A Robust Optimization Framework for the Day-Ahead Scheduling of Active Distribution Networks including Energy Storage Systems

In this paper we present an adaptive robust optimization framework for the day-ahead scheduling of Active Distribution Networks (ADNs) where the controlled devices are distributed Energy Storage Systems (ESSs). First, the targeted problem is formulated using a two-stage optimization approach. The first-stage decisions determine the amount of import/export energy from the external grid at each hour, as well as energy exchanges for each ESS. The second stage deals with the intra-day control, given the first stage decisions. In order to effectively consider the impacts of uncertainties, the problem is transformed into a `min-max-min' formulation. Here, we minimize the first (day-ahead scheduling) and second stage (intra-day operation) costs while uncertainties are maximally affecting the cost function of the second stage. The Benders dual cut algorithm is employed for the solution of the optimization problem. IEEE 34 bus standard network is the benchmark grid for assessing the performances and effectiveness of the developed robust optimization process.

Stochastic Day-ahead Optimal Scheduling of Active Distribution Networks with Dispersed Energy Storage and Renewable Resources

Mostafa Nick, Mario Paolone

This paper focuses on the problem of the probabilistic optimal day-ahead scheduling of energy resources in Active Distribution Networks (ADNs). These resources include both dispersed energy storage systems (DESSs) and volatile renewable embedded generators. Technical constraints related to both energy resources and electrical network are modeled and taken into account in the proposed optimization problem. The paper first proposes a convex formulation of a specific optimal power flow (OPF) used to compute the resources schedule. Its objective function aims at achieving the minimum of the following quantities: network and DESSs losses, energy cost imported from the external grid, and deviations from the day-ahead scheduled power flow with the same external grid. In addition, the ability of using the substation transformer tap-changer is incorporated into the problem with a suitable cost function. The initial OPF formulation is then enhanced thanks to the use of the Mixed Integer Second Order Cone Programming approach in order to formulate a stochastic AC-OPF. The uncertainties of the problem are due to the forecast errors of the PV generation, load consumption and energy prices. The applicability and the effectiveness of the proposed scheduling approach are tested by using a modified version of the IEEE 34 buses test feeder.

IEEE2014

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

Mostafa Nick

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.

EPFL2016

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

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

Mostafa Nick

EPFL2016

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

Mostafa Nick, Mario Paolone

SCCER-FURIES2017