3.1. Analysis of Power Characteristics of Aggregated IAC Load in DR
Figure 4 shows a schematic diagram of the load rebound. The black line is the load baseline. The red line shows the load as load rebound occurs. In order to participate in a DR project at noon in summer, the setting temperature of all IACs shall be raised uniformly at the beginning of a peak load in a day (
). After the DR task is completed, the setting temperature shall be uniformly set back at the end of the peak load (
). The frequency of each compressor is increased and the total power will rise instantly.
Therefore, it can be seen that the total power of the aggregated IAC load is closely related to the setting temperature. The operating status of the aggregated IAC load is aggregated by the operating status of individual IACs, which are directly affected by the setting temperature sequence. The setting temperature sequence of the aggregated IAC load can be represented by a matrix
T of the following form:
Each row in the matrix represents each individual IAC in the aggregated IAC load. Each column in the matrix represents a moment. Any element
in the matrix represents the setting temperature of the
-th IAC at time
. For the
-th IAC, when not participating in the DR project, the setting temperature is kept constant while in operation, that is:
where
and
are the start and end time of operation respectively, and
is the original setting temperature.
When participating in the DR project, the setting temperature should be increased to meet the demand of load reduction, that is:
where
and
are the start and end time of DR respectively,
is the setting temperature of DR.
As can be seen from the above, the direct cause of the load rebound is the unreasonable setting of and , while only determines the load reduction. Therefore, the determination of the DLC strategy includes two aspects. First of all, the setting temperature of each IAC in the DR period should be determined according to the specific load reduction requirements. Then, the reasonable control of and is considered to suppress load rebound.
3.2. Determination of the Setting Temperature
It is assumed that each IAC has entered a steady state operation state before the DR project. The initial operating frequency of the
-th IAC compressor
is determined by its original setting temperature
. The initial active power can be given by:
When participating in DR, the active power can be given by:
where
is the frequency of the compressor when participating in DR, which is directly determined by
.
The load reduction of the aggregated IAC load can be given by:
where
N is the number of individual IAC. Set
equal to the DR target to obtain a set of indefinite equations about
. In order to consider users’ comfort, each temperature setting adjustment should be as small as possible, that is, to minimize the variance of the adjustment of the setting temperature. The variance of the adjustment of the setting temperature can be given by:
The optimal solution of each can be obtained by minimizing . The thus obtained can be used to adjust the setting temperature in a minimum range to ensure users’ comfort while ensuring the DR target.
3.3. A Temperature-Queuing Method to Suppress Load Rebound
After determining the DR target, DLC can be used to directly adjust the setting temperature of the aggregated IAC load to achieve load reduction. However, the general DLC method can easily cause load rebound. Therefore, it is of great significance to deeply study the control methods to suppress load rebound under the premise of ensuring the DR target.
The method of loose control for users is generally considered. In a given period of time, users can freely control their own and , so that the DR items of each IAC are staggered in the form of random distribution. However, the problem is that the load aggregator weakens its ability to control the IAC load. The intelligent control terminal of IAC will no longer play the original control function, and may be unable to achieve the DR target as expected.
For this reason, using the temperature-queuing method should be considered to ensure that each
and
are staggered.
Figure 5 shows a schematic diagram of the simplest equally spaced queuing method. The start and end times of each IAC are equidistantly arranged in a later order, so as to avoid load rebound. However, it is difficult to obtain the optimal solution of the total power curve in this way. Thus, it is necessary to adopt intelligent algorithms to solve the optimal solution of the final staggered arrangement of
and
. The genetic algorithm is used to solve the problem.
A genetic algorithm mainly includes several steps of population initialization, fitness function calculation, selection, crossover and mutation. The optimization process is shown in
Figure 6. The main parameters of the genetic algorithm used in this paper are shown in
Table 1.
It is worth noting that a large maximum number of iterations is set to ensure that a convergent optimal solution is obtained. The ETP model is used to model the IAC load which ensures that the steady-state operation process fluctuates within the dead zone temperature. The above guarantees the stability of the proposed model.
For the aggregated IAC load containing
individual IAC, the solution variables are
and
(
), and a chromosome can then be coded as:
When setting the code value in the genetic algorithm, each
and
need to be constrained so that the DR project can be carried out within the specified time interval, which is:
where
and
are the earliest and latest moments when DR starts, and
and
are the earliest and latest moments when DR ends.
For the final total power curve, it is expected to meet the following two basic requirements:
The total power should change at a certain rate at the start and end of the DR period instead of instantly dropping to the total standby power or rising to the total cooling power, corresponding to time
and
in
Figure 4, which can be represented by:
where
is the final total power,
and
are the maximum rate of change of the total power respectively at the start and end of the DR period.
The total power should be as close as possible to the baseline load after the end of the DR period, corresponding to the period
to
in
Figure 4, which can be represented by:
where
is the baseline load,
is the rebound limit coefficient.
Fitness value is the basis for selection. The higher the fitness, the more likely the individual is to survive. The second requirement is then selected as the main fitness function of the genetic algorithm, and the first requirement is selected as the constraint.
The main function of the fitness function considering the requirement
b can be represented by:
The penalty function considering the first requirement can be represented by:
where
is the range that meets the requirements.
The fitness function can be finally represented by:
All of the above constitute a complete DLC strategy of aggregated IAC load to regulate the frequency of the microgrid. It can be seen from the above content that, compared with the strategy in [
14], the biggest advantage of the strategy proposed in this paper is that it avoids precise identification of the operating state space. This strategy only needs to read the setting temperature data, which greatly improves the feasibility.