arXiv subjects

Christian A. Hans

Publications and source records attributed to Christian A. Hans.

18 recordsLinked to original sources

arXiv2026

Data-Driven Active Power Flow Modeling: A Behavioral Systems Approach

The increasing decentralization of power systems driven by a large number of renewable energy sources poses challenges in power flow optimization: Partially unknown power line properties can render model-based approaches unsuitable. With the increasing deployment of sensors, data-driven methods rise as a promising alternative, offering flexibility to adapt changes and deal with unknown properties. In this paper, we propose a novel data-driven representation of nonlinear active power flow equations for radial grids based on Willems' Fundamental Lemma. Our approach allows for direct integration of input/output data into active power flow optimization, enabling cost minimization and constraint enforcement without requiring explicit knowledge of the electrical properties of the grid. Moreover, we derive a computationally tractable convex relaxation and show in a numerical case study that our approaches yield results that are identical to optimal active power flow formulations with known parameters.

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arXiv2026

Saturation-aware robust optimal operation control of microgrids based on minimum-regret optimization

This paper studies robust optimal operation control problems for microgrids with a high share of renewable energy sources. The main goal is to ensure an optimal operation in the presence of a wide range of scenarios of uncertain infeed of renewable sources and uncertain load demand. We formally state a minimum-regret robust model predictive control (MPC) problem and address it by making effective use of a hierarchical microgrid control structure. In detail, we consider an enhanced primary control layer composed of droop control and an autonomous limitation of power and energy. We prove that this enables us to use constant power setpoints to achieve an optimal operation under certain conditions. To obtain a tractable controller, we then combine the abovementioned constant saturation-aware setpoints with an energy management system, which solves a robust unit commitment problem within a model predictive control framework. In a case study, we finally demonstrate the viability of the control design.

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arXiv2026

Graph Neural Ordinary Differential Equations for Power System Identification

With the shift towards decentralized energy generation, the increasing complexity of power systems renders physics-based modeling challenging. At the same time the growing amount of available measurement data opens the door for obtaining models in a data-driven manner. A modern method to do so are neural ordinary differential equations (NODEs), offering a framework for continuous time system identification. Recent extensions, so called graph NODEs impose a structural inductive bias that has the potential to improve generalization of the learned representation. In this work, we employ graph NODEs and extend them with novel ideas to develop message-passing graph NODEs (MPG-NODEs) for identification of coupled systems with heterogeneous node dynamics and edge couplings. This encompasses state-of-the-art machine learning architectures to infer latent representations of unmeasured states from past measurements, local node and edge embeddings to account for heterogeneity as well as an autoregressive scheme to allow for piecewise constant control inputs. We apply MPG-NODEs to identify voltage and frequency dynamics of power systems and compare them to a monolith NODE under identical measurement assumptions. Our case study on the IEEE 9-bus system indicates that the proposed MPG-NODE offers a much more flexible framework with transfer learning options that allow to add or remove powerlines and units with little to no retraining.

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arXiv2025

Augmented Neural Ordinary Differential Equations for Power System Identification

Due the complexity of modern power systems, modeling based on first-order principles becomes increasingly difficult. As an alternative, dynamical models for simulation and control design can be obtained by black-box identification techniques. One such technique for the identification of continuous-time systems are neural ordinary differential equations. For training and inference, they require initial values of system states, such as phase angles and frequencies. While frequencies can typically be measured, phase angle measurements are usually not available. To tackle this problem, we propose a novel structure based on augmented neural ordinary differential equations, learning latent phase angle representations on historic observations with temporal convolutional networks. Our approach combines state-of-the art deep learning techniques, avoiding the necessity of phase angle information for the power system identification. Results show, that our approach clearly outperforms simpler augmentation techniques.

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arXiv2025

$\mathcal{H}_\infty$ Loop-shaping for Power Tracking Control of Wind Turbines

In this paper, we present an advanced wind turbine control scheme for power maximization as well as for active power control, which is designed using $\mathcal{H}_\infty$ loop-shaping. Our approach involves the synthesis of two separate controllers for two different operating modes. To ensure smooth transitions between these modes, we implement a bumpless transfer strategy that reduces transient effects. A comprehensive case study demonstrates the efficacy of our control scheme, showing significant improvements in power tracking accuracy and a reduction in mechanical wear. Moreover, our control strategy comes with robust stability guarantees.

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arXiv2024

Identification of Power Systems with Droop-Controlled Units Using Neural Ordinary Differential Equations

In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and electric vehicles, as well as a shift towards active distribution grids. Obtaining physically-based models for simulation and control synthesis can therefore become challenging. Differential equations, where the right-hand side is represented by a neural network, i.e., neural ordinary differential equations (NODEs), have a great potential to serve as a data-driven black-box model to overcome this challenge. This paper explores their use in identifying the dynamics of droop-controlled grid-forming units based on inputs and state measurements. In numerical studies, various NODE structures used with different numerical solvers are trained and evaluated. Moreover, they are compared to the sparse identification of nonlinear dynamics (SINDy) method. The results demonstrate that even though SINDy yields more accurate models, NODEs achieve good prediction performance without prior knowledge about the system's nonlinearities which SINDy requires to work best.

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arXiv2024

Robust LQ Optimal Control for Wind Turbine Power Tracking Operation

In this paper, a robust linear quadratic optimal control approach for accurate active power tracking of wind turbines is presented. For control synthesis, linear matrix inequalities are employed using an augmented wind turbine state model with uncertain parameters. The resulting controller ensures robust stability in different operating regions. In a case study, the novel approach is compared to existing controllers from literature. Simulations indicate that the controller improves power tracking accuracy while leading to similar mechanical wear as existing approaches.

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arXiv2024

Data-driven model predictive control of battery storage units

In many state-of-the-art control approaches for power systems with storage units, an explicit model of the storage dynamics is required. With growing numbers of storage units, identifying these dynamics can be cumbersome. This paper employs recent data-driven control approaches that do not require an explicit identification step. Instead, they use measured input/output data in control formulations. In detail, we propose an economic data-driven model predictive control (MPC) scheme to operate a small power system with input-nonlinear battery dynamics. First, a linear data-driven MPC approach that uses a slack variable to account for plant-model-mismatch is proposed. In a second step, an input-nonlinear data-driven MPC scheme is deduced. Comparisons with a reference indicate that the linear data-driven MPC approximates the nonlinear plant in an acceptable manner. Even better results, however, can be obtained with the input-nonlinear data-driven MPC scheme which provides increased prediction accuracy.

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arXiv2024

Hierarchical distributed scenario-based model predictive control of interconnected microgrids

Microgrids are autonomous clusters of generators, storage units and loads. Special requirements arise in interconnected operation: control schemes that do not require individual microgrids to disclose information about their internal structure and operating objectives are preferred for privacy reasons. Moreover, a safe and economically meaningful operation shall be achieved in presence of uncertain load and weather-dependent availability of renewable infeed. In this paper, we propose a hierarchical distributed model predictive control approach that satisfies these requirements. Specifically, we demonstrate that costs and safety of supply can be improved through a scenario-based stochastic control scheme. In a numerical case study, our approach is compared to a certainty equivalence and a prescient scheme. The results illustrate good performance as well as sufficiently fast convergence.

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arXiv2024

Predictions and Decision Making for Resilient Intelligent Sustainable Energy Systems

Future energy systems are subject to various uncertain influences. As resilient systems they should maintain a constantly high operational performance whatever happens. We explore different levels and time scales of decision making in energy systems, highlighting different uncertainty sources that are relevant in different domains. We discuss how the uncertainties can be represented and how one can react to them. The article closes by summarizing, which uncertainties are already well examined and which ones still need further scientific inquiry to obtain resilient energy systems.

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arXiv2024

Model predictive control of wakes for wind farm power tracking

In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows to track a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows to estimate the rotor effective wind speeds at downstream turbines based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

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arXiv2024

A Predictive Operation Controller for an Electro-Thermal Microgrid Utilizing Variable Flow Temperatures

We propose an optimal operation control strategy for an electro-thermal microgrid. Compared to existing work, our approach increases flexibility by operating the thermal network with variable flow temperatures and in that way explicitly exploits its inherent storage capacities. To this end, the microgrid is represented by a multi-layer network composed of an electrical and a thermal layer. We show that the system behavior can be represented by a discrete-time state model derived from DC power flow approximations and 1d incompressible Euler equations. Both layers are interconnected via heat pumps. By combining this model with desired operating objectives and constraints, we obtain a constrained convex optimization problem. This is used to derive a model predictive control scheme for the optimal operation of electro-thermal microgrids. The performance of the proposed operation control algorithm is demonstrated in a numerical case study.

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arXiv2023

Model Predictive Control of Wind Turbines with Piecewise-Affine Power Coefficient Approximation

In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind conditions. In contrast, the presented controller is based on one unified control law that works for all wind conditions. The inherent nonlinearity of wind turbines is addressed through a piecewise-affine approximation of the power coefficient, which is modelled in a mixed-integer fashion. The presented controller is compared to a state-of-the-art baseline controller in a numerical case study using OpenFAST. Simulation results show that the presented controller ensures accurate reference power tracking. Additionally, damage equivalent loads are reduced for higher wind speeds.

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arXiv2022

LQ Optimal Control for Power Tracking Operation of Wind Turbines

In this paper, an approach for active power control of individual wind turbines is presented. State-of-the-art controllers typically employ separate control loops for torque and pitch control. In contrast, we use a multivariable control approach. In detail, active power control is achieved by using reference trajectories for generator speed, generator torque, and pitch angle such that a desired power demand is met if weather conditions allow. Then, a linear quadratic (LQ) optimal controller is used for reference tracking. In an OpenFAST simulation environment, the controller is compared to a state-of-the-art approach. The simulations show a similar active power tracking performance, while the LQ optimal controller results in lower mechanical wear. Moreover, the presented approach exhibits good reference tracking and by improving the reference trajectory generation further performance increases can be expected.

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arXiv2021

Saturation-Aware Model Predictive Energy Management for Droop-Controlled Islanded Microgrids

In this paper, we propose a minimax model predictive control (MPC)-based energy management system that is robust with respect to uncertainties in renewable infeed and load. The MPC formulation includes a model of low-level droop control with saturation at the power and energy limits of the units. Robust MPC-based energy management systems tend to under-utilize the renewable energy sources to guarantee safe operation. In order to mitigate this effect, we further consider droop control of renewable energy sources. For a microgrid with droop-controlled units, we show that enhancing droop feedback with saturation enlarges the space of feasible control actions. However, the resulting controller requires to solve a mixed-integer problem with additional variables and equations representing saturation. We derive a computationally tractable formulation for this problem. Furthermore, we investigate the performance gained by using droop with saturation, renewable droop and combination of both in a case study.

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arXiv2021

Optimal operation of microgrids with risk-constrained state of charge

In this paper we present a stochastic scenario-based model predictive control (MPC) approach for the operation of islanded microgrids with high share of renewable energy sources. We require that the stored energy remains within given bounds with a certain probability using risk-based constraints as convex approximations of chance constraints. We show that risk constraints can generally be cast as conic constraints and, unlike chance constraints, can control both the number and average magnitude of constraint violations. Lastly, we demonstrate the risk-constrained stochastic MPC in a numerical case study.

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arXiv2019

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors.

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arXiv2019

Very Short Term Time-Series Forecasting of Solar Irradiance Without Exogenous Inputs

This paper compares different forecasting methods and models to predict average values of solar irradiance with a sampling time of 15 min over a prediction horizon of up to 3 h. The methods considered only require historic solar irradiance values, the current time and geographical location, i.e., no exogenous inputs are used. Nearest neighbor regression (NNR) and autoregressive integrated moving average (ARIMA) models are tested using different hyperparameters, e.g., the number of lags, or the size of the training data set, and data from different locations and seasons. The hyperparameters and their effect on the forecast quality are analyzed to identify properties which are likely to lead to good forecasts. Using these properties, a reduced search space is derived to identify good forecasting models much faster.

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