Optimization Configuration of Distributed Multi-Energy Complementary Energy Systems

This paper points out the uncertainty of existing optimization models due to factors such as environmental and equipment output, which have a significant impact on the accuracy and rationality of system planning. Therefore, this paper establishes a full-working-condition-mathematical model for distributed multi-energy complementary energy systems and constructs an optimization configuration mathematical model with the total annual cost of the system as the optimization objective. Subsequently, an energy supply equipment optimization configuration method for distributed multi-energy complementary energy systems is proposed. Finally, the effectiveness of the proposed optimization configuration method is verified through case studies. This research will have important guiding significance for the construction and operation of distributed multi-energy complementary energy systems.


Introduction
With the continuous development of renewable energy and energy storage technologies, efficient utilization of energy and overall improvement of the power system can be achieved by using these new energy technologies [1].Distributed multi-energy complementary energy systems, as a coupling system that integrates multiple types of energy such as electricity, gas, heating, and cooling, is a feasible solution for achieving the goals and is also a promising development path for modern power systems [2][3].
There have been studies on the optimization configuration for distributed multi-energy complementary energy systems.[4] proposed an Emission operational strategy for a cooling, heating, and power systems integrated energy system, which reduced CO 2 emissions compared to the primary energy operational strategy, but did not integrate the natural gas network into the research object in the target system.[5] introduced the main features, modelling methods, and evaluation indicators of multienergy coupling systems.[6] proposed an optimized scheduling model for a comprehensive energy system with combined cooling, heating, and electric energy supply, wind power, and integrated natural gas system safety constraints into the optimization scheduling strategy.[7] took a multi-energy coupling system considering renewable energy consumption as the research object and proposed a two-stage mixed integer planning method to achieve joint optimization of equipment selection and capacity configuration in the multi-energy systems.[8] established a Bi-level optimal planning model for an electric-hydrogen multi-energy coupling system with the upper and lower targets of optimal system configuration cost and hydrogen cost, and achieved optimal equipment configuration based on the optimal hydrogen supply price.
The researches were based on ideal energy usage scenarios under ideal conditions for energy system optimal configuration.However, the optimization model based on ideal conditions is not accurate enough due to the impact of environmental and equipment output, which has a significant impact on the accuracy and rationality of system planning.This paper focuses on distributed multi-energy complementary energy systems and establishes a full-working-condition mathematical model for the system's main equipment.On this basis, a full-working-condition mathematical modelling of distributed multi-energy complementary energy systems is conducted.Secondly, an optimization configuration mathematical model is constructed with the objective of the total annual cost of the system, and an energy supply equipment optimization configuration method of distributed multi-energy complementary system is proposed.Finally, the effectiveness of the optimization configuration method is verified through case studies.

Full Working Condition Models
A distributed multi-energy complementary energy system is an energy conversion and supply system that is based on the concept of cascade energy utilization and is set up near users to provide electricity as well as heating and cooling functions.It utilizes equipment such as gas turbines and gas engines that run on natural gas to generate electricity.The waste heating contained in the high-temperature flue gas emitted by this equipment is recovered and utilized for winter heating and to drive equipment such as absorption refrigerators for summer cooling.In addition to the main equipment mentioned above, auxiliary equipment such as electric chiller machines, gas boilers, and energy storage equipment are generally equipped to increase the stability and reliability of the system's energy supply.The typical structure of a distributed multi-energy complementary energy system is shown in Figure 1.

Gas generator
The gas generator is the core component for implementing tri-generation of cooling, heating, and power.Commonly used gas generators include gas turbines, microturbines Stirling engines, fuel cells, etc.Among them, the mathematical models and constraints of the gas engine and the gas turbine are as follows: GT GT GT e e g GT GT GT h h g The power generation efficiency and heat production efficiency of the gas generator are related to the PLR, ambient temperature, and local altitude.Under standard conditions, the relationship between the power generation efficiency and heat production efficiency of the gas generator is commonly expressed by the following functions: in Equations ( 3) and ( 4), ( ) ( ) GT f t are the PLR of the gas engine and the gas turbine.

Gas boiler
As gas boilers operate efficiently and stably, it is generally assumed that their operating efficiency remains constant under partial load, i.e., the heat output and input energy (consumed fuel chemical energy) maintain a linear relationship.The energy supply mathematical model can be represented as: The mathematical model of a gas boiler mainly refers to the changes in its heating efficiency with different load ratios (heat supply).

Waste heat boiler
The mathematical model of the waste heat boiler can be expressed as follows: The mathematical model indicates that the full working conditions of the waste heat boiler mainly refer to the variation of its energy conversion coefficient with different part-load ratios (steam energy).

Absorption chiller
The mathematical model of the absorption chiller is:

Wind power and photovoltaic power generation
Like wind and photovoltaic power generation, when the output of photovoltaic and wind power generation systems is excessive, it is difficult in absorbing the excess power.Currently, it is permissible to reduce the power output.Therefore, the actual output of photovoltaic and wind power generation systems satisfies the following constraints.

Heat pump
The heat pump (HP) typically retrieves low-grade heating energy from the environment and converts it into high-grade heating energy through electric work.The mathematical model of the heat pump [9-10] can be expressed as follows: in Equation (9), a , b and c are regression coefficients.

Energy storage equipment
The characteristics of the energy storage equipment can be described by several aspects, including the equipment capacity, maximum energy storage state, energy storage output power, energy self-discharge rate, and energy storage efficiency.The mathematical model for the energy storage equipment charging and discharging can be expressed as follows: in Equation ( 10), t Δ is the time interval from t to 1 t + .
The energy efficiency of energy storage equipment varies with different working conditions, where charge η and discharge η are not constants but functions of the charging and discharging power, respectively.The mathematical expression for this function is: Moreover, the energy storage equipment should satisfy the constraints of capacity limits: ( ) NESP-2023 Journal of Physics: Conference Series 2592 (2023) 012029

Objective function
The model is based on the objective function of the annual total cost.The annual total cost includes the annual investment cost, the annual operation cost, the annual energy cost, and the annual environmental cost.

Nomenclature
in Equation ( 13), k is the period, K is the set of all periods in the year, and k t is the number of hours per year in the k -th period.

Equipment capacity constraints.
For the energy storage system, the equipment capacity is a continuous variable; for other equipment, there are multiple models available for each equipment, but only one model can be selected at most, and the selected number of units should not exceed the maximum allowed.Therefore, equipment capacity is a discrete variable that depends on the model and the number of units.Therefore, the following constraints apply: GE,GT,GB,WB , AC,HP,PV,WT GE,GT,GB,WB 1 , AC,HP,PV,WT in Equation ( 14), λ is a binary variable indicating whether to select the equipment, with 0 indicating not to select and 1 indicating to select.

Equipment operating characteristic constraints.
Within the upper and lower limits of the equipment output, the operating characteristics of the equipment can be approximately represented by a linear relationship between the input energy and the output.It is assumed that at any time, the load level of all equipment in the same category that is in operation is the same.In addition, the amount of equipment in operation at any time should be less than the number of equipment selected for that category.Therefore, the following constraints are: equi.outequi.
,GT,GB, , , WB,AC,HP GE,GT,GB,WB , , A The operational characteristic constraints of photovoltaic, wind turbines, and energy storage systems can refer to sections 2.5, 2.6, and 2.7 and are not repeated here.

System energy flow balance constraint.
The required electricity and heating of the distributed multi-energy complementary system can be produced internally or purchased from the External electricity network (heating network), while the required cooling can be produced internally.In addition, the flue gas generated by the system is recovered and utilized by the waste heat boiler and the lithium bromide absorption chiller, and the unrecoverable heat is discharged into the atmosphere in the form of flue gas.Therefore, the power of various energy types in the system should satisfy the following constraints:

P
is the amount of exhaust heat from the gas turbine generator that cannot be utilized and is discharged into the atmosphere.

Numerical Examples
Simulation is conducted for a distributed multi-energy complementary energy system, and based on oneyear operation data of the system, three typical operating scenarios of the system are summarized.
In a distributed multi-energy complementary system, the input energy sources include wind energy, solar energy, purchased electricity, heat energy, and natural gas.Among them, the cost of generating electricity using solar and wind energy is 0, while the cost of purchased electricity, heat energy, and natural gas is 1.2 CNY/kWh, 0.5 yuan/kWh, and 0.5 CNY /kWh, respectively.The selling price of electricity to the external grid is 0.2 CNY /kWh.The lifespan, single machine investment cost, operating cost, and single unit capacity of each piece of equipment in the system are shown in Table 1.The distributed multi-energy complementary energy system can directly supply power to the load through the external electricity network and internal wind and photovoltaic equipment, or supply power to the electric load through gas engines and gas turbines.The system can directly supply heat to the heat load through external heating networks, gas boilers, and gas engines, or supply heat through waste heat boilers driven by flue gas.In addition, the system can provide cooling through heat pumps and absorption chillers.Based on the typical operating scenarios and equipment parameters of the system, the optimal planning and configuration of the distributed multi-energy complementary energy system can be obtained, as shown in Table 2.According to the optimal planning and configuration results of the distributed multi-energy complementary energy system, the power balance diagrams of cold power, heat power, and electrical power in each typical scenario in the system can be obtained, as shown in Figure 2 (a), 2 (b), and 2 (c), respectively.Since there is no cooling demand in winter, the power balance of cold power only exists in summer and transitional seasons.When the chiller unit's cooling supply is insufficient or the system's cold load demand is lower than the minimum cooling capacity that the chiller unit can provide, the heat pump will be used to meet the system's cold load demand.
According to Figure 2 (b), there is a high demand for heat power in winter, so the external purchase of heat is higher, and almost all available equipment participates in supplying heat.In summer and transitional seasons, the supply of heat is mainly provided by internal combustion engines and heat pumps, and the external purchase of heat is minimal.
According to Figure 2 (c), the electric load demand in the system is mainly met by wind and solar power.Gas turbines, gas engines, and purchasing from external electricity networks are used to adjust the imbalance between renewable energy generation and electric load demand.

Conclusions
By using the proposed planning method, the optimal planning and configuration of the distributed multienergy complementary energy system is obtained.In the case study, the optimized configuration scheme of the distributed multi-energy complementary energy system can realize the cascade utilization of energy and multi-energy complementarity, alleviate the electricity shortage during peak periods, reduce the operating energy consumption costs and the penalties for renewable energy abandonment, thus improving the economic and environmental benefits of the system.By using a full-working-condition model to optimize the system configuration, the real-time operating characteristics of the equipment can be more accurately reflected.
is the functional expression of the full-working-condition characteristic parameters of the energy storage equipment.a , b and c are regression coefficients.

Figure 2
Figure 2 Power balance diagramAccording to Figure2(a), the cooling load demand in the system is mainly met by the chiller unit.When the chiller unit's cooling supply is insufficient or the system's cold load demand is lower than the minimum cooling capacity that the chiller unit can provide, the heat pump will be used to meet the system's cold load demand.According to Figure2(b), there is a high demand for heat power in winter, so the external purchase of heat is higher, and almost all available equipment participates in supplying heat.In summer and transitional seasons, the supply of heat is mainly provided by internal combustion engines and heat pumps, and the external purchase of heat is minimal.According to Figure2(c), the electric load demand in the system is mainly met by wind and solar power.Gas turbines, gas engines, and purchasing from external electricity networks are used to adjust the imbalance between renewable energy generation and electric load demand.

Table 1
Equipment installation parameters

Table 2
Optimal configuration results