Tillmann Mühlpfordt

Solving stochastic AC power flow via polynomial chaos expansion

The present contribution demonstrates the applicability of polynomial chaos expansion to stochastic (optimal) AC power flow problems that arise in the operation of power grids. For rectangular power flow, polynomial chaos expansion together with Galerkin projection yields a deterministic reformulation of the stochastic power flow problem that is solved numerically in a single run. From its solution, approximations of the true posterior probability density functions are obtained. The presented approach does not require linearization. Furthermore, the IEEE 14 bus serves as an example to demonstrate that the proposed approach yields accurate approximations to the probability density functions for low orders of polynomial bases, and that it is computationally more efficient than Monte Carlo sampling.

Nonlinear Model Predictive Missile Control with a Stabilising Terminal Constraint

Abstract In this paper, an MPC scheme for a missile pitch axis autopilot is proposed. The scheme uses a nonlinear prediction model to give it an ability to push the controlled missile very close to its operating limits, and is stabilised through the use of an ellipsoidal terminal constraint. Tracking performance and computational load of the scheme are compared to that with a linear prediction model and other types of terminal constraint. Specifically, the choice of ellipsoidal, polytopic, or no terminal constraint is discussed. The terminally constrained nonlinear MPC scheme achieves comparable solution times to that with a linear prediction model, whilst being more aggressive to give a superior tracking performance.

Towards Distributed OPF using ALADIN [in press]

This paper discusses the application of the recently proposed augmented Lagrangian alternating direction inexact Newton (<sc>aladin</sc>) method to non-convex ac optimal power flow problems (<sc>ac</sc>-<sc>opf</sc>) in a distributed fashion. In contrast to the often used alternating direction of multipliers method (<sc>admm</sc>), <sc>aladin</sc> guarantees locally quadratic convergence for <sc>ac</sc>-<sc>opf</sc>. Numerical results for 5–300 bus test cases indicate that <sc>aladin</sc> is able to outperform the <sc>admm</sc> and to reduce the number of iterations by about one order of magnitude. We compare <sc>aladin</sc> to numerical results for the <sc>admm</sc> documented in the literature. The improved convergence speed comes at the cost of increasing the communication effort per iteration. Therefore, we propose a variant of <sc>aladin</sc> that uses inexact Hessians to reduce communication. Additionally, we provide a detailed comparison of these <sc>aladin</sc> variants to the <sc>admm</sc> from an algorithmic and communication perspective. Moreover, we prove that <sc>aladin</sc> converges locally at a quadratic rate even for the relevant case of suboptimally solved local nonlinear programs.

Optimal power flow: An introduction to predictive, distributed and stochastic control challenges

Abstract The Energiewende is a paradigm change that can be witnessed at latest since the political decision to step out of nuclear energy. Moreover, despite common roots in Electrical Engineering, the control community and the power systems community face a lack of common vocabulary. In this context, this paper aims at providing a systems-and-control specific introduction to optimal power flow problems which are pivotal in the operation of energy systems. Based on a concise problem statement, we introduce a common description of optimal power flow variants including multi-stage problems and predictive control, stochastic uncertainties, and issues of distributed optimization. Moreover, we sketch open questions that might be of interest for the systems and control community.

On solving probabilistic load flow for radial grids using polynomial chaos

The uncertain nature of electric energy production from distributed generation based on renewable resources has to be considered when managing and operating distribution grids. In several cases, this uncertainty can be described using non-Gaussian random variables, requiring appropriate probabilistic load flow techniques. The present paper proposes a method that, exploiting Polynomial Chaos Expansion and Galerkin projection, allows a reformulation of the probabilistic load flow for radial grids as an enlarged deterministic problem. For radial grids, the well known Backward-Forward-Sweep method is applicable. This method does not require any model simplification or assumptions on the probability density function of the input random variables, i.e. it is applicable to non-Gaussian uncertainties. We draw upon a real 84-node grid and compare results against those obtained from Monte Carlo simulation.