Exact Convex Modeling of the Optimal Power Flow for the Operation and Planning of Active Distribution Networks with Energy Storage Systems

The distribution networks are experiencing important changes driven by the massive integration of renewable energy conversion systems. However, the lack of direct controllability of the Distributed Generations (DGs) supplying Active Distribution Networks (ADNs) represents a major obstacle to the increase of the penetration of renewable energy resources characterized by a non-negligible volatility. The successful development of ADNs depends on the combination of i) specific control tools and ii) availability of new technologies and controllable resources. Within this context, this thesis focuses on developing practical and scalable methodologies for the ADN planning and operation with particular reference to the integration of Energy Storage Systems (ESSs) owned, and directly controlled, by the Distribution Network Operators (DNOs). In this respect, an exact convex formulation of Optimal Power Flow (OPF), called AR-OPF, is first proposed for the case of radial power networks. The proposed formulation takes into account the correct model of the lines and the security constraints related to the nodal voltage magnitudes, as well as, the lines ampacity limits. Sufficient conditions are provided to guarantee that the solution of the AR-OPF is feasible and optimal (i.e., the relaxation used is exact). Moreover, by analyzing the exactness conditions, it is revealed that they are mild and hold for real distribution networks. The AR-OPF is further augmented by suitably incorporating radiality constraints in order to develop an optimization model for optimal reconfiguration of ADNs. Then, a two-stage optimization problem for day-ahead resource scheduling in ADNs, accounting for the uncertainties of nodal injections, is proposed. The Adaptive Robust Optimization (ARO) and stochastic optimization techniques are successfully adapted to solve this optimization problem. The solutions of ARO and stochastic optimization reveal that the ARO provides a feasible solution for any realization of the uncertain parameters even if its solution is optimal only for the worst case realization. On the other hand, the stochastic optimization provides a solution taking into account the probability of the considered scenarios. Finally, the problem of optimal resource planning in ADNs is investigated with particular reference to the ESSs. In this respect, the AR-OPF and the proposed ADN reconfiguration model, are employed to develop optimization models for the optimal siting and sizing of ESSs in ADNs. The objective function aims at finding the optimal trade-off between technical and economical goals. In particular, the proposed procedures accounts for (i) network voltage deviations, (ii) feeders/lines congestions, (iii) network losses, (iv) cost of supplying loads (from external grid or local producers) together with the cost of ESS investment/maintenance, (v) load curtailment and (vi) stochasticity of loads and renewables production. The use of decomposition methods for solving the targeted optimization problems with discrete variables and probable large size is investigated. More specifically, Benders decomposition and Alternative Direction Method of Multipliers (ADMM) techniques are successfully applied to the targeted problems. Using real and standard networks, it is shown that the ESSs could possibly prevent load and generation curtailment, reduce the voltage deviations and lines congestions, and do the peak shaving.

Sizing and siting of a utility scale distributed battery energy storage system

Mostafa Nick, Mario Paolone

The report focuses on the development of a practical and scalable methodology for the planning and operation of Active Distribution Networks (ADNs) with particular reference to the integration of Energy Storage Systems (ESSs) owned, and directly controlled, by the Distribution Network Operators (DNOs). In this respect, an exact convex formulation of the Optimal Power Flow (OPF) problem, called Augmented Relaxed OPF (AR-OPF), is first proposed for the case of radial power networks [1]-[3]. The proposed formulation takes into account the correct model of the lines (i.e., the non-approximated two-port Π model) and, therefore, the full AC load flow equalities. Moreover, the security constraints related to the nodal voltage magnitudes, as well as the lines ampacity limits, are suitably incorporated into the AR-OPF using a set of more conservative constraints. Therefore, the AR-OPF is characterized by a slightly reduced space of feasible solutions where the removed space is in correspondence of the ones close to the technical limits of the grid. Sufficient conditions have been identified to guarantee that the solution of the AR-OPF formulation is feasible and optimal, i.e., the relaxation used in the formulation is exact [1]. Moreover, by analyzing the exactness conditions, it is revealed that they are mild and hold for real distribution networks operating in feasible region. Then, by making use of the AR-OPF method, we formulate a specific optimization problem associated to the optimal resource planning and operation in ADNs with particular reference to the case of Battery Energy Storage Systems (BESSs). In this respect, it is assumed that the ESSs are owned, and directly controlled, by the DNOs. The objective function is augmented aiming at finding the optimal trade-off between technical and economic goals. In particular, the proposed procedures accounts for (i) network voltage deviations, (ii) feeders/lines congestions, (iii) network losses, (iv) cost of supplying loads (from external grid or local producers) together with the cost of ESS investment/maintenance, (v) load curtailment and (vi) stochasticity of loads and renewables production. The use of decomposition methods for solving the targeted optimization problems with discrete variables and probable large size is also investigated (see [3] for further details). More specifically, Benders decomposition and Alternative Direction Method of Multipliers (ADMM) techniques are successfully applied to the solution of the targeted problems. The developed technique is the applied to the siting and sizing problem of the BESS in the electrical distribution feeder of Onnens (medium voltage) that is expected to be used as demonstration sites for the Phase II of the SCCER-FURIES.

SCCER-FURIES2017

Optimal siting and sizing of distributed energy storage systems via alternating direction method of multipliers

Mostafa Nick, Mario Paolone

Energy Storage Systems (ESSs) has an important role in Active Distribution Networks (ADNs). Within this context this paper focuses on the problem of ESSs optimal siting and sizing. Following similar approaches already proposed by the Authors, this paper uses a multi-objective procedure to account various ancillary services that can be provided by ESSs. The proposed procedure takes into account the voltage support and network losses minimization along with minimization of the cost of energy from external grid. For the case of large-scale problems, accounting networks with large number of nodes and scenarios, the selection of the solution methodology is a non-trivial problem. In this respect, the paper proposes and discusses the applicability of the Alternative Direction Method of Multipliers in order to provide an efficient algorithm for large-scale networks that also provide a solution to the optimality aspect. A real large-scale network with real profiles of load and distributed photovoltaic generation is used as the case study to analyze the effectiveness of the proposed methodology.

Power Systems Computation Conference2014

Sizing and siting of a utility scale distributed battery energy storage system

Mostafa Nick, Mario Paolone

SCCER-FURIES2017