Comprehensive Benefit Evaluation Analysis of Multi-Energy Complementary Off-Grid System Operation

Abstract

In the future, China’s demand for centralized industrial development in remote areas will gradually increase, but the operation evaluation analysis of off-grid systems applicable to the development of such areas has not yet matured, and it is an urgent challenge to improve the operation mechanism of off-grid systems and then conduct a comprehensive benefit evaluation of off-grid systems. First of all, this paper focuses on the problem that the existing dimensions of the benefit evaluation of multi-energy complementary off-grid systems are not refined and comprehensive enough, and takes into account their high safety and reliability requirements, as well as the potential impacts on local industries and people’s lives after their completion, and then constructs a more complete comprehensive benefit evaluation indicator system for multi-energy complementary off-grid systems. Secondly, the subjective and objective weighting method based on the combination of the AHP (analytic hierarchy process) and AEM (anti-entropy method) is used to assign weights to the evaluation indicators. Finally, based on the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) comprehensive evaluation method, a comprehensive benefit evaluation of a multi-energy complementary off-grid system under different operation schemes is conducted, and the example results show that the size of the relative closeness under different operation schemes has a maximum difference of 0.5592, which verifies that the proposed evaluation indicator system and the multilevel evaluation method can comprehensively evaluate and analyze the strengths and weaknesses of multi-energy complementary off-grid systems under different operation schemes, and provide theoretical guidance and decision-making support for the further promotion and construction of multi-energy complementary off-grid systems.

1. Introduction

Achieving the sustainable development of resources and the environment and reducing greenhouse gas emissions is a common goal of all societies. A multi-energy complementary off-grid system, as a kind of system that provides power security for the production and development of alpine areas, has an important strategic position in green and low-carbon transformation. At present, a scientific and perfect evaluation indicator system has not yet been established for multi-energy complementary off-grid systems. Therefore, there is an urgent need to establish a set of more detailed and comprehensive evaluation systems for analyzing the comprehensive benefits of multi-energy complementary off-grid systems, which has important theoretical value and practical significance for promoting the clean energy consumption of energy bases in Northwest China.

The optimal operation of a multi-energy complementary off-grid system involves the supply, conversion, and storage of each energy source. Regarding the comprehensive benefit evaluation of multi-energy complementary systems, domestic and foreign scholars have also conducted many research studies.

Domestic and foreign studies on the comprehensive benefit evaluation of multi-energy complementary systems mainly focus on three aspects: the system’s economic benefits, technical reliability, and environmental benefits. Reference [1] introduces a small-scale power generation system composed of photovoltaics, battery energy storage, and garbage power generation, and evaluates its economic and technological reliability. Reference [2] establishes a comprehensive benefit evaluation indicator system for a pumped-storage power station from the point of view of the system’s operation effect, economic benefit, and environmental benefit, and constructs a comprehensive evaluation model based on TOPSIS to quantitatively analyze the comprehensive benefits of the pumped-storage power station in the multi-energy complementary system. Reference [3] proposes a dimensionless numerical indicator to evaluate the linkage between three energy sources by utilizing the complementarity among the three resources, namely, hydropower, photovoltaic power, and wind power; reference [4] comprehensively analyzes solar energy, wind energy, hydropower, geothermal energy, and biomass energy, and carries out a comparative study from the perspectives of economic benefits, technical reliability, environmental benefits, and development prospects; reference [5] proposes an MECS optimization method that integrates reliability, economy, and environmental performance, and applies the MCMC method for reliability evaluation; reference [6] proposes a new framework based on synergy theory and introduces current techno-economic evaluation indicators to validate the framework; reference [7] constructs a hybrid renewable energy system (HRES) and evaluates its management using decision algorithms and 13 case studies, analyzing economic, technological, and environmental aspects; reference [8] uses machine learning techniques to resolve uncertainties in renewable energy systems and thus analyze the economics and technical reliability of the system.

China’s research on the comprehensive benefit evaluation of multi-energy complementary systems started late, and the current research mainly focuses on small-scale multi-energy complementary systems such as park microgrids. Reference [9] proposed a comprehensive evaluation scheme for many types of microgrid systems characterized by an open range, focusing on the technical benefits as well as the economic benefits during the construction of a microgrid comprehensive evaluation indicator system, and introducing mapping functions, such as Arctangent mapping functions, to quantitatively analyze it. Reference [10] constructed a comprehensive benefit evaluation model for microgrids from the perspectives of the economy, environmental protection, and technology, and used the analytic hierarchy process and entropy weighting method to combine and assign weights to them. Reference [11] used the ANP algorithm to optimize the weight coefficients of the indicators in a comprehensive evaluation indicator system of microgrid planning in order to simplify a comprehensive evaluation model of a microgrid system.

Through an analysis of the above references, it is found that most of the current studies on multi-energy complementary off-grid systems are limited to cost considerations and energy saving and emission reduction methods in the context of the “dual-carbon” goal, and the evaluation dimension is focused on economic and environmental benefits. However, as the country’s demand for the development of remote areas with abundant industrial production resources but weak power construction gradually increases, the existing benefit evaluation system of multi-energy complementary microgrid systems can hardly meet the needs of the benefit evaluation of industrial production in remote areas without access to large power grids; thus, there is an urgent need to consider the more important social benefits in the off-grid environment and further analyze the potential social development prospects after the completion of the system to encourage the development of related industrial chains in the local area, improve the production and lives of the local residents, etc. In addition, an off-grid system has higher requirements for the safety and reliability of the system’s operation, so it is necessary to increase the power supply reliability of these systems and electric power production safety at the technical reliability level so as to fully maximize the safety and reliability of system operation. Therefore, a more detailed and comprehensive evaluation indicator system for multi-energy complementary off-grid systems has not yet been established.

Against this background, this paper proposes a more refined and comprehensive benefit evaluation system for multi-energy complementary off-grid systems based on comprehensive consideration of the operational characteristics of multi-energy complementary off-grid systems. In view of the high safety and reliability requirements of off-grid systems, the power supply reliability of these systems and electric power production safety are added to the technical reliability evaluation dimensions, which can better reflect the safety and reliability of off-grid systems. In view of the potential social development prospects of off-grid systems in terms of the development of the local industry chain and the improvement of the production and lives of the local residents, the evaluation dimension of the social benefits to the local community is added to the indicators, and an overall system of indicators for the evaluation of the benefits is established with the four aspects of economic benefits, technological reliability, environmental benefits, and social benefits in a detailed and comprehensive manner. Secondly, in view of the characteristics of the comprehensive benefit evaluation of this system, such as the large number of indicators and the open range, a corresponding standardization strategy is designed according to the different characteristics of the evaluation indicators. Then, the AHP and the AEM are introduced to calculate the weights of the indicators once each, and normalization of the indicators is performed through classification and quantification with fuzzy algorithm normalization processing, and then, the subjective and objective weighting method based on the AHP-AEM is used for combined weighting processing. Finally, on this basis, the TOPSIS-based comprehensive benefit evaluation solution method is proposed to evaluate and analyze the comprehensive benefits, and the method is verified to comparatively analyze the advantages and disadvantages of the multi-energy complementary system under different operation schemes through an analysis of examples.

2. Establishment of a Comprehensive Benefit Evaluation System for Multi-Energy Complementary Off-Grid Systems

2.1. Ideas for Constructing a Comprehensive Efficiency Evaluation Indicator System for Off-Grid Systems

The comprehensive benefit evaluation indicator system for multi-energy complementary off-grid systems constructed in this paper aims to find the advantages and disadvantages of the benefits of each part of multi-energy complementary systems in a synergistic and optimized operation, and to analyze the comprehensive benefits of the system under different operation schemes. The design flow of the comprehensive benefit evaluation indicator system of multi-energy complementary off-grid systems is shown in Figure 1.

2.2. Construction of Comprehensive Benefit Evaluation Indicators for Multi-Energy Complementary Off-Grid Systems

For the multi-energy complementary off-grid integrated benefit evaluation configuration, the core issue is whether the implementation of the comprehensive benefit evaluation configuration scheme is good or not (target layer), i.e., whether the safety of the comprehensive benefit evaluation scheme is established or not. To this end, based on the research on the optimal capacity configuration for off-grid systems, and referring to the relevant information [12,13], four key issues (criterion layer) are proposed, i.e., whether the program environment adheres to the standard, whether the program economy is good, whether the program technicality is reasonable, and the nature of the program sociality; based on the four key issues and analyzing the connotation of the four key issues, 13 indicators in the connotation index layer (connotation layer) can be derived, which form a comprehensive integrated benefit evaluation indicator assessment system for multi-energy complementary off-grid-type systems comprising 1 target layer, 4 guideline layers, and 13 connotation index layers, as shown in Figure 2 below.

(1)

Economic benefit evaluation indicators

1.

Life cycle cost

The utilization of the life cycle cost can take into account all the costs of each piece of equipment in the system from its initial procurement and construction to its end-of-life disposal, including the respective equivalent investment and operation and maintenance costs. The specific investment costs of the system are also related to the design capacity of the system, as shown in Equations (1)–(4):

$$F_{\mathrm{IA}}=F_{\mathrm{IN}}+F_{\mathrm{M}}$$

(1)

$$F_{\mathrm{IN}}={\displaystyle \frac{T}{8760}}{\displaystyle \sum _{i=1}^I{X}_i{c}_i{S}_{i,\mathrm{equ}}}$$

(2)

$$F_{\mathrm{M}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum {\alpha }_i{P}_i(t)}}$$

(3)

$$X_i={\displaystyle \frac{m{(m+1)}^N}{{(1+m)}^N-1}}$$

(4)

where $F_{\mathrm{IA}}$ is the life cycle cost of the system; $F_{\mathrm{IN}}$ is the annual equivalent investment cost of the system; $F_{\mathrm{M}}$ is the operation and maintenance cost of the system; $X_i$ is the annual equivalent investment conversion coefficient for the equipment in the system; $I$ is the unit investment cost of the respective equipment within the system; $c_i$ is the annual equivalent investment cost of the system; $S_{i,\mathrm{equ}}$ is the optimal capacity of each device designed within this system; ${\alpha }_i$ is the operating cost of the ith device; $P_i(t)$ is the power of the ith device at moment t; $m$ is the discount rate; and $N$ is the life cycle of the system.

2.

Internal rate of return

The internal rate of return (IRR) of the system can be obtained from the discount rate corresponding to the system when the sum of the net present values of each year of this multi-energy complementary off-grid system equals zero, which is expressed as shown in Equation (5):

$${\displaystyle \sum _{t=1}^T{(CI-CO)}_n{(1+IRR)}^{-T}}=0$$

(5)

where $CI$ is the inflow of money into the system in year $n$; $CO$ is the outflow of money from the system in year $n$; $T$ the computational cycle of the system; and $IRR$ is the internal rate of return of the system.

3.

Period of investment recovery

The period of investment recovery of the multi-energy complementary off-grid system equipment is considered from the perspective of time to characterize the investment years that can be covered by the economic income of the project, and can be divided into two indicators: the static investment recovery period and the dynamic payout period of investment. The specific expressions are shown in Equations (6) and (7):

$${\displaystyle \sum _{a=0}^{T_{\mathrm{DPP}}}\left[\left(A_{\mathrm{cin}}(n)-A_{\mathrm{count}}(n)\right){(1+r)}^{-n}\right]}=0$$

(6)

$${\displaystyle \sum _{a=0}^{T_{\mathrm{APP}}}\left[A_{\mathrm{cin}}(n)-A_{\mathrm{count}}(n)\right]}=0$$

(7)

where $T_{\mathrm{DPP}}$ is the dynamic payout period of investment for the system’s equipment; $T_{\mathrm{APP}}$ is the static investment recovery period for the system’s equipment; $A_{\mathrm{cin}}(n)$ is the comprehensive income in year $n$; $A_{\mathrm{count}}(n)$ is the total investment in year $n$; and $r$ is the annual interest rate.

(2)

Environmental benefit evaluation indicators

1.

Equivalent environmental cost

The pollutant emission coefficients of the respective energy equipment within the integrated energy off-grid-type system and the environmental evaluation standards for pollutant gases in the traditional electric power industry [14,15,16] are shown in

Table 1. Pollutant emission factors for different energy equipment.

Pollutant Emission	$\mathbf{Pollutant}\mathbf{Emission}\mathbf{Factors}\mathbf{for}\mathbf{Individual}\mathbf{Energy}\mathbf{Equipment}{\mathit{\chi }}_{\mathit{c}}$[g·(kW·h)−1]
	Traditional Coal-Fired	Gas Turbine	Gas Boiler	Photovoltaic	Wind Power
NOX	3.0942	0.6178	0.2554	0.0000	0.0000
SO2	3.9442	0.0009	-	0.0000	0.0000
CO	-	0.1713	-	0.0000	0.0000
CO2	86.4525	184.1830	227.0000	0.0000	0.0000

and

Table 2. Environmental evaluation criteria for polluting gases in the conventional power industry.

Type of Pollutants Emitted	$\mathbf{Environmental}\mathbf{Value}{\mathit{V}}_{\mathit{C}}$/(yuan/kg)	$\mathbf{Penalty}\mathbf{Amount}{\partial }_{\mathit{C}}$(yuan/kg)
NOX	6.7493	1.6178
SO2	4.8583	0.8174
CO	0.8096	0.1298
CO2	0.0184	0.0082

below. In this paper, the emission coefficients of the respective pollutants of the two tables, the environmental benefits, and the penalty amount are combined, and they are uniformly discounted to the equivalent environmental benefits, which are expressed as shown in Equation (8) below:

$$C_{\mathrm{W}}={\displaystyle \sum _i{\displaystyle \sum _c{P}_{\mathrm{ex}}{\chi }_c(V_C+{\partial }_C)}}$$

(8)

where $P_{\mathrm{ex}}$ is the amount of electricity generated by the system’s thermal power; ${\chi }_c$ is the emission factor for category c pollutants; $V_C$ is the environmental value of category $C$ pollutants; and ${\partial }_C$ is the cost of the penalty to be paid for Class $C$ pollutants.

2.

Carbon dioxide emission reduction rate

In the context of achieving the goal of “double carbon”, this paper takes the carbon dioxide emission reduction rate as the object of consideration in terms of its environmental benefits. The main pollutant gas emitted by traditional energy equipment is carbon dioxide, and the use of multi-energy complementary systems can greatly reduce the emission of carbon dioxide. At the same time, the hydrogen produced at the terminal can also be transported to other equipment, which will lead other industries to realize the cleanliness of terminal energy use. The main source of carbon emissions of the multi-energy complementary system constructed in this paper is the emission from power generation with gas turbines and other equipment in the off-grid system, which is expressed as shown in Equation (9):

$$E_{{\mathrm{co}}_2}={\displaystyle \sum _{t=0}^T{\omega }_{\mathrm{grid}}{W}_{\mathrm{grid}}(t)}$$

(9)

where $E_{{\mathrm{co}}_2}$ is the carbon dioxide emissions of the system; ${\omega }_{\mathrm{grid}}$ is the CO₂ conversion factor for procured fossil energy generation; and $W_{\mathrm{grid}}(t)$ is the amount of fossil energy generated by the system at time t.

The reduction rate of CO₂ for the multi-energy complementary off-grid-type system is shown in Equation (10) below:

$$F_{{\mathrm{co}}_2}={\displaystyle \frac{C_{{\mathrm{co}}_2}^{\mathrm{coal}}-E_{{\mathrm{co}}_2}}{C_{{\mathrm{co}}_2}^{\mathrm{coal}}}}$$

(10)

where $F_{{\mathrm{co}}_2}$ is the CO₂ reduction rate of the system, and $C_{{\mathrm{co}}_2}^{\mathrm{coal}}$ is the emission of CO₂ from a conventional distributed generation system.

3.

Space occupancy

Space occupancy refers to the fact that the energy generation equipment and storage equipment of each subsystem in a multi-energy complementary off-grid system need to occupy a certain amount of land area, which will have a certain impact on the external environment. The difference in the number of pieces of equipment used in different operational programs will also result in a different space occupancy, which also reflects the difference in the impact of the system on the environment.

(3)

Technical reliability evaluation indicators

1.

Clean energy consumption rate

In this paper, the clean energy consumption capacity of a multi-energy complementary off-grid system is evaluated from the three perspectives, the clean energy abandonment rate ${\alpha }_{\mathrm{q}}$, clean energy penetration rate ${\zeta }_{\mathrm{x}}$, and clean energy reduction rate ${\delta }_{\mathrm{s}}$, which are expressed as shown in Equations (11)–(13):

$${\alpha }_{\mathrm{q}}={\displaystyle \sum _{t\in T}\frac{P_{\mathrm{tot}}(t)-P_{\mathrm{use}}(t)}{P_{\mathrm{tot}}(t)}}$$

(11)

$${\zeta }_{\mathrm{x}}={\displaystyle \frac{(W_{\mathrm{RF}}-W_{\mathrm{R}})}{W_{\mathrm{RF}}}}$$

(12)

$${\delta }_{\mathrm{s}}={\displaystyle \frac{S_{\mathrm{RES}}}{P_{\mathrm{L},\mathrm{m}}}}$$

(13)

where $P_{\mathrm{tot}}(t)$ is the annual generation of clean energy within the system; $P_{\mathrm{use}}(t)$ is the amount of clean energy consumed by the system load in a year; $W_{\mathrm{RF}}$ is the ideal power generation for the system; $W_{\mathrm{R}}$ is the actual power generation of the system; $S_{\mathrm{RES}}$ is the actual installed capacity of the system; and $P_{\mathrm{L},\mathrm{m}}$ is the peak power of the internal load of the system.

2.

The power supply reliability of the system

A multi-energy complementary off-grid system needs to maintain its own stability to ensure the reliability of the power supply. Taking into account the strong volatility of wind power and photovoltaic output, which will lead to frequency flicker oscillation of the system and so on, in order to reflect the ability of the system to meet the power loads in various situations, the power supply reliability of this multi-energy complementary off-grid system is evaluated mainly from the three perspectives, outage frequency $f_{\mathrm{SIF}}$, outage time $S_{\mathrm{SID}}$, and power supply reliability $A_{\mathrm{SSA}}$, as formulated in Equations (14)–(16):

$$f_{\mathrm{SIF}}={\displaystyle \frac{{\displaystyle \sum _{m\in E}{\lambda }_{m,e}{N}_{m,e}}+{\displaystyle \sum _{m\in H}{\lambda }_{m,h}{N}_{m,h}}}{{\displaystyle \sum _{m\in E}{N}_{m,e}}+{\displaystyle \sum _{m\in H}{N}_{m,h}}}}$$

(14)

$$S_{\mathrm{SID}}={\displaystyle \frac{{\displaystyle \sum _{m\in E}{M}_{m,e}{N}_{m,e}}+{\displaystyle \sum _{m\in H}{M}_{m,h}{N}_{m,h}}}{{\displaystyle \sum _{m\in E}{N}_{m,e}}+{\displaystyle \sum _{m\in H}{N}_{m,h}}}}$$

(15)

$$A_{\mathrm{SSA}}=1-{\displaystyle \frac{{\displaystyle \sum _{m\in E}{M}_{m,e}{N}_{m,e}}+{\displaystyle \sum _{m\in H}{M}_{m,h}{N}_{m,h}}}{\mathrm{Y}\left({\displaystyle \sum _{m\in E}{N}_{m,e}}+{\displaystyle \sum _{m\in H}{N}_{m,h}}\right)}}$$

(16)

where $E$ is the collection of load points in the distribution network; $H$ is the collection of system load points; $m$ is the $m$th load point; $h$ is the system load point; $e$ is the distribution network load point; $M_{m,e}$ is the outage time of the load point in the distribution network; $M_{m,h}$ is the time when the load point in the system is out of supply; ${\lambda }_{m,e}$ is the failure rate at the $m$th load point of the distribution network;${\lambda }_{m,h}$ is the failure rate at the $m$th load point of the system; $N_{m,e}$ is the number of users at the $m$th load point of the distribution network; $N_{m,h}$ is the number of users at the $m$th load point of the system; and $\mathrm{Y}$ is the number of hours in a year, 8760 h.

3.

Electric power production safety

The safety of power production in a multi-energy complementary off-grid system is evaluated from two perspectives: the safety of the production equipment within the system and the safety of the employees working under the system.

4.

System operation flexibility

Since this multi-energy complementary off-grid system contains energy storage equipment inside, the system power supply capacity $S_{\mathrm{P}}$, the maximum regulated capacity of the contact transmission line $S_{\mathrm{W}}$, and the ratio of the capacity of the energy storage devices $S_{\mathrm{S}}$ to the maximum load of the system $P_{\mathrm{L},\max }$ are defined as the operational flexibility of the system, which is expressed as shown in Equation (17) below:

$$K_{\mathrm{yun}}={\displaystyle \frac{(S_{\mathrm{P}}+S_{\mathrm{S}}+S_{\mathrm{W}})}{P_{\mathrm{L},\max }}}$$

(17)

where $S_{\mathrm{P}}$ is the power capacity that can be flexibly adjusted within the system; $S_{\mathrm{S}}$ is the capacity of the energy storage equipment in the system; $S_{\mathrm{W}}$ is the maximum regulated capacity of the contact transmission line; and $P_{\mathrm{L},\max }$ is the peak power of the internal load of the system.

(4)

Social benefit evaluation indicators

1.

Provision of employment opportunities

The current employment rate in China is low, and improving the national employment rate is also a social issue of concern. After the beginning of the project, it will provide a certain number of jobs for local residents. So, the number of jobs provided after the implementation of the project has also become one of the investigation indicators to examine the social benefits of the multi-energy complementary system.

2.

Enhancing resident satisfaction

Resident satisfaction represents the real feelings of the local residents after the implementation of the multi-energy complementary off-grid system project for the improvement of local social and environmental benefits. The main purpose of building the off-grid system is to provide a clean and stable power supply to the local community, and to improve the reliability of local residents’ electricity consumption on the basis of protecting the environment. After the project is implemented, the higher the satisfaction of local residents, the better the social benefits of the project.

3.

Leading the development of the local regional economic industry

The main benefits of completing the multi-energy complementary off-grid system project are driving the development of the local economic industry and the expansion of the local economic environment, as well as driving the development of the relevant local industrial chain. As the system contains hydrogen storage subsystems, the implementation of the project can greatly promote the development of the local hydrogen industry, including hydrogen storage, manufacturing, transportation, etc.; at the same time, regarding the country’s policy support, it also provides a forward-looking platform to the relevant clean energy power generation industry.

The stronger the project’s demonstration of advanced technology is, the more it can promote the development of the relevant industrial chain, with strong social benefits. Therefore, driving the development of the local regional economic industry has also become an important indicator for measuring the social benefits of the system after its implementation.

3. Analysis of the Combination of Indicators for Evaluating the Comprehensive Benefits of Multi-Energy Complementarity

3.1. Analytic Hierarchy Process

The analytic hierarchy process (AHP) [17] is a widely used subjective weight calculation method. It is suitable for multi-objective complex decision-making, and the calculation steps consists of five parts: establishing a hierarchical structure, constructing an interval judgment matrix, solving index weights, performing consistency verification, and calculating the overall comprehensive weights [18].

After determining the interconnection between the target layer, criterion layer, and connotation layer, the interval judgment matrix can be established. This involves the pairwise comparison of indicators within the same hierarchical level to assess their relative importance, yielding the following judgment matrix:

$$A=\left[\begin{array}{l}{a}_{11}{a}_{12}\cdots a_{1n}\\ a_{21}{a}_{22}\cdots a_{2n}\\ \cdots \cdots \cdots \cdots \\ a_{n1}{a}_{n2}\cdots a_{nn}\end{array}\right]$$

(18)

where $a_{ij}$ is the relative importance of $U_i$ versus $U_j$ based on the consideration of some factors; $a_{ij}=\left[a_{ij}^{-},a_{ij}^{+}\right]$, $a_{ji}=\left[{\displaystyle \frac{1}{a_{ij}^{+}}},{\displaystyle \frac{1}{a_{ij}^{-}}}\right]$; $a_{ij}^{+}$ is the upper limit of the result; and $a_{ij}^{-}$ is the lower limit of the result.

At the same time, the judgment matrix should have the following properties: $a_{ij}>0$; $a_{ij}={\displaystyle \frac{1}{a_{ji}}}$; $a_{ii}=1$.

We calculate the weight vector of the indicator set through the judgment matrix and normalize it, as formulated in Equation (19) below:

$${\overline{a}}_{ij}={\displaystyle \frac{a_{ij}}{{\displaystyle \sum _{i=1}^n{a}_{ij}}}}$$

(19)

Subsequently, each row of the normalized judgment matrix $A$ is further summed to find the summation value $M_i$ for each row of matrix $A$.

$$M_i={\displaystyle \sum _{j=1}^n{\overline{a}}_{ij}}i=1,2,\cdot \cdot \cdot ,n$$

(20)

Finally, we calculate the indicator weights ${\omega }_i$ for each indicator of matrix $A$.

$${\omega }_i={\displaystyle \frac{M_i}{{\displaystyle \sum _{j=1}^n{M}_j}}},i=1,2,\cdot \cdot \cdot ,n$$

(21)

If the judgment matrix is not able to satisfy the consistency requirement, it will face a situation where the solution cannot proceed, so it needs to be checked for consistency.

The consistency indicator $CI$ is met:

$$CI={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(22)

The stochastic consistency ratio $CR$ of the judgment matrix $A$ is satisfied:

$$CR={\displaystyle \frac{CI}{R1}}$$

(23)

where ${\lambda }_{\max }$ is the maximum eigenvalue of the judgment matrix $A$; $n$ is the order of the judgment matrix; and $R1$ is the average random consistency indicator.

If the obtained matrices satisfy the consistency checks, the overall weights can be calculated after computing the weights of each layer.

3.2. Anti-Entropy Method

The entropy-based anti-entropy method (AEM) [19] is formulated in Equation (24) below:

$$h_i=-{\displaystyle \sum _{i=1}^k{K}_i\ln (1-K_i)}$$

(24)

where $0\le K_i\le 1$, and ${\displaystyle \sum _{i=1}^k{K}_i}=1$. $h_i$ and $h$ have opposite characteristics; the greater the degree of disorder in the system, the greater the anti-entropy.

The objective weight vector $W^{,,}=\left(w_1^{,,},w_2^{,,},\cdot \cdot \cdot ,w_s^{,,}\right)$ for each evaluation indicator is calculated using the AEM. $w_i^{,,}$ is calculated as formulated in Equation (25) below:

$$w_i^{,,}={\displaystyle \frac{h_i}{{\displaystyle \sum _{i=1}^s{h}_i}}}$$

(25)

The steps of the AEM are briefly described based on the previous object of the comprehensive benefit evaluation indicator system of the multi-energy complementary off-grid-type system [20]:

The objective decision matrix $A’$ is derived based on the comprehensive benefit evaluation indicator system of the multi-energy complementary off-grid system, where $A’=\left(x_{ij}\right)\left(i=1,2,\dots ,m,j=1,2,\dots ,n\right)$ is formulated in Equation (26):

$$A’=\left[\begin{array}{llll}{x}_{11}& x_{12}& \cdot \cdot \cdot & x_{1n}\\ x_{21}& x_{22}& \cdot \cdot \cdot & x_{2n}\\ \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot \\ x_{m1}& x_{m2}& \cdot \cdot \cdot & x_{mn}\end{array}\right]$$

(26)

where $n$ is the number of operating scenarios for a multi-energy complementary off-grid system; $m$ is the number of indicators for the comprehensive benefit evaluation of the multi-energy complementary off-grid system; and $x_{ij}$ is the original value of the $j$ th metric in the first optimization strategy.

In order to facilitate the calculation, the cost type of the indicator type is converted into the benefit type by consistent treatment, as formulated in Equation (27):

$$x_{ij}^{\ast }={\displaystyle \frac{1}{x_{ij}}}$$

(27)

The standardized calculation of the indicators for assessing the comprehensive benefits of a multi-energy complementary off-grid system was carried out immediately after the transformation was completed:

$$P_{ij}={\displaystyle \frac{x_{ij}^{\ast }}{{\displaystyle \sum _{i=1}^m{x}_{ij}^{\ast }}}}$$

(28)

where $P_{ij}$ represents the standardized data for each evaluation indicator of the comprehensive benefit evaluation of the multi-energy complementary off-grid system.

The entropy of the comprehensive benefit evaluation indicator of the $j$ th multi-energy complementary off-grid-type system is found through arithmetic, and is formulated in Equation (29):

$$e_j=-{\displaystyle \sum _{i=1}^m{P}_{ij}\ln \left(1-P_{ij}\right)}\left(j=1,2,\dots ,n\right)$$

(29)

where $e_j$ is the entropy of the $j$th comprehensive benefit evaluation indicator of multi-energy complementary off-grid-type system.

The coefficient of variation of the comprehensive benefit evaluation indicator of the $j$ th multi-energy complementary off-grid-type system is shown in Equation (30):

$$g_j=1-e_j$$

(30)

where $g_j$ is the coefficient of variation of the $j$th comprehensive benefit evaluation indicator of the multi-energy complementary off-grid-type system.

Finally, the weights of the indicators for the comprehensive benefit evaluation of the multi-energy complementary system are measured, as formulated in Equation (31):

$${\omega }_j={\displaystyle \frac{g_j}{{\displaystyle \sum _1^n{g}_j}}}$$

(31)

where ${\omega }_j$ is the weight value of the $j$th comprehensive benefit evaluation indicator of the multi-energy complementary off-grid system.

3.3. Classification and Quantification with Fuzzy Algorithm Normalization Processing

In this paper, the constructed comprehensive benefit evaluation indicators of multi-energy complementary off-grid systems are categorized into three kinds: those with a specific numerical limit, those with a fixed minimum and without a maximum, and those with maximum optimization-seeking saturation with a minimum and without a maximum.

Generally, those with specific numerical limits are taken to be 0 and 1, while the fixed minimum for the fixed-minimum-without-maximum class is taken to be 0, and the normalization transformation is performed with reference to Equation (32):

$$f(x)={\displaystyle \frac{2}{\pi }}\arctan x$$

(32)

For the maximum optimization-seeking saturation with a minimum and no maximum, its maximum is generally not explicitly limited, but it can be wrapped and quantized around 1 by using the segmentation function when it is larger than 1, which is expressed as formulated in Equation (33) below:

$$f(x)=\left\{\begin{array}{ll}x& x\le 0.99\\ {\displaystyle \frac{2}{\pi }}\arctan 65x& x>0.99\end{array}\right.$$

(33)

After classifying each sub-indicator of the comprehensive benefit evaluation indicator system of this multi-energy complementary off-grid system into the above three types, fuzzification processing is carried out by using the membership function $\mu (x)$, where $\mu (x)\in [0,1]$. Since the indicators are classified into two categories, benefit and cost, when the indicator $k$ in the evaluation index layer of the comprehensive benefit of this multi-energy complementary system belongs to the benefit-type indicator, the specific expression of the membership function $\mu (x)$ is formulated as in Equation (34):

$${\mu }_k\left(x\right)={\displaystyle \frac{f_{k,\min }-f_k\left(x\right)}{f_{k,\max }-f_{k,\min }}}$$

(34)

When the indicator $k$ in the evaluation indicator layer of the comprehensive benefits of this multi-energy complementary system belongs to the cost-type indicator, the specific expression of the membership function ${\mu }_k(x)$ is formulated as in Equation (35) below:

$${\mu }_k\left(x\right)={\displaystyle \frac{f_{k,\max }-f_k\left(x\right)}{f_{k,\max }-f_{k,\min }}}$$

(35)

where $f_{k,\min }$ is the minimum value of the evaluation indicator $k$, and $f_{k,\max }$ is the maximum value of the evaluation indicator $k$.

After obtaining $\mu (x)$, weighted summation can be performed to derive the optimization function of the indicators of the comprehensive benefit evaluation system of this multi-energy complementary off-grid system:

$$F_{\mathrm{CB}}=\max {\displaystyle \sum _k{G}_k{\mu }_k\left(x\right)}$$

(36)

where $G_k$ is the weighting coefficient of each indicator in the comprehensive benefit evaluation indicator system, and $G_k\ge 0$, ${\displaystyle \sum _k{G}_k}=1$ is satisfied.

3.4. Combination Weight Calculation Based on AHP and AEM

Based on the classification and quantification with the fuzzy algorithm to complete the normalization of the indicators, the subjective and objective weighting method is used to determine the combination of weights, and a multi-level indicator weighting model based on the hierarchical analysis anti-entropy weighting method is established to analyze the comprehensive benefits of multi-energy complementary off-grid systems. It lays the foundation for the subsequent comprehensive benefit evaluation.

We determine the combined weight coefficients of the two weights based on the AHP and AEM, which are calculated as formulated in Equation (37):

$$\left\{\begin{array}{l}{\epsilon }_i={\displaystyle \frac{{\omega }_i}{\left({\omega }_i+{\omega }_j\right)}}\\ {\delta }_i={\displaystyle \frac{{\omega }_j}{\left({\omega }_i+{\omega }_j\right)}}\end{array}\right.$$

(37)

where ${\epsilon }_i$ is the weighting coefficient of the AHP, and ${\delta }_i$ is the weighting coefficient of the AEM.

The final combination weight value ${{\omega }^{\prime }}_i$ is found through the combination calculation, which is formulated in Equation (38):

$${\omega }_i^{\prime }={\displaystyle \frac{{\epsilon }_i{\omega }_i+{\delta }_i{\omega }_j}{{\displaystyle \sum _{i=j=1}^n\left({\epsilon }_i{\omega }_i+{\delta }_i{\omega }_j\right)}}}, (i=j=1,2,\cdot \cdot \cdot ,n)$$

(38)

3.5. Comprehensive Evaluation Method Based on TOPSIS

The TOPSIS evaluation method [21] is often referred to as the ideal point method. In this paper, based on the values of the weights of the comprehensive benefit evaluation indicators of the multi-energy complementary off-grid system, the comprehensive benefits of each operation scheme of this objective are evaluated using the TOPSIS method [22]. The specific calculation flowchart is shown in Figure 3, and the detailed steps are as follows:

• Weight the standardized raw data of each evaluation indicator of the comprehensive benefit evaluation of the multi-energy complementary off-grid system to obtain the weighting matrix, which is formulated in Equation (39):

  $$R=\left(\begin{array}{cccc}{P}_{11}{\omega }_1& P_{12}{\omega }_2& \cdots & P_{1n}{\omega }_n\\ P_{21}{\omega }_1& P_{22}{\omega }_2& \cdots & P_{2n}{\omega }_n\\ \cdots & \cdots & \cdots & \cdots \\ P_{m1}{\omega }_1& P_{m2}{\omega }_2& \cdots & P_{mn}{\omega }_n\end{array}\right)=\left(\begin{array}{llll}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ r_{m1}& r_{m2}& \cdots & r_{mn}\end{array}\right)$$

  (39)

  where $P_{mn}$ is the standardized data of each evaluation indicator of the comprehensive benefit evaluation of the system; ${\omega }_n$ is the weight of the $n$th operation scheme; $n$ is the number of operation schemes of the multi-energy complementary off-grid system; and $m$ is the number of comprehensive benefit evaluation indicators of the multi-energy complementary off-grid system.
• Determine the positive and negative ideal points of the comprehensive benefit evaluation indicator of the multi-energy complementary off-grid-type system, as formulated in Equations (40) and (41):

  $$r_j^{+}=\left\{\left(\underset{1\le i\le m}{\max }{r}_{ij}\left|j\in J_1\right.\right),\left(\underset{1\le i\le m}{\min }{r}_{ij}\left|j\in J_2\right.\right)\left|j=1,2,\cdot \cdot \cdot ,n\right.\right\}$$

  (40)

  $$r_j^{-}=\left\{\left(\underset{1\le i\le m}{\min }{r}_{ij}\left|j\in J_1\right.\right),\left(\underset{1\le i\le m}{\max }{r}_{ij}\left|j\in J_2\right.\right)\left|j=1,2,\cdot \cdot \cdot ,n\right.\right\}$$

  (41)

  where $r_j^{+}$ is the set of positive ideal schemes; $r_j^{-}$ is the set of negative ideal schemes; $J_1$ is the set of benefit-based indicators; and $J_2$ is the set of cost-based indicators.
• Calculate the Euclidean distance, as formulated in Equations (42) and (43):

  $$d_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^n{\left(r_{ij}-r_j^{+}\right)}^2}}\left(i=1,2,\cdot \cdot \cdot ,m\right)$$

  (42)

  $$d_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^n{\left(r_{ij}-r_j^{-}\right)}^2}}\left(i=1,2,\cdot \cdot \cdot ,m\right)$$

  (43)

  where $d_i^{+}$ is the distance from the operating scheme to the positive ideal point, and $d_i^{-}$ is the distance from the operating scheme to the negative ideal point.
• Calculate the relative closeness of each operation scheme of the multi-energy complementary off-grid system. The specific formula is as follows (44):

  $$C_i={\displaystyle \frac{d_i^{-}}{d_i^{+}+d_i^{-}}}\left(i=1,2,\cdot \cdot \cdot ,m\right)$$

  (44)

  where $C_i$ is the relative closeness of each operating scheme and satisfies $0\le C_i\le 1$.

The relative closeness of each scheme is calculated using the above equation, and the optimal scheme for the comprehensive benefits is judged based on the relative closeness.

4. Results and Discussion

This section includes the case study and result presentation, as detailed below.

According to the comprehensive benefit evaluation indicator system of multi-energy complementary off-grid systems constructed above, a comprehensive benefit evaluation and a comparative analysis of the three different operation schemes given are carried out.

Operation Scheme 1: No wind, PV, or hydrogen storage equipment is involved in regulation, and only hydropower is operated separately, allowing hydropower to meet the system’s load demand as much as possible within certain constraints, thus reducing the amount of fossil energy purchased from outside the system.

Operation Scheme 2: This scheme involves hydro–wind–photovoltaic joint operation without adding hydrogen storage equipment. The double-layer capacity optimization allocation model constructed in this case does not have to consider the variables and constraints related to hydrogen storage equipment, and only the hydro–wind–photovoltaic constraints are included in the solution.

Operation Scheme 3: Hydropower plants are used as the basis for joint wind–solar-hydrogen storage operation, and capacity optimization is allocated based on a conventional dual-layer model.

4.1. Indicator Data Access

Based on the interrelationships of the indicators in the diagram of the comprehensive benefit evaluation indicator system of the multi-energy complementary off-grid-type system established in Figure 1 and Figure 2, a hierarchical structure of indicator evaluation is established. The nature of each indicator is analyzed in terms of costs and benefits with qualitative and quantitative aspects.

By reviewing relevant information and literature for analysis, the three operational schemes developed are organized and summarized, resulting in quantitative index data of the three operational schemes for the comprehensive benefit evaluation of the multi-energy complementary off-grid system, as shown in

Table 3. Quantitative indicator data for comprehensive benefit evaluation of multi-energy complementary off-grid system.

Name of Evaluation Indicator	Operation Scheme 1	Operation Scheme 3	Operation Scheme 3
Life cycle cost C1/CNY 10,000	68,015.4	76,974.1	77,162.4
Internal rate of return C2/%	7.25%	7.98%	8.91%
Period of investment recovery C3/year	14.5	13.9	13.1
Equivalent environmental cost C4/(CNY 10,000 /year)	22.56	24.67	28.94
Carbon dioxide emission reduction rate C5/(tons/year)	103,225.1	147,165.1	151,623.5
Clean energy consumption rate C7/%	90.1	95.3	99.4
Provide employment opportunities C11/person	52	58	64
Resident satisfaction C12/%	82.3	85.6	87.1

below:

The qualitative indicators are handled by inviting relevant industry experts to evaluate the qualitative indicators in accordance with the qualitative indicator evaluation criteria [23] shown in

Table 4. Qualitative evaluation indicator levels for comprehensive benefit evaluation of multi-energy complementary system.

Evaluation Grade	Score Range
Excellent	[90, 100]
Good	[75, 90)
Average	[60, 75)
Poor	[0, 60)

below, and we take the average value as the reference standard. The results of the scores of the qualitative evaluation indicators are shown in

Table 5. Qualitative indicator data for comprehensive benefit evaluation of multi-energy complementary off-grid system.

Name of Evaluation Indicator	Operation Scheme 1	Operation Scheme 2	Operation Scheme 3
Space occupancy C6	84.7	81.3	80.9
Power supply reliability of system C8	78.5	86.7	92.4
Electric power production safety C9	88.5	87.9	83.2
System operation flexibility C10	84.3	89.1	91.5
Lead development of local regional economic industry C13	87.4	89.6	90.7

below.

4.2. Calculation and Analysis of Comprehensive Benefit Evaluation Results Based on TOPSIS

The indicator data obtained to calculate the weighting matrix for the comprehensive benefit evaluation of the multi-energy complementary off-grid-type system are shown in

Table 6. Weighted matrix of TOPSIS comprehensive benefit evaluation indicator.

Name of Evaluation Indicator	Operation Scheme 1	Operation Scheme 2	Operation Scheme 3
Life cycle cost C1	0.0081	0.0084	0.0103
Internal rate of return C2	0.0095	0.0098	0.0114
Period of investment recovery C3	0.0673	0.0791	0.0842
Equivalent environmental cost C4	0.0064	0.0089	0.0095
Carbon dioxide emission reduction rate C5	0.0247	0.0278	0.0284
Space occupancy C6	0.0057	0.0043	0.0038
Clean energy consumption rate C7	0.0211	0.0225	0.0229
Power supply reliability of system C8	0.0235	0.0306	0.0384
Electric power production safety C9	0.0248	0.0224	0.0216
System operation flexibility C10	0.0146	0.0162	0.0217
Provide employment opportunities C11	0.0089	0.0094	0.0097
Resident satisfaction C12	0.0084	0.0092	0.0098
Lead development of local regional economic industry C13	0.0314	0.0356	0.0379

below:

We calculate the positive and negative ideal points for each indicator according to Equations (40) and (41), then use Equations (42) and (43) to calculate the Euclidean distance between each operating plan and the positive and negative ideal points, as shown in

Table 7. Euclidean distances from positive and negative ideal points for each operating scheme.

Name of the Operational Scheme	Euclidean Distance to the Positive Ideal Point	Euclidean Distance to the Negative Ideal Point
Operation Scheme 1	0.0314	0.0009
Operation Scheme 2	0.0267	0.0053
Operation Scheme 3	0.0016	0.0314

:

Based on Equation (44), the relative closeness of each operational scheme of the multi-energy complementary off-grid-type system is calculated as shown in

Table 8. Relative closeness of the operational schemes.

Name of the Operational Scheme	Relative Closeness Value	Sorted
Operation Scheme 1	0.2658	3
Operation Scheme 2	0.6374	2
Operation Scheme 3	0.8250	1

below:

From Table 7, it can be seen that the Euclidean distance to the positive ideal point for operation scheme 3 is 0.0016, the Euclidean distance to the negative ideal point is 0.0314, and the size of the calculated relative closeness is 0.8250, which is the largest among the three schemes, so the scheme has the best comprehensive benefit evaluation. Considering that operation scheme 3 is a combined operation, the utilization of hydrogen storage equipment can greatly improve the operational yield of the system as well as the clean energy consumption rate while suppressing the instability of the wind power and photovoltaic output. In this paper, the comprehensive benefits of the constructed multi-energy complementary off-grid system are evaluated from four perspectives: economic benefits, environmental benefits, technological reliability, and social benefits. The superiority of operation scheme 3 is verified, which shows that the joint operation has broad application prospects.

In addition, as the traditional indicator evaluation system is less involved in indicators of the power supply reliability of the system, electric power production safety, and resident satisfaction, under the background conditions of operation scheme 3, which is based on hydropower plants and operates together with combined wind–solar hydrogen storage, the expansion of the scale of production led to the peak load exceeding the designed capacity by 12%. In addition, regarding the traditional evaluation system, because of its focus on economic benefits and environmental benefits, considering that the cost of power generation did not rise significantly, the change in the value of the relative closeness was about 0.0013 under the solution method using the same combination of subjective and objective assignment based on the combination of the AHP and AEM, as well as the TOPSIS comprehensive evaluation method; this shows that there is short-term overloaded operation of the system compared to the normal operation of the system. The comprehensive evaluation results calculated by the traditional evaluation system did not change significantly, which shows that the traditional evaluation system is not sensitive to load demand changes; however, the evaluation system constructed in this paper takes into account the safety and reliability of off-grid system operation and the security of residents’ production and lives, and under the same background conditions, the relevant qualitative index scores plummeted, and the value of relative closeness changed to about 0.0071; it can be seen that compared with the traditional evaluation system, the evaluation system constructed in this paper provides an early warning of sensitivity to the changes in the load demand under off-grid conditions, which indicates that the constructed evaluation system has good practical application value.

5. Conclusions

(1) Considering the higher safety and reliability requirements of off-grid systems and the impact of their social benefits, this paper constructs a more perfect and comprehensive multi-level evaluation indicator system for analyzing the comprehensive benefits of multi-energy complementary off-grid systems.

(2) For the constructed evaluation indicator system, the subjective and objective weighting method combined with the AHP and AEM is utilized to determine the weights of each indicator, and a comprehensive benefit evaluation analysis of each operation scheme is carried out based on the TOPSIS method. Through example verification, it is found that the relative closeness values of operation schemes 1, 2, and 3 are 0.2658, 0.6374, and 0.8250, respectively. As the larger relative closeness in the TOPSIS method indicates the higher degree of closeness of the scheme to the ideal optimal solution, it is further verified that the proposed evaluation indicator system and multilevel evaluation method can more comprehensively evaluate and analyze the advantages and disadvantages of the multi-energy complementary off-grid system under different operation schemes, and at the same time, compared with the traditional evaluation indicator system, it is found that the constructed evaluation indicator system is able to provide better warnings as it has higher sensitivity to changes in load demand.

(3) For the evaluation dimension of social benefit in this paper, it is mainly reflected by some qualitative indicators. In future research, we will study more scientific quantitative methods to further improve it, and at the same time, we will also try to take into account the risks of the planning, operation, construction, and subsequent management of off-grid systems so as to further improve the value of its commercial application. In addition, in-depth research will be conducted on more appropriate comprehensive evaluation methods to make evaluations more reasonable and scientific.