Research on multi-objective planning method for comprehensive energy system based on optimal weight analysis

A method for determining the optimal target weight by using a fuzzy membership function is proposed to address the subjectivity of target weight selection. This method first establishes the planning objectives and constraints of the comprehensive energy system and linearizes the nonlinear model based on the Big-M method. Then, multiple objectives are given weights and transformed into a single objective to obtain a target solution set composed of different weights. Based on this, a fuzzy membership function is proposed to determine the optimal weight of the objective and determine the maximum comprehensive satisfaction solution. The example results verify the feasibility of this method.


Introduction
Integrated energy system planning requires both economic and environmental objectives.At present, the heuristic algorithm is often used to solve multi-objective programming of integrated energy systems.In [1], particle swarm optimization was used to solve the problem of renewable microgrid configuration in order to solve the optimal unit capacity.In [2], the particle swarm optimization algorithm was used to solve the economic scheduling problem of cogeneration units to obtain the optimal power and heat source output.In [3], an improved epsilon-constraint algorithm was used to solve the multi-objective extended programming model of the electric-gas interconnection integrated energy system, and the optimal planning scheme was selected by fuzzy decision-making.Although the heuristic algorithm has strong adaptability and low requirements on the model, it has problems with convergence time and unstable calculation results [4].
Some scholars convert the multi-objective programming model into single-objective programming and then solve it.In [5], the gray Wolf algorithm and Pareto front-end thought were used to transform the multi-objective programming into the single-objective programming model.However, it is difficult for the Pareto method to scientifically and effectively determine the weights between objective functions 2 with different dimensions [6].Based on the above problems, this paper presents a method to determine the optimal target weight by using the fuzzy membership function.Firstly, the objective and constraint conditions of integrated energy system planning are established.Then the multi-objective is transformed into a single objective by giving weight to it, and the target solution set composed of different weights is obtained by using the Cplex solver.Finally, the fuzzy membership function is used to determine the optimal weight of the target, and then the maximum solution of comprehensive satisfaction is determined.

Objective function
The objective function is established with economy and carbon emission as targets respectively.

Economic objective
The goal is to minimize the sum of the investment and construction, operation and maintenance, power and gas purchase, and carbon transaction costs of the whole life cycle equipment in a typical scenario of an integrated energy system [7].The expression of the total cost is as follows: ( ) where Finv is the cost of equipment investment and construction, including the investment cost of various coupling equipment; Fom is equipment operation and maintenance cost; Fbuy is the cost of purchasing electricity and natural gas; Ftra is the stepped carbon trading cost.

Carbon Emission Objective
The goal is to minimize the sum of carbon dioxide emissions in the whole life cycle of new energy unit power generation, gas consumption capacity of the gas unit and power purchase process [8], and the target expression of carbon emissions is as follows: where Y is the planned operating period of the system; D is the number of typical scenarios; d  is the day of the d typical scenario; EIES,a,t is the total carbon emissions of the system at time t.

Constraint condition
The constraint conditions of integrated energy systems mainly include energy balance constraints and operation constraints of coupling equipment.

Energy balance constraint
In the operation process, energy balance constraints should be met to ensure that the supply meets the energy consumption of the terminal load and the operation of the coupled equipment, including the relevant constraints of four kinds of energy: electricity, heat, cold, and gas [9].The relevant expression is as follows: where Pe,buy,t is the power purchased at time t; PWT,t, PPV,t, and PGT,t are respectively the output power of Wind Turbine (WT), photovoltaic (PV), and Gas Turbine (GT) at time t; Psto,t and Pdis,t are the power supply and discharge power of the energy storage device at time t; PL,t , QL,t , and CL,t correspond to the electric load, hot load and cold load at  respectively.

Coupling device operation constraints.
In addition to energy balance constraints, inequality constraints such as output and slope climbing must be satisfied during the operation of the coupled equipment in the system.The operating constraints of the equipment are analyzed as follows.
Operation constraints of new energy units: The operating constraints of new energy units mainly include the upper limit of the generating power of the unit itself and the maximum power at the corresponding time in typical scenarios, the expression as follows: where PPW,max is the upper limit of WT or PV power generation; PPW,d,t is the maximum power at the corresponding moment of the d-th typical scenario of the Wind Turbine unit or photovoltaic unit.
Operating constraints of gas units: GT and Gas Boiler (GB) operation constraints include unit output and climbing constraints.The expression is as follows: , , where GGBT,max is the upper limit of input power of GT or GB; DGGBT,min is the lower climbing limit of GT or GB; DGGBT,max indicates the climbing upper limit of GT or GB.Operation constraint of refrigeration equipment: The operating constraints of the Absorbent Chiller (AC) and Electric Chiller (EC) include unit output and climb constraints, and the constraint expression is similar to that of gas units.
Operation constraint of energy storage equipment: The charging and discharging power of the energy storage device is limited by the storage capacity of the device itself and the upper limit of the charging and discharging power, and the device cannot charge and discharge at the same time.The expression is as follows: ,min , ,max j j j t j j S W W S W  , , , , , 0 j sto t j sto t j sto j , , , , , 0 where j refers to an energy storage device; Sj,min and Sj,max are the proportion of minimum and maximum stored energy of the energy storage device, respectively; Wj,t is the energy stored by the energy storage device at time t; Pj,sto,t and Pj,dis,t are the energy storage and discharge power of the energy storage device at time t respectively; Bj,sto,t and Bj,dis,t are 0-1 variables, Bj,sto,t=1 when the device is storing energy and Bj,dis,t=1 when it is releasing energy; Kj,sto and Kj,dis are the maximum upper limit ratio of energy storage and energy discharge of the energy storage device respectively.

Determining multi-objective optimal solutions
To avoid the influence of artificial weight selection on the planning results, this paper proposes to use the fuzzy membership function to screen the solution with the highest comprehensive satisfaction from the solution set composed of different weight planning results [10].The expression is as follows: ( ) ,max , ,max ,min where μhi is the satisfaction of the h-th weight corresponding to the planning result and the i-th planning objective; Fi(Φh) is the planning result; Fi,max and Fi,min are the maximum and minimum values of the ith planning target results respectively; μh is the comprehensive satisfaction of the h-th planning result to all planning objectives; H is the number of weights to be selected; L is the number of objectives, and the value of this paper is 2.

Multi-objective planning optimization process of the integrated energy system
The planning process of the integrated energy system includes the identification of typical scenarios on both sides of source and load, construction of objective functions and constraints, linearization of the model, assignment of different weights to the objectives to solve, determination of the optimal solution, and analysis of the planning results.The relevant process is shown in Figure 1.

Example analysis
Taking an industrial park as an example, a 10-year system planning case analysis was carried out according to the flow chart in Figure 1 to verify the feasibility of the proposed method.The parameters of integrated energy system coupling equipment are shown in Table 1, and the parameters of energy storage equipment are shown in Table 2.The electricity price is based on the time-of-use electricity price.In addition, the price of natural gas is 0.3 yuan/kWh, the basic price of carbon trading is 0.1 yuan/kg, and the price growth rate is 20%.

Typical scene identification
Four typical wind turbine and photovoltaic unit output scenarios are selected in spring, summer, autumn and winter, as shown in Figure 2 and Figure 3 respectively.Based on 4 typical scenarios, this paper studies multi-objective planning of integrated energy systems and obtains the results of weight and planning objectives.

Weight selection and planning target results
The multi-objective programming process, which uses the fuzzy membership function to determine the optimal object weight, is used to select the weight and solve the object.The corresponding interval range of target weights is [0, 1], the interval length of 0.025 is used to assign different weights to economic goals and carbon emission goals, and 41 sets of solutions for planning cost and carbon emission goals are obtained.The solution set is shown in Figure 4, and the satisfaction of different weights on all results is shown in Figure 5.As can be seen from Figure 4, in the weight [0, 1] range, the cost of the planning model ranges from 1.36×10 8 yuan to 1.63×10 8 yuan.The carbon emission range is 1.29×10 8 kg~1.36×10 8 kg.When the economic cost weight decreases from 1 to 0, the planning cost gradually increases and the carbon emission gradually decreases.It is difficult to meet the requirements of low cost and low carbon emissions at the same time.As can be seen from Figure 5, for the 0.025 coefficient interval and 0.05 coefficient interval, when the carbon emission weight is 0.8, the comprehensive satisfaction value obtained is the largest.Therefore, the carbon emission target weight is 0.8, and the economic target weight is 0.2 as a compromise solution, wherein the total planning cost is 1.37362×10 8 yuan and the total carbon emission is 1.305×10 8 kg.

Conclusions
This paper proposes a method to determine the optimal objective weight by using the fuzzy membership function and constructs a multi-objective programming process for the integrated energy system.First, the objective function and constraint conditions are determined, then different weights to each objective are assigned to solve, and finally, the most weight and optimal solution are determined.Combined with the actual calculation example, the method is verified.The results show that by assigning weights to multiple objectives, transforming them into a single-objective programming model, and using the fuzzy membership function to determine the optimal solution, the subjectivity of weight selection in traditional methods is avoided, and the scientific nature of weight assignment is guaranteed.Finally, through a numerical example, the feasibility of obtaining the target solution by using the optimal target weight method proposed in this paper is verified.

start
Build an integrated energy system planning model, including objective functions and decision variables Assign different target weights to solve Determining the Optimal Solution by Fuzzy Membership Function Analyze planning results Finish Big-M method model linearization

Figure 1 .
Figure 1.Flowchart of multi-objective planning for integrated energy system.

Figure 2 .Figure 3 .
Figure 2. Typical daily data of wind Turbine output

Figure 4 .
Figure 4. Programming model cost and carbon emissions under different weights.

Table 2 .
Parameters of Energy Storage Equipment.