Determination of Weights for the Integrated Energy System Assessment Index with Electrical Energy Substitution in the Dual Carbon Context

Abstract

Electrical energy substitution is an important way to achieve the optimization of the energy consumption structure as well as to alleviate environmental problems, and it is also an important source of benefits of the integrated energy system. However, there are few works that study the effects of electrical energy substitution on the construction of the integrated energy system (IES) and electrical energy substitution work without incentives carried out in the IES. To this end, this paper proposed a G1 method with constructing consistency matrix to determine the evaluation index weights for the IES with electrical energy substitution. Specifically, we firstly construct the evaluation index system for the IES including electrical energy substitution indicators, low-carbon indicators, technical indicators and economic indicators as well as their secondary indicators. Then, a tri-level evaluation index system of target-criteria-indicator benefits is established based on pertinent standards and norms, taking the practical operability into account. Finally, a G1-method-constructed consistency judgment matrix is proposed. Compared with the G1 method, it is simple and practical, and the weight calculation results are more in line with the reality, which effectively solves the consistency problem of the judgment matrix. The rationality and feasibility of the proposed weight calculation method are verified by the calculation and analysis of an example.

1. Introduction

Electricity has the advantages of cleanliness, safety and convenience. Implementing electrical energy substitution is of great significance for promoting the energy consumption revolution, implementing the national energy strategy, and promoting the development of energy cleanliness. This is also an important measure to increase the proportion of thermal coal, control the total consumption of coal and reduce air pollution [1]. Steadily promoting electrical energy substitution is conducive to the formation of a new electric power consumption market with higher composition levels and a wider scope, the expansion of electric power consumption scale, the improvement of China’s electrification level, the improvement of people’s quality of life, the development of related equipment in the manufacturing industry and the expansion of new economic growth points [2,3].

The integrated energy system (IES) is conducive to mitigating the effects of climate change by decarbonizing the energy system through technical and policy means [4], which has attracted wide attention from researchers. A bi-level optimal configuration strategy for a community-integrated energy system with coordinated planning and operation based on energy supply–demand responses and robustness adjustable scenarios is proposed in [5]. The work in [6] develops a low-carbon economic dispatch method for the IES to tackle the uncertainty of energy efficiency. A multi-time period optimal dispatching scheme for IES incorporating green certificate trading and carbon emission right trading is proposed in [7]. Current studies on IESs mainly focus on the planning, optimal operation and scheduling of IESs and the effects relevant policies have on IES operating costs and emission reductions; hence it is of great significance to comprehensively evaluate the benefit of an IES. To carry out the comprehensive evaluation of the integrated energy system (IES), one can quantify the advantages of IESs and achieve energy efficient utilization, reliable operation of the system and optimized resources disposition. Many scholars have researched the evaluation of the integrated energy system. The evaluation methodologies and performance assessment criteria for multi-energy systems were summarized in [8]. A novel evaluation framework for IESs based on the System-of-Systems approach for systems analysis coupled with an indicator-based approach for evaluation is presented in [9]. Some representative works are listed in

Table 1. The development of research in the evaluation index for IESs.

Ref.	Year	Evaluation Index	Weight Calculation Method	Method Strength
[10]	2009	economic, energetic, environmental	AHP and PROMETHEE	different evaluation methods may give different results
[11]	2012	energy, economic, environmental and integrated	-	a wise practice
[12]	2015	economic, energy consumption, environment	information entropy and expert assessment	objective and practical
[13]	2017	reliable energy supply, natural gas accommodation, peak-cutting and valley-filling, renewable overcapacity	-	-
[14]	2018	technology, economy, environment, society	rank correlation analysis and entropy information	simple and practical
[15]	2019	economic, reliability, renewable accommodation, environmental	Mixed Scatter-Monte Carlo sampling	high evaluation efficiency and effectively identify weaknesses in IES
[16]	2021	economic, load peak valley ratio, carbon emission	AHP and PROMETHEE	-
[17]	2022	economy, environmental protection, energy efficiency, reliability, technology	integrated the Best–worst Method and the CRITIC	excellent robustness and effective
[18]	2023	technology, economy, environment, society	TFN and AHP	intuitive and consistent with reality, and high data information utilization rate

, including the publication year, evaluation index and weight calculation method.

The above works evaluated IESs from the perspective of the economy, environment, technology, reliability, etc., especially in the context of carbon peaking and carbon neutrality, which are conductive to the decarbonizing and economic development of an IES. An evaluation index system from multiple dimensions of economy, environmental protection, energy efficiency, reliability and technology was proposed in [19], the case results proved the scientificity and effectiveness of the index system. A district energy evaluation index system was established in [20] using energy efficiency, the economy, and the environment; the results indicated the evaluation system had good maneuverability and could guide the optimization of the system. A comprehensive evaluation criteria system for an industrial park’s integrated energy system project from four aspects, namely economy, reliability, energy utilization, and environment was established in [21]. Case results indicated that the system contributes in selecting the most suitable alternative among multiple choices. However, existing studies did not take the benefit of electrical energy substitution carried out in the IES into account when evaluating. The authors of [22] established the quantitative calculation model of regional electrical energy substitution potential evaluation index system on the basis of considering the influencing factors and regional differences of electrical energy substitution potential, but did not relate them to IESs. Most of the research on electrical energy substitution is aimed at the benefits of typical equipment construction in large cities or rural areas to the power system. Few studies analyze the effect of integrated energy system construction in combination with electrical energy substitution work.

The method of calculating index weights of the IES directly affects the evaluation results of the IES; hence, it is crucial to choose an appropriate calculation method to calculate index weights for the evaluation of the IES. At present, the analytic hierarchy process (AHP) is widely used in the evaluation of the integrated energy system index system [10,16,18]. A combination of the AHP, entropy weight method and set pair analysis was used in [23] to evaluate the user-side IES planning scheme. The results indicated that the method can realize the optimization of multiple design schemes. The AHP-entropy weight method was used in [24] to calculate each index weight, and proved this method can improve the accuracy and scientificity of index weight. It is necessary to correct the inconsistent judgment matrix when using the AHP, and it is necessary to test until the consistency condition is met after the correction, which will increase the amount of calculation. Furthermore, too many modifications do not better reflect the intent of the decision maker. Hence, other scholars proposed the G1 method, which is utilized to determine the importance of each criterion through expert stratification to obtain subjective weight [25,26].

Inspired by the above-mentioned works, this paper aims at comprehensively evaluating IESs on the basis of the positive influence of electrical energy substitution on construction. Furthermore, the effect of an integrated energy system in the context of carbon peaking and carbon neutrality, and comprehensive details on economic, energy consumption, societal, reliability and environmental impacts are taken into account. This establishes an evaluation index system including electrical energy substitution index, low-carbon index, technical index and economic index and further calculates the weights of each index. Compared with the existing related research, the main contributions of this paper are as follows:

(1)

Electrical energy substitution is introduced to the industrial-park-integrated energy system and a correlated indicators model for electrical energy substitution is established.

(2)

A target-criteria-indicator tri-level index system is established taking the five influential factors of economy, energy consumption, society, reliability and environmental protection into account comprehensively.

(3)

The G1 method of constructing a consistency matrix is used to calculate the weights of the established index systems. Case studies indicates that compared with the G1 method, the weight acquired via the proposed method is more genuine.

The remainder of this article is structured as follows: Section 2 describes the model of the evaluation index for an IES. Section 3 presents the method of calculating the weight of indexes. Case studies and the results comparison are presented in Section 4. Section 5 summarizes the paper.

2. Integrated Energy System Evaluation Index

2.1. Integrated Energy System Structure

IESs can be divided into wide-area-level, regional-level and park-level energy systems [27], among which industrial parks include three parts: energy input, multi-energy coupling and energy utilization, and the key point of its research is the conversion, distribution and storage relationship between multiple energy sources. Through rational planning of coupling equipment configuration capacity, deep coupling and gradient-efficient utilization of energy can be realized. Thus, energy savings and emission reduction can be realized on the premise of meeting users’ energy demands and the balance of supply and demand of the system, so as to improve the utilization level of clean energy power.

IESs can promote multi-energy coupling and synergistic optimization, while solving the problem of clean energy consumption and making the energy consumption structure of the system more reasonable. The physical structure and energy coupling relationship of the industrial-park-integrated energy system constructed in this paper are shown in Figure 1. It can be observed from Figure 1 that in the park, load demands include electric, heat, natural gas and cold load. The electric load demand is supplied by distributed power generation, the combined heat and power (CHP) unit, the battery and the grid. The thermal load demand is supplied by the combined heat and power (CHP) unit and the heat storage tank. The natural gas load demand is supplied by the natural gas company. The cold load demand is supplied by the electric chillers. The CHP unit consumes natural gas to generate electric power and heat power coupling the electrical network, heating and natural gas network. Electric chillers couple the electric network and cold network via consuming electric power to generate cold power. Furthermore, it should be noted that as a flexible resource, the battery can change its operation mode according to the balance state of power supply and electric load demand, which is particularly conductive to accommodating renewable power.

2.2. Quantitative Model of Evaluation Indicators

In this paper, following the principles of scientific, comprehensive, independent, applicable and operable index construction, the evaluation index model is constructed from four aspects of electrical energy substitution.

2.2.1. Electrical Energy Substitution Indicators

The electrical energy substitution index represents the integrated energy system at the terminal electrification level, which is mainly reflected in the utilization rate of clean energy, the proportion of terminal electricity consumption, the effective substitution of electric power, the effective substitution of electrical energy, etc.

(1)

Comprehensive energy utilization rate ${\eta }_{ce}$ [28]: the ratio of the total energy used by the system to the total energy supplied.

$${\eta }_{ce}=\frac{E_{load}}{E_{in}}=\frac{E_e+{\beta }_h{Q}_h+{\beta }_c{Q}_c+{\beta }_g{Q}_g}{{\displaystyle \sum _{n=1}^{N_{DG}}{E}_{DG,n}}+\frac{E_{grid}}{1-\xi }+{\beta }_g{\displaystyle \sum _{j=1}^{J_e}{G}_{g,j}}}$$

(1)

where $E_{load}$ is the total system load, which is also the total energy used. $E_{in}$ is the sum of the energy input to the integrated energy system. $E_{grid}$ is the electricity purchased from the grid. $G_{g,j}$ is the amount of natural gas consumed by natural gas equipment J. $J_e$ is the number of gas-fired equipment. ${\beta }_g$ is the conversion factor for natural gas. $\xi$ is the network loss rate of the main network. $E_e$, $G_g$, $Q_c$ and $Q_h$ are the electrical, natural gas, cold and thermal loads of the system, respectively. ${\beta }_g$, ${\beta }_c$ and ${\beta }_h$ are the conversion factors of natural gas, cold and heat energy, respectively.

(2)

The proportion of clean energy supply ${\eta }_{DG}$ [29]: this reflects the system’s ability to consume new energy generation. Increasing the proportion of clean energy supply has an important impact on reducing energy costs, alleviating the problem of wind power and photovoltaic power curtailment, and reducing environmental pollution.

$${\eta }_{DG}=\frac{E_{DG}}{E_{in}}=\frac{{\displaystyle \sum _{i=1}^N{E}_{DG,i}}}{{\displaystyle \sum _{i=1}^N{E}_{DG,i}}+\frac{E_{grid}}{1-\zeta }+{\beta }_g{\displaystyle \sum _{j=1}^{J_e}{G}_{g,j}}}$$

(2)

(3)

The terminal electrical energy ratio ${\eta }_e$ [29]: there are various types of loads in the integrated energy system of the industrial park. As the application of electrical energy substitution equipment can be re-flected in the index of terminal energy proportion, the larger the index value, the higher the electrification level of the industrial park.

$${\eta }_e=\frac{E_e}{E_{load}}=\frac{E_e}{E_e+{\beta }_g{G}_g+{\beta }_c{Q}_c+{\beta }_h{Q}_h}$$

(3)

where $E_{load}$ is the total system load, which is also the total energy used. $E_e$, $G_g$, $Q_c$ and $Q_h$ are the electrical, natural gas, cold and thermal loads of the system, respectively. ${\beta }_g$, ${\beta }_c$ and ${\beta }_h$ are the conversion factors of natural gas, cold and heat energy, respectively.

(4)

Effective replacement power $E_{es}$ [29]: this is a visual reflection of the improvement of power consumption and optimization of the energy structure of the integrated energy system.

$$E_{es}=\alpha {\displaystyle \sum _{i=1}^M{E}_{es,i}}$$

(4)

where $E_{es,i}$ is the electricity replaced by the electrical energy substitution equipment in m. $\alpha$ is the percentage of clean energy generation; M is the total number of electrical energy substitution equipment pieces.

2.2.2. Low-Carbon Indicators

Thermal power generation is a major emitter of carbon dioxide, and in order to achieve carbon compliance and carbon neutrality, the power system reform must be carried out first. With the deterioration of the global environment and the impact of the energy crisis, low-carbon problem has become the focus. This paper selects three secondary indicators of energy consumption per unit of GDP, carbon dioxide emission reduction, and carbon dioxide capture, storage and utilization (CCUS) technology as low-carbon indicators.

(1)

Energy consumption per unit of GDP $C_{GDP}$: this is the main indicator reflecting the level of energy consumption and the status of energy saving and consumption reduction.

$$C_{GDP}=\frac{E_{total}}{GDP}$$

(5)

where $C_{GDP}$ is the consumption per unit of GDP, $E_{total}$ is the total primary energy consumption. Emissions of carbon dioxide will decrease as a result of lower primary energy consumption and lower energy consumption per unit of GDP.

(2)

Carbon dioxide emissions $Ec{o}_2$ [23]: this is obtained by summing the estimated amount of CO₂ emissions due to various energy consumptions.

$$Ec{o}_2=\frac{44}{12}{\displaystyle \sum _{\mathrm{i}=1}^n\left(A_i\times CC{F}_i\times H{E}_i\times CO{F}_i\right)}$$

(6)

where $\frac{44}{12}$ is the molecular weight ratio of carbon dioxide to C. $A_i$ is the actual consumption of different energy sources after the conversion of the standard coal factor. $CC{F}_i$ is the carbon content per unit calorific value of different energy sources. $H{E}_i$ is the heat content per unit of the corresponding energy source. $CO{F}_i$ is the carbon content share of different energy sources.

(3)

CCUS technology A: carbon dioxide emissions reduction per unit of power generation after adopting CCUS technology in the power system.

$$A=(Q_1+Q_2)\cdot C_h$$

(7)

where $Q_1$ and $Q_2$ are the carbon capture rate and utilization rate of CCUS technology, respectively, $C_h$ is the installed capacity of the generator set before replacement.

2.2.3. Technical Indicators

With the rapid development of industrial parks, the demand for comprehensive energy in society is increasing. Through the conversion of supply and demand and the cascade utilization of energy, the increment of energy efficiency can be realized, and the energy efficiency of the system can be maximized. The technical indicators correspond to the construction and operation effects of energy equipment configured in the planning scheme.

(1)

Relative energy saving rate ${\mu }_e$ [30]: this can reflect the energy consumption saved by the integrated energy system after the introduction of electrical energy substitution technology; the higher the relative energy saving rate, the better the result.

$${\mu }_e=\frac{P_f-P_1}{P_f}$$

(8)

where $P_f$ is the total energy consumption of the conventional integrated energy system. $P_1$ is the total energy consumption of the integrated energy system after the electrical energy substitution.

(2)

Energy storage allocation rate ε [30]: the total ratio of energy storage capacity connected to the grid to the total installed capacity of new energy.

$$\epsilon =\frac{{\displaystyle \sum _{a=1}^A{C}_a}}{P_{\mathrm{z}}}$$

(9)

where $C_a$ is the energy storage capacity of the energy source in a; $P_z$ is the total installed capacity of photovoltaic power 26708.6.

(3)

Load point failure rate ${\lambda }_z$ [31] is represented as follows:

$${\lambda }_z=\frac{N_z}{{\displaystyle \sum _{t=1}^{8760}{T}_{UZ}}}$$

(10)

where ${\lambda }_z$ is the number of outages caused by faults in the system at load point z per year, in units of times/year, $T_{UZ}$ is the time that load point z is under continuous operation, $N_z$ is the total number of outages at load point z.

(4)

Average annual power outage time $U_z$ [31] is represented as follows:

$$U_z=\frac{{\displaystyle \sum _{t=1}^{8760}{T}_{DZ}}}{{\displaystyle \sum _{t=1}^{8760}{T}_{DZ}}+{\displaystyle \sum _{t=1}^{8760}{T}_{UZ}}}$$

(11)

where $U_z$ denotes the sum of the time in hours/year that load point z is out of service due to a failure of the original system, $T_{DZ}$ denotes the time that load point z is in a continuous state of outage.

(5)

Average power supply availability [31] is described as follows:

$$ASAI=\frac{{\displaystyle \sum _{z\in G}8760\times N_z}-{\displaystyle \sum _{z\in G}{U}_z{N}_z}}{{\displaystyle \sum _{z\in G}8760\times N_z}}$$

(12)

where ASAI represents the ratio of the number of hours in the system in which the customer excludes outages per unit of time to the number of hours the customer needs to supply energy.

(6)

Expected value of system power shortage [31] is described by the following equation:

$$EENS=8760\times {\displaystyle \sum _{z\in G}{P}_{az}{U}_z}$$

(13)

where EENS is the amount of power supply per unit time in the system that the load does not receive after a customer outage due to a fault, the unit is kW$\cdot$h/year, $P_{az}$ represents the average load value of load point z.

2.2.4. Economic Indicators

The planning stage of the park-integrated energy system is characterized by the economic efficiency of the system in terms of the costs required in the process of construction and operation. Four indicators characterize the economy of system construction: initial investment construction cost, operation and maintenance cost, payback period and return of unit energy supply.

(1)

Initial investment construction cost [29]: the initial investment refers to the initial construction equipment investment of the park:

$$C_{inv}={\displaystyle \sum _{i=1}^{N_c}{c}_i^{inv}\cdot ca{p}_i}+{\displaystyle \sum _{j=1}^{N_s}{c}_j^{inv}\cdot E_j}$$

(14)

where $N_c$ is the number of energy conversion equipment units i. $c_i^{inv}$ is the unit capacity investment cost of energy conversion equipment. $N_s$ is the number of energy storage equipment units. $c_j^{inv}$ is the unit capacity investment cost of energy storage equipment j. $ca{p}_i$ is the configuration capacity of energy conversion equipment i. $E_j$ is the configuration capacity of energy storage equipment j.

(2)

Operation and maintenance cost [29]: the operation and maintenance cost include the energy consumption cost and equipment maintenance cost during the operation of the equipment.

$$C_{OP}={\displaystyle \sum _{y\in Y}{\displaystyle \sum _{l\in L}{\displaystyle \sum _{t\in T}{D}_l\cdot \left(c_t^E\cdot P_{y,l,t}^{SYS}+c_t^G\cdot G_{y,l,t}^{SYS}\right)}}}$$

(15)

$$C_{MA}={\displaystyle \sum _{y\in Y}{\displaystyle \sum _{l\in L}{\displaystyle \sum _{t\in T}{D}_l\cdot \left(\begin{array}{l}{c}_{BAT}^{MA}\cdot \left|P_{y,l,t}^{BAT}\right|+c_{HS}^{MA}\cdot \left|S_{y,l,t}^{HS}\right|\\ +c_{CS}^{MA}\cdot \left|C_{y,l,t}^{CS}\right|+{\displaystyle \sum _{m=1}^{M_{eq}}{c}_{eq,m}^{MA}{P}_{y,l,t}^{eq,m}}\end{array}\right)}}}$$

(16)

where $C_{OP}$ is the operating cost of the system. $C_{MA}$ is the maintenance cost of the system. $D_l$ is the annual duration of the equipment operation days. $c_t^E$ and $c_t^G$ are the unit prices of electricity and natural gas at time t, respectively. $c_{BAT}^{MA}$, $c_{HS}^{MA}$ and $c_{CS}^{MA}$ are the unit maintenance costs of electric, thermal and cold energy storage equipment, respectively. $P_{y,l,t}^{BAT}$, $S_{y,l,t}^{HS}$ and $C_{y,l,t}^{CS}$ are the operating powers of electric, thermal and cold energy storage equipment, respectively. $c_{eq,m}^{MA}$ and $P_{y,l,t}^{eq,m}$ are the unit maintenance cost and operating power of energy conversion device m, respectively.

(3)

Income index of unit energy supply [32]: the revenue per unit of energy supply is the ratio of the system revenue from the sale of electricity, heat and cooling to the system’s supply of electricity, heat and cooling energy to customers.

$$A=\frac{S_e+S_h+S_c}{Q_{ele}+Q_{hot}+Q_{cold}}$$

(17)

where $S_e$ is the revenue from electricity sales. $S_h$ is the revenue from heat sales. $S_c$ is the revenue from cooling sales.

(4)

Investment payback period [30]: the payback period is the time required to make the accumulated economic benefits equal to the initial investment cost. The payback period is the number of years to recover the investment through the return flow of funds. In general, the shorter the payback period time, the more profitable the project will be.

$$T_p=m-1+\frac{\left|F_l\right|}{F_m}$$

(18)

where m is the year when the cumulative net cash flow is zero or positive for the first time, F is cumulative net cash flow of last year and $F_m$ is net cash flow of the year. In practice, the construction time of electrical energy substitution projects is shorter and the use time is longer; currently, China’s electrical energy substitution projects are still in the development stage, and the benchmark payback period in the electric power industry is generally set to 10 years. If the payback period of a certain electrical energy substitution project is less than 10 years, the profit of the project is still good.

3. Indicator Weight Calculation Method

3.1. G1 Method

(1)

Determine the order relationship of indicators.

The experts rank the indicator set $\left\{A_1,A_2,A_3,\cdots A_n\right\}$ according to its importance as a criterion from highest to lowest $A_1^{*}>A_2^{*}>A_3^{*}>\cdots >A_n^{*}$, denoted as $A_i^{*}>A_j^{*}$, where $A_i$ indicates that the importance of the evaluation indicator relative to a criterion is greater than or equal to $A_j$.

(2)

The importance of adjacent indicators is assigned.

The relative importance between two adjacent indicators, $A_i^{*}$ and $A_{i+1}^{*}$, is denoted by Equation (19)

$$r_k=\frac{{\omega }_i}{{\omega }_{i+1}}$$

(19)

where ${\omega }_i$ and ${\omega }_{i+1}$ are the weight of indicators i and i + 1, respectively.

The indicator weights are unknown before calculation, but $r_k$ can give the results by expert evaluation of the importance of the two indicators, and the relative importance of the indicators $r_k$ is shown in

Table 2. Relative importance of two adjacent indicators.

${\mathit{r}}_{\mathit{k}}$	Explanation
1.0	Indicator $A_{k-1}$ has the same importance as indicator $A_k$
1.1	Indicator $A_{k-1}$ and $A_k$ are between equally important and marginally important
1.2	Indicator $A_{k-1}$ is slightly more important than indicator $A_k$
1.3	Indicator $A_{k-1}$ and $A_k$ are between slightly important and relatively important
1.4	Indicator $A_{k-1}$ is very important compared to indicator $A_k$
1.5	Indicator $A_{k-1}$ and $A_k$ are between relatively important and very important
1.6	Indicator $A_{k-1}$ is more important than indicator $A_k$
1.7	Indicator $A_{k-1}$ is extremely important compared to indicator $A_k$
1.8	Indicator $A_{k-1}$ and $A_k$ are between more important and extremely important

.

(3)

Calculate the weights of the indicator set.

According to Equation (19), on the basis of the relative importance between two adjacent indicators, we have the following:

$${\displaystyle \prod _{i=k}^n{r}_i}=\frac{{\omega }_{k-1}}{{\omega }_k}\frac{{\omega }_k}{{\omega }_{k+1}}\cdots \frac{{\omega }_{n-2}}{{\omega }_{n-1}}\frac{{\omega }_{n-1}}{{\omega }_n},k\ge 2$$

(20)

$${\displaystyle \sum _{k=2}^n\left({\displaystyle \prod _{i=k}^n{r}_i}\right)}={\displaystyle \sum _{k=2}^n\frac{{\omega }_{k-1}}{{\omega }_n}}$$

(21)

Since the sum of the weights of all indicators in the indicator set is 1, from Equation (21) and ${\displaystyle \sum _{k=1}^n{\omega }_k}=1$:

$$1+{\displaystyle \sum _{k=2}^n\left({\displaystyle \prod _{i=k}^n{r}_i}\right)}=1+{\displaystyle \sum _{k=2}^n\frac{{\omega }_{k-1}}{{\omega }_n}}=\frac{{\omega }_n}{{\omega }_n}+{\displaystyle \sum _{k=2}^n\frac{{\omega }_{k-1}}{{\omega }_n}}=\frac{1}{{\omega }_n}{\displaystyle \sum _{k=1}^n{\omega }_k}=\frac{1}{{\omega }_n}$$

(22)

According to Equation (23), by first calculating the weight ω_n of the last indicator, the weights of the remaining other indicators can be derived from Equation (20). The index weight coefficients are obtained directly from the G1 method as follows:

$${\omega }_n={\left[1+{\displaystyle \sum _{k=2}^n\left({\displaystyle \prod _{i=k}^n{r}_i}\right)}\right]}^{-1}$$

(23)

$${\omega }_{k-1}=r_k{\omega }_k$$

(24)

3.2. G1 Method for Constructing the Consistency Matrix

The elements of each row of the judgment matrix represent the expert’s judgment on the relative importance of each level of indicators, which is expressed using numbers and written in matrix form. By analyzing the values of the matrix, it is possible to derive an ordinal relationship between the relative importance of indicators in each row of the matrix; this ordinal relationship is denoted by $S_i$.

Regarding analysis of the n sequential relations obtained from the initial judgment matrix, if the sorting results of the n sequential relations are consistent it is possible to construct a consistent judgment matrix. If the sorting results of the n sequential relations are inconsistent, the constructed judgment matrix must be an inconsistent matrix.

If the judgment matrix is inconsistent, the expert needs to rethink the judgment given by the indicator, find out the inaccuracy of the judgment given the reason and establish the final sequential relationship. Then, one can construct the consistency judgment matrix according to the final sequential relationship. There are n-1 independent elements (excluding diagonal elements) located in different rows and columns in the consistency judgment matrix, and other elements can be represented by a combination of n-1 independent elements.

Based on the final sequential relations given by the above experts, the consistency matrix is constructed as follows.

$$x_1\ge x_2\ge x_3\ge \cdots \ge x_n$$

(25)

Let the rational judgments of experts re-giving the ratio of the importance of evaluation indicators A and B, respectively, C, as follows.

$${\omega }_{l-1}/{\omega }_l=r_l$$

(26)

A is the weight coefficient corresponding to indicator B. The above Equation (27) represents the ratio of judgments between two neighboring indicators in the sequential relation, that is, between two indicators with the smallest degree of relative importance difference, so it can fully reflect the subtle judgments of experts and make the other judgments obtained through these ratios more accurate. After giving all n − 1 ratio judgments (i.e., own ratio is 1), the values of all other elements in the judgment matrix can be obtained proportionally by independent elements. For indicators (i < j; i, j = 1,2,..., n) the relationship is as follows.

$$\widetilde{a_{ij}}=\frac{{\omega }_i}{{\omega }_j}={\displaystyle \prod _{l=i+1}^j{r}_l}\left(l=2,3,\dots ,n\right)$$

(27)

$$\widetilde{a_{ij}}=\frac{1}{\widetilde{a_{ji}}}$$

(28)

The consistency matrix can be constructed from the above formula. Through the above calculation method, the final order relationship between indicators is analyzed and established, and the consistency matrix is constructed. According to the properties of the constructed consistency matrix column, for each column element, the weight coefficient of the indicator is

$${\omega }_j=\frac{1}{{\displaystyle \sum _{j=1}^n{a}_{ij}}}$$

(29)

4. Main Results: Case Study

In order to verify the reasonableness of the index system of the integrated energy system and the method of determining index weights proposed in this paper, an industrial park in Yunnan Province was selected for the comprehensive implementation of electrical energy substitution work for experimental analysis. the parameters of the indicators can be found in [32] but others are from Yunnan Power Grid Co, Ltd. that are not publicly available due to privacy, and the index weights were determined by the G1 method and the G1 method of constructing a consistency matrix, respectively.

Table 3. Index name and its nomenclature.

Indicator		Nomenclature
Secondary indicator	Electricity substitution indicators	$U_1$
	Low-Carbon Indicators	$U_2$
	Technical Indicators	$U_3$
	Economic Indicators	$U_4$
Three-level indicator	Comprehensive energy utilization rate	$I_1$
	The proportion of clean energy supply	$I_2$
	The terminal electrical energy ratio	$I_3$
	Effective replacement power	$I_4$
	Energy consumption per unit of GDP	$I_5$
	Carbon dioxide emissions	$I_6$
	CCUS technology	$I_7$
	Relative energy saving rate	$I_8$
	Energy storage allocation rate	$I_9$
	Load point failure rate	$I_{10}$
	Average annual power outage time	$I_{11}$
	Average power supply availability	$I_{12}$
	Expected value of system power shortage	$I_{13}$
	Initial investment construction cost	$I_{14}$
	Operation and maintenance cost	$I_{15}$
	Income index of unit energy supply	$I_{16}$
	Investment payback period	$I_{17}$

presents the index name and its nomenclature.

A questionnaire was used to invite six experts (three professors from university and three engineers from the energy industry) with different professional backgrounds to rank the importance of each indicator in the above index system from multiple perspectives and in all directions.

4.1. Index Weights Determined by the G1 Method for Constructing a Consistency Matrix

(1)

Secondary indicator

The secondary indicator includes electrical energy substitution indicators, low-carbon indicators, reliability indicators, and economic indicators. The final sequential relationship is determined according to the joint deliberation of five experts: U₃ ≥ U₁ ≥ U₂ ≥ U₄. At the same time, the importance ratio between the two adjacent indicators after re-comparing is given as follows: I₃₁ = 2, I₁₂ = 1, I₂₄ = 2.

According to the scoring conditions of the nine-level scale method, the judgment matrix of the first-level indicators is derived as

$$C=\left[\begin{array}{llll}1& 1& 1& 1\\ 1& 1& 1/2& 2\\ 2& 2& 1& 4\\ 1/2& 1/2& 1/4& 1\end{array}\right]$$

The obtained weights of each indicator are

$$U_1=0.2222,U_2=0.2657,U_3=0.4155,U_4=0.1347$$

(2)

Three-level indicator

The electrical energy substitution indicator sequence relationship is I₂ ≥ I₄ ≥ I₁ ≥ I₃. The importance ratio between its two adjacent indicators is I_2–4 = 2, I_4–1 = 3, I_1–3 = 1. In turn, the other elements of the judgment matrix are derived, from which the weights of the electrical energy substitution indicators are calculated:

W₁ = [0.1538,0.3529,0.1538,0.2727]

The low-carbon indicator sequence relationship is I₆ $\ge$ I₇ $\ge$ I₅. The importance ratio between its two adjacent indicators is I_6–7 = 1, I_7–5 = 2. In turn, the other elements of the judgment matrix are found, and then the weights of each indicator are found:

W₂ = [0.2,0.4,0.4]

The technical indicators sequence relationship is I₉ > I₁₀ > I₁₃ > I₈ > I₁₁ > I₁₂. The importance ratio between its two adjacent indicators is I_9–10 = 1, I_10–13 = 1, I_13–8 = 1, I_8–11 = 2, I_11–12 = 2. In turn, the other elements of the judgment matrix are derived, from which the weights of each indicator are found:

W₃ = [0.2105,0.2105,0.2105,0.2105,0.105,0.075,0.2105]

The sequential relationship of economic indicators is I₁₇ $\ge$ I₁₄ $\ge$ I₁₆ $\ge$ I₁₅. The importance ratio between its two adjacent indicators is I_17–14 = 2, I_14–16 = 1, I_16–15 = 2. In turn, the other elements of the judgment matrix are derived, from which the weights of each indicator are found:

W₄ = [0.222,0.111,0.222,0.444]

From the initial weights of the criterion layer and the initial weights of the scheme layer, the single ranking of the constructed consistency matrix can be derived, and based on this, the total ranking is calculated.

4.2. Comparison of Calculation Results for Both Methods

Figure 2 depicts the weights of secondary indicators (namely criteria layer) calculated by the G1 method and the G1 method used for constructing a consistency judgment matrix. It can be observed that the weight ranking of secondary indicators calculated by both methods is U₃ ≥ U₂ ≥ U₁ ≥ U₄, which indicated that according to experts’ willingness, technical indicators are the most critical in the process of comprehensively evaluating IESs. In this paper, technical indicators include relative energy saving rate, energy storage allocation rate, load point failure rate, average annual power outage time, average power supply availability and expected value of system power shortage, which fully demonstrates that the reliability of IESs should be given more attention. It also can be observed that compared with the G1 method, the weight of each indicator determined by the G1-method-constructed consistency judgment matrix is bigger. Comprehensively taking the sequential relationship and the relative importance between the two adjacent indicators of secondary indicators into account, the weight of each index determined by the G1 method’s constructed consistency matrix is more reasonable. It also can be observed from Figure 2 that for the criterion layer, the weights of low carbon and reliability criteria are higher, both of which exceed 25%. This is because there are indicators with larger weights under the above two criteria, and the number of subordinate indicators of reliability is large. The electrical energy substitution index takes the second place, and it is also an important factor affecting the benefit of the construction for IESs. The results of index weight show that the integrated energy construction should be dominated by reliability, focusing on environmental protection and energy, and can accelerate the construction of energy-saving and eco-friendly systems at the expense of proper economic benefits.

Figure 3 shows three-level indicators weight calculation results of the two methods. It can be found that the index weights determined by the G1 method and the G1 method with constructing consistency matrix are similar, which indicates that the results calculated by both methods are essentially the same given the same experts’ willingness. Among the index weights calculated by the two methods, the largest different index is I4, namely effective replacement power, the absolute error of the weight is 0.012, and the relative error is 0.14, respectively. According to the analysis of the relative importance among the indicators, the weights obtained by using the G1 method with constructing consistency matrix are more consistent with reality. For the index layer, the weights of most indicators are concentrated between 6% and 8%, the values are relatively average and there are no obvious important indicators. Among them, the proportion of clean energy supply, carbon dioxide emissions, relative energy-saving rate, average power supply availability and CCUS technology have higher weights. The average annual power outage time, operation and maintenance cost and comprehensive energy utilization rate have low weights, and their subjective weights are low, which indicates the experts believe that these three indicators have little impact on the benefits and have low relative importance. The subordinate indicators of low-carbon and technical guidelines are the most important indicators for experts with subjective empowerment exceeding 7%. Based on the above analysis, compared with the G1 method, the G1 method with constructing consistency matrix can better reflect the wishes of experts, and is more reasonable when calculating the weight of the index.

5. Conclusions

At present, there are few studies on the implementation of electrical energy substitution devices into IESs, and it is impossible to analyze the benefits and optimization results of integrated energy systems with electrical energy substitution as the core. Aiming at this problem, this paper established an evaluation index system of integrated energy systems with electrical energy substitution, and the G1 method with constructing consistency matrix is proposed to determine the indexes’ weights. Through example verification, the following conclusions are obtained.

(1)

Compared with the G1 method, the weight of each index in the proposed index system determined by the G1 method and a constructed consistency matrix is more reasonable and more consistent with reality. Moreover, the proposed method is convenient and fast to determine the weight coefficients of indexes.

(2)

On the basis of ensuring reliability, IESs should build a green consumption model with clean energy on the source side and electrical energy on the user side, promote the implementation of an electrical energy substitution strategy and CCUS technology to reduce carbon dioxide emissions, and realize the configuration and optimization of different types of energy through technical performance to improve energy utilization.