Multiple heating loads participate in the system power regulation control strategy

With the addition of a high proportion of new energy and power electronic equipment, the power system has shown characteristics such as low inertia and significant energy output fluctuation, which has brought great challenges to power/frequency regulation and control of the power system. Therefore, this article uses the inertia characteristics of heat energy on the load side and exerts reasonable start-stop control to play a positive and beneficial role in the power regulation of the power system. Firstly, the room temperature variation process was transformed into a lumped parameter equivalent model. A lumped parameter heat transfer model of a single typical load was built in Simulink, and its dynamic characteristics were analyzed by symbolic calculation. Based on this, a time-domain simulation was carried out to explore the influence of the law of system parameters and external input on the change of system state quantity. Based on time domain simulation, the behavior of the heating load is analyzed. Then, the effects of typical and multiple loads on system power regulation at different outdoor temperatures are studied. It is found that when the average outdoor temperature decreases, the sustainable time of system power upturn will increase, and the sustainable time of downturn will decrease. The power curve of multiple loads simultaneously is more stable, and the adjustment ability is stronger. The reasonable and flexible control method of load switch setting, namely the coherent characteristic load power regulation strategy, realizes the sustainable power optimization of the load to the system in the specified period.


Introduction
With the promulgation of the national "double carbon" goal, the power industry is undergoing major changes [1], with major changes occurring on both the source, grid, and load sides [2].The access to a high proportion of new energy and power electronic equipment not only places requirements on the active control capabilities of the "source side" but also puts a huge demand on the flexible and adjustable resources of the "load side" [3].With the support of the national clean heating policy, household electric heating is gradually applied on a large scale.As an important flexible load resource, it has unlimited potential in the demand response of the power system.It is bound to become an important adjustable load in the operation of the power system resources [4].
However, electric heating loads are highly random and dynamic.Large-scale disorderly access to the distribution network can easily cause peak loads, causing an imbalance in power supply and demand.This will lead to increased power generation costs, difficulty peaking the power grid, and limited power supply.Electricity and other problems [5], in severe cases, will also affect the power supply reliability and operational stability of the power system.Therefore, it is necessary to reasonably regulate the power consumption of temperature-controlled loads without affecting the comfort experience of residents.This can provide adjustment capabilities for the power system and reduce the electricity costs of temperaturecontrolled loads through auxiliary service revenue.
To provide a basis for the calculation of temperature control load, some scholars consider from the perspective of thermodynamics and propose an equivalent thermodynamic model to represent the temperature change process of building rooms [6][7][8]; Song et al. consider the temperature change process of building rooms [9]; for widely distributed loads, centralized control, decentralized control, and aggregator-based control models have been proposed; Zhang et al. and Gao et al. proposed a load aggregator model and used the load aggregator to control the load so that the dispatched tasks are consistent with the load aggregator [10][11]; Zhu explores the application of large-scale heating loads in power system power regulation based on genetic algorithms [12].The actual load output remains the same.However, these control strategies require the power grid dispatching center to collect user information and process it, and then the control center issues instructions to control the load.However, during peak power consumption periods, the number of devices increases, and the control area becomes wider.These control methods will make load adjustment more difficult [14].
To this end, this article will focus on the problem of heating load power regulation, intends to describe the dynamic relationship between electric heating load power input and temperature, evaluate the power/electricity characteristics of single/multiple heating loads participating in power grid regulation and economic benefits, and propose a coordinating method based on the unique load power adjustment strategy to achieve sustainable power optimization in the peak-cutting and valley-filling intervals.

Equivalent model of room temperature variation process
The interaction of the heating power of the electric heating equipment and the outdoor temperature determines the temperature change process of a building room.The room temperature change process can be approximately represented by the lumped parameter equivalent model shown in Figure 1.

Analytical analysis of model dynamic and stable characteristics
The lumped parameter ordinary differential equation describing the room temperature change process is shown in Equation (1).Preliminary analysis shows that it is a second-order linear differential equation with two inputs [13], so it can be written as a matrix, as shown in Equation (2).

∋(
wall t π are the system state variables.It can be initially seen that the input matrix is diagonal, and the two inputs will affect the two state variables independently of each other.However, the state matrix A is not diagonal, and the two-state variables will have an interactive relationship.The analytical solution of the system is directly obtained through MATLAB symbolic calculation.Through simplification, it is obtained that when time falcon tends to infinity, the steady-state solution of the state space is: ∋ ( When the system has inputs S out π , the relationship between each state variable and the input in the system's steady state will satisfy Equation (3).The model's thermal resistance parameters will significantly impact the relationship between the steady-state solutions in the steady-state situation.Based on the eigenvectors, the system can be further diagonalized to analyze the dynamic rules of the system.However, the above analysis does not consider the relationship between the input and the system output (or state variable), so it is not convenient for subsequent power adjustment of the heating load.Therefore, we will only elaborate on the analysis.Subsequently, from a time domain perspective, the system's changing rules and power adjustment capabilities of the load switch under a specific control rate will be analyzed, and the correctness of the aforementioned analytical analysis will be reflected to a certain extent [15].
For Equation (1), we build the corresponding equation model in the Simulink environment, build a model simulation of one room, and expand it to 600 rooms, as shown in Figure 2. where int π is the indoor temperature at the current moment, t S is the load switch state at the current moment, and 1 t S , is the load switch state at the previous moment.

Heating load power adjustment switching strategy based on coherence characteristics
In the case of multiple loads participating in power regulation, the total power, the up-regulated power, and the down-regulated power all change periodically; the up-regulated power and the down-regulated power are complementary.The changing characteristics of the total and down-regulated power with the average outdoor temperature are relatively similar.When the outdoor temperature changes, the ability of multiple loads to adjust power will also change significantly.We use simulation to analyze the total power consumption under different outdoor temperatures and use six loads as the analysis objects for different outdoor temperatures.The results are shown in Figure 3.It can be seen from the figure that as the average outdoor temperature decreases to meet the indoor temperature range condition constraints, the power output duration of the electric heating equipment will increase, and the total power consumption will still show periodic changes.Its duration will gradually increase, and power consumption will gradually increase.The control strategy of the system switch remains the same for each load, as shown in Equation ( 4).However, the switching control strategies of different systems are not necessarily the same.By reasonably and flexibly setting the control method of the load switch, the load can play a role in the peak-cutting and valley-filling of the system within a specified period.The load power adjustment up and down changes the energy absorbed or released by the system by changing the state of the switch during the temperature change of the system.Therefore, a more general control strategy can be regarded as a real-time change of the parameters in Equation (4).To reasonably set the opening section of the switch to achieve power regulation, it is necessary to study the switching control strategy for different loads.The most critical feature that characterizes different loads is the initial indoor temperature, that is, the relationship between the initial temperature of the room and the load switch is sought.

Total electrical power
Therefore, if the initial temperature of a specific room is T, then the index is defined to characterize the load initial value temperature level to satisfy: Considering the time constant of the load rising and falling, a gradient compensation term is introduced to correct the relationship between the initial temperature of the room and the load switch.During the peak cutting stage, the upper-temperature range of each load is calculated as follows: ))   (6) In the valley filling stage, the lower temperature range of each load is calculated as follows: ) ) *   (7)  In the peak-shaving stage, the temperature control range of each load is calculated as min T ∋ ( ; while in the valley filling stage, the temperature control range of each load is calculated as Based on the relationship between the initial temperature of the room and the load switch, corresponding control strategies can be adopted during the corresponding peak-shaving and valley-filling stages so that the inertia of the thermal load can be better utilized to realize the regulation of power grid power.

Power regulation effectiveness verification
When the number of loads increases, the differences in the system due to different initial indoor temperatures will also be reflected.The fixed and same control strategy for different loads will result in a fixed waveform, as shown in Figure 4.However, according to the changes in the initial indoor temperature, selecting the upper and lower limits of the switching changes will make the power adjustment capabilities of each system consistent, as shown in Figure 5.This article applies the proposed method to a peak-shaving and valley-filling scenario with 600 sets of room heating loads within 24 ℎ a day.Among them, the initial indoor temperature of 600 sets of loads conforms to a uniform distribution within the specified temperature.After time domain simulation, the power adjustment curve and indoor temperature changes within the specified period are drawn, as shown in Figure 6 (taking the valley filling upward adjustment from 0 to 4 points as an example).6 that in the valley filling stage from 0 o'clock to 4 o'clock, the continuous maximum adjustment power of the load increase is 681 kW , 697 kW , 710 kW at the temperature of −10℃, −5℃, and 0℃ respectively; at the temperature from 16 o'clock to 20 o'clock, during the peakcutting stage, the continuous maximum regulating power of load reduction is 320. 2 kW , 302 kW , and 291 kW at temperatures −10℃, −5℃, and 0℃ respectively.In summary, the calculated data conforms to the rules above and is relatively reasonable, verifying the accuracy of the proposed control method.

Conclusion
This article conducts technical and economic analysis of the participation of electric heating loads in the power regulation of the power system.The high proportion of new energy access has led to a scarcity of power system regulation capabilities, and there is an urgent need to develop new regulation resources, such as thermal power bottomless peak shaving, construction of pumped storage power stations, configuration energy storage, and regulation capabilities in excavation loads, etc. Modern electric loads contain many temperature-controlled loads (such as air conditioners and heating).Due to the existence of thermal inertia of buildings, the power consumption of temperature-controlled loads can be reasonably adjusted without affecting the comfort experience of residents, which can not only provide regulating capabilities for the power system but also reduce the electricity cost of temperature-controlled loads through auxiliary service revenue.Through the analysis of the dynamic characteristics of the room temperature change process model and the analysis of the ability of single/multiple electric heating loads

Figure 1 .
Figure 1.Schematic diagram of an equivalent model of room temperature variation process.

Figure 2 .
Figure 2. SIMULINK simulation model.To satisfy the temperature control interval constraints of the temperature change process, the load switch input S of the system will be determined based on Equation (4).

Figure 3 .
Figure 3.Total power consumption of multiple machine loads at different outdoor temperatures.It can be seen from the figure that as the average outdoor temperature decreases to meet the indoor temperature range condition constraints, the power output duration of the electric heating equipment will increase, and the total power consumption will still show periodic changes.Its duration will gradually increase, and power consumption will gradually increase.The control strategy of the system switch remains the same for each load, as shown in Equation (4).However, the switching control strategies of different systems are not necessarily the same.By reasonably and flexibly setting the control method of the load switch, the load can play a role in the peak-cutting and valley-filling of the system within a specified period.The load power adjustment up and down changes the energy absorbed or released by the system by changing the state of the switch during the temperature change of the system.Therefore, a more general control strategy can be regarded as a real-time change of the parameters in Equation (4).To reasonably set the opening section of the switch to achieve power regulation, it is necessary to study the switching control strategy for different loads.The most critical feature that characterizes different loads is the initial indoor temperature, that is, the relationship between the initial temperature of the room and the load switch is sought.Therefore, if the initial temperature of a specific room is T, then the index is defined to characterize the load initial value temperature level to satisfy: Room temperature

Figure 4 .Figure 5 .
Figure 4. Phase shift characteristics of indoor temperature with different loads.

Figure 6 .
Increase the power curve and increase the indoor temperature under different outdoor average temperatures.(a) Adjust the power curve upward at 0℃; (b) 0℃ raise the indoor temperature; (c) Adjust the power curve upward at -5℃; (d) -5℃ raise the indoor temperature; (e) Adjust the power curve upward at -10℃; (f) -10℃ raise the indoor temperature.It can be seen from Figure