1. Introduction
With the shortage of fossil energy and the deterioration of the natural environment, renewable energy sources (RESs) represented by wind power and photovoltaic (PV) have been rapidly developed. With higher distributed energy resources integration, the traditional distribution network is gradually becoming an active distribution network (ADN) and the optimal operation of the distribution network is facing new challenges [
1,
2,
3]. Active power optimization and reactive power optimization (RPO) are two important aspects of system optimization. Active power optimization is also called economic dispatch, which often aims to minimize the total day-ahead or real-time operation cost by deciding the output of distributed generations (DGs) and charge–discharge power in the distribution system. RPO is an important measure to ensure safe and economic operation of distribution network, which can regulate the system voltage profile and power flow, as well as reduce the active power losses [
4,
5].
The RPO for ADN is often formed as a mixed integer nonlinear programming (MINLP) problem, which should deal with both continuous control variables such as DG output and discrete control variables, such as capacitor banks (CBs) and on-load tap changer (OLTC) [
6,
7]. Meanwhile, the RPO problem is essentially nonconvex due to the nonconvex and nonlinear power flow equations, which are difficult to solve. Various methods have been proposed to cope with this problem, which can be divided into two categories: Heuristic algorithms and analytical methods [
8]. The heuristic algorithms have attracted much attention because they are relatively easy to implement. A chaotic particle swarm optimization (PSO) was employed in [
9] to minimize the system losses using voltages of wind power generator, tap changers, and shunt compensators. Shaw et al. [
10] proposed a gravitational search algorithm for the reactive power scheduling, with the aim of minimizing the active power losses. A multi-objective reactive power scheduling model was proposed in [
11], where the hybrid fuzzy multi-objective evolutionary algorithm was utilized to obtain the Pareto front. A novel cuckoo search algorithm was used in [
12] to overcome optimal power flow problems and enhance the operation capacity of hydrothermal power systems. However, the obvious drawbacks of the heuristic algorithm are that they often require long calculation time and it is easy for them to fall into local optimum. Therefore, more researchers focus on the exploration of the analytical methods. Traditional analytical methods include gradient descent, interior point methods, quadratic programming, etc. However, due to the nonconvexity of power flow equations, these traditional methods can only guarantee a local optimal solution [
13]. Thus, convex programming methods are more desirable. The second-order cone programming (SOCP) relaxation, which is based on the branch flow model, is a promising convexification method because of its lower computational complexity [
14,
15]. The accuracy of SOCP relaxation has been verified in references [
16,
17,
18].
Although a great number of methods have been proposed in the literature, they did not take the joint active and reactive power scheduling into consideration. Actually, the R/X ratio of the distribution system is large, the P–Q is not decoupled, and active power scheduling affects the voltage as well. In addition, apart from active power output, the inverter-based DG is allowed to provide reactive power as an ancillary service to further reduce power losses and improve the network voltage level [
19,
20,
21]. Therefore, a joint dispatch of active and reactive resources for ADN is highly desired to take full advantage of renewable energies to reduce the operation cost and active power losses, as well as improve the voltage stability.
It is worth noting that, with the large-scale wind power and PV access to distribution network, the random and intermittent nature of such resources may have an adverse effect on distribution network [
22]. As a flexible power supply, the energy storage system (ESS) provides a new idea to mitigate the power fluctuations of intermittent RES. The application of ESS in ADN may provide auxiliary services and enhance system reliability, as well as improve system economy [
23,
24]. As one typical DG, the distributed ESS was applied to improve voltage profile in [
25,
26]. A coordinated dispatch problem of a wind farm with ESS was proposed in [
27]. The results indicate that ESS can greatly improve the dispatchability of wind farm. The integration of ESSs with different capacities into the power grid has been studied in [
28] to analyze the improvements in the power quality. Reference [
29] has formulated a stochastic programming framework to choose optimal energy and reserve bids for ESS owners based on the electricity market. Chen et al. [
30] considered the unit commitment problem for microgrids; the optimal capacity and operation strategy of ESS for both the grid-connected and islanded modes of microgrids were analyzed. Reference [
31] investigated the coordinated optimal dispatch of ESS with renewable energies in microgrids to minimize the electricity costs. Fan et al. [
32] analyzed the stochastic optimal operation of microgrid with ESS; the influences of ESS on the optimization results were fully investigated.
Based on the above discussions, a coordinated optimization model for ADN with ESSs is proposed in this paper, where the active and reactive power are handled simultaneously. In particular, the reactive power capabilities of DGs and ESS are fully utilized to minimize power losses and improve voltage profiles.
The remainder of this paper is organized as follows:
Section 2 describes the mathematical formulation of the coordinated optimization problem for ADN with ESS. The SOCP relaxation method is used to transform the original MINLP problem into a tractable mixed integer SOCP (MISOCP) problem in
Section 3.
Section 4 presents the case studies. Finally,
Section 5 concludes the paper.
5. Conclusions
This paper proposed a dynamic coordinated optimization model for joint dispatch of active and reactive resources in ADN with ESSs. Taking the power losses, the operation cost, and the voltage deviation of the distribution network into consideration, an MINLP optimization model was formulated, which was further transformed into an MISOCP model by SOCP relaxation to reduce the difficulty of problem solving. The comparison with the original MINLP model (solved by PSO) on 33- and 69-bus distribution network shows the effectiveness and efficiency of the proposed method.
The main contributions and the conclusions are summarized as follows:
(1) The power losses, the operation cost, and the voltage deviation can be improved significantly after the coordinated active-reactive optimization.
(2) The SOCP relaxation is used to transform the original MINLP model into a MISOCP model, thus reducing the difficulty of problem solving and verifying the exactness of SOCP relaxation.
(3) ESSs help to reduce the total operation cost of an ADN effectively.
(4) The reactive power regulation of DGs and ESSs play an important role in improving the system security and economy.