Response potential and coordinated dispatching of rural residentials’ temperature control load participating in demand-side response

With the continuous expansion of household electricity consumption, the impact of household electricity on the power system is also increasing. TCL (Temperature Control Load) accounts for a large proportion of household electrical loads such as AC (Air Conditioning) and EWH (Electric Water Heater) and is an indispensable electrical load in households. For the temperature control load participating in DR (Demand side Response), this article first analyzes the basic physical model of TCL and uses the Monte Carlo method to aggregate multiple temperature control loads. Then, by combining the aggregation model with the willingness and controllability of rural users to participate in DR and analyzing the response potential from the user’s education level, family income, age, and controllability, the potential obtained is more in line with the actual situation. Finally, a scheduling model is established with the goal of economic optimization. From the results, when both AC and EWH participate in the demand-side response, the total operating cost of the system is the lowest.


Introduction
In recent years, the demand for electricity has increased year by year, which has brought great challenges to the power grid [1] .In order to relieve the power supply pressure of the power grid during the peak period, the power grid encourages power users to actively participate in DR [2] .Nowadays, the proportion of household electricity consumption is increasing year by year, in which the temperature control load accounts for about 50% of the household electricity load, and the TCL has good thermal insulation performance, so it is particularly appropriate for the temperature control load to participate in the DR in the household load [3] .The main research objects of this paper are ACs [4] and EWHs [5] , which are most commonly used in temperature control loads.
This paper uses the Monte Carlo method to aggregate the temperature control load [6] .Since there are few considerations in responding to potential users, this paper comprehensively considers the education level, family income, age, and controllability of rural household users to assess the potential of load participation in DR and takes the new rural area as an example [7][8] .Combined with the clean energy resource endowment in rural areas [9] , the impact of temperature control load participating in where a is the inductive sensitivity.By solving Equation (1), it can be obtained that the startup cycle T on and the shutdown cycle T off of the air conditioner are respectively: on on on set a ln(1 ) 2 2

Aggregation model of the AC load
Load aggregation is to integrate the power load of a region by some method, which is convenient for the dispatching center or load aggregator to achieve the goal of common control.Therefore, it is necessary to establish the aggregation model of household TCL.The aggregate power of N ACs at time t is: where P agg (t) is the aggregate power at time t, which depends on the switching state of N ACs.
In the steady state, the aggregate power of the AC is related to its operating duty cycle, which can be expressed as: on , on, on , off , Considering that the number of ACs N is large enough, and each air conditioner operates independently, when the external temperature is constant, according to the law of large numbers, the aggregate power of N ACs can be approximately expressed as: agg on, 1 ( ) ( ) We take Equations ( 3) and ( 4) into Equation ( 6) for inequality transformation: on, on, on , on, on, We take Equations ( 3) and (4) into Equation ( 8) for inequality transformation: a s e t , a s e t , on, According to Equations ( 6) and ( 9), the upper and lower limits of the aggregate power of N ACs are: a s e t , u agg 1 (X) a s e t , d agg 1 (Y) The final aggregate power of the AC load can be expressed as: (1 ) , [0,1]

Single physical model of EWH load
The difference between TCLs such as EWHs and ACs is that users of EWHs use water, which will affect the water temperature of EWHs.Therefore, the impact of water use should be considered when building models of electric water heaters.When there is no water use behavior at time t, the exponential mathematical model of the electric water heater at this time is the same as the model of air conditioning.
When the user uses water at time t, an equal amount of cold water will flow into the electric water heater.At this time, the mathematical model of the water temperature of the EWH is: where θ before,t is the water temperature before use, ℃; θ in,t is the temperature of cold water flowing into the electric water heater, ℃; M is the capacity in the electric water heater tank, L; d t is the water consumption at time t, L.

Load aggregation model of EWH
The parameters randomly distributed in this section are rated power, equivalent heat capacity, equivalent thermal resistance, and indoor temperature.Therefore, the approximate solution of the load aggregate power of the electric water heater can be calculated from the arithmetic mean of the parameters subject to the probability distribution according to the Monte Carlo method.
( ) where E(θ room,N) ), E(R N ), E(C N ), and E(P n,N ) are the expected values of indoor temperature, equivalent thermal resistance, equivalent heat capacity, and rated power respectively; s t is the switch state variable function of the EWH.Then, according to Equation (1), the operation state of the whole cycle, namely the switch state of the EWH, can be calculated.) where t on is the operating duty cycle in the operating cycle; T is the operation cycle; P is the approximate aggregate power; N is the aggregate quantity of EWH.

Response potential of TCL based on user willingness and controllability
The  where 0 ≤ a 1 <a 2 <a 3 ≤ 1, 0<a 4 ≤ 1; ω1, ω2, and ω3 represent the increase in the educational level of users from low to high; ω4 is the threshold value of user's willingness affected by family income; E is the education level of users; I is family income; A is the average age of the family.ϕE, ϕI, ϕA, and ϕ respectively represent the influence coefficient of education level, family income, average age, and subjective influence coefficient; μ i,t is the influencing factor of user willingness.
We adjust the value range of the set temperature according to the user's willingness: , , , , max,0 min,0 ( ) where P bp,min and P bp,max are the lower limit and upper limit of biogas output respectively; V min and V max are the lower limit and upper limit of biogas digester capacity respectively, which determine the biogas output power.
 Battery restraint ( ) P are the power before and after reduction of the air conditioner at time t.

Objective function
The coordinated dispatching model takes the lowest operation cost and compensation cost of each generator unit as the objective function: where ( ) buy C t is the power purchase price of the power grid at time t ; w K , pv K and bp K are cost coefficients of wind power generation, photovoltaic power generation and biogas power generation respectively; ( ) buy P t is purchase power for the grid.

Potential analysis of temperature control load response
The number of ACs and EWHs participating in the polymerization is 10000.Table 1   Τ i n [26,28]   Considering the thermal comfort of air conditioning users, the value range of the initial temperature setting value of the AC in this paper is [24.8℃,27.3℃] [10] .Taking into account the temperature required by the users of the EWH for domestic water and the comfort degree of the bath water, the initial setting value range of the EWH in this paper is [42℃, 50℃] [11] .Considering the income, education and age of rural areas [9] , combined with the time-sharing electricity price [10] , the response potentials of the AC and the EWH are shown in Figure 1.As is shown in Figure 1, the potential of temperature control load to participate in demand side response is greatly affected by the enthusiasm of users.Therefore, when evaluating the load response potential of a region, the enthusiasm of users to participate in the response is an indispensable consideration.Figures 2-3 show the results of coordinated dispatching, where Figure 2 shows the load reduction after the AC participates in the dispatching, and Figure 3 shows the load reduction after the EWH load participates in the dispatching.After solving, the optimal dispatching cost of the power grid is 21836 CNY, and the optimal dispatching costs of only ACs participate in scheduling and only EWHs participating in scheduling are 23361 CNY and 22554 CNY respectively.It can be seen that when the AC and EWH participate in the coordinated dispatching at the same time, the operation cost of the power grid is the lowest.

Conclusion
This paper studies TCL's participation in DR from three aspects: temperature control load model, response potential of TCL participating in DR, and scenario analysis of TCL participating in coordinated dispatching, and draws the following conclusions:  Considering the ability of users to participate in DR in terms of education level, age, income, and controllability of users can more accurately reflect the response potential of users in this region.
 When the AC and EWH participate in the coordinated dispatching at the same time, the dispatching cost of the whole system is the lowest, and the lowest cost is 21836 CNY.Therefore, it is necessary for TCL to participate in DR.
Air conditioning response potential (b) Response potential of electric water heater Figure 1.Response potential of temperature control load NESP-2023 Journal of Physics: Conference Series 2592 (2023) 012063 IOP Publishing doi:10.1088/1742-6596/2592/1/0120637 The dispatching model in Chapter 4 of this paper is a coordinated dispatching model considering the resource endowment of a new rural area.Considering the actual situation in rural areas, 1000 ACs and 1000 EWHs are selected to participate in the coordinated dispatching.The output constraint of the power grid is [0, 1000 kW].The number of biogas digesters is 100, the biogas output is limited to [0, 900 kW], and the maximum volume of each biogas digester is 8 m 3 .The battery charge discharge constraint is [-250 kW, 250 kW].

Figure 2 .
Figure 2. Air conditioning load reduction Figure 3. Load reduction of electric water heater influencing factors of user participation in DR include the duration of electricity usage in the region, the education level of users in the region, household income, and age.Based on the above influencing factors, this section establishes a willingness model for users to participate in demand side response.
the upper and lower limits of the set temperature, which can be obtained by Equation (16).In this paper, α is 0.5; L cut,max represents the maximum response potential value.For the electric water heater, the highest set temperature means the maximum aggregate power at this time; on the contrary, the lowest set temperature means the minimum aggregate power at this time: where P net (t) , P pv (t) , P w (t) , and P bp (t) are respectively the power supply of the power grid, photovoltaic power supply, wind power supply, and biogas at time t; P bat (t) is the output of the battery at time t, with a positive charge and negative discharge; L base (t) , L ac (t) and L dr (t) are respectively the base load, air conditioning load, and electric water heater load at time t. Grid supply constraint ( ) ) and Table2respectively show the range of various parameters for the polymerization of air conditioners and electric water heaters: