1. Introduction
Owing to the great pressure of the global energy crisis and environmental pollution [
1], much effort has been devoted to integrating different kinds of distributed generations (DGs) into microgrids (MGs) in order to reduce carbon emissions and improve power quality [
2]. MGs could operate in grid-connected or islanded mode, managing all kinds of DGs effectively [
3]. This is an ideal way to realize local coordination control and optimized operation of multi-DGs, including micro-gas turbines (MTs), diesel engines (DEs), fuel cells (FCs), photovoltaics (PVs), wind turbines (WTs), small hydropower and some energy storage devices such as flywheels, super capacitors and accumulators [
4]. Most of the existing MGs are designed to work primarily under on-grid mode, excluding emergency situations [
5]. However, the impact of hybrid renewable energy sources (HRES) to power system should be paid much attention. Researches such as the unsymmetrical faults [
6], improvement of transient stability [
7], ground fault current [
8] were conducted for MG and they are beneficial to the application of renewable energies. On the other hand, more and more attention is drawn to study the stand-alone MG for its capability to supply power economically in some other particular applications, such as MGs for islands or remote areas without power grids [
9,
10].
For a small but important power system like MG, the problems of voltage balance [
11], fault current limit and power system stability are also very important. All in all, the power quality [
12] must be guaranteed through a series means such as storage coordination [
13], dynamic control [
14] or demand response (DR) [
15]. Fortunately, all these operation requirements could be included into the optimized operation model as constraints. In order to take full advantages of stand-alone MGs and promote their popularization, researchers around the world have devoted momentous efforts to the optimal operation of stand-alone MGs [
16]. However, the uncertainty of renewable power generation because of weather conditions [
17,
18,
19] and load demand challenges the economic operation a lot. Because of the uncertainty, the predicted data of renewable energy and demand is subject to errors, which negatively affect the optimized generation schedules and operation plans [
20,
21]. As a result, the economic operation cannot be realized and even the power balance would be broken in extreme conditions such as storms, abnormally high or low temperatures, or part damage of distribution facilities.
To mitigate the impact of uncertainty on optimized operation, energy storage devices were introduced to ensure the safety and reliability of the MG with consideration of their lifetime characteristics [
22]. However, the advantage of fast responses for batteries was not used to its full extent and the environmental benefit was not included in the optimization objective. Secondly, the stochastic scheduling method was applied in the MG’s optimized operation to decrease the unfavorable effects brought by the uncertainty [
23,
24,
25]. To a certain degree, the impacts of uncertainty were impaired by transferring the optimal operation into a deterministic optimization problem with a large number of stochastic scenarios. However, the fundamental issue of uncertainty was not resolved because the stochastic method merely dealt with the problem by considering more scenarios while no one could take all scenarios into account due to the complexity of the environment. Another trouble was that the computed burden increased accordingly. Thirdly, with the development of DR, the demand side has been proved an effective tool to improve system reliability and maintain power balance by responding to the dispatch information [
26,
27,
28]. The applications of DR strategies may help to settle the intermittency of renewable resources by devoting to the balance between energy supply and demand, thus minimizing the operation costs and providing a more reliable grid management [
29]. Although DR was considered in studies such as [
30,
31,
32], the expense for DR was not taken into account and the constraints for DR were not described in the optimized model.
To address these problems and realize the optimized operation of stand-alone MG, this paper establishes a multi-objective optimized model for a stand-alone MG, consisting of PV, WT, FC, DE, MT and an energy storage system (ESS) based on the coordinated operation among sources-load-ESS and an improved dispatch strategy of the MT’s CCHP operation mode. It should be pointed that multi-types of micro sources and ESS are considered at the same time so as to improve the stability and flexibility of stand-alone MG by providing various choices to satisfy the power balance and coping with emergency circumstances. And the installation cost increase of this structure is following therefore. Controllable load (CL) is taken into account as DR resources to improve the reliability. The optimized model is divided into two-time scales in order to deal with the uncertainty of load demand and renewable power generation. The first time scale model is day-ahead optimization, which is to seek a global optimal solution for all the generation resources, CL and ESS, based on the day-ahead predicted data. The renewable integration could be further optimized if storage systems are coupled with DR in order to enlarge load-shifting capacity [
33,
34]. Therefore, the coordinating operation of ESS and CL are introduced into the second time scale model, called real-time optimization, to adjust the optimized schedule considering the real-time weather condition and demand based on the day-ahead scheduling.
In terms of the optimization solution, various algorithms are developed recently, such as basic particle swarm optimization (PSO) [
35], ε-constraint method [
36] and non-dominated sorting genetic algorithm II (NSGA-II) [
37]. All these algorithms achieved relatively good result in the setting of MGs and models. However, the performance needs to be further studied when it comes to different scenarios. PSO is a stochastic and population-based evolutionary algorithm and has gained popularity in the optimized operation of MGs due to its superiorities of having few constraints on fitness function, simple principle, easy coding and rapid convergence speed [
38]. However, when major fluctuations occur in the base data of optimized model resulting from different scenarios during stand-alone MG’s optimized operation, two problems would appear in PSO algorithm: (i) the local and global search ability is not good enough to find an excellent solution in a relatively short time; (ii) the premature phenomenon would occur due to the loss of population diversity in the later iterations. Moreover, conditions could be worse especially for the model with complex variables and intricate scenarios [
39]. Chaotic optimization (CO) has a strong local search capability profiting from the characteristics of randomness, ergodicity and inherent regularity [
40] which would be effective to the optimization problem with many variables and the nature of chaos could also decrease the impact that comes from renewable energy or load uncertainty. In addition, an adequate elite retention strategy (ERS) could further improve the solution quality, as well as the convergence speed, even under the inconstant conditions [
41]. In order to solve the problems of poor search ability and premature in PSO, this paper introduces a duel-step modification (search improvement process and CO) and ERS into PSO to present a Search Improvement Process-Chaotic Optimization-Particle Swarm Optimization-Elite Retention Strategy (SIP-CO-PSO-ERS). SIP-CO-PSO-ERS was applied to solve the day-ahead scheduling model, while linear programming was used to deal with the real-time scheduling model due to the simplicity of its model which contains fewer decision variables and constraints.
The main contributions of this paper can be summarized as follows:
A new two-time scale multi-objective optimization model which aims to optimize the operation cost, load cut compensation and environmental benefit of stand-alone MGs that consists of electric, thermal and cooling energy styles based on CL and multi-DGs; the synergetic response of CL and ESS (battery in this paper) in real-time scheduling offsets the operation uncertainty quickly, and the improved dispatch strategy for CCHP enhances the system economy, guaranteeing comfort feel;
A duel-step modification and ERS are introduced into PSO to present SIP-CO-PSO-ERS, which has a strong search capability and fast convergence speed; four typical scenarios are designed according to diverse situations to verify the adaptation of SIP-CO-PSO-ERS and proposed optimized model.
This paper focuses on the achievement of the presented points and is organized as follows.
Section 2 gives descriptions of the two-time scale model.
Section 3 gives a detail explanation of the proposed SIP-CO-PSO-ERS method. Simulation is given in
Section 4 to illustrate the advantages and validity of the proposed algorithm and model.
Section 5 gives a conclusion.
3. SIP-CO-PSO-ERS Algorithm
For a multi-objective optimization problem, the best condition is to find the absolute optimal solution. However, subgoals are usually contradictory with each other and it’s impossible to find a common solution that makes all the sub-goals achieve optimal values at the same time. Therefore, the multi-objective model is transformed into a weighted single-objective model to optimize the whole system’s operation cost. Considering that the model of the first time scale has been converted into single-objective optimization model, this paper proposes SIP-CO-PSO-ERS to solve the day-ahead scheduling model. Fewer decision variables and constraints simplify the model in the second time scale. Linear programming in MATLAB/Optimization Tool (R2011B, MathWorks, Natick, MA, USA) was conducted to solve the real-time scheduling model.
3.1. Basic PSO Algorithm
PSO is a meta-heuristic intelligent algorithm on the basis of population search [
49]. The individuals of population update their velocity vectors according to their own speed, individual optimal solution
pbest and population optimal solution
gbest to converge to global optimal solution during all the iterations. The velocity and position for particle
i at moment
t are updated as follows:
where
w is the inertia weight for PSO;
c1 and
c2 are both learning factors;
r1 and
r2 are random numbers between 0 and 1;
d is the dimension of the optimization problem;
pi,j and
pg,j represent the individual and population optimal solution.
vi,j(
t) and
vi,j(
t + 1) are the velocity vectors for particle
i in the
j-th dimension at moment
t and
t + 1; accordingly,
xi,j(
t) and
xi,j(
t + 1) are the position vectors for particle
i in the
j-th dimension at moment
t and
t + 1.
Due to the full use of individuals’ and group’s experience, the PSO algorithm is able to approach the optimal solution with a relatively high convergence efficiency [
50]. Because of the consideration of CL and multi-scenarios, more decision variables, constraints, and intricate data for variable scenarios complicate the optimization model. Therefore, the PSO exhibits the problems of premature, poor local and global search ability when solving the optimized operation model of stand-alone MG [
51]. Specially, a fall into the local optimum because of the oscillation around certain local optimums with inappropriate step lengths would occur. In addition, the convergence speed is slow in later iterations because the optimum search goes beyond the constraints easily when there is great fluctuation in predicted data from different scenarios, causing the process to repeat several times until the constraints are all satisfied. However, the MG’s day-ahead optimized scheduling requires not only a faster solution speed to meet the dispatch timeliness, but also an excellent search performance to satisfy dispatch accuracy. Reasonable modification must be developed to improve the properties of basic PSO. In this paper, a dual-step modification consisting of SIP and CO is introduced into PSO as well as ERS.
3.2. Search Improvement Process (SIP)
Considering that a local optimum cannot take full advantages of different DGs for a stand-alone MG in economy and environmental protection, the total ability of PSO in both global and local optimizing must be improved. SIP was conducted on all the particles during the optimization to improve the global search ability for PSO. The global search ability improvement of proposed SIP is based on [
52]:
- (1)
Increasing the population’s diversity by mutations and cross operations.
- (2)
Promoting all the particles to move toward the best promising local or global individuals.
After the update of both velocity and position vectors for particle i, a modified process was carried out as follows:
- (1)
Find out the best individual Xbest and the worst individual Xworst through the calculation of fitness function.
- (2)
For each particle
i, two particles
Xm and
Xn are selected from the particle swarm randomly such that m ≠ n ≠ i, then the following two particles are generated by cross style:
where Δ is a random number between 0 and 1,
X1cross and
X2cross are two new particles obtained by cross.
- (3)
A mutation process is implemented after the cross to get five new particles, and the
j-th dimensions of
X1muta,
X2muta,
X3muta,
X4muta and
X5muta are obtained by:
where
k1,
k2, …,
k8,
λ1 and
λ2 are all random numbers range from 0 to 1; Equation
λ1 +
λ2 = 1 is satisfied.
- (4)
Then the best particle among X1muta, X2muta, X3muta, X4muta and X5muta is selected by fitness values to compare with Xi. If it is better than Xi, replace Xi with the selected particle; otherwise, Xi will remain in the initial position. After SIP, CO will be conducted.
3.3. Chaotic Optimization (CO)
The ergodicity and randomness characteristics of chaos could realize local deep search [
53]. Better local optimized ability is achieved by searching the space near superior individuals. The basic principle for chaotic optimization-particle swarm optimization (CO-PSO) to strength the local search ability is mapping the chaotic variables into the optimized variables’ space linearly. For a given optimization target, the search process is corresponding to the traversal process of chaotic orbit. The steps of chaotic search in this paper are indicated as:
- (1)
Suppose
k = 0, and map the decision variables
xjk,
j = 1, 2…
d into chaotic variables
sjk between 0~1 for every dimension of the solution.
xmax,j and
xmin,j are the upper and lower search bounds of the
j-th dimension:
- (2)
Calculate the chaotic variables of the next iteration:
- (3)
Convert the chaotic variables
sjk+1 into decision variable
xjk+1 by the following formula:
- (4)
Assess the new obtained solution by xjk+1. Make a decision by different result: if the new obtained solution is better than the initial one or the chaotic search has reached the maximum iteration, the new obtained solution will be the final result of chaotic search; otherwise, set k = k + 1 and turn to Step 2.
In this paper, the first 20% of the best particles during each iteration are chaotic searched in order to further excavate the adaptability of excellent particles and improve the local search ability of optimization algorithm.
3.4. Elite Retention Strategy (ERS)
The premature of an optimization algorithm is caused by the loss of population diversity, which is due to the population’s pattern simplification in later iteration. It is an obstacle to find the global optimal solution during the stand-alone MG’s optimized operation. ERS is a procedure to preserve the optimal individuals, or a part of excellent individuals during each iteration, and replace the worst individuals at the beginning of next iteration. The ERS could avoid the loss of better solutions generated during each iteration and maximize the advantages of superior individuals. That is to say, poor solutions will be superseded as soon as possible. In addition, the population diversity is guaranteed because of the reservation of initial particles at the beginning of each iteration as well as the connection between two generations. Through this process, the premature phenomena will be impaired and the convergence speed is accelerated. In this paper, ERS is integrated into basic PSO algorithm. Specifically, the top 10% of the best individuals are reserved at the beginning of each iteration. Then the last 10% of the population in next-generation individuals will be replaced correspondingly.
3.5. Detailed Procedures of SIP-CO-PSO-ERS
Figure 5 exhibits the structure of presented algorithm and the detailed procedures of SIP-CO-PSO-ERS in this paper are given as follows:
- (1)
Initialize the position and velocity of each particle in the population.
- (2)
Assess the fitness of each particle by objective function calculation.
- (3)
Preserve current particles’ positions and fitness values into pbest of each particle; preserve the position and fitness value of the optimal individual in current population into gbest.
- (4)
Save the top 10% of the best individuals whose fitness values are the best.
- (5)
Execute the SIP on all particles.
- (6)
Evaluate the fitness of each particle and search the top 20% of best individuals with CO; update pbest and gbest of the whole population.
- (7)
If the solution has reached the required search accuracy or the maximum iteration, stop the chaotic search and export the result, otherwise, turn to step 8.
- (8)
Update the position and speed of each particle; evaluate all particles’ fitness values and replace the last 10% individuals with the worst fitness by the best individuals preserved in step 4, then turn to step 3.
3.6. The Limitations of Proposed SIP-CO-PSO-ERS
SIP-CO-PSO-ERS has many advantages such as better adaptability, fast convergence speed and excellent search ability. However, limitations are also existed, as follows:
- (1)
SIP-CO-PSO-ERS consists of different procedure modules due to the algorithm integration. As a result, it’s really hard work for programmers to write the program correctly. Any errors in the code would lead to a wrong operational result. More time should be spent on the programming so as to ensure the correct code;
- (2)
The particles that are generated randomly increase the operation time to some extent. When the proposed model and SIP-CO-PSO-ERS are applied in a specific MG, initial values of particles could be given according to MG’s historical operation states so as to decrease the iteration numbers and operation time.
3.7. The Framework of Stand-alone MG’s Optimized Operation
Figure 6 shows the integrated framework of this study about the optimized operation for proposed stand-alone MG in detail. The final dispatch scheme is obtained by the results of day-ahead and real-time scheduling models.