Christian A. Hans

Droop-controlled inverter-based microgrids are robust to clock drifts

Clock drift in digital controllers is of great relevance in many applications. Since almost all real clocks exhibit drifts, this applies in particular to networks composed of several individual units, each of which being operated with its individual clock. In the present work, we investigate the effect of clock drifts in inverter-based microgrids. Via a suitable model that incorporates this phenomenon, we prove that clock inaccuracies hamper synchronization in microgrids, in which the individual inverters are operated with a fixed uniform constant electrical frequency. In addition, we show that the well-known frequency droop control renders stability of a lossless microgrid robust with respect to clock inaccuracies. This claim is established by using stability results reported previously by the authors for lossless inverter-based microgrids with ideal clocks. We also discuss the effect of clock drifts on active power sharing. The analysis is illustrated via a simulation example.

Scenario-based model predictive operation control of islanded microgrids

We propose a model predictive control (MPC) approach for the operation of islanded microgrids that takes into account the stochasticity of wind and load forecasts. In comparison to worst case approaches, the probability distribution of the prediction is used to optimize the operation of the microgrid, leading to less conservative solutions. Suitable models for time series forecast are derived and employed to create scenarios. These scenarios and the system measurements are used as inputs for a stochastic MPC, wherein a mixed-integer problem is solved to derive the optimal controls. In the provided case study, the stochastic MPC yields an increase of wind power generation and decrease of conventional generation.

Minimax Model Predictive Operation Control of Microgrids

Abstract Due to the steady growth of decentralised distributed generation, the operational management of small, local electricity networks (microgrids) is becoming an increasing challenge to meet: How to provide an operational control for microgrids with a high share of renewable energy sources (RES) that is robust to perturbations? In this paper we address an optimal control problem (OCP) that maintains all of the stated properties in the presence of an uncertain load and RES infeed in islanded operation. Assuming that the uncertainty is within a bounded region along a given load and RES trajectory prediction, the problem is posed as a worst-case hybrid OCP, where the RES output can be curtailed. We propose a minimax (MM) model predictive control (MPC) scheme that adjusts according to the present uncertainty and can be formulated as a mixed-integer linear program (MILP) and solved numerically online.

Modeling, Analysis, and Experimental Validation of Clock Drift Effects in Low-Inertia Power Systems

Clock drift in digital controllers is of great relevance in many applications. Since almost all real clocks exhibit drifts, this applies in particular to networks composed of several individual units, each of which being operated with its individual clock. In the present paper, we demonstrate via extensive experiments on a microgrid in the megawatt range that clock drifts may impair frequency synchronization in low-inertia power systems. The experiments also show that—in the absence of a common clock—the standard model of an inverter as an ideal voltage source does not capture this phenomenon. As a consequence, we derive a suitably modified model of an inverter-interfaced unit that incorporates the phenomenon of clock drifts. By using the derived model, we investigate the effects of clock drifts on the performance of droop-controlled grid-forming inverters with regard to frequency synchronization and active power sharing. The modeling and analysis is validated via extensive experiments on a microgrid in the megawatt range.

Approximate closed-loop minimax model predictive operation control of microgrids

We address an optimal control problem for a microgrid in islanded operation with bounded uncertain load and renewable infeed. While model predictive control (MPC) with worst-case cost evaluation is often employed to obtain robust optimal control laws in the presence of bounded disturbances, it suffers from an inherent conservativeness. To counteract this phenomenon, we propose an approximate closed-loop minimax MPC scheme, where the renewable energy sources output can be curtailed. The MPC is formulated as a mixed-integer linear program, solved online and applied in a receding horizon fashion. In the case study, the approximate closed-loop approach yields a better prediction accuracy and performance than the corresponding open-loop scheme.

Steady state evaluation of distributed secondary frequency control strategies for microgrids in the presence of clock drifts

Secondary frequency control, i.e., the task of restoring the network frequency to its nominal value following a disturbance, is an important control objective in microgrids. In the present paper, we compare distributed secondary control strategies with regard to their behaviour under the explicit consideration of clock drifts. In particular we show that, if not considered in the tuning procedure, the presence of clock drifts may impair an accurate frequency restoration and power sharing. As a consequence, we derive tuning criteria such that zero steady state frequency deviation and power sharing is achieved even in the presence of clock drifts. Furthermore, the effects of clock drifts of the individual inverters on the different control strategies are discussed analytically and in a numerical case study.

Minimax model predictive operation control of grid-connected microgrids

Microgrids (MGs) are a promising solution to global energy challenges. Robust and reliable operation while maximizing infeed from renewable sources and reducing the use of thermal generation are important objectives in the control of MGs. In this paper, two model predictive control strategies are applied to operate a grid-connected MG in the presence of bounded uncertainties in an optimal way. One is a certainty-equivalence and the other a minimax approach. They differ in the disturbance model used for renewable energy source infeed and load. To find an optimal operation strategy, a mixed-integer quadratic program is solved online. In a numerical case study, the results of two approaches are analyzed. The simulation shows, that compared to the performance of the certainty-equivalent case, the minimax approach is robust to disturbances and allows a secure operation of MGs in grid-connected mode.

Optimal adaptive predictive control of a combustion engine

This paper deals with the optimal tracking control of a spark ignited combustion engine. The overall controller consists of an (a priori given) feed-forward part that steers the system close to the desired trajectory and an optimal adaptive predictive controller for the tracking error dynamics. The latter is based on estimating a linear model along the desired trajectory online, which is then used in a model predictive control (MPC) scheme that systematically incorporates the input and state constraints in the design process. The provided feed-forward control and its respective combination with an infinite linear-quadratic regulator (LQR) and the adaptive MPC are compared in simulation. The results demonstrate a decrease in fuel consumption at the price of a minor performance loss in terms of tracking the desired torque cycle, while avoiding disadvantageous operation of the engine at all times.

Hierarchical distributed model predictive control of interconnected microgrids

In this work, we propose a hierarchical distributed model predictive control strategy to operate interconnected microgrids (MGs) with the goal of increasing the overall infeed of renewable energy sources. In particular, we investigate how renewable infeed of MGs can be increased by using a transmission network allowing the exchange of energy. To obtain an model predictive control scheme, which is scalable with respect to the number of MGs and preserves their independent structure, we make use of the alternating direction method of multipliers leading to local controllers communicating through a central entity. This entity is in charge of the power lines and ensures that the constraints on the transmission capacities are met. The results are illustrated in a numerical case study.