Optimal operation of cold-heat-electricity multi-energy collaborative system based on price demand response

1 Introduction

In recent years,environmental pollution and energy crisis have become increasingly acute.Multi-energy collaborative systems have emerged as an effective way to address these problems and have become an important sector in the energy field.Research on the coordinated planning and operation of multiple energy components,such as electricity,heating,and gas,is an important area of focus.The energy hub model serves as an input-output dual-port model that describes the energy supply,load demand,network switching,and coupling relationships in a multi-energy system.It can integrate cooling,heating,electricity,gas and other energy components.Such a system can optimally allocate energy by making full use of the complementary coupling characteristics of various energy sources.Additionally,it can solve the problems associated with large-scale renewable energy consumption and energy cascade utilization.The energy hub model is widely used in multi-energy system planning and operation analysis [1-2].

Current domestic and foreign studies on multi-energy collaborative systems focus on optimization scheduling,capacity allocation,benefit evaluation,and reliability analysis.Dong,Zhang,and Shang [3]have designed a multienergy optimal scheduling method with a combined cooling,heating,and power (CCHP) system.The primary objectives of the method are to reduce cost and carbon emissions.Lin et al.[4]have built a multi-objective optimal power flow model for a multi-energy system aimed at minimizing economic cost and pollutant emissions.Zeng et al.[5]have built a multi-objective collaborative optimization model for a multi-energy system with the goal of minimizing the total cost and power shortage rate and maximizing the emission reduction rate.Jabbari,Tahouni,Ataei,and Panjeshahi [6]have targeted the minimization of annual operating cost and used a genetic algorithm to optimize the capacity of each element in a CCHP system.Guo et al.[7]established a twolayer optimization planning and design model.The outer model calculated the construction and installation capacity of energy conversion equipment and energy storage units in the energy hub.The inner model optimized the typical daily operating conditions.Cui [8]has built a comprehensive set of benefit evaluation indices of a multi-energy system from the perspective of economy,energy saving,and environmental protection,based on the analysis of energy hubs.Koeppel and Andersson [9]have established a Markov state space transition diagram of multi-energy system components and proposed a general energy hub reliability assessment model to evaluate the power supply availability of the system.Xu,Hou,Jia,and Yu [10]have established an optimal load reduction model for a multienergy system and proposed a reliability assessment model based on the Monte Carlo method.

With the increase in the load demand of users and the variety of load types,more flexible controllable load participation in the demand response(DR) has become an important means of relieving the imbalance of power supply and demand.Current domestic and foreign studies on DR mainly focus on two aspects,electricity cost and incentive mechanisms.Callaway and Hiskens [11]consider the dispatch of temperature-controlled load and electric vehicles in response to electricity cost movements as a result of load forecasting.The advantages and disadvantages of centralized,hierarchical,and distributed control scheduling methods were also compared.The Federal Energy Regulatory Commission [12]and Conejo,Morales,and Baringo [13]have presented a calculation method of the price elasticity coefficient for large industrial and commercial users to separate user groups.The method was developed through a series of steps,such as determining the types of DR projects,clustering the analysis of electricity consumption characteristics of users,identifying DR project participation rates,calculating price elasticity,and evaluating the DR potential of users.In a study of DR based on the incentive mechanism,Wang,et al [14]established an optimal purchase model of interruptible load with the minimum power cost as the objective function.The model considered two types of interruptible loads.The purchasing strategy of interruptible loads was arranged according to the predicted electricity price and users’ quotations in the equilibrium market.Guo et al.[15]studied the deviation electricity evaluation based on interruptible load contracts and used the interruptible load as a basis for proposing the optimal operation purchase model of the electricity sales company.Through the adjustment of the interruptible load,both the positive deviation quantity and cost were reduced.

In summary,there have been few studies on the impact of price-based power DR on the optimal operation strategy of multi-energy collaborative systems that are based on market elasticity.Therefore,this study proposes an optimization model of the multi-energy collaboration system that considers the price-based DR.The model is based on results from previous studies and the coupling and conversion characteristics of multiple energy sources in the multi-energy collaboration system.First,the main components and equipment models of the multi-energy collaborative system are introduced,and a price-based DR model based on market elasticity is established.To achieve the lowest daily operating cost of the system operator,an optimal scheduling model of the multi-energy collaborative system is then built.Finally,based on actual data,an example analysis is carried out.

2 Overview of multi-energy collaborative system

2.1 Main components of multi-energy collaborative system

The multi-energy collaborative system is an integrated energy system that uses the coupling mechanism of each energy sub-system in space and time [16].Additionally,it is a system that adopts the operating mechanism of “part for use and part for sale” to achieve multi-energy complementarity and energy cascade utilization.It is one of the most important ways to solve China’s energy dilemma.The multi-energy collaborative system based on the energy hub model consists of the input and output side of energy,and equipment for energy production,energy conversion,and energy storage [17].The multi-energy collaborative system can be either grid-connected or grid-isolated.This study focuses on the grid-connected operation of a multienergy collaborative system and adjusts the output of each unit to the lowest system operating cost,including wind power,photovoltaic units,CCHP,and other units.The system is connected to the power grid at the same time and trades electricity according to market rules.

The multi-energy collaborative system described in this paper consists of two major stakeholders,the system operator and the integrated energy user.The roles of each stakeholder in the system operation are described as follows:

(1)The system operator is both a dispatch center of the multi-energy collaborative system and an operator.While maintaining the stable operation of the system,it can obtain energy sales revenue by selling energy to users.System operators can improve their economic benefits by configuring equipment for energy production,energy coupling conversion,and energy storage,and developing a scheduling strategy based on DR.In addition,they can ensure the normal supply of energy and carry the operating and maintenance costs of their and energy producers’equipment.

The specific production equipment model is shown as follows:

where Ee,and are the output power of renewable energy,wind turbines,and photovoltaic units respectively,in kW.

where is the output power of the wind turbine fan in kW;vci,vco,and vr are the cut-in wind speed,cut-out wind speed,and rated wind speed,respectively in m/s; Pr is the rated output power in kW;and a and b are the wind speed correlation coefficients.

where ξ is the actual light radiation intensity;θ is the incident angle of the light on the solar panel;ηm is the efficiency of the maximum power point tracking controller;Ap is the area of the solar panel;and ηp is the efficiency of the solar panel.

where is the electric power output of the gas turbine;qgas is the calorific value of natural gas;ηeGT is the efficiency of the gas turbine;is the power consumption of the natural gas used in the gas turbine;is the output heat power of the waste heat boiler;ηWHBh is the efficiency of the waste heat boiler;is the heat output of the gas boiler at time t; is the efficiency of the gas boiler;and,is the natural gas consumption power of the gas boiler.

A) Electricity storage equipment model:

where is the electricity storage capacity at time t in kWh;α is the self-loss rate of the electricity storage equipment;is the electricity storage capacity at time t-1in kWh;the charge and discharge power,respectively,at time t in kW;are the charge and discharge efficiency,respectively;are the charge and discharge states,respectively,variable 0 or 1;and,Δt is the charge and discharge time (= 1h in this study).

B) Heat storage equipment model:

where EtTSS is the heat storage capacity at time t in kWh;β is the self-loss rate of the heat storage equipment;is the heat storage capacity at time t-1in kWh;are the charge and discharge heat power,respectively,at time t in kW;are the charge and discharge efficiency,respectively;are the heat storage and heat release status,respectively,variable 0 or 1;and,Δt is the charge and discharge time (= 1h in this study).

(2) The integrated energy users are those who have cooling,heating,and power load demand,and the load demand has coupling characteristics.This study focuses on rational integrated energy users who do not have energy production and storage elements.Therefore,when external price signals change,such users can independently adjust part of the non-rigid electrical load demand to reduce their energy cost to a minimum.

2.2 Energy hub model

The Energy Hub (EH) is an interface platform between the source,network,and load in a multi-energy collaborative system.It includes the mutual conversion,distribution,and storage of various forms of energy to achieve the optimal configuration of energy resources.Therefore,it provides theoretical support for the planning,design,and operation optimization of multi-energy collaborative systems.EH can adjust the output and operating status of different equipment depending on the optimization goals of the model and in this way satisfies the demand of the corresponding load.In this study,we examine the EH based on the CCHP and consider the four energy components of electricity,gas,heating,and cooling.The input-output coupling relationship is shown as:

where Le,Lc,and Lh are the user’s electricity load demand of electricity for general use,cooling,and heating,respectively;ηe is the average conversion efficiency of the power transformer;Ee is the total electricity generated by wind and photovoltaic units;Egas is the amount of natural gas entering the system;and,k is the distribution coefficient.Components of the energy hub and the specific energy flow in the system are shown in Fig.1.

2.3 Analysis of electric-heat-cold load coupling characteristics

The energy flow diagram in Fig.1 shows the main energy coupling equipment,such as the lithium bromide absorption chiller,the heat pump,and the electric chiller refrigerator.They are used to obtain the coupling characteristics between the various energy sources.The lithium bromide absorption chiller uses the waste heat in the production process for refrigeration operations through a heat transfer process.It is the key component of cooling and heating coupling.The heat pump is an electric-toheating device that extracts a small amount of low-grade heat energy existing in groundwater and transfers the heat through heating pipes.The electric chiller is an electricto-cooling device that produces cooling capacity when consuming electrical energy.

(1) Lithium bromide absorption chiller model

where is the cold power output by the lithium bromide chiller at time t in kW;is the thermal power consumed at time t in kW;and,is the cooling efficiency of the lithium bromide chiller.

(2) Heat pump model

where is the thermal power output by the heat pump at time t in kW;is the electrical power consumed by the heat pump at time t in kW;and,is the efficiency of electricity for heating.

(3) Electric chiller model

where is the cold power output by the electric chiller at time t in kW; is the electric power consumed by the electric chiller at time t in kW;and, is the efficiency of the electric chiller.

Fig.1 Schematic of internal energy flow process of multi-energy system

3 DR model based on market elasticity

3.1 Market elasticity model

Both incentives and pricing are used to manage DR.In this study,we focus on the price-based DR model.Based on the flexible load of users,the market elasticity model is used to establish a time-of-use (TOU) price-based DR model.According to economic principles,market elasticity includes self-elasticity and cross-elasticity.Self-elasticity is used to measure the impact of current single-period electricity price changes on electricity demand.Cross-elasticity,on the other hand,is used to measure the impact of multi-period electricity price changes on multi-period electricity demand.The self-elasticity coefficient and cross-elasticity coefficient of electric load are:

where ε(i ,i) is the self-elasticity;ε(i ,j) is the crosselasticity;p0(i) is the original price at time i;q0(i) is the original electric load at time i;p (i) is the price at time i;q (i) is the electric load at time i;p (j) is the price at time j;and,q (j) is the electrical load at time j.

3.2 DR model

(1) Single-period DR model

The electricity load amount changed by the user’s participation in the DR is as follows:

To calculate the load demand q i() after the user participates in the DR,the power value B q i(()) of the user’s electricity consumption q i() and the net profit L i() obtained from the user’s electricity consumption are defined as [18,19]:

The partial derivative of q i() at both ends can be obtained as:

Substitute the original electric load q0(i) into the above equation:

The Taylor expansion of the power value can be obtained as:

Based on the above model,let equation (17) be equal to 0 to get a single-period DR model.

(2) Multi-period DR model

By introducing g cross-elasticity and expanding equation (18),a multi-period DR model based on market elasticity can be obtained as:

(3) Final DR model

The final DR model can be obtained by combining the single-period and multi-period DR models:

where ηDR is the percentage of customer’s responsiveness,which is a constant parameter.

4 Operating model of multi-energy collaborative system

4.1 Objective function

This study aims to minimize the daily operating cost of the system,including equipment operation and maintenance cost COM,electricity cost CE,and gas cost CG.The specific optimization objective function of a grid-connected multienergy collaborative system is as follows:

(1) Operation and maintenance cost

where is the operating and maintenance cost per unit of output power of equipment m;Etm is the output power of equipment m at time t;and T is the scheduling time.

(2) Electricity cost

where pe,t is the electricity cost at time t;and,is the power purchased at time t.

(3) Gas cost

where pgt, is the gas cost at time t and the calorific value of natural gas is 9.7 kWh/m3.

4.2 Constraint condition

(1) Power balance constraints

(A) Electric power balance constraint

where is the electric load of the user before DR at time t and Δqt is the amount of load changed by users participating in DR.

(B) Thermal power balance constraint

whereis the actual heating load of users at time t.

(C) Cold power balance constraint

where is the actual cooling load of users at time t.

(2) Tie line constraints

where Pgrid,min and Pgrid,max are the minimum and maximum interactive power of the distribution network,respectively,and Ptgrid, is the interactive power of cooling,heating,electricity,and the distribution network at time t.

(3) Energy storage device constraints

where are the maximum and minimum capacity of the electricity storage device,respectively,and are the minimum and maximum capacity of the heat storage device,respectively.

(4) Equipment output constraints

(5) Unit climbing constraint

whereis the upper climbing limit of equipment m.

5 Example analysis

5.1 Basic parameters of the example

In the calculation example,the actual data fora day in summer in an industrial park in the north were selected,and the time scale was 1 h.The CPLEX solution was called in the MATLAB environment to verify the rationality and effectiveness of the model established in this study.Fig.2 shows the typical daily electricity,heating,and cooling load curves and the renewable energy (wind power and photovoltaic units) output curve.To make full use of the renewable energy and maximize the use of wind and light as energy sources,we assumed that priority should be given to ensure the full consumption of renewable energy.The electricity cost while connected to the grid was the same as the electricity sale price on the same day,and the TOU electricity price was used,as shown in Table1.The selfelasticity and cross-elasticity are shown in Table2.The specific parameters of each device are shown in Table3 and Table4 [20,21].

Fig.2 Renewable energy output and load curve

Table1 Energy price (yuan/kWh)

Project type Time period Electricity cost Heating cost Gas cost Peak period 8:00-11:00,16:00-20:00 1.2 0.3 0.25 Off-peak period 6:00-8:00,11:00-16:00,20:00-22:00 0.7 Valley period 22:00-6:00(the next day) 0.4

Table2 Self-elasticity and cross-elasticity

Peak period Off-peak period Valley period Peak period 40 -90 -75 Off-peak period -90 40 100 Valley period -75 -100 40

Table3 Main parameters of energy storage equipment

Equipment Electric energy storage Heat energy storage Configuration capacity (kWh) 1,500 1,500 Efficiency (charge/discharge) 0.9 0.9 Self-loss coefficient 0.0035 0.0035 Upper and lower limit of energy storage ratio 0.9/0.1 0.9/0.1 Initial capacity (kWh) 750 750 Operation and maintenance costs (yuan/kW) 0.0018 0.0018

Table4 Main parameters of energy storage equipment

Equipment Configuration capacity (kWh)Electric/heat efficiency Energy Efficiency Ratio Uphill/downhill rate (kW/h)Output upper/lower limit Operation and maintenance costs (yuan/kW)Gas boiler1,0000.93—5001,000/00.020 Gas turbine1,0000.3—5001,000/00.020 Waste-heat boiler1,0000.8—5001,000/00.025 Electric chiller1,000— 4 5001,000/00.025 Heat pump1,000— 4.5 5001,000/0 0.025 Absorption chiller1,000— 0.7 5001,000/0 0.025

5.2 Example result

To verify the effectiveness of the model established in this study,four scenarios (Table5) were built for comparison based on the configuration of energy storage equipment and the DR setting.With the system operator’s lowest daily operating cost as the optimization goal,we want to determine the optimal scheduling strategy.

Table5 Four scenarios

Scenarios 1 2 3 4 Electricity storage equipment ×√√√Heat storage equipment ××√√Demand response (DR) ×××√

(1) Scenario 1

Scenario 1 is basic,i.e.,without any storage equipment or DR of the user.The electric power balance,thermal power balance,and cold power balance in this scenario are shown in Fig.3(a),(b),and (c).As can be seen from Fig.2,since the output of renewable energy has the characteristics of anti-peak-load regulation,the output during the times 0:00-4:00,12:00-16:00,and 21:00-24:00 was higher,and 22:00-6:00 of the next day was the valley period when the electricity cost was lower.Therefore,the gas turbine and waste heat boiler did not operate all the time,as the renewable energy output and purchased electricity were able to meet the power demand of the system,and the heat load was mainly satisfied by the heat pump.The output electric power of the gas turbine was mainly concentrated in the period of high electricity cost (8:00-11:00 and 17:00-20:00).While meeting the demand of system electric load,the surplus heat was recovered by the waste heat boiler to supply heat for the system.The cooling load demand of the system was mainly satisfied by the electric chiller.In the period of low heat demand (10:00-16:00),part of the heat load was converted into the cooling load by the absorption chiller to meet part of the cooling demand.In this scenario,the system’s gas consumption was 27,588.4kWh,and the electricity consumption was 13,781.5kWh.

Fig.3 Scenario 1

(2) Scenario 2

Scenario 2 added electricity storage equipment to scenario 1.The electric power balance,thermal power balance,and cold power balance in this scenario are shown in Fig.4(a),(b),and (c).Compared with the basic scenario,the electricity storage equipment discharged in the period of high electricity cost,charged during the period of low electricity cost,and carried part of the electrical load demand,so the output of the gas turbine unit,heat recovered by the waste heat boiler,and the power purchased during the period of high electricity cost were significantly reduced.The heat load demand of the system was mainly met by the heat pump,and only a small part was met by the gas boiler.The output of the electric chiller and absorption chiller remained almost constant.The cooling load demand of the system was still mainly met by the electric chiller.In this scenario,the gas consumption of the system was 26,761.2 kWh,and the electricity consumption was 13,971.6 kWh.

Fig.4 Scenario 2

(3) Scenario 3

Compared with scenario 1,scenario 3 added electricity storage and heat storage equipment.The electric power balance,thermal power balance,and cold power balance in this scenario are shown in Fig.5(a),(b),and (c).Compared with scenario 2,the output power of the electricity storage equipment in scenario 3 was reduced during the valley and off-peak periods,whereas the purchased power was increased,and the output power of the gas turbine was reduced.The main reason was that the heat storage equipment carried part of the heat load demand,which led to the output reduction of the waste heat boilers and gas turbines.The heat load demand of the system was met mainly by the heat pump with higher energy efficiency.The output of the electric chiller and the absorption chiller changed a little.During 16:00 to 17:00,when the electricity cost was high,the output of the absorption chiller increased,whereas that of the electric refrigerator decreased.However,the cooling load demand of the system was still mainly met by the electric chiller.In this scenario,the gas consumption of the system was 26,403.8 kWh,and the electricity consumption was 14,114.1 kWh.

Fig.5 Scenario 3

(4) Scenario 4

Scenario 4 added the user’s price-based DR to Scenario 3.The user adjusted the electricity load according to the cost of electricity,which alleviated the system peak regulation and reduced the user’s own electricity cost.The electric power balance,thermal power balance,and cold power balance are shown in Fig.6(a),(b),and (c).Compared with the previous three scenarios,the user’s electricity load changed in the different periods.The electricity consumption increased during the low electricity cost period and decreased during the high electricity cost period.The total DR was about 5% of the original load.Consequently,the amount of electricity generated by the gas turbines,purchased from the grid,and output from the power storage equipment all decreased significantly.The thermal power output of the waste heat boiler and the heat storage equipment were reduced,resulting in an increase in the heat output of the heat pump.The output changes of the gas boiler,electric chiller,absorption chiller,electricity,and heat storage equipment were relatively small.In this scenario,the gas consumption of the system was 24,220.4 kWh,and the electricity consumption was 13,796.2 kWh.

Fig.6 Scenario 4

According to the results of the above four scenarios,and thanks to the TOU user DR mechanism,the total daily operating cost of the system was significantly reduced.The results are summarized in Table6.

Table6 Gas cost,electricity cost,and total daily operating cost of the system (unit/yuan)

Gas cost Electricity cost Total daily operating cost Scenario 1 6,897 9,820 17,904 Scenario 2 6,690 9,140 15,964 Scenario 3 6,601 9,242 15,946 Scenario 4 6,055 8,486 14,608

However,when the percentage of the customer’s responsiveness is less than 100%,the operating cost of the system will increase accordingly.The specific results are shown in the following table.

Table7 System operating costs under different percentage of customer's responsiveness (unit/yuan)

Gas cost Electricity cost Total daily operating cost ηDR =100% 6,055 8,486 14,608 ηDR =90% 6,120 8,526 14,761 ηDR =80% 6,245 8,647 14,875

6 Conclusions

In this study,the main objective was to minimize the daily operating cost by adopting the optimal scheduling of a multi-energy cooperative system.To do this,we used pricebased DR to develop a scheduling optimization model fora multi-energy collaborative system operating strategy.After comparing and analyzing the optimization results of multiple scenarios,the main conclusions can be summarized as:

(1) Using market elasticity to derive a price-based DR can effectively combine the power supply and the user demand sides.The price sensitivity of users can then be used to guide them on how to reduce and transfer their electricity load,thus significantly reducing the operating cost of the system.

(2) The operating mode of the multi-energy collaborative system that coordinates energy storage and power DR was more efficient than the multi-energy collaborative system with only energy storage equipment.It can reduce the cost of power purchased from the outside and the total operating cost of the system.

Acknowledgments

This paper is supported by State Grid Corporation Technology Project (5400-201956447A-0-0-00).

Declaration of Competing Interest

We declare that we have no conflict of interest.