Aggregate scheduling potential evaluation of large-scale air conditioning loads

As an adjustable load, the air conditioning (AC) load is a high-quality resource for power system operation regulation. However, due to the large number of AC loads and the heterogeneity among individual users, the scheduling potential of AC loads is difficult to accurately calculate. An aggregate scheduling potential evaluation of large-scale AC loads is proposed. Firstly, according to the operation characteristics of ACs, the aggregation models of central ACs and household split-type ACs are constructed by using the equivalent thermal parameter model and Monte Carlo sampling method respectively. Secondly, based on the proposed aggregation models of large-scale AC loads, the AC loads are rescheduled by resetting the set temperature, and the scheduling potential calculation model of central ACs and residential ACs is obtained. Finally, case studies show that AC loads have considerable scheduling potential when the indoor temperature is maintained within the range of human comfort.


Introduction
Due to the continuous development of renewable energy with uncertainties, the regulation demand for power systems is gradually increasing [1][2].Meanwhile, with the further advancement of urban electrification, flexible load resources on the user side represented by air conditioning (AC) loads show a rapid growth trend [3].The application of large-scale flexible loads has brought abundant regulation means to the power system operation regulation.However, the amount of AC loads is huge and dispersive.If a single AC load participates in the regulation of power grids, it will bring the curse of dimensionality problem [4].Therefore, aggregating large-scale AC loads to participate in the power grid regulation through aggregators is a promising method.In addition, since the power grid, load aggregators, and AC users belong to different stakeholders, the power grid cannot directly schedule the AC loads.At this time, the scheduling potential of large-scale air conditioning loads has become the primary problem that needs to be solved for AC loads to participate in power grid operation regulation.
Although some researchers have focused on AC loads participating in power grid operation regulation, they mainly focus on scheduling strategies and control strategies.In [5], a controller based on brain emotion learning is proposed to provide control signals for ACs to effectively participate in power system frequency regulation.In [6], a multi-area power system frequency regulation model considering regulating services is proposed, provided by large-scale ACs.In [7], a coordinated frequency modulation control strategy with Inverter AC units for primary frequency modulation and fixed frequency AC units for secondary frequency modulation is proposed.From the perspective of AC users, considering the characteristics of thermal appliances and customer convenience in a smart home environment, a smart heating and AC scheduling method is developed for home energy management systems [8].In [9], an adaptive optimization scheduling strategy for residential ACs based on a deep reinforcement learning method is proposed, which can adaptively learn the state transition probability in the case of tolerance violations, to make economic decisions.Considering that the AC load in the smart-building virtual power plant (VPP) has good regulatory potential, a dayahead bidding model for the VPP to participate in both the energy and frequency regulation market is established [10].However, all the above studies ignore the impact of AC loads' scheduling potential on scheduling and control strategies.
In reality, the power grid and AC loads belong to different stakeholders, and AC loads cannot be directly dispatched.When ACs participate in the power system regulation, the upper and lower limits of the output power are the key constraints for formulating the scheduling strategies.Therefore, this paper proposes the corresponding aggregation models and scheduling potential evaluation method for a large number of central AC loads and household split-type air conditioning loads.

Model of AC load characteristics
The working goal of ACs is to maintain a constant indoor temperature and provide users with a comfortable temperature environment.In essence, the intermittent output of the compressor in ACs inhales the low-pressure steam and compresses it into the high-pressure steam, which will achieve the purpose of the exchange of indoor and outdoor gas heat, to maintain the indoor ambient temperature within the set temperature range.Taking the refrigeration mode as an example, the working characteristics of ACs can be shown below: t tt ss ,Χ .In the actual operation process, the ACs' power consumption is very complex.To simplify the load model of a single AC, it can be assumed that the power consumption during operation is only 0 [11].Therefore, the real-time consumption of an AC can be expressed as follows: The second-order differential equation of the equivalent thermal parameter (ETP) model can be used to model the temperature change of the indoor environment where the AC is located.
x Ax Bu y Cx Du where Ca and Cs represent the specific heat capacity of gas and solid in the room, respectively; Rs and Rh are the indoor solid and the house equivalent thermal resistances, respectively; ηP i s t h e temperature control power of the AC; η is the energy efficiency coefficient of the AC; To, Tin, and Tm are the outdoor gas temperatures, indoor gas temperatures, and the indoor solid temperature, respectively.Due to the complexity of solving the second-order differential equations, the simulation operation time is too long when the AC load aggregation scale is large.To improve the calculation speed and avoid the complexity of the calculation process, it can be simplified into a discrete first-order model.Assuming that the AC is in the refrigeration state, the above second-order differential equation can be simplified to the discrete first-order equation.
where T t in , T t+1 in , and T t+1 o represent the indoor temperature at time t, the indoor temperatures at time t+1, and the outdoor temperatures at time t+1, respectively; R and C are the equivalent thermal resistance and equivalent heat capacity of the first-order model, respectively.

3.1Aggregation model of central AC loads
For large-scale central ACs in commercial and office areas, the operation states of ACs are uniform, and the targe t tem pe rature in e ach room of the building is the same .The refore , the equivalent thermodynamic model of ACs in multiple single rooms can be extended to obtain the aggregate equivalent thermodynamic model of ACs.The aggregation model is also a first-order equation.Compared with the single AC model, the equivalent values ηeq, Peq, Req, and Ceq are used to replace each corresponding parameter.
When the air conditioning cluster reaches the set target temperature, AC units will run in a stable state.At this time, Tin is the same as the set target temperature Tset, and Tin can be regarded as no longer changing.In the stable operation state, the AC cluster satisfies: Considering that there is a standby power Pres when a central AC is turned on but not at the output state, the discrete equation and steady-state operation equation of the AC need to be modified, as shown in Equations ( 7) and ( 8).
' o in eq eq res res eq eq If the specific parameters and temperature control target of cluster central AC are known, the room temperature and AC power characteristics can be simulated according to Equations ( 7) and (8).

Aggregation model of household split-type AC loads
Due to the individual randomness of AC users' behavior in residential areas, the above equivalent thermodynamic model is difficult to apply.In this paper, the Monte Carlo method is adopted to simulate the AC load characteristics of residential areas, and then the aggregated power of AC in residential areas is obtained by aggregating and stacking their power: () where n denotes the total number of residential ACs; Pall (t) is the aggregate power of residential AC at time t; P t i represents the power of AC i at time t.

Scheduling potential of large-scale AC loads
On the one hand, because buildings often have heat storage functions, the short-term change of AC loads will only bring a small range of fluctuations in room temperature.On the other hand, the comfortable ambient temperature of the human is a certain range.So, the scheduling ability can be obtained by resetting the AC temperature to change the AC output in the short term.

4.1Scheduling potential of cluster central AC loads
The scheduling potential of cluster central AC is not a fixed power value, but a power sequence in a certain range corresponds to the scheduling time.It is assumed that the scheduling duration of the scheduling instruction given to the cluster central AC is tdu, the outdoor temperature always remains unchanged during the scheduling period, the indoor temperature has stabilized at the AC temperature set value Tset1 before the scheduling, the room temperature will rise to the new set value Tset2 during the scheduling period tdu, and the output power of the aggregate AC is Pdu.According to Equation ( 7), the relationship between scheduling time tdu and the above parameters can be obtained.

∋ ( ∋ (
According to the thermodynamic parameters of the equivalent model and the set temperature of the AC, the output power of the aggregate AC during the scheduling period can be calculated.

4.2Scheduling potential of cluster household split-type AC loads
The average aggregation power of the cluster AC in residential areas, when the set temperature is 23℃, is defined as the power reference value Pref, and the average aggregation power after adjusting the set temperature is Pnew.Then the scheduling potential Prd can be expressed as the difference between the two average aggregation powers, and the proportion p of the scheduling potential of aggregate ACs after resetting the target temperature to the power reference value is defined as: If the AC load power at a certain set temperature is obtained by simulation calculation, the fitting relationship between the parameter p and the se t tempe rature adjustment Δt and the scheduling potential of cluster split-type AC loads can be calculated.

Case studies
Case studies are carried out by using the data of central ACs in a hotel and a residential area in Wuhan, China.Figure 1 shows the typical daily temperature variation curve of the city in summer.The operating parameters of the selected hotel central ACs are as follows: the rated power Peq is 532 kW, the standby power is Pres=0.45Peq, the equivalent energy efficiency coefficient of the units is 3.8, the equivalent thermal resistance is =0.0135C/kW eq R ↓ , and the equivalent heat capacity is C =21.85 kWh/ C eq ↓ .The residential area has 3, 000 households and the parameters of the ACs are shown in Table 1.    2 and 3, it can be seen that the proposed models can effectively simulate the variation characteristics of large-scale AC loads with the outdoor temperature and temperature set value.

Scheduling potential of large-scale ACs
Based on the proposed AC aggregation models, the scheduling potential of central AC load and residential AC load under different conditions is further analyzed.
The daily AC load of the hotel is rescheduled, and the scheduling time for each temperature reset is 1 hour.Figure 4 shows the hotel's central AC load curve before and after rescheduling.The conclusion can be drawn from Figure 4 that the rescheduling strategy can ensure that the indoor temperature is stable in the comfortable environment of the human body while reducing the AC loads, to obtain the scheduling potential of AC loads.
Furthermore, the scheduling potential of residential AC loads is analyzed based on the aggregation model of household split-type AC loads.The indoor set temperature is set to the human comfort level of 22~27 C ν , and the AC loads of 3, 000 residents in one day are rescheduled to obtain the upper and lower limits of AC loads in the residential area.The lower limit of AC loads in the residential area corresponds to the indoor set temperature of 22 C ν , and the upper limit of AC loads in residential areas corresponds to the indoor set temperature of 27 C ν , as shown in Figure 5.It can be seen that the AC loads in the residential area have great scheduling potential, and the maximum power scheduling range will reach 700 kW.

Conclusion
This paper mainly studies the evaluation method of the scheduling potential of large-scale AC loads participating in the power grid regulation.The aggregation physical models of central AC and household split-type AC are proposed respectively from the operation characteristics of AC loads, which can reflect the relationship between the consumption curve of large-scale AC loads with the outdoor and the set temperatures.On this basis, the large-scale AC load power is adjusted by resetting the set temperature under the comfortable indoor temperature of the human body, and the aggregate scheduling potential of large-scale AC loads is obtained.

where
Tin is the indoor temperature; Tset is the temperature set value of the AC; δ is the temperature control interval; Tmax and Tmin are the upper and lower limits of the working temperature of the AC respectively; st represents the switching working state of the AC at time t.If min in TT ′ , the AC is off and st=0; If max in TT ″ , the AC is on and st=1; If min max in T TT ′′ , =

Figure 2 .
Figure 2. Load power curve of ACs in the hotel.

Figure 3 .
Figure 3. Load power curve of ACs in the residential area.By comparing the aggregated power curves of AC clusters calculated by the proposed aggregation models with the actual power curves in Figures2 and 3, it can be seen that the proposed models can effectively simulate the variation characteristics of large-scale AC loads with the outdoor temperature and temperature set value.

Figure 4 .
Figure 4. Hotel central AC load curve before and after rescheduling.The conclusion can be drawn from Figure4that the rescheduling strategy can ensure that the indoor temperature is stable in the comfortable environment of the human body while reducing the AC loads, to obtain the scheduling potential of AC loads.Furthermore, the scheduling potential of residential AC loads is analyzed based on the aggregation model of household split-type AC loads.The indoor set temperature is set to the human comfort level of 22~27 C

Figure 5 .
Figure 5. Scheduling potential of residential AC loads.
So, the scheduling potential of the cluster central AC Prd can be obtained as: