1. Introduction
The microgrid, as is defined by the Consortium for Electric Reliability Technology Solutions (CERTS), is the integration of interconnected load and distributed energy resources and acts as a single controllable entity with respect to the traditional power grid [
1,
2]. However, due to the high intermittence of renewable energy sources (RESs), new challenges have been posed to the operation and control of microgrid.
In order to overcome this problem, battery energy storage systems (BESSs) [
3] are installed in microgrids due to their fast dynamic responses and accurate performances in absorbing excessive power and compensating for insufficient power. In [
4], a BESS was used to provide fast active power compensation and improve performances of load frequency control. In [
5], a novel state-of-charge-based control strategy is proposed to smooth the output fluctuation of a hybrid system. Finally, in [
6], a cooperation control strategy for wind power and battery storage is proposed to provide frequency regulation. The supply–demand balance can be well guaranteed through an appropriately designed control strategy of BESSs. Additionally, the rotating inertia of a microgrid is significantly reduced due to the widely use of power electronic converters, which will result in greater frequency oscillation if there exists supply–demand mismatch [
7,
8]. Hence, in order to stabilize system frequency during the optimal control process, it’s significantly important to employ more effectively control strategies.
Generally, there are three main control strategies, including centralized control strategy [
9,
10], decentralized control strategy (DCS) [
11,
12], and distributed control strategy. The centralized control strategy, which is implemented through a central controller, requires global information of a microgrid. That is to say, a complex communication network and a powerful central controller are essential. Additionally, microgrid will be broken down by the single-point fault of the central controller. In contrast, components based on fully decentralized control strategy are only controlled by the local information and do not need to communicate with each other, which enhances system robustness. However, because of the deficiency of broader available information, it is not effective to use all available resources of microgrid for optimization [
13]. Conversely, DCS only needs the information obtained from the local communication network.
Recently, there are various DCSs for microgrid operation and control. In [
14], an incremental cost consensus algorithm is proposed to illustrate the use of distributed control in a microgrid, and the algorithm was extended by considering the generator capacity. Then, in [
15], based on the incremental cost consensus algorithm, an improved distributed control strategy is proposed through changing the updating rules to minimize total power loss. Similarly, in [
16], another improved distributed control strategy based on the consensus algorithm is proposed for microgrid optimal control. Moreover, the distributed cooperative control strategy proposed in [
17] also effectively maintains total power balance and minimizes total power loss. Then, inspired by the dynamic average consensus estimation method, an optimal control strategy is proposed in [
18] to minimize the generation cost of components in a distributed manner. With further investigation of the distributed algorithm, authors in [
17,
18] propose a novel distributed strategy in [
13] to coordinate multiple BESSs under wind uncertainties. The fully distributed power dispatch method proposed in [
19] achieves rapid frequency recovery and minimizes generation cost for a microgrid, in which a subgradient-based consensus algorithm is used to recover frequency and an average consensus algorithm is used to eliminate frequency disturbance caused by measurement error. However, although the aforementioned literatures can realize distributed optimal control of microgrid, the fluctuation of frequency can be further controlled during the optimal control process.
Microgrids based on the previous optimal methods still have small supply–demand deviation after the optimization process. It can be neglect in traditional power systems. However, the frequency of a microgrid changes more rapidly and sharply with the existence of supply–demand mismatch. Additionally, considering the stochastic characteristic of wind turbine generators and other renewable energy sources, it’s necessary to propose a more available control strategy which can provide faster frequency recovery during optimization process. Therefore, this paper proposes a novel distributed optimal control strategy to realize the minimization of BESS cost, and to simultaneously provide fast frequency recovery. The multi-agent system (MAS) framework [
20] and the consensus-based optimization algorithm are employed in this paper. Furthermore, the measurement of supply–demand mismatch is replaced by the control signal calculated by a supplementary controller based on the improved linear active disturbance rejection control (ILADRC) algorithm [
21] to realize fast frequency recovery. Compared with methods in [
14,
16] and other literatures, the frequency stability of a microgrid can be better guaranteed based on the proposed method.
This paper is arranged following:
Section 2 introduces consensus algorithm and ILADRC theory.
Section 3 formulates the problem. The proposed control strategy and its implementation are described in
Section 4. Simulation results and analysis are shown in
Section 5. Finally, conclusions are drawn in
Section 6.
3. Problem Formulation
A framework of an islanded microgrid is presented in
Figure 1, which consists of multiple BESSs, two wind power generators, and three load demands. In a system’s stable state, the active power balance of an islanded microgrid can be represented as:
where
,
, and
are the output power of
BESS, RES, and load demand, respectively. Furthermore,
,
, and
are the index sets of BESSs, RESs, and load demands, respectively.
Although the wind power generator can make contributions to the frequency regulation through the inertia control strategy, the output power cannot be accurately controlled due to its intermittent nature. Additionally, the wind power generator is almost undispatchable. In contrast, because of the fast dynamic responses and accurate performances, the BESSs can be dispatched to eliminate the supply–demand mismatch caused by the intermittence of RESs and unpredicted fluctuation of load demand.
The cost function for BESSs is often modeled as:
where
C is the cost, and nonnegative
and
are the cost coefficients.
and
are the lower and upper bounds of
BESS power output, respectively.
Then, the optimal control problem of BESSs can be described as follows:
The traditional solution of this situation is to use the Lagrange multiplier method, and the Lagrange function for the optimal problem can be constructed as:
where
is the Lagrange multiplier associated with the equality constraint.
The Lagrangian operator
is minimized when the following equation is satisfied:
which yields the following optimal solution:
Then, through substituting Equation (
15) into Equation (
10), the optimized incremental cost of each component can be represented as:
Furthermore, considering of the generation constraints of each component, the optimal solution is given as [
23]:
where
is the optimal incremental cost.
The above solution can be solved through the centralized control strategy. However, due to the timely communication and calculation manner, the centralized control strategy cannot provide the desired responses under unexpected and rapidly changed disturbances. In contrast, the distributed control strategy is flexible, scalable, reliable, and cost-effective to implementation, and it is wildly adopted to maintain system stability and provide optimal control performances.
With the theory of consensus algorithm, the optimal control problem can be solved by Equation (
18):
where
r is the incremental cost.
Given that all the components are operating in a stable state at
, and following the consensus algorithm, the optimal incremental cost will converge to Equation (
19) at
.
where
T is a convergent period to obtain the optimized incremental cost with a consensus algorithm.
However, as described in Equation (
20), the result obtained by the consensus algorithm in one convergent period is not equal to that calculated by the Lagrange multiplier method with a centralized control strategy. That is to say, the supply–demand balance is broken. The supply–demand mismatch is described by Equation (
21).
In order to deal with the above problem, an improved distributed approach was proposed by [
14], and the updating rule for the leader agent follows:
where
is the convergence coefficient, which controls the convergence speed of the leader agent.
Then, [
16] modified the updating rules for agents coordination, which are represented as:
In the initial state,
. After completing one convergent period,
, then
works to eliminate the supply–demand mismatch until
. As is shown in Equation (
24), the optimal incremental cost converges to that calculated by central control strategy.
5. Simulation Results and Analysis
The simulation results are described in this section and the simulations are testing in an islanded microgrid with a configuration of five BESSs, two WTGs, and three load demands. The parameters of the BESS are summarized in
Table 1, and the parameters of the WTG and load demand are summarized in
Table 2. The wind turbine generator used in this work is the doubly-fed induction generator, which will not be introduced in detail in this paper. The supplementary controller parameters are shown in
Table 3. All the simulations are testing in MATLAB/Simulink and the step time is 0.01 s.
Furthermore, this study adopted the rate of change of frequency (RoCoF) and the integral of time-weighted absolute value of the error (ITAE) to be the evaluation indexes of system frequency stability. The RoCoF and ITAE are described by Equations (25) and (26), respectively.
5.1. Case A
In this case, performances of the proposed method at initial state are investigated. The initial power output of BESSs are shown in
Table 1. The fluctuation of supply–demand and WTG power output are supposed to be stable and their initial values are shown in
Table 2. The response of total active power deviation and microgrid frequency deviation are described in
Figure 11. As is shown in
Figure 11, the frequency based on the proposed distributed strategy can be recovered to its normal value in 2.7 s. And the overshoot of frequency is 0.0006 Hz, it’s better than those derived by other methods. The detailed comparison results are shown in
Table 4. Obviously, microgrid system with the proposed distributed strategy has better frequency recovery capability and desired optimal performances. The convergence curve of incremental cost is described in
Figure 12 and the active power of each BESS is shown in
Figure 13.
5.2. Case B
The validity of the proposed method in handling the situation with unpredicted fluctuation of load demand is demonstrated. Suppose that WTG power is stable, and the load demand suddenly increases from 1.0 p.u. to 1.1 p.u. at 10 s. The total active power deviation can be well eliminated by all three distributed control strategies, as is shown in
Figure 14b.
However, the overshoot of frequency based on the proposed control strategy is 0.0115 Hz, which is smaller than 0.0617 Hz and 0.0148 Hz obtained through the methods in [
14,
16], respectively. Additionally, the settling time of the system frequency with the proposed control strategy, which is 4.9 s, is shorter than that based on the other methods. The convergence curve of incremental cost and the power of BESSs are described in
Figure 15 and
Figure 16, respectively. Simulation results in
Table 5 indicate the significant importance of the supplementary controller with the ILADRC algorithm. The supplementary controller can compensate for the deviation of frequency faster, and the incremental cost of the BESSs can also converge to the optimization value simultaneously.
5.3. Case C
In the practical environment, unpredictable disturbances cannot be neglected anymore. Then, the anti-disturbance ability of the distributed optimal control strategy is of significant importance. So, the system performances under stochastic power output of the WTGs are investigated. The total load demand is supposed to be stable at 1.0 p.u.
The stochastic characteristic of wind power is shown in
Figure 17. The comparison results of supply–demand mismatch and frequency deviation are described in
Figure 18. From comparison results shown in
Table 6, it can be found that frequency fluctuation with the proposed method is in an extremely smaller range than that based on other methods, which demonstrates the superior anti-disturbance capability of the proposed method. The power of the BESSs and the convergence curve of incremental cost are shown in
Figure 19 and
Figure 20, respectively.
6. Conclusions
In an islanded microgrid, the system frequency changes more rapidly and sharply than that in a traditional power grid while supply–demand mismatch occurs. Therefore, this paper proposes a novel distributed optimal control strategy of BESSs in an islanded microgrid, which can provide optimal control performances and simultaneously realize faster frequency recovery, compared with previous studies. A multi-agent system based on the consensus algorithm is adopted in the proposed control strategy. A supplementary controller based on the ILADRC algorithm is employed to greatly enhance the frequency stability. The validity of the proposed distributed strategy is demonstrated by adequate simulation experiments, comparing the proposed method with two previous methods.
On the one hand, the proposed control strategy realizes the maximum welfare of the BESSs in a microgrid, so it makes economic sense. On the other hand, practically, the proposed method guarantees the microgrid stability while the components are operating at minimum cost, which ensures system security and consumers’ experience. Based on the above aspects, this work realizes the economic operation of a microgrid without reducing power quality, and it even greatly enhances system stability.
In future work, the proposed distributed optimal control strategy can be improved for a system with more realistic constraints. Furthermore, it also has the potential to solve multi-microgrid optimal control problem.