Philipp Fortenbacher

Philipp Fortenbacher, Johanna L. Mathieu, Göran Andersson

Due to high power in-feed from photovoltaics, it can be expected that more battery systems will be installed in the distribution grid in near future to mitigate voltage violations and thermal line and transformer overloading. In this paper, we present a two-stage centralized model predictive control scheme for distributed battery storage that consists of a scheduling entity and a real-time control entity. To guarantee secure grid operation, we solve a robust multi-period optimal power flow (OPF) for the scheduling stage that minimizes battery degradation and maximizes photovoltaic utilization subject to grid constraints. The real-time controller solves a real-time OPF taking into account storage allocation profiles from the scheduler, a detailed battery model, and real-time measurements. To reduce the computational complexity of the controllers, we present a linearized OPF that approximates the nonlinear AC-OPF into a linear programming problem. Through a case study, we show, for two different battery technologies, that we can substantially reduce battery degradation when we incorporate a battery degradation model. A further finding is that we can reduce battery losses by 30% by using the detailed battery model in the real-time control stage.

Philipp Fortenbacher, Martin Zellner, Göran Andersson

This paper proposes a novel algorithm to optimally size and place storage in low voltage (LV) networks based on a linearized multiperiod optimal power flow method which we call forward backward sweep optimal power flow (FBS-OPF). We show that this method has good convergence properties, its solution deviates slightly from the optimum and makes the storage sizing and placement problem tractable for longer investment horizons. We demonstrate the usefulness of our method by assessing the economic viability of distributed and centralized storage in LV grids with a high photovoltaic penetration (PV). As a main result, we quantify that for the CIGRE LV test grid distributed storage configurations are preferable, since they allow for less PV curtailment due to grid constraints.

Philipp Fortenbacher, Göran Andersson

This paper presents a novel method to describe battery degradation. We use the concept of degradation maps to model the incremental charge capacity loss as a function of discrete battery control actions and state of charge. The maps can be scaled to represent any battery system in size and power. Their convex piece-wise affine representations allow for tractable optimal control formulations and can be used in power system simulations to incorporate battery degradation. The map parameters for different battery technologies are published making them an useful basis to benchmark different battery technologies in case studies.

Philipp Fortenbacher, Turhan Demiray

This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear power flow approximation and consider a convex reformulation of the power losses in the form of absolute value functions. We show four ways how to incorporate this approximation into LP/QP based OPF problems. In a comprehensive case study the usefulness of our OPF methods is analyzed and compared with an existing OPF relaxation and approximation method. As a result, the errors on voltage magnitudes and angles are reasonable, while obtaining near-optimal results for typical scenarios. We find that our methods reduce significantly the computational complexity compared to the nonlinear AC-OPF making them a good choice for planning purposes.

Philipp Fortenbacher, Turhan Demiray

In this paper we present a novel tractable method to compute reduced and aggregated distribution grid representations that provide an interface in the form of active and reactive power (PQ) capability areas for improving transmission service operator - distribution service operator (TSO-DSO) interactions. Based on a lossless linear power flow approximation we derive polyhedral sets to determine a reduced PQ operating region capturing all voltage magnitude and branch power flow constraints of the entire distribution grid. To demonstrate the usefulness of our method, we compare the capability area obtained from the polyhedral approximation with an area generated by multiple optimal power flow (OPF) solutions for different distribution grids. While the approximation errors are reasonable, especially for low voltage (LV) grids, the computational complexity to compute the PQ capability area can be significantly reduced with our proposed method.

Philipp Fortenbacher, Turhan Demiray, Christian Schaffner

This paper presents a new method to determine the susceptances of a reduced transmission network representation by using nonlinear optimization. We use Power Transfer Distribution Factors (PTDFs) to convert the original grid into a reduced version, from which we determine the susceptances. From our case studies we find that considering a reduced injection-independent evaluated PTDF matrix is the best approximation and is by far better than an injection-dependent evaluated PTDF matrix over a given set of arbitrarily-chosen power injection scenarios. We also compare our nonlinear approach with existing methods from literature in terms of the approximation error and computation time. On average, we find that our approach reduces the mean error of the power flow deviations between the original power system and its reduced version, while achieving higher but reasonable computation times.

Philipp Fortenbacher, Andreas Ulbig, Göran Andersson

In this paper we present a novel methodology for leveraging Receding Horizon Control (RHC), also known as Model Predictive Control (MPC) strategies for distributed battery storage in a planning problem using a Benders decomposition technique. Longer prediction horizons lead to better storage placement strategies but also higher computational complexity that can quickly become computationally prohibitive. The here proposed MPC strategy in conjunction with a Benders decomposition technique effectively reduces the computational complexity to a manageable level. We use the CIGRE low voltage (LV) benchmark grid as a case study for solving an optimal placement and sizing problem for different control strategies with different MPC prediction horizons. The objective of the MPC strategy is to maximize the photovoltaic (PV) utilization and minimize battery degradation in a local residential area, while satisfying all grid constraints. For this case study we show that the economic value of battery storage is higher when using MPC based storage control strategies than when using heuristic storage control strategies, because MPC strategies explicitly exploit the value of forecast information. The economic merit of this approach can be further increased by explicitly incorporating a battery degradation model in the MPC strategy.