Energy management of cooperative microgrids: A distributed optimization approach

https://doi.org/10.1016/j.ijepes.2017.10.021Get rights and content

Highlights

  • Direct energy exchange among microgrids can reduce the energy cost.

  • The consideration of distribution networks is necessary for system stability.

  • The effects of topologies of the direct energy exchange network are studied.

  • The cooperation among microgrids depends on their locations and demand profiles.

  • The proposed distributed algorithm works for large systems.

Abstract

The cooperation of multiple networked microgrids (MGs) can alleviate the mismatch problem between distributed generation and demand and reduce the overall cost of the power system. Energy management with direct energy exchange among MGs is a promising approach for improving energy efficiency. However, existing methods on microgrid cooperation usually overlook the underlying distribution network with operating constraints (e.g., voltage tolerance and power flow constraints). Hence the results may not be applicable to actual systems. This paper studies the energy management problem of multiple MGs that are interconnected by both the direct current (DC) energy exchange network and the alternating current (AC) traditional distribution networks. In our problem, each MG is equipped with renewable energy generators as well as distributed storage devices. In order to handle the non-convex power flow constraints, we exploit the recent results of the exact optimal power flow (OPF) relaxation method which can equivalently transform the original non-convex problem into a second-order cone programming problem and efficiently determine the optimal solution successfully. The objective of our problem is to minimize the overall energy cost in a distribution network consisting of multiple MGs, with the practical operating constraints (e.g., power balance and the battery’s operational constraints) explicitly incorporated. Considering the privacy and scalability, we propose a distributed algorithm with convergence assurance based on the alternating direction method of multipliers (ADMM). We also implement our method based on the model predictive control (MPC) approach in order to handle the forecasting errors of the renewable energy generation. Simulations are made for different MG exchange topologies on three radial distribution network testbeds. Numerical results demonstrate that certain topologies are more favorable than others, and the cooperation strategy for the energy exchange is significantly affected by the MGs’ locations in the distribution network.

Introduction

Microgrids (MGs) are localized grids which accommodate a variety of distributed energy resources (DERs) and different types of energy users. They are believed to be a promising paradigm that can improve the utilization of DERs and also users’ benefits [1]. However, in order to ensure the stability and reliability of MGs, many tough problems need to be resolved, among which, the mismatch between the distributed generations and loads due to the intermittent nature of DERs (e.g., photovoltaic (PV) generators and wind turbines (WT)) is a key issue and draws lots of attention. In order to handle this, several approaches can be employed.

One solution is to take advantage of distributed storage (DS) devices (e.g., batteries), which however suffer from two drawbacks: a huge capital investment increases dramatically with DS capacities, and significant energy transfer loss occurs due to the inefficiency of charging and discharging processes. Therefore, relying solely on DS units is not enough. Another promising solution is the direct energy exchange among neighboring and cooperative MGs by dedicated energy exchange network (denoted as EEN hereinafter). An EEN is composed of direct power lines connecting a cluster of geographically correlated MGs, enabling energy sharing and trading among them [2]. By exploiting the diversified distributed generation and consumption profiles, EENs have the following advantages: first, reduced power transmission loss thanks to the short distance between MGs, and second, lower energy bills for the MGs because the internal energy trading price is higher than the buyback price, while lower than the selling price of the utility company [3], [4]. Thanks to these advantages, MGs will have enough incentives to cooperate with each other in order to minimize the overall cost of the system [5] and benefit from the energy sharing via the EEN. In fact, the similar concept of the peer-to-peer direct current (DC) EEN among MGs has been proposed in [6], [7], and this DC EEN is in parallel to the underlying AC distribution network. Accordingly, we add the structured relationship between these two networks in Fig. 1. From the figure, we can see that each MG is connected to the traditional AC distribution network and at the same time, they are interconnected by a dedicated DC EEN. The EEN enables the direct energy exchange among MGs and the connection to the distribution network can ensure the balance between supply and demand for each MG.

The coordinated energy management of networked MGs with energy sharing has been warmly discussed in the literature [8], [5], [9], [10], [11], [12], [13], [14], [15]. Gregoratti et al. [5] developed a distributed convex optimization framework for energy trading between islanded MGs, where all MGs cooperate with one another to minimize the total cost of the system. Lakshminarayana et al. [8] analyzed the tradeoff between the use of storage and the cooperation by energy sharing among DG resources with the objective of minimizing the time average cost of the energy exchange within the grid. A problem in these prior works is that the transmission loss incurred by the energy sharing is either ignored [8], [5], [9], [10], [11] or oversimplified by a linear model [12], [13], both of which are not realistic in practice. In contrast to these, some recent works considered the energy sharing problem of MGs with a more accurate loss model [14], [15], by using a quadratic function of the energy transferred. Another issue in [8], [5], [9], [10], [11], [12], [13], [14], [15] is that their models were proposed in an abstract way with the underlying distribution networks neglected. In fact, the MGs, if not operated in an islanded mode such as those in remote areas, are connected with the main grid via the points of common coupling (PCC) through the distribution networks. For this reason, the associated power flow constraints and other system operational constraints [16], [17], [18] of the distribution networks should be taken into account such that the obtained scheme can be applicable to actual systems and truly benefits users with the stability [19] and reliability of the system ensured.

In this paper, motivated by the above considerations, we present a model for the energy management of cooperative MGs with energy sharing under distribution networks [20]. The context of our problem is the day-ahead market with a time-of-use (TOU) pricing mechanism. In our problem, there is a local area operator (LAO) in charge of constructing the EEN, for the purpose of reducing the system power loss and improving the energy efficiency. Moreover, the MGs are equipped with DERs (i.e., solar panels and wind turbines) and DS units (i.e., batteries). In this way, the MGs can fulfill their demands by not only their own distributed resources but also the supply from the EEN and the main grid. The objective of our problem is to minimize the overall system cost, which includes: (i) the money paid for the power fed into the network, (ii) the power loss in the distribution network, (iii) the direct energy exchange cost, and (iv) the battery’s operational cost, while satisfying all the corresponding constraints, such as system operational constraints on power flow and voltage, and the batteries’ operational constraints.

Our problem is formulated as a non-convex optimization problem since the resistive power losses in the distribution network are considered in an alternative current (AC) power flow model, and thus, an exact solution may be too complex to compute [5]. To handle the non-convex optimal power flow (OPF) problem more efficiently, in this paper we exploit the recent results of the exact OPF relaxation method from [21]. In particular, this method matches the property of our model well, thus enabling us to equivalently transform the original non-convex problem into a second-order cone programming problem and efficiently determine the optimal solution successfully (without suffering from any relaxation loss).

To solve the energy management problems of MGs, many centralized solutions have been used [9], [10], [12]. However, due to some disadvantages (e.g., poor scalability and privacy concerns) of the centralized solutions, distributed methods are more desirable [22]. For this reason, we develop a distributed algorithm to solve our problem based on the alternating direction method of multipliers (ADMM) [5], [23] by leveraging the specific structure of our formulation, such that the MGs and LAO only need to communicate with their direct neighbors and hence the communication overhead can be quite low. Moreover, the convergence of the algorithm is assured.

We apply our model on three radial distribution systems (34-bus, 69-bus and 119-bus) and perform extensive numerical tests. Specifically, the fast convergence rate of our proposed algorithm is demonstrated with appropriate chosen parameters. Furthermore, the results show that different MGs can cooperate with each other according to their distinct and/or complementary consumption profiles to minimize the total cost of the system. In addition, simulations are conducted for different EEN topologies, which show that, depending on the relative positions of MGs in the distribution network, some specific EEN topologies may be more advantageous. Moreover, considering the uncertainty of the renewable energy input, we also implement our method based on the model predictive control (MPC) approach in order to handle the forecasting errors of the renewable energy generation. The results show that with estimation errors, performance loss of our method is still acceptable.

There are several works in the literature that have studied the interaction of multiple MGs with the distribution networks [17], [24], [25], [26], [27], [28], [29]. In [17], [24], the authors propose a control strategy for the coordinated operation of networked microgrids (MGs) in a distribution system. They formulate the problem as a stochastic bi-level optimization problem in which the upper level problem is solved by the distribution operator in order to guarantee the operational constraints while the lower level problem is to minimize the operation costs of MGs. In [25], [26], [27], a bi-level optimal operation model for distribution networks with grid-connected MGs have been presented. The upper-level model determines the optimal dispatch of the distribution network to achieve its power loss reduction and voltage profile improvement, while the lower-level model determines the optimal operation strategy of distributed generators in MGs considering the utilization of renewable power. However, in [25], although the operation of multiple grid-connected MGs are considered, only the interaction between the distribution network and MGs is studied without considering any power exchange among MGs. By contrast, in [26], [27], the cooperative interaction among MGs with expanded energy storage systems are taken into account in addition to the interaction with the distribution network. Specifically, the cooperation among MGs is modeled by an interactive energy game matrix based on priority-based game theory to take full advantage of the remaining dispatchable capacity in energy storage systems and distributed generators. In [26], the impact of the large integration of renewable energy resources is considered and analyzed. Moreover, the authors in [27] introduce the responsive reserve of distributed generators to the model to improve the system operation. Additionally, the authors in [28] propose an optimal energy scheduling framework for the energy exchange among multiple microgrids while considering the security constraints. In their framework, there are two layers: a distributed network layer which solves the OPF problem and a market layer which coordinates the energy transaction among multiple MGs. Furthermore, in [29], a distributed algorithm for the energy management of networked MGs based on the on-line alternating direction method of multipliers algorithm is proposed. Their objective is to coordinate the power scheduling of various components in the MGs while satisfying the underlying power network operation constraints.

Compared with our work, there are several issues in these related works. The most remarkable one is that although the problems in those literature have considered networked MGs with a distribution system, there is no direct energy exchange network among MGs. Specifically, they only allow the MGs to exchange energy through the distribution network. In contrast, in our work both the DC EEN as well as the interaction between the MGs and the distribution network are taken into account. Therefore, the energy management for the coordination between the EEN and the traditional distribution networks is studied in our work, which is one of our key contributions. In addition, although the similar concept of the peer-to-peer DC energy exchange network among MGs has been proposed in [6], [7], the detailed energy management problem involving these two networks has not been studied. Hence, our work tries to make the first attempt to fill this gap in the literature.

Furthermore, the problem formulation in our work is more practical in several aspects when compared to those works in the literature. For example, in [17], [24], [29], linearized power flow equations for distribution networks are used, while in our work, an AC power flow model has been adopted which is more accurate. Moreover, in [17], [24], [28], [29], the DS devices are not considered, while our model involves DS devices because they are becoming more and more important with the increasing penetration of renewable energy resources.

In addition, although in [24], [28], distributed algorithms are proposed for the energy management of networked MGs, there is no theoretical proof of the convergence. The lack of the convergence guarantee may raise concern about the reliability of their methods. In [29], an on-line ADMM algorithm is leveraged for solving their problem. Compared to their work, one important contribution of our work is that we have proved that the primal decision variables converge to the optimal values. This is stronger than a general convergence result of the ADMM algorithm applied to a convex problem where only the objective value are guaranteed to converge to the optimal value.

We summarize the main contributions of our work as follows.

  • 1.

    The energy management for multiple MGs that are interconnected by both the DC EEN and the AC distribution network has been studied. In our problem, the distributed storage devices are taken into account such that the energy can be stored and released in order to help complement the instant energy deficiency or surplus at different time of the day. Moreover, the AC power flow equations without any approximation are used to accurately model the power flow and operational constraints of the distribution networks.

  • 2.

    We propose a distributed approach such that the disadvantages of centralized methods (e.g., poor scalability, privacy concerns and high communication overhead) can be avoided with the assurance of convergence of our proposed algorithm. Another advantageous feature of our ADMM-based algorithm is that we prove that the primal decision variables converge to the optimal values, which is stronger than a general convergence result of the ADMM algorithm.

The rest of the paper is organized as follows. In Section 2, the MG EEN and the distribution network are modeled. The problem formulation as well as its relaxed version is discussed in Section 3. The distributed algorithm is described in Section 4. Numerical results are presented in Section 5, followed by conclusions in Section 6.

Section snippets

MG direct energy exchange network model

We consider a set of N MGs, denoted by M={MGn:nN}, where N={1,,N}, and W={in:nN} denotes the corresponding index set of MGs, where in denotes the index of MGn in the distribution network. The time horizon is discretized, and t{1,2,,H} denotes the time slot (t,t+Δ], where H is the total number of time slots of interest. Each MG is connected to a bus of the underlying distribution network by the PCC, and is equipped with a battery as well as DERs (PV generators and WTs). These MGs are also

Problem formulation and exact relaxation

In this work, we consider the MGs which are willing to cooperate with each other to reduce the overall cost. These MGs have the sufficient incentive because the benefit of the overall cost reduction will be shared among the MGs such that each MG can pay a lower energy bill. The detailed mechanism for pricing and profit sharing in the EEN is beyond the scope of this paper, while our previous work about the pricing for hybrid energy trading market [3] is an example.

The objective of our problem is

Distributed algorithm

We focus on developing a distributed algorithm for solving the problem P-relaxed in this section, which has many advantages over a centralized method in terms of scalability, privacy, etc. In our approach, each agent (MG or LAO) only needs to communicate with its neighbors and there is no central node. Additionally, the proposed distributed method can be proved to converge to the optimal solution. Specifically, our problem can be reformulated into a global variable consensus optimization (

A 34-bus radial distribution network

We apply our energy management model on a 34-bus radial distribution network, as shown in Fig. 4. It is noted that in this figure, while each MG is represented by a circle and connected to the distribution network via a point of common coupling, it does not mean that a MG only has one node. In fact, a MG can include several nodes of the network inside of it and in this paper, we mainly focus on the cooperation and interaction among MGs and the main grid. Therefore, the topology inside a MG is

Conclusions

In this work, we studied the energy management problem for cooperative MGs with direct energy exchange under the distribution network and developed a distributed algorithm. We formulated the energy management problem as a practical yet non-convex optimization problem to minimize the total system cost. After exploiting an exact relaxation of the non-convex constraint, we equivalently transformed this problem into an SOCP problem and thus made it efficiently solvable. Then convergence of our

Acknowledgment

This work was supported by the Hong Kong Research Grants Councils General Research Fund under Project 16209814 and Project 16210215.

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