PD = 20%, ST = 0.8, SD = 10%
CSSA	PD = 20%, ST = 0.8, SD = 10%
RSSA	$\mathrm{PD}=20\%, \mathrm{ST}=0.8, \mathrm{SD}=10\%, {\alpha }_{init}=0.1,{\alpha }_{final}=1.2$

, and the other parameters were consistent, except for the parameters in the table. The experiments were carried out in an Intel Core i5 CPU, 2.20 GHz, 4 GB RAM, Windows10 64-bit test environment, and written using Matlab software. To guarantee the objectivity of the experimental outcomes, the population number of each algorithm was established to be 100, and the greatest number of iterations was 500. The name and parameter settings of each test function are shown in

Table 2. Benchmarking function.

Test Function		Dimension	Scope	${\mathit{F}}_{\mathit{m}\mathit{i}\mathit{n}}$
$f_1$	Generalized Rosenbrock’s Function	30	(−30, 30)	0
$f_2$	Step Function	30	(−100, 100)	0
$f_3$	Generalized Schwefel’s Problem 2.26	30	(−500, 500)	−12,600
$f_4$	Generalized Penalized Function 1	30	(−50, 50)	0
$f_5$	Generalized Penalized Function 2	30	(−50, 50)	0
$f_6$	Kowalik’s Function	4	(−5, 5)	−0.000307

. In Table 2, $f_1$–$f_2$ are unimodal test functions used to test the algorithm’s convergence speed and accuracy. $f_3$–$f_5$ are multimodal test functions that test the global quest capacity to avoid premature convergence. $f_6$ is a fixed dimension test function to test the ability of the algorithms to balance exploration and development. The CEC-2021 test function’s name and parameter settings are shown in

Table 3. CEC-2021 test function.

Test Function		Dimension	Scope	${\mathit{F}}_{\mathit{m}\mathit{i}\mathit{n}}$
$f_7$	Bent cigar Function	10	(−100, 100)	0
$f_8$	Schwefel’s Function	2	(−100, 100)	0
$f_9$	Lunacek bi-Rastrigin Function	2	(−100, 100)	700
$f_{10}$	Rosenbrock’s plus Griewangk’s Function	2	(−100, 100)	0
$f_{11}$	Composition Function 1	2	(−100, 100)	0
$f_{12}$	Composition Function 2	2	(−100, 100)	0

.

4.3.2. Testing of the Improved SSA

In this section, based on the above parameter settings and the benchmark test functions, each algorithm was implemented 30 times independently on each test function. The optimal value, the mean, and the standard variance of the algorithm optimization consequence were obtained and compared with the RSSA algorithm optimization results. Among them, the general average was used to reflect the solving speed and accuracy of the algorithm, and the standard variance was used to reflect the robustness of the optimization process of the algorithm. The results are shown in

Table 4. Experimental results of test functions.

Function	Algorithm	Best	Ave	Std
$f_1$	PSO	8.28	46.51	35.90
	WOA	27.80	28.43	0.17
	GWO	26.15	27.97	0.97
	ABC	5040	15,400	6320
	SSA	2.15 × 10−6	8.88 × 10−4	1.69 × 10−3
	CSSA	4.01 × 10−6	2.94 × 10−4	3.77 × 10−4
	RSSA	1.04 × 10−11	1.85 × 10−5	2.99 × 10−5
$f_2$	PSO	2.16 × 10−9	4.13 × 10−3	4.13 × 10−4
	WOA	0.03	0.49	0.16
	GWO	0.03	0.89	0.41
	ABC	1.31	2.17	$5.27$× 10−1
	SSA	8.54 × 10−9	4.23 × 10−6	8.90 × 10−6
	CSSA	2.34 × 10−6	1.82 × 10−6	3.46 × 10−6
	RSSA	2.44 × 10−15	9.78 × 10−7	3.17 × 10−6
$f_3$	PSO	−8797.80	−7.85×103	7.12 × 102
	WOA	−12,569.30	−10,385.25	1608.52
	GWO	−7859.90	−6076.012	1015.45
	ABC	−5840.33	−5167.70	255.76
	SSA	−8793.88	−7675.75	596.51
	CSSA	−12,569.49	−12,539.73	89.70
	RSSA	−12,569.49	−12,569.49	1.68 × 10−3
$f_4$	PSO	1.47 × 10−2	4.85 × 10−2	1.21 × 10−1
	WOA	7.37 × 10−3	3.39 × 10−2	2.18 × 10−2
	GWO	8.34 × 10−3	5.16 × 10−2	3.35 × 10−2
	ABC	2.69 × 101	3.65 × 102	9.26 × 102
	SSA	5.32 × 10−10	2.09 × 10−7	3.36 × 10−7
	CSSA	9.11 × 10−11	8.259 × 10−8	1.86 × 10−7
	RSSA	5.56 × 10−13	1.06 × 10−8	3.48 × 10−8
$f_5$	PSO	5.16 × 10−1	7.63	9.09
	WOA	1.29 × 10−1	4.75 × 10−1	2.24 × 10−1
	GWO	0.25	0.87	0.37
	ABC	4.94×101	1.04 × 103	9.30 × 103
	SSA	9.66 × 10−9	2.53 × 10−6	3.38 × 10−6
	CSSA	7.80 × 10−11	3.54 × 10−6	7.33 × 10−6
	RSSA	4.82 × 10−13	4.34 × 10−7	1.13 × 10−6
$f_6$	PSO	6.31 × 10−4	8.97 × 10−3	9.19 × 10−3
	WOA	3.10 × 10−4	8.08 × 10−4	5.13 × 10−4
	GWO	3.94 × 10−4	1.93 × 10−3	4.93 × 10−3
	ABC	5.70 × 10−4	7.00 × 10−4	4.30 × 10−5
	SSA	3.08 × 10−4	3.23 × 10−4	6.95 × 10−5
	CSSA	3.07 × 10−4	3.13 × 10−4	6.30 × 10−6
	RSSA	3.07 × 10−4	3.10 × 10−4	3.24 × 10−6
$f_7$	PSO	7852.25	2.52 × 104	8965.5
	WOA	1.56 × 103	2.96 × 103	1.27 × 103
	GWO	1.09 × 104	2.04 × 104	7.23 × 103
	ABC	2.45 × 10−4	1.60 × 10−3	2.20 × 10−3
	SSA	1.59 × 103	2.79 × 103	4.47 × 103
	CSSA	3.49 × 103	1.08 × 104	1.01 × 104
	RSSA	1.62 × 10−3	3.80 × 10−4	4.00 × 10−4
$f_8$	PSO	0.312	12.01	8.01
	WOA	8.23 × 10−6	38.25	49.80
	GWO	0.31	60.96	76.71
	ABC	0.13	3.25	2.07
	SSA	1.81 × 10−12	2.05	5.28
	CSSA	0.31	4.50	8.17
	RSSA	0	1.68	2.13
$f_9$	PSO	700.99	701.61	0.94
	WOA	700.00	702.11	0.79
	GWO	702.02	702.27	0.29
	ABC	700.95	7.02 × 102	9.01 × 10−1
	SSA	700.00	701.89	0.67
	CSSA	702.02	702.13	0.51
	RSSA	700.00	701.50	0.08
$f_{10}$	PSO	0.01	0.01	0.02
	WOA	0.02	0.02	0.02
	GWO	2.17 × 10−6	2.20 × 10−3	7.10 × 10−3
	ABC	1.90 × 10−3	1.29 × 10−2	1.12 × 10−2
	SSA	0	0.01	0.03
	CSSA	0.01	0.01	0.01
	RSSA	0	2.00 × 10−3	6.20 × 10−3
$f_{11}$	PSO	0.01	3.26	5.25
	WOA	1.1 × 10−4	3.28	5.26
	GWO	7.21 × 10−3	20.47	43.14
	ABC	1.85 × 10−9	1.43 × 10−8	1.23 × 10−8
	SSA	3.53 × 10−7	1.12 × 10−6	8.01 × 10−7
	CSSA	0	0	0
	RSSA	0	0	0
$f_{12}$	PSO	55.23	80.06	63.36
	WOA	6.64 × 10−2	90.04	31.61
	GWO	100.00	110.03	31.72
	ABC	5.31	17.82	11.35
	SSA	2.05 × 101	40.02	51.64
	CSSA	1.04 × 101	18.85	20.76
	RSSA	0	1.00 × 101	2.06 × 101

.

The above optimization results were analyzed. For the single peak test function $f_1$–$f_2$, the average value obtained with the RSSA algorithm was closer to the optimal solution than those obtained with the other six algorithms, which shows that the RSSA algorithm had a higher speed and accuracy in solving single-peak-function problems. The standard variance of the RSSA algorithm was lower, indicating that the data fluctuation was minor and the algorithm was robust in the optimization process. The mean and standard variance of the RSSA algorithm were lower than those of the other six algorithms, suggesting that the RSSA algorithm has superior global searchability and the ability to avoid premature convergence. For the multi-dimensional fixed-dimensional test function $f_6$, the RSSA algorithm and the CSSA algorithm had the same optimal solution. Nevertheless, the average value of the former was closer to the theoretical global optimal solution, indicating that the RSSA algorithm’s solution was more accurate than the CSSA algorithm’s solution. For the CEC-2021 test function, the RSSA algorithm generally outperformed the remaining six algorithms, which also shows that after embedding the sharing factor and random walk strategy, the sparrow algorithm showed an improved ability to balance global exploration and local development.

To more intuitively reflect the dynamic convergence characteristics of the RSSA algorithm, in Figure 4 we present the convergence curves of six benchmark functions under seven optimization algorithms and functions $f_1$–$f_6$, along with the waveforms of the corresponding Figure 4a–f. The convergence curve shows that RSSA has strong convergence, whether faced with a single-peak or multi-peak function. Compared with the other six algorithms, the convergence curve was always lower, indicating that the RSSA algorithm had a swifter convergence speed and superior solution precision. The optimized results were closer to the theoretical global optimal value. To compare the convergence accuracy and speed of the algorithm more intuitively, in this paper we present the convergence curve of the CEC-2021 test function based on the number of iterations and the fitness value. Here, the iterative convergence curve of six test functions was selected for display, as shown in Figure 5, and the waveforms for functions $f_7$–$f_{12}$ are shown in the corresponding Figure 5a–f. Compared with the other six algorithms, the convergence curve of RSSA was always lower, which indicates that RSSA had a faster convergence speed and higher convergence accuracy. The optimized results were closer to the theoretical global optimal value, and the improvement effect was evident and efficacious.

4.4. The Multi-Objective RSSA Algorithm

4.4.1. Multi-Objective Optimization Problems and Related Concepts

Multi-objective optimization problems (MOPs) consider multiple relevant factors in solving optimization problems. For the MOPs of N optimization objectives, the general mathematical description is as follows:

$$\mathit{min}f\left(x\right)=\mathit{min}\left\{f_1\left(x\right),f_2\left(x\right),f_3\left(x\right),\cdots ,f_n\left(x\right)\right\},n=1,2,\cdots ,N$$

(45)

$$g_i\left(x\right)\le 0,i=1,2,\cdots ,k$$

(46)

$$h_j\left(x\right)=0,j=1,2,\cdots ,k$$

(47)

where $f_i$ denotes the i-th objective optimization function, $N$ is the number of optimization objectives. Equation (46) expresses the inequality constraints, and Equation (47) expresses the equality constraints.

For the decision variables x, y, if $f_i\left(x\right)\le f_i\left(y\right),\left(i=1,2,\cdots ,n\right)$, and there is at least one $i$ such that $f_i\left(x\right)<f_i\left(y\right)$, then x is said to be dominant or x dominates y, denoted by $x\propto y$. If other individual solutions do not dominate $x^{*}$ in the decision space, then $x^{*}$ is named a non-dominant solution. The congregate of all non-dominant solutions obtained by means of the multi-objective RSSA is the Pareto optimal solution ensemble.

4.4.2. Multi-Objective RSSA Based on Non-Dominated Solution Set

Figure 6 presents a flowchart depicting the simplified process of the multi-objective RSSA predicated on a non-dominated solution set.

Compared with the original SSA algorithm, the multi-objective RSSA algorithm based on the non-dominated solution set offers two main improvements:

(1)

In this paper, we have changed the original sparrow algorithm from a single-objective algorithm to a multi-objective algorithm. The method we adopted was to introduce the concept of a non-dominated solution set into the original sparrow algorithm. According to the updating of the different individual positions of sparrows, the non-inferior solution sets under different iteration times are stored in the external file, the non-dominated relation judgment and solution set updates are carried out with the number of iterations, and the final non-dominated solution set is obtained by solving.

(2)

The sparrow algorithm itself has been improved. Given the uneven distribution of the population in the traditional sparrow algorithm, in this study we use a sinusoidal chaotic map to generate a uniformly distributed original sparrow population in the space. In this paper we introduce the sharing factor and random walk strategy, aiming to solve the problems of the unsatisfactory global search aptitude and the accessibility of the local optimum in the traditional sparrow algorithm. The introduction of a sharing factor aims to strengthen the information exchange between domain individuals and improve the global search ability. The introduction of the random walk strategy mainly helps to balance the SSA algorithm’s global and local search aptitude in the iterative process. At the start of the iteration, the bounds of the random walk are significant, which is conducive to improving the global searchability. After many iterations, the bounds of the walk become smaller, which improves the algorithm’s local search capacity with regard to the optimal position.

5. Simulation Example and Analysis

5.1. Example Introduction

In this paper, we have selected a CCHP microgrid with grid-connected operation as the research object. The simulation environment was anb Intel Core i5 CPU, 2.20 GHz, 4 GB RAM, Windows10 64-bit system. The time-of-use prices are shown in

Table 5. Time-of-use prices.

Time (h)	${\mathit{C}}_{\mathit{b}\mathit{u}\mathit{y}}$$(\mathbf{CNY}/\mathbf{kW}·$h)	${\mathit{C}}_{\mathit{s}\mathit{e}\mathit{l}\mathit{l}}$$(\mathbf{CNY}/\mathbf{kW}·$h)
0:00–7:00, 23:00–24:00	0.1599	0.1230
10:00–15:00, 18:00–21:00	0.7749	0.6150
7:00–10:00, 15:00–18:00, 21:00–23:00	0.4551	0.3567

[49], and the parameters of each micro-source are shown in

Table 6. The parameters of each micro-source in the CCHP system.

Microsource	Parameters	Value	Microsource	Parameters	Value
WT	$P_{max}$	50 kW	AC	$P_{max}$	200 kW
	$C_{WT{\_}_{om}}$	$0.043 \mathrm{CNY}/\mathrm{kW}·$h		$C_{AC\_om}$	$0.0156 \mathrm{CNY}/\mathrm{kW}·$h
PV	$P_{max}$	25 kW	WHB	$P_{max}$	200 kW
	$C_{PV\_om}$	$0.0096 \mathrm{CNY}/\mathrm{kW}·$h		$C_{WH{\_}_{om}}$	$0.0023 \mathrm{CNY}/\mathrm{kW}·$h
MT	$P_{max}$	100 kW	EH	$P_{max}$	80 kW
	$C_{M{T}_{\_om}}$	$0.1685 \mathrm{CNY}/\mathrm{kW}·$h		$C_{eh{\_}_{om}}$	$0.02 \mathrm{CNY}/\mathrm{kW}·$h
GB	$P_{max}$	100 kW	EC	$P_{max}$	80 kW
	$C_{GB{\_}_{om}}$	$0.0018 \mathrm{CNY}/\mathrm{kW}·$h		$C_{ec{\_}_{om}}$	$0.03 \mathrm{CNY}/\mathrm{kW}·$h

. The relevant equipment parameters and data were obtained from [49,50,51,52,53]. In this study, we chose typical summer and winter days for analysis, and the prediction values of the wind turbine, photovoltaic, and load outputs for typical summer and winter days are shown in

Table 7. Forecast values of wind turbine, photovoltaic, and load outputs on a typical day in summer.

t (h)	${\mathit{P}}_{\mathit{p}\mathit{v}} \left(\mathbf{kW}\right)$	${\mathit{P}}_{\mathit{w}\mathit{t}} \left(\mathbf{kW}\right)$	${\mathit{Q}}_{\mathit{c},\mathit{l}\mathit{o}\mathit{a}\mathit{d}} \left(\mathbf{kW}\right)$	${\mathit{Q}}_{\mathit{h},\mathit{l}\mathit{o}\mathit{a}\mathit{d}} \left(\mathbf{kW}\right)$	${\mathit{P}}_{\mathit{l}\mathit{o}\mathit{a}\mathit{d}} \left(\mathbf{kW}\right)$
1	0	353.9651	272	0	382
2	0	670	320	0	342
3	0	647.3837	278	0	328
4	0	531.8952	344	0	334
5	0	327.1645	294	68.4	294
6	0	230.8035	560	184.4	358
7	1.01	216.0075	576	254	464
8	18.86	127.2004	650	278	492
9	53.72	129.4397	664	310	480
10	142.49	198.7832	670	322	454
11	345.87	254.406	706	336	466
12	527.69	92.4375	744	402	536
13	556.12	204.0917	760	450	558
14	417.86	106.7044	772	418	590
15	459.76	21.392	780	354	512
16	211.5	29.692	712	294	510
17	20.05	38.5502	740	248	526
18	1.22	107.1555	716	288	506
19	0	178.8319	708	394	480
20	0	546.2307	678	424	466
21	0	552.3908	556	480	580
22	0	650	538	440	512
23	0	551.9069	528	346	476
24	0	526.5944	416	244	454

and

Table 8. Forecast values of wind turbine, photovoltaic, and load outputs on a typical day in winter.

t (h)	${\mathit{P}}_{\mathit{p}\mathit{v}} \left(\mathbf{kW}\right)$	${\mathit{P}}_{\mathit{w}\mathit{t}} \left(\mathbf{kW}\right)$	${\mathit{Q}}_{\mathit{c},\mathit{l}\mathit{o}\mathit{a}\mathit{d}} \left(\mathbf{kW}\right)$	${\mathit{Q}}_{\mathit{h},\mathit{l}\mathit{o}\mathit{a}\mathit{d}} \left(\mathbf{kW}\right)$	${\mathit{P}}_{\mathit{l}\mathit{o}\mathit{a}\mathit{d}} \left(\mathbf{kW}\right)$
1	0	471.9535	0	472	332
2	0	629.49	0	444	342
3	0	863.1783	0	408	328
4	0	709.1936	0	414	338
5	0	436.2193	68	370	290
6	0	174.4046	184	438	358
7	4.12	288.01	254	482	460
8	148.05	169.6005	278	490	488
9	286.29	172.5862	310	434	480
10	339.51	265.0443	322	414	450
11	342.25	339.208	336	400	464
12	457.12	123.2499	402	366	530
13	155.72	272.1223	450	356	552
14	242.78	142.2726	418	332	594
15	247.86	28.5226	354	320	512
16	236.3	39.5894	294	350	510
17	110.24	51.4003	248	394	524
18	0.43	142.8739	288	400	518
19	0	238.4425	394	406	606
20	0	428.3076	424	446	534
21	0	736.5211	480	498	566
22	0	520.4211	440	488	510
23	0	602.5435	346	476	439
24	0	463.977	244	468	425

. In this example, the RSSA algorithm was used for optimizing the solution. The values of each parameter were as follows: the population amount NP was 100, the number of iterations was 500, the warning value ST was 0.8, the discoverer group consisted of 20% of the sparrows, and the vigilance group consisted 10% of the total sparrows. In this paper we set the scheduling cycle $\mathrm{T}=24$ and the scheduling interval $\Delta t=1 \mathrm{h}$.

5.2. Weight Coefficient

The introduction of the weight coefficient transforms the multi-objective issue into a single-objective problem. Its purpose is to weigh the operation cost and environmental cost and consider the operation cost of the microgrid, as well as the ecological cost [54]. Under different market policies, the values of ${\omega }_1$ and ${\omega }_2$ can be adjusted accordingly to the adjustment of the operation strategy, in order to minimize the microgrid’s total cost. In this paper, we take the operation of the microgrid on a typical summer day as an example to study the weight coefficient. A comparison of the microgrid operation costs and environmental costs under different weight coefficients is presented in

Table 9. Relationship between weight coefficient and objective function.

Number	${\mathit{\omega }}_1$	${\mathit{\omega }}_2$	Minimum Comprehensive Cost
			Running Cost (CNY)	Environmental Cost (CNY)
1	1.0	0	11,759	5852
2	0.9	0.1	11,775	5822
3	0.8	0.2	11,806	5790
4	0.7	0.3	11,832	5755
5	0.6	0.4	11,857	5717
6	0.5	0.5	11,887	5667
7	0.4	0.6	11,945	5657
8	0.3	0.7	11,989	5645
9	0.2	0.8	12,034	5634
10	0.1	0.9	12,076	5620
11	0	1.0	12,116	5613

.

As shown in Table 9, as ${\omega }_1$ decreased and ${\omega }_2$ increased, the emphasis on environmental protection increased, the operating cost gradually increased, and the ecological cost gradually decreased. Number 1 and number 11, two cases of weight coefficient values, corresponded to two single-objective models. Meanwhile, the operation and environmental prices obtained for the minimum comprehensive operation level were slightly higher than those obtained under the single-objective model. When only considering the minimum operating cost, the environmental cost was the largest; and when only considering the minimum ecological price, the maximum operating cost was observed. By measuring total costs, one can better coordinate the balance between running costs and environmental costs. In the process of CCHP dispatching, decision-makers can reasonably adjust the value of the weight coefficient according to the specific operating conditions, which can ensure the economic operation of the CCHP microgrid and cause the microgrid operation to develop in an environmentally friendly direction. The equal weight method can show the same ideal effect as the optimal weight method in multi-objective optimization [55]. Therefore, in the following example analysis, we assume that ${\omega }_1={\omega }_2=1/2$ to analyze the objective function and operation of the microgrid.

5.3. Analysis of Optimization in Typical Summertime Conditions

Under the conditions of a typical summer day, the RSSA algorithm was utilized to optimize the scheduling of the CCHP microgrid. Figure 7 presents the optimal output of each apparatus in the microgrid.

As shown in Figure 7, during the 01:00–05:00 period, the wind energy output first meets the power burden requirements of the microgrid, but the wind power output is greater than the power load demand, resulting in excess wind power. At this time, the production of the biomass gasification device is increased to absorb the extra wind power, and the biomass gasification process is carried out. The syngas generated during the gasification process is stored in the gas storage tank. The electricity price is the valley-hour price. Compared with the gas turbine power supply to the microgrid, there is an economic benefit to purchasing electricity from the public power grid. The demand for cold and heat loads at night is relatively low. So at this time, buying electricity from the grid drives electric refrigerator and electric heating to meet users’ needs. After 06:00, the demand for electricity load gradually increased, and the system no longer generated excess wind power. Therefore, the gasification device was closed, and the gas storage tank began to vent. The gas turbine started working, and the gas turbine generated electricity by burning syngas to supply part of the electricity load. At 12:00–15:00 and 12:00–21:00, the system power load reached its peak, and the gas turbine, wind power, and photovoltaic power generation were still unable to meet the demands of the power load, so it was necessary to buy power from the grid to make up for the power load shortage. After 07:00, the need for cooling gradually increased. Absorption chillers and waste heat boilers started to work, absorbing the high-temperature flue gas generated by gas turbine power generators, and generating cold/heat energy to meet the cold/heat load requirements of the microgrid. Suppose that absorption chillers and waste heat boilers cannot meet the entire power operation’s cold/heat load requirements. In that case, gas boilers are refueled to meet the heat load requirements, and electric refrigeration consumes the power generated by gas turbines to provide for the cold load requirements of the microgrid. At 21:00–24:00, the microgrid had extra wind power, and the biomass gasification device began to absorb this excess wind power. At this time, the grid’s electricity price was relatively low. Electricity was obtained from the public grid to drive electric refrigeration and electric heating to meet the microgrid’s cooling and heating load requirements.

During the entire operating cycle, the battery was charged and discharged under the guidance of the time-of-use price. The battery was charged when the electricity price reached the valley price at night, and the battery was discharged when the electricity price reached its peak during the day. The battery was charged from 23:00 to 24:00 to restore storage at the beginning of the scheduling period.

As shown in

Table 10. Comparison of optimization results of different algorithms in a typical day in summer.

Optimization Object	PSO	SSA	CSSA	RSSA
Running Cost (CNY)	12,182	12,125	11,899	11,887
Environmental Cost (CNY)	5970.3	5824.4	5679.1	5667
Comprehensive Cost (CNY)	9076.15	8974.7	8789.05	8777

, on a typical summer day, compared with PSO, SSA, and CSSA, the effect of using the RSSA algorithm was an improvement in performance. Compared with PSO, the operating cost decreased by 2.4%, and the environmental price decreased by 5.1%. Compared with SSA, the operating expense decreased by 2.0%, and the ecological cost decreased by 2.7%. Compared with CSSA, running costs decreased by 0.1%, and environmental costs decreased by 0.21%. The above simulation results indicate that the RSSA algorithm had more senior convergence precision than PSO, SSA, and CSSA, and was able to solve the CCHP model stably to obtain the optimal comprehensive cost of the microgrid.

5.4. Analysis of Optimization in Typical Wintertime

Given the heating situation in winter, when the waste heat boiler cannot meet the thermal load of the microgrid, supplementary combustion from gas boilers provides the heat load. The simulation outcomes of typical winter days are demonstrated in Figure 8.

The gas turbine adopts the following thermal load (FTL) operation mode in the winter heating season. When the microgrid adopts the operation mode of FTL, we can obtain the corresponding power generation by calculating the residual heat of the flue gas generated by the gas turbine when the cooling and heating load is satisfied. At this time, the gas turbine should first meet the microgrid’s cooling and heating load demand. If the maximum power operation cannot meet its hot and cold demand, it is necessary to start the gas boiler to supply the heating load that is experiencing a shortage. Figure 8 shows that during the period of 01:00–05:00, the wind power output in the microgrid was greater than the power load demand, resulting in excess wind power. The way to absorb wind power was the same as that employed in summer. In this period, the electricity price was the valley price, meaning that electricity was purchased from the grid and electric heating was used to supply the micro-grid with energy to meet the heat load demands. From the 06:00 period, the demand for electricity load gradually increased, and the system no longer produced excess wind power. Therefore, the gasification device was closed; the gas storage tank began to discharge, the gas turbine started working, and the gas turbine supplied part of the electricity load through burning syngas power generation. In the periods of 10:00–15:00 and 18:00–21:00, electricity prices were at their peak, and the economic benefit of power grid purchasing was far less than that of the use of the gas turbine, so the gas turbine’s output was the largest in this period. The electrical load of the microgrid was supplied by daytime wind power, photovoltaic, and gas turbine power generation, and insufficient purchases from the grid. The waste heat boiler absorbed high-temperature flue gas generated via gas turbine power generation to supply the heat load. When the waste heat boiler could not meet the demands of the heat load, supplemental combustion from the gas boiler was used to meet the heat load shortage of the microgrid, and the heat load of the microgrid was supplied by the waste heat boiler and gas boiler. From 21:00–24:00, the gas turbine stopped working, and the fan power generators met the electric load demand in the microgrid. However, the electric load demand of the microgrid was lower than the output of the fan. At this time, the microgrid generated excess wind power, so the biomass gasification device started to work and store extra wind power in the form of stable chemical energy. There were small cooling load and heat load demands on the microgrid. At this moment, the electricity price of the grid was low, and electricity was taken from the grid to drive electric refrigeration and heating to meet the microgrid’s cooling and heating load demands.

As shown in

Table 11. Comparison of optimization results of different algorithms for a typical day in winter.

Optimization Object	PSO	SSA	CSSA	RSSA
Running Cost (CNY)	8492.9	8462.6	8222.5	8215.1
Environmental Cost (CNY)	4778	4640.8	4489.7	4480.8
Comprehensive Cost (CNY)	6635.45	6551.7	6356.1	6347.95

, on a typical winter day, compared with PSO, SSA, and CSSA, the RSSA algorithm displayed better optimization results. Compared with PSO, the operating cost decreased by 3.2%, and the environmental price decreased by 6.2%. Compared with SSA, the operating expense decreased by 2.9%, and the ecological cost decreased by 3.4%. Compared with CSSA, the operating cost decreased by 0.09%, and the environmental price decreased by 0.2%. The above simulation results indicate that it was easier to obtain an excellent solution with RSSA than with PSO, SSA, or CSSA. Thus, the effectiveness and superiority of RSSA in practical engineering applications have been further illustrated.

5.5. Non-Dominated Solution Set and Weighted Multi-Objective Comparison Results

According to the model established in the second chapter of this paper and the typical examples in the analysis of samples in Section 5.3 and Section 5.4, in this section we used the RSSA predicated on the non-dominated concept for the model. Using Matlab programming software, we obtained the optimization results of the multi-objective RSSA algorithm for the CCHP microgrid on a representative summer day, as shown in Figure 9.

As shown in

Table 12. Comparison of optimization results of different schemes for a typical day in summer.

Optimization Object	Running Cost (CNY)	Environmental Cost (CNY)	Comprehensive Cost (CNY)
Minimum Running Cost	11,500.2	6512.1	9006.15
Minimum Environmental Cost	13,685.5	4490.9	9088.2
Minimum Comprehensive Cost	12,361.1	5216.3	8788.7

, the optimization results under different schemes can be analyzed based on the Pareto solution set of the multi-objective RSSA for typical summer days.

The optimization results of the multi-objective RSSA for the CCHP microgrid on a typical winter day are shown in Figure 10.

As shown in

Table 13. Comparison of optimization results of different schemes for a typical day in winter.

Optimization Object	Running Cost (CNY)	Environmental Cost (CNY)	Comprehensive Cost (CNY)
Minimum Running Cost	7459.6	5412.3	6435.95
Minimum Environmental Cost	9512.3	3856.5	6684.4
Minimum Comprehensive Cost	8580.2	4126.5	6353.35

, the optimization results under different schemes can be analyzed based on the Pareto solution set of the multi-objective RSSA for a typical winter day.

In this section we compare and analyze the optimization results of Table 10, Table 11, Table 12 and Table 13. To make the comparison more objective, the total cost shown in Table 12 and Table 13 is the optimal compromise solution obtained using the same proportion as in the weight multi-objective method. As can be seen from the non-dominated solution set and the multi-objective weight comparison results: (1) the non-dominated solution set pays more attention to the impact of conflicts between objectives and seeks the frontier on the basis of the multi-objective dominance relationship. The multi-objective weight approeach pays more attention to the optimization solution from the overall perspective and the reduction of the overall cost. The critical optimization is the target value—the operation cost that significantly influences the results. Therefore, in the comparison of the optimal results, it can be seen that the running costs in the optimal weight results are smaller than those in the non-dominated solution set, and the weight algorithm can be used to obtain a solution that is more in line with expectations and which offers better comprehensive benefits. (2) The multi-objective non-dominated solution set algorithm was obtained under the same parameters, such as the number of cycles and the population. It can be seen that the optimal results of the comprehensive cost gained by the algorithm still outperformed those of the PSO, SSA, and CSSA algorithms, and the optimization performance of the algorithm was thus further verified. (3) As shown in the results presented in Table 12 and Table 13, the cost of the non-dominated solution set was slightly higher than that of the weighted multi-objective approach. In this paper we have mainly studied the economic dispatch of the CCHP microgrid, focusing on a more economical optimization model; therefore, we used the linear weighting method to optimize the established model.

6. Conclusions and Future Directions

In this study, we aimed to achieve the economic operation of a CCHP-type microgrid system in grid-connected mode in a particular place. A research model of operation accounting for operation costs and environmental pollution costs as part of a multi-objective strategy was constructed. A CCHP system with a biomass gasification device can store excess wind power in the form of biomass gasification syngas when extra wind power is generated at night and can release syngas during the day for gas turbine power generation. At the same time, the flue gas waste heat generated through gas turbine power generation, which is recycled and used for heat generation in a waste heat boiler and for refrigeration in an absorption refrigerator, can be used to realize the cascade utilization of energy in the microgrid. In this paper, we developed the RSSA algorithm to optimize the solution and obtain the optimal output of each micro-source at each time in the scheduling cycle, as well as to assess the total cost of microgrid operation.

When using the traditional sparrow algorithm, it is easy to fall into the local optimum, and the algorithm has a poor global search ability. In this study we improved upon the SSA algorithm as follows:

(1) Sinusoidal chaos was used to initialize the population and to uniformize the initial population distribution.

(2) In this study, a sharing factor was added to the discoverer location update formula so that the discoverer could exchange information between individuals in the field in the search process for food sources to better search for the optimal location.

(3) In this study, we used the random walk strategy to form a new individual to ameliorate the algorithm’s local search aptitude in the optimal location and improve its performance combined with the microgrid model.

Finally, the analysis of an example showed that on typical summer days, the operation cost of a microgrid using RSSA was 2.4% lower than that obtained using the PSO algorithm optimization process, and the environmental price was 5.1% lower. The operation cost of the microgrid under the RSSA was 2.0% lower than that under the SSA algorithm optimization process, and the environmental price was 2.7% lower. Compared with CSSA, RSSA reduced the operation cost of the microgrid by 0.1% and the ecological cost by 0.21%. On typical winter days, the operational cost of a microgrid using RSSA was 3.2% lower than that obtained using the PSO algorithm optimization approach, and the environmental cost was 6.2% lower. The operation cost of the microgrid using RSSA was 2.9% lower than that obtained using SSA optimization, and the environmental cost was 3.4% lower. Compared with CSSA, the use of RSSA reduced the operation cost of the microgrid by 0.09% and the ecological cost by 0.2%. Comparing the optimization results of RSSA, PSO, CSSA, and SSA in typical summer and winter days, the RSSA algorithm was more economical than the PSO, SSA, and CSSA algorithms.

For the optimal economic scheduling of a CCHP microgrid, we optimized the structure, operational strategy, and optimization algorithm of the CCHP microgrid to a certain extent and thus made some progress. However, this is only a preliminary study on the optimal scheduling of CCHP microgrids, and the research presented in this paper needs to be continued and improved.

(1) In this study, we report on an improved biomass gasification device based on the traditional CCHP microgrid structure. As a form of renewable energy, biomass energy is easy to obtain and abundant, but its distribution is uneven and it has poor controllability. Therefore, this research still needs to be further strengthened and improved.

(2) Due to the volatility of distributed energy sources such as wind power and photovoltaic power generation, specific errors occur in the prediction of the power output of photovoltaic and wind power, which would have a certain impact on the optimal scheduling of the CCHP microgrid. Therefore, in subsequent research works, the uncertainty of wind power and photovoltaic output should be considered.

(3) In regard to the construction of the CCHP microgrid, the types of batteries are not discussed in detail in this paper. Nowadays, the application of lithium batteries has improved the performance of batteries in energy storage. For the same capacity, the volume of a lithium battery is much smaller than that of a lead-acid battery, and the weight of a lithium battery is less than 40% of that of a lead-acid battery. Therefore, the energy storage capacity of lithium batteries is more significant, despite having the same volume. Thus, in the future economic dispatch of CCHP microgrids, the question of whether introducing lithium batteries as energy storage devices can improve the economy of the microgrid’s operation requires further research and analysis.