Optimization modeling method for coal-to-electricity heating load considering differential decisions

1 Introduction

When large-scale electric heating equipment is utilized,the peak-to-valley difference of the load curve is increased,which decreases both economic benefits and power grid stability performance,considering problems such as the low penetration rate of renewable energy production methods[1].Because of its good flexibility,the electric heating load could be utilized for peak shaving and valley filling by proper guiding or control via methods such as the demand response (DR) mechanism.DR assists in alleviating problems of power grid operation efficiency.Therefore,using electric heating load as a DR source has become an attractive prospect.However,because this application depends on automatic control device,incentive-based DR is difficult to implement.Fortunately,with the increasing maturity of the power market,price-based DR may appeal to users participating in load regulation.Thus,it may become the preferred strategy of many kinds of users.

The traditional methods used to model price DR behavior are mainly based on consumer psychology [2],electricity price elasticity matrices [3],and data mining[4].The general DR characteristic model is obtained by data processing.However,unlike the fixed-load response behavior of centralized industrial and commercial users,the distributed residential load DR is more autonomous and random.Thus,diverse user needs cannot be satisfied by the general model.Recent studies have focused on the management of family energy systems and energy efficiency plants.Some literature [5,6] considers consumer electrical appliances including energy-storing appliances (batteries and air conditioners),transferable electrical appliances(cleaning appliances and electric vehicles),and other pricemotivated loads.In order to minimize the electric cost expenditure of users and the fluctuation of system load,a DR resource-control model is established to optimize the user's electric curve,considering consumer satisfaction.The participation of appliances for air conditioning is closely related to thermal comfort.Considering the indirect energy-storage characteristics of air conditioning,the multiobjective load optimal operation model for economics and comfort level is presented in the literature [7] and achieves optimal load control.

In the modeling of thermostatically controlled load DR behavior [8-11],different users have different correlations between comfort and economy,but few studies have thoroughly addressed this difference.Therefore,the new factor in this study is the refinement of user classification and the establishment of a load-response DR model based on load factors,housing structures,and the external environment.Defining the electric heating load with heat storage in the residential side as the DR load and considering the thermal energy storage characteristics and thermal comfort demand of buildings,models of thermal comfort temperature demand and load multi-objective optimization operation are established.A fuzzy decision method is proposed to select differentiated multi-objective optimization schemes.The establishment of a DR model for electric heating developed through this analysis is an important basis for the development of electricity price mechanism and load forecasting in the implementation of the coal-to-electricity transition.

2 Modeling of thermal load demand based on differentiated optimal comfort

Simulation of the thermal load demand of buildings is the basis for DR fulfillment by thermostatically controlled loads.Traditional modeling methods of heat load demand mainly include two aspects:the thermophysical characteristic modeling of buildings and the simulation of external meteorological factors.Considering differences in user production and living needs,user comfort can be quantified in modeling thermal load demand.

Factors affecting the thermal process of a building include both external and human factors.Fig.1 shows the mode of action of various factors affecting the thermal process of a building.External influences include outdoor and indoor factors.Defining the building envelope as the boundary,outdoor influencing factors mainly include meteorological conditions (outdoor air temperature and humidity,solar irradiance,wind speed and direction,etc.) and the ambient surface temperatures around the building (sky effective temperature,ground temperature,and adjacent building surface temperature),which mainly affect the building thermal process through heat transfer by the envelope.Indoor influencing factors include various indoor calorific values (indoor lighting installations and the heat dissipation and dispersion of human bodies and equipment),which affect the heat process by convection or radiation.Human factors include the heating system type and ventilation frequency.

Considering the above factors,the time-varying equation of air temperature in the building space formed by the envelope structure can be described as

Fig.1 Factors influencing building thermal process

where cpaρaVa is the heat capacity of air in the building space (J/℃),qjwall is the amount of heat transferred by the jth wall surface,n is the number of inner surfaces,qwin is the amount of heat through window radiation,qcov is the heat of air from indoor heat sources by convection,qvent is the heat brought into a room by air exchange between indoor and outdoor air or between adjacent rooms,and qhvac is the heat from a heating system.

The specific calculation formula for each thermal disturbance term is as follows:

(1) The heat from outdoor environment transferred by the jth wall surface qjwall:

where Fj is the inner surface area of the wall j in a building(m2), hin is the heat transfer coefficient of wall inner surfaces and indoor air (W/m2·K),tj(τ) is the temperature of wall j at the τth moment,and ta(τ) is the indoor temperature at the τth moment.

(2) The transferred heat considering window shading coefficient qwin:

where Ajwin is the window area,Dj is the solar heat gain factor of the jth window,Cjwin is the cooling load coefficient of window glass,and Zjwin is the window shading coefficient.

(3) The air exchange heat transferred by outdoor air and adjacent rooms qvent:

where qout(τ) is the heat exchange between outdoor air and indoor air,qadj(τ) is the heat exchange between indoor and adjacent room air,Gout and Gadj are the ventilation volumes between indoor and outside and between adjacent rooms,and tout(τ) is the outdoor temperature at the τth moment.

(4) The total heat produced by internal interference factors (equipment,lighting,and personnel):

The total heat produced by internal interference factors affects the indoor temperature both directly and indirectly through the indoor air.The factors include the indoor equipment qe(τ),lighting ql(τ),and personnel qp(τ),where Ce is the equipment cooling load coefficient,Ne is the dissipated heat of equipment per unit area,A is the room area,Cl is the lighting cooling load coefficient,Nl is the dissipated heat of lighting per unit area,qxr and qqr are the sensible and latent heat dissipation of personnel,respectively,Cxr is the cooling load coefficient for sensible heat gain,n is the population of the unit,and φ is a clustering coefficient.

(5) The heat produced by heating equipment

This refers to the heat required for indoor heatproduction equipment and specifically that for electric heating equipment in this paper.

3 A multi-objective optimization model of electric heating load characteristics considering DR

Heat energy,which is converted from electric power to meet users' heating demands,can be divided into two types:direct heating and heat accumulation.The electric heating load has a good DR potential because of its thermal energy storage characteristics.In traditional DR processes,most aim to reduce load,sacrifice user comfort,and reduce participation in DR.In this section,considering electricity price signal and the most comfortable indoor temperature within a 24-h period,a multi-objective optimization model for electric heating equipment with heat energy storage is investigated.It can optimize the operation of equipment in one day.The model treats heating economy and comfort as the goals,and the optimal control cycle is 24 h.The decision variables are the power consumption of an electric boiler in 1 h and the heat power of the storage system in 1 h,represented by Pe,0,t and Pe,1,t,respectively.

Objective 1 is to minimize electric heating costs,represented by J1:

where Pe,0,t is the power consumption of electric boiler during the t-th period,Pe,1,t is the consumption of heat storage and heating modules during the t-th period, cg is the peak electricity price,cg is the valley electricity price,tf is the peak period of the electricity price,and tg is the valley period of the electricity price.

The optimization of objective 1 is often performed at the expense of user heating comfort,so it is necessary to consider objective 2 to balance user heating demand.Objective 2 quantifies the user heating comfort level and introduces the user comfort index based on the deviation of the actual value from the expected value of the indoor temperature in the heating season,which indicates the user heating comfort J2:

where Tset is the user-defined expected indoor temperature expectation and Tt is the actual indoor temperature during the t-th period.

Constraint:

(1) The constraint of thermal load balancing:

where Hload,t is the user heat load demand at the t-th period.

(2) The upper and lower limit constraints of direct heating equipment are shown as (9):

where is the upper limit of the direct-heating equipment.

(3) The capacity status constraints of the heat energy storage system:

a.capacity constraint:

b.status constraint:

(4) The heat power constraints of the heat storage system:

where is the upper limit of heat storage power,Pf,t is the heat releasing power at the t-th period,and is the upper limit of releasing power.

(5) The operation constraint of the heat storage system:

where Ce,1 is the heat power of heat storage,η0 is the heating efficiency of electric heating equipment,η1 is the heat storage efficiency of heat storage,and St is the heat storage of the heat storage system at the t-th moment.

4 Fuzzy decision model and solution method

Based on the above multi-objective optimization model for electric heating equipment with heat storage,the traditional solution method uses a fixed-preference factor to allocate the object weight,transforming the multi-objective optimization solution into a single target optimization problem.However,this method is strongly subjective and cannot accurately represent user demand.Considering differences in user DR behaviors,a fuzzy decision model with differential weight is proposed in this section to optimize the load curve.

4.1 Differential weight

The basic data of user characteristics and heating behavior are collected by questionnaire.These data mainly consist of load variation,the expense of daily heating,and temperature.Based on the Pearson coefficient correlation analysis,the load variation and user characteristics can be analyzed.Then the three characteristics with the maximum correlation coefficient are regarded as the major influencing factors,k (k = 1,2,3),with the correlation coefficient εk.According to the historical data of heating electricity and indoor temperature in each category,the preference coefficients of user i for economy C and comfort ΔD are βC,k,i and βΔD,k,i.Therefore,the preference weight of objectives considering the differential of user demand is

4.2 Fuzzy decision model

Because of the differences in the dimensions of each objective,the functions for each objective are different and not comparable.According to the method of dimensionless treatment of indicators based on fuzzy comprehensive evaluation,a membership function is introduced for the dimensionless processing of multi-objective functions.Combined with the differential weight,the optimal operation scheme of a user corresponds to the minimum deviation of the expected scheme.

According to the solution of the gamultiobj multiobjective optimization toolbox,a non-inferior solution set for the acceptable power supply under a certain configuration can be obtained as a Pareto-optimal set.The comprehensive decision is made using the differential preference weights of users.In order to ensure that the value of the objective function of different dimensions has the same effect on the decision index,an interval membership function for the alternatives j (j= 1,2,3,...) is proposed,and its normalized expression is shown in (15):

where fmax and fmin are the upper and lower limit,respectively,of the target function within the interval,and fj is the actual value of the target function for alternative j.

The scheme of the middle point of each target function in the Pareto-optimal solution interval is assumed as the expected scheme accepted by most users under the same heating equipment configuration,represented as ( fC,ex,fΔD,ex):

The minimum value of the Euclidean distance of the expected scheme in the alternative scheme is used as the decision index,and modeled as

where:

The fuzzy decision model comprises (17),(18),and(19).The deviation value of the alternative from expected scheme,considering different user preferences,can be calculated,and the scheme with the lowest deviation value is the optimal scheme.

5 Result analysis

To test the effectiveness of the scheme proposed in this paper,a district of S region is regarded as the actual scene,and the optimal model and decision model are solved by using the gamultiobj toolbox in MATLAB 2014a.Then the electric heating load curve and the electricity characteristics indices (economy and comfort) can be analyzed in the heating period.

5.1 Example parameters

The example treats one household of the distributed electric heating community as the research object and simulates 100 typical users in the community.All users are classified by influence factors of DR.Among them,for office workers,middle-income households with areas of＜60 m2 account for 32%,and low-income households account for 20%.For households with old people and children,the middle-income households of 60-120 m2 account for 20%,and high-income households of ＞120 m2 accounting for 18%.Other vacant spaces of ＜60 m2 account for 10%.All users adopt electric boilers with heating storage as heating equipment with the rated boiler power,heat storage tank power,and heat storage capacity of 50 kW,25 kW,and 180 kW·h,respectively.

5.2 Simulation results

5.2.1 Heat load demand curves under different thermal comfort temperatures

With the specified building characteristic parameters and outdoor meteorological environment,combined with equation (1),the two ends of the equation are obtained to determine the thermal load demand.The heat load demand curves under different thermal comfort temperatures are shown in Fig.2.

Fig.2 Thermal load demand curve

5.2.2 The multi-objective optimization results

Taking office workers and middle-income households with areas of ＜60 m2 as the research object,the optimum temperature is 22℃.The characteristics of electric heating are optimized in MATLAB,and the Pareto-optimal solution set for heating expense and comfort is calculated by the algorithm converging after about 200 iterations.From Fig.3,the optimized heating expense is ～10-20 ¥/day and the temperature deviation is ±1- 3℃.

Taking the heating power and characteristics of electric heating users in area S as data samples,the correlation coefficients of the influence factors can be calculated by (14):ε1= 0.2,ε2= 0.5,and ε3= 0.1.According to the collected data for user heating behavior information (daily heating and indoor temperature),the preference weight of each category is calculated by the maximum likelihood estimation method.The preference weights of users are among (0.46,0.47).By the model of fuzzy decision among schemes in (17),the best scheme is (15.5,1.83) which has the minimum deviation from the ideal scheme.

Fig.3 Pareto-optimal solution set

Based on the classification of users in an area and the above method,the differentiated preference factors for different users can be solved.Then the load characteristics of each category can be calculated and the best schemes for different users can be decided as well.The preference factors and the best plans for various users are shown in Table1.

Table1 Preference factors and best plans for various users(cf /cg = 4.883)

Category Preference factors Best plan/(¥,℃)Ⅰ.Office worker,Middle income,＜60 m2 (0.46,0.47) (15.5,1.83)Ⅱ.Office worker,Low income,＜60 m2 (0.59,0.33) (11.46,2.6)Ⅲ.Old people and children,Middle income,60-120 m2 (0.42,0.55) (19.96,1.9)Ⅳ.Old people and children,High income,＞120 m2 (0.22,0.65) (24.21,1.43)Ⅴ.Vacant house,Middle income,＜60 m2 (0.51,0.40) (12.05,2.5)

According to the best plan for each type of user decision in Table1,the daily power consumption curves of various users are shown in Fig.4:

It can be seen from Fig.4 that the daily load curves of various users in the community show shapes with low,middle,and high heads.In the period from 8:00 to 20:00,community electricity consumption is lower and the heat storage system is mainly used for heating.Electricity consumption is increased during the low-price period from 20:00 to 8:00.For office workers,low-income households,and other users who do not have high comfort requirements,at the peak of electricity price,electricity expenses can be reduced at the expense of comfort to reduce the electric load to near zero,while users with higher comfort demand still have small electricity demand during peak hours.

Fig.4 Daily load curve for single households in different categories

Then,the community load curve is obtained by superimposing the various optimized load curves.As is shown in Fig.5,compared with the traditional fixed-value weight-distribution method,the load DR participation is much higher.

Fig.5 Daily load curve of community

From Fig.5,the total daily load of the community is 26.87 MW/day by using the proposed method,and the fixed-preference decision method is 43.28 MW/day.The total daily load is thus decreased by 37.9% using the proposed method.This is because,in the research community,most users such as office workers and middle-income families have greater economic preferences.Under the premise of meeting basic heating demand,the expense of electricity consumption and the demand for electric load are reduced.Therefore,by using the differential decision method,the decision is made according to the requirements of user preference,and the daily electricity curve is similar to the actual heating power curve.The accuracy of the load model is thus improved greatly.

Fig.6 The Pareto curves of different heat storage tank capacities

5.2.3 Analysis of capacity configuration of heat storage tank

With changes in the storage tank capacity of the electric heating equipment,the results are shown in Fig.6:

Fig.6 shows that increasing the capacity of storage tank generally optimizes both heating expense and comfort.However,for increases in capacity beyond a certain extent,the heating comfort decreases at the same expense.This is because,during the peak price period,in order to meet the operating characteristics of ST= S0,meeting heating comfort would cause thermal power loss; therefore,comfort deviates.The simulation shows that the optimal heat storage tank capacity is 180 kW·h,which could guide the capacity configuration of heat storage tanks for distributed electric heating users.

5.2.4 Impact of peak valley electricity price ratio on decision results

The above analysis of the optimal operation strategy of the “coal-to-electricity”load is based on the peak-valley pricing mechanism.Under the same basic parameters of the above example and setting a different peak-valley price ratio δ on the given price,the influence of the peak-valley electricity price ratio on user DR behavior is analyzed with the proposed model.

From the results,larger peak-valley price ratios(pf /pg) correspond to greater user response,and more load transferred in the peak-valley period.

If δ is equal to 1,user expense is reduced only when power consumption in the valley price period exceeds that in the peak period.From Fig.7 and 8,with the increase of the peak-valley price ratio,the response degree of users is increased,the degree of peak clipping is obvious,and the user expense is decreased.However,when the ratio increases to a certain extent,these indices tend to stabilize.

Fig.7 Influence of peak-valley price ratio on heating economy

Fig.8 Influence of peak-valley price ratio on electricity consumption

6 Conclusion

To solve problems such as surge loads and increases in the peak-valley differences of power grids caused by the assessment of large-scale “coal-to-electricity”loads,an optimal operation model for electric heating load considering DR is established to optimize the objects of economy and comfort.Differences between comfort demands and response behaviors are considered for modeling and the validity of the proposed method is verified by simulations.From the results,compared to the traditional modeling method,the optimized result of user electrical behavior is more consistent with their own needs when considering these differences.The accuracy of the proposed model is higher than the traditional one,allowing greater controllability and predictability to access the regional“coal-to power”load.This research is important for power grid planning and operation.The above analysis indicates that the influence of different peak-valley electricity price mechanisms on load characteristics of cost-sensitive users is greater.Therefore,it is necessary to study differential pricing methods for different electric heating users.