Dispatch-aware planning of energy storage systems in active distribution network

Highlights

• The optimal allocation of ESSs is determined to achieve the dispatchability of an ADN.

• The control-aware approach is embedded for the maximum exploitation of ESSs capacity.

• The benefit of ESSs is evaluated through the ADN operation modeled by the PWL-OPF.

• The Benders decomposition is applied to solve the complexity of the planning problem.

Abstract

This paper proposes a procedure for the optimal siting and sizing of energy storage systems (ESSs) within active distribution networks (ADNs) hosting a large amount of stochastic distributed renewable energy resources. The optimization objective is to minimize the ADN’s day-ahead computed dispatch error. The allocation of ESS is determined while taking advantages from their operational features regarding the ADN’s dispatchability. The proposed ESS planning is defined by formulating, and solving, a scenario-based non-linear non-convex optimal power flow (OPF). The OPF problem is converted to a piecewise linearized OPF (PWL-OPF). The ESS control strategy is designed to fully exploit the energy capacity of the ESS. It is integrated within the PWL-OPF to achieve the ADN’s dispatchability regarding all operating scenarios. The Benders decomposition technique is employed to tackle the computational complexity of the proposed planning problem. The problem is decomposed into two sub-ones: a master problem where the allocation of the ESSs is decided, and several subproblems where the dispatchability of ADN with the support of the allocated ESS is evaluated through the scenario-based OPF. To validate the proposed method, extensive simulations are conducted on a real Swiss grid embedding significant PV generation capacity.

Introduction

The constant increase of spinning reserve in nowadays power systems is one of the technical concerns related to the increasing proportion of electricity production from distributed stochastic resources [1]. The security of the power system has been traditionally sustained by central procurement of regulating power from fast generating units. However, the growing uncertainty associated to power generation of stochastic resources calls for higher expenses for the procurement of conventional reserve. In this respect, the recent literature has advocated the provision of flexibility from active distribution networks (ADNs) such as demand-side management and energy storage systems (ESSs) [2]. In particular, there has been increasing interest in using ESSs in ADNs to compensate for the uncertainty of non-dispatchable local resources (e.g., [3], [4]). Efforts have been made to achieve dispatchability of the ADNs in view of the inherent advantages such as reduction of the bulk system reserve provision [1] and mitigation of the imbalance penalty charges imposed on distribution system operators (DSOs) [5], [6].

The dispatchability signifies the capability of the ADN active power flow through the grid connecting point (GCP) with the transmission netowrk to strictly follow a day-ahead power schedule composed of discrete intervals, henceforth called dispatch plan. Due to the inherent stochasticity of prosumption¹, the realized active power infeed at the GCP varies from the dispatch plan. The magnitude of the difference is defined as dispatch error. When ESSs are exploited to compensate the dispatch error, a DSO of an ADN can have a sufficient capability to control the network infeed through the GCP close to the dispatch plan, thereby avoiding high penalties for power imbalance [7]. Based on the probabilistic forecast of the prosumption and forecast errors, the Authors of [5] computed an optimal dispatch schedule by minimizing the power exchange through the GCP, while limiting the occurrences of dispatch error during the total operation horizon. Meanwhile, a robust optimization approach with an emphasis on control strategy for ESS was proposed in [6]. The Authors suggested an operational procedure to obtain a dispatch plan taking into account the ESS control strategy that can maximize the ESS exploitation to cope with the prosumption forecasting uncertainty. However, the algorithm proposed in [5], [6] did not take into account the network model and associated operational constraints, which may lead to solutions that are physically inapplicable during the real operation. The operational constraints were addressed to compute an optimal dispatch plan in [8], but the model did not involve any control strategy of ESS. In [9], the Authors presented a control-aware optimal placement and sizing of ESSs by embedding receding horizon control strategies within a linearized optimal power flow (OPF). However, the objective of the problem was to maximize the photovoltaic utilization, rather than achieving the dispatchability of the targeted grid.

Notably, the above mentioned studies clearly state that the feasibility of the formulated problems regarding the imbalance constraint is heavily dependent on the ESS capacity. There have been papers in probabilistic estimation of the required ESS capacity to compensate the renewable generation uncertainty to pre-defined extent from the prosumer’s side [10], [11]. However, regarding the purpose of achieving the dispatchability of the ADN, it is necessary to evaluate the optimal allocation of ESS in the view of DSOs’ economic profit by considering the trade-off between its investment cost and the expected advantages, while respecting the technical requirements for the preferred operational condition of the ADN.

Based on this fundamental observation, the Authors of this paper proposed an OPF-based ESS planning strategy to achieve the dispatchability of ADNs in [12]. The objective of the ADN is defined as to minimize the dispatch error during the ADN operation horizon. The optimization problem regarding the ESS allocation consists of a two-stage decision process. The first-stage decision is associated with the investment of ESS which is determined by the location and the capacity of the ESSs energy reservoirs and power ratings. The second-stage decision is related to the daily operation of ADN with allocated ESSs concerning several operating scenarios.

Meanwhile, the control strategy of ESS can profoundly influence the ESS allocation by providing an efficient way to use their capacity for handling the local resources’ uncertainties [13]. Therefore, it is worth exploring the impact of the control aspect of ESSs while optimizing their capacity. However, to the best of the Authors’ knowledge, the previous literature has not focused on this specific problem. In this respect, this paper is an extension of [12] with an emphasis on the integration of ESS control scheme within the planning problem.

The operation of ESS must adhere to the chosen control strategy while ensuring operational conditions of the ADN to be technically feasible. Therefore, the performance and reliability of the planning tools for ADNs can be guaranteed only when the operational conditions of the system are accurately modeled through a proper OPF model. Among various approaches, we focus on convex AC-OPF models in view of their superiority in guaranteeing the optimality of the solution.

One of the consolidated approaches for the convexification of the AC-OPF is provided by relaxation methods, such as semi-definite programming (SDP) [14] or second-order cone programing (SOCP) proposed for radial grids [15]. The SOCP relaxation is preferred in several studies for solving the ESS sizing problem thanks to its computational efficiency and tractability [16], [17]. The Author of [18] pointed out the drawbacks of the SOCP relaxation method such as the possible inexactness of the solution in the cases of reverse line power flows and the cases where the upper bound of nodal voltage and line ampacity constraints are binding. Then, the Authors proposed the so-called Augmented Relaxed OPF (AR-OPF), which is capable to guarantee the exactness of the solution by constructing an augmented conservative set of constraints. In [12], the AR-OPF model has been leveraged for solving the optimization problem of the ESS allocation by achieving the ADN dispatchability. The objective function for the given problem has been deliberately modified to comply with a prerequisite condition of the AR-OPF objective function in order to guarantee the exactness of the solution. The condition states the objective function should strictly increase with the grid losses.

In this paper, embedding the ESS control strategy requires the optimization problem to have more flexibility with repsect to the objective function. It should be noted that integrating the control scheme within the AR-OPF problem might violate the prerequisite condition on the objective function for the exactness of the solution. In this regard, we choose to utilize an alternative convexification approach through linear approximation of the original power flow equations. The linear approximated model makes the OPF problem more tractable at the expense of the exactness of the formulation (i.e., the optimal solution of the approximated model may not be equivalent to the optimal solution of the original OPF problem). The first approach employs the linear approximation of nodal voltages and current flows as function of nodal power injections [19], [20]. Another approach relies on approximating the nonlinear terms in the power flow equations, such as piecewise linearized OPF (PWL-OPF). The piecewise linearization method is widely used in tackling various research interests in power system thanks to its flexibility of implementation [21], [22], [23]. It can achieve the optimal solution of reasonable quality, with minor approximation error from the original OPF solution.

In this context, PWL method is employed for the ESS control-aware planning problem. Moreover, it is noteworthy that the proposed planning strategy can be applicable not only in radial grids but also in meshed grids by using PWL-OPF model. Unlike the existing work relying on the PWL method, we take into account the shunt element of the lines in the PWL-OPF model, which can bring a significant impact on line current especially in the networks with underground coaxial cables. Moreover, we embed the operational strategy for ESS to utilize its energy capacity optimally to cope with uncertainty in the power flow through the distribution feeder. The planning problem is formulated as a mixed-integer linear programming (MILP) problem, which is notorious for its computational intractability. In this respect, the Benders decomposition is employed [24]. The contributions of the paper are listed below.

• The optimal allocation of ESSs is determined based on an piecewise linear approximation of the full AC-OPF to achieve the dispatchability of an ADN hosting a high capacity of stochastic renewable generation.

• The control-aware approach embeds the maximum exploitation of ESSs capacity, and is integrated into the ESSs planning problem.

The structure of the paper is as follows: in Section 2, we describe the proposed method and the differences with respect to our former work [12]. In Section 3, the proposed problem formulation and solution approach are described, followed by a specific case study illustrated in Section 4. Finally, Section 5 concludes the paper.