Dealing with uncertainty in planning of energy storage systems in power distribution networks

In the last decades, power systems are undergoing major modifications, mostly driven by the climate change. This increasing awareness has brought national policies to meet the necessities of reducing CO2 emissions and the use of fossil fuels by incentivizing renewable energy sources. At the same time, the latest advances in the field of distributed energy resources, including more efficient photovoltaic, wind and energy storage systems, have raised the interest in taking full advantage of these technologies, for instance to reduce grid power losses. As a consequence, these new challenging environmental and economic targets set by government policies are driving a dramatic transformation of power supply in electricity systems, with traditional thermal power plants getting off the stage, replaced by distributed generation. Moreover, non-dispatchable distributed energy resources such as wind and photovoltaic systems, with their dependance on weather and climate conditions, introduce new sources of uncertainty in power system operation. Energy storage systems represent a solution for enhancing grid performance, reliability, flexibility and security in the presence of renewables. Charging of the storage devices installed in a distribution grid may help avoid or mitigate the reverse power flow upstream the transformers in case of an excess of generation from distributed generators, without resort to curtailment of generated power. Moreover, use of ESSs may help smooth the fast voltage variations arising as one of the tangible effects of sudden changes in energy production and/or demand patterns. This thesis addresses the problem of the optimal energy storage system allo- cation in power distribution networks with high penetration of renewables. This is a problem which has received increasing attention in the literature, due to the numerous benefits that the use of energy storage systems brings to the power system and its stakeholders. The considered decision problem consists of defining the number of storage units to be deployed, their locations (placement) and sizes (sizing). This decision is made at the planning stage, when the future realizations of demand and generation in the network are unknown. In this thesis uncertainty is accounted for by formulating the allocation problem in a scenario-based stochastic optimal power flow framework. The high dimensionality of the sources of uncertainty involved, puts additional burden on the solution of the allocation problem which, even in the deterministic case, is subject to the combinatorial complexity intrinsic in the placement problem, and the nonconvexity of power flow equations. The main contribution of this thesis is therefore to cope with the prohibitive computational complexity of the large-scale mixed-integer nonconvex optimization problems formulated for optimal allocation. This is done along two directions. On the one hand, the thesis proposes a scenario- reduction technique which makes it possible to solve at the optimum the sizing problem over a large set of scenarios by solving a smaller problem over a selected set of scenarios. On the other hand, the combinatorial nature of optimal placement problems is overcome through a near-optimal placement strategy with well-defined performance guarantees based on submodularity theory and greedy methods. The proposed techniques take advantage of recent developments on convex relaxations and linear approximations of power flow equations to tackle the solution of the considered optimal power flow problems. Numerical results and sensitivity analyses are reported to show the effectiveness of all the procedures and approaches presented in this thesis