Optimal sizing and placement of energy storage systems and on-load tap changer transformers in distribution networks
Introduction
The emission targets of Paris climate agreement will require two major transformations in the electricity sector: (1) increasing the generation from renewable energy sources at the distribution level; (2) electrifying the transportation sector, namely by replacing internal combustion engine vehicles by electric vehicles (EVs). However, this revolution at the edge of the electricity system brings new challenges to the planning and operation of distribution networks, such as reverse power flows along with voltage and congestion problems, which will require a significant upgrade of grid assets as well as optimization-based tools for economically plan and operate them. Grid-connected energy storage and on-load tap changer (OLTC) transformers will play an important role in this infrastructure upgrade, as they are flexible control mechanisms that are becoming economically competitive. Thus, the optimal placement and sizing of energy storage systems and OLTC transformers will be vital to reduce investment and operation costs of distribution system operators (DSOs).
Electricity system planning methodologies have started to consider energy storage for different purposes including frequency regulation [1], energy arbitrage [2], microgrid applications [3], voltage regulation [4], and alleviate grid congestions [5]. At the transmission level, Dvorkin et al. [2] proposed a bi-level optimization model to size and place an energy storage device to perform energy arbitrage. In a later work [1], the application of the energy storage was extended to the provision of frequency regulation services. In the microgrid paradigm, several optimization models under the form of mixed-integer linear problems have been proposed to size and place energy storage devices for the provision of multiple services, such as energy arbitrage [6], [7], peak shaving, and reliability services to ensure the safe operation of the microgrid in grid-connected and islanded modes [8]. At medium voltage (MV) distribution level, planning methodologies consider energy storage as an instrument to perform voltage regulation [4], [9] and alleviate network congestions [5], [10]. Yang et al. [9] presented a heuristic based on power flows to size energy storage, while Alnaser et al. [5] addressed the same problem by presenting an optimization model with the non-convex formulation of the optimal power flow (OPF). Both works are exclusively focused on the sizing problem. Placement involves representing the network constraints, which has been addressed by other authors either using second-order cone programming (SOCP) [10], [11], metaheuristics [4] or linear models [12], [13]. Placement and sizing were simultaneously addressed in [14], [15] with optimization models based on the SOCP-OPF. In fact, as discussed in previous works [16], [17], the OPF relaxation via SOCP convexifies the power flow equations, allowing the OPF model to be applicable to large-scale problems.
OLTC transformers have been traditionally used by DSOs to automatically control voltages at the HV/MV substations [18], [19]. However, the installation of OLTC at the MV/LV transformer is becoming more common with the increasing adoption of distributed energy resources by low voltage (LV) consumers. This can be seen in recent studies considering OLTC transformers in distribution network planning and operation [20], [21]. Armendáriz et al. [20] proposed a network optimization model to place MV/LV OLTC transformers and later [21] the author presented a coordinated planning strategy to demonstrate the benefit of OLTC transformer investments in microgrid/utility boundary locations. Hosseinpour and Bastaee [22] included network equations and solved the problem of OLTC transformer placement, applying the non-convex formulation of the OPF, while using a metaheuristic to solve the non-linear problem. In a later work, Xie et al. [23] solved the problem of optimal placement of OLTC transformers using SOCP-OPF.
This paper proposes a novel optimization model to support DSOs in the planning of MV distribution networks. The aim is to improve the network operation and mitigate possible network problems, such as undervoltages and overvoltages that may arise from the high integration of distributed energy resources at the LV level. Two smart grid technologies are considered in the planning problem: energy storage devices to perform energy arbitrage and voltage regulation; and OLTC transformers to perform voltage regulation.
The proposed optimization model defines the optimal mix, placement, and sizing of energy storage devices and MV/LV OLTC transformers that mitigate network technical problems and minimize overall investment and operation costs. Investment costs include fixed and variable components of new energy storage devices and MV/LV OLTC transformer installations while operation costs include network energy losses, energy storage arbitrage and tap changes of OLTC transformers located at HV/MV and MV/LV substations. The non-convex formulation of the OPF is relaxed to a constrained SOCP model, while the non-linear OLTC model is exactly linearized via binary expansion scheme and big-M method. These two transformations make the optimization problem solvable via mixed-integer quadratically constrained programming.
In the scope of distribution network planning, the proposed optimization model improves the state-of-the-art in the following points:
- 1.
it considers the joint sizing and placement of energy storage devices and MV/LV OLTC transformers, which differs from approaches only focused on energy storage devices [9], [14] or OLTC transformers [20], [21]. The joint optimization of these two technologies produces a more affordable planning strategy than the individual optimization of the technologies, as shown in the results section. To the authors’ knowledge, no paper in the literature has presented an optimization formulation targeting planning problems that simultaneously consider OLTC transformers and energy storage devices;
- 2.
it exploits a SOCP-OPF model constrained by the LinDistFlow formulation [24] to ensure that the OPF solutions have physical meaning for extreme scenarios of network operation characterized by undervoltages and overvoltages. The solutions of the classic SOCP-OPF [15] may lose physical meaning in the mentioned scenarios, as discussed in [25]. This paper analyzes scenarios of undervoltages, overvoltages, and reverse power flows;
- 3.
it is applicable to real-scale MV distribution grids, as demonstrated in the results section for a 118-bus test system. Alternative approaches to real-scale distribution grids exploit linear OPF models [12], [13] and metaheuristics [4], [22]. However, the linear models and metaheuristics present drawbacks. The metaheuristics do not ensure the global optimality of the OPF problem and the linear models may produce technically infeasible solutions, as shown in the results section.
In short, the proposed optimization model improves the planning of real-scale MV distribution grids by defining a more affordable and flexible plan for the placement and sizing of energy storage devices and MV/LV OLTC transformers.
The remaining paper is organized as follows: Section 2 reviews the non-convex formulation of the OPF for distribution grids with OLTC transformers; 3 Optimization model for sizing and placement of energy storage devices and on-load tap changer transformers, 4 Candidate buses, critical-days, and design-days present the methodology for the optimal sizing and placement of energy storage devices and OLTC transformers; the case study and results are described in 5 Case study, 6 Results; Section 7 is the conclusion.
Section snippets
Non-convex formulation of the optimal power flow for radial distribution networks
This section reviews the non-convex formulation of the OPF for radial networks with OLTC transformers.
Optimization model for sizing and placement of energy storage devices and on-load tap changer transformers
The aim of this optimization model is to support DSOs in the planning of the MV distribution networks. The model defines the optimal mix, size, and placement of energy storage devices and MV/LV OLTC transformers in MV distribution networks by minimizing the overall investment and operation costs. The investment costs include the placement and sizing of energy storage devices and MV/LV OLTC transformers. The operation costs consider energy network losses and costs associated with the coordinated
Candidate buses
Part of the candidate buses to place energy storage devices and MV/LV OLTC transformers can be manually selected by the DSO based on decision constraints. However, even with this pre-selection, the planning problem can end up with hundreds of candidate buses for each technology penalizing the computational efficiency of the optimization problem. Thus, the authors propose a heuristic method to reduce the candidate buses based on selective power flow evaluations that explore the control space of
General description
The proposed optimization model is tested using the MV distribution network described in Fig. 4. Two scenarios of integration of distributed energy resources are evaluated:
- 1.
scenario 1: considers the integration of 14,937 EVs in Area 2 (see Fig. 4). It is assumed that 50% of the consumers in Area 2 have one EV. The EVs are not controlled by any market agent or DSO.
- 2.
scenario 2: considers the integration of 59 MWp of photovoltaic units (PVs) in Area 1. It is assumed that each consumer in Area 1 has
Identification of candidate buses for placing energy storage devices and on-load tap changer transformers
Table 5 presents the candidate buses for placing MV/LV OLTC transformers and energy storage devices. The number of candidate buses is reduced but is still much higher than the final number of buses with placed technologies (see Fig. 8).
Fig. 6 presents the voltage violations identified in scenario 1. The voltage violations were identified by the heuristic algorithm. The integration of EVs generates undervoltages in Area 2 (see Fig. 4). The bus 76 presents the lowest voltage value (0.84 p.u.) and
Conclusion
The widespread integration of distributed energy resources will produce reverse power flows, overvoltage and undervoltage problems in the distribution grids. This paper proposes a new optimization model to plan MV distribution networks characterized by a high integration of distributed energy resources. The optimization model defines the optimal mix, size, and placement of energy storage devices and MV/LV OLTC transformers with the objectives of mitigating network technical problems and
Acknowledgments
The authors of this publication would like to acknowledge Dan Ton and Ali Ghassemian, Program Managers at the U.S. Department of Energy, for the support granted to this work through the Microgrid R&D Program and the Advanced Grid Modeling Program. The work of José Iria was also supported by Fundação para a Ciência e Tecnologia with the Ph.D. Scholarship PD/BD/113716/2015.
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