Andreas Venzke

Andreas Venzke, Lejla Halilbasic, Uros Markovic et al.

High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized approach or an iterative approximation of non-linearities. This paper proposes a semidefinite relaxation of a chance constrained AC-OPF which is able to provide guarantees for global optimality. Using a piecewise affine policy, we can ensure tractability, accurately model large power deviations, and determine suitable corrective control policies for active power, reactive power, and voltage. We state a tractable formulation for two types of uncertainty sets. Using a scenario-based approach and making no prior assumptions about the probability distribution of the forecast errors, we obtain a robust formulation for a rectangular uncertainty set. Alternatively, assuming a Gaussian distribution of the forecast errors, we propose an analytical reformulation of the chance constraints suitable for semidefinite programming. We demonstrate the performance of our approach on the IEEE 24 and 118 bus system using realistic day-ahead forecast data and obtain tight near-global optimality guarantees.

Florian Thams, Andreas Venzke, Robert Eriksson et al.

Power system security assessment methods require large datasets of operating points to train or test their performance. As historical data often contain limited number of abnormal situations, simulation data are necessary to accurately determine the security boundary. Generating such a database is an extremely demanding task, which becomes intractable even for small system sizes. This paper proposes a modular and highly scalable algorithm for computationally efficient database generation. Using convex relaxation techniques and complex network theory, we discard large infeasible regions and drastically reduce the search space. We explore the remaining space by a highly parallelizable algorithm and substantially decrease computation time. Our method accommodates numerous definitions of power system security. Here we focus on the combination of N-k security and small-signal stability. Demonstrating our algorithm on IEEE 14-bus and NESTA 162-bus systems, we show how it outperforms existing approaches requiring less than 10% of the time other methods require.

Andreas Venzke, Spyros Chatzivasileiadis

High Voltage Direct Current (HVDC) systems interconnect AC grids to increase reliability, connect offshore wind generation, and enable coupling of electricity markets. Considering the growing uncertainty in power infeed and the complexity introduced by additional controls, robust decision support tools are necessary. This paper proposes a chance constrained AC-OPF for AC and HVDC grids, which considers wind uncertainty, fully utilizes HVDC control capabilities, and uses the semidefinite relaxation of the AC-OPF. We consider a joint chance constraint for both AC and HVDC systems, we introduce a piecewise affine approximation to achieve tractability of the chance constraint, and we allow corrective control policies for HVDC converters and generators to be determined. An active loss penalty term in the objective function and a systematic procedure to choose the penalty weights allow us to obtain AC-feasible solutions. We introduce Benders decomposition to maintain scalability. Using realistic forecast data, we demonstrate our approach on a 53-bus and a 214-bus AC-DC system, obtaining tight near-global optimality guarantees. With a Monte Carlo analysis, we show that a chance constrained DC-OPF leads to violations, whereas our proposed approach complies with the joint chance constraint.

Andreas Venzke, Lejla Halilbasic, Adelie Barre et al.

The integration of large-scale renewable generation has major implications on the operation of power systems, two of which we address in this work. First, system operators have to deal with higher degrees of uncertainty due to forecast errors and variability in renewable energy production. Second, with abundant potential of renewable generation in remote locations, there is an increasing interest in the use of High Voltage Direct Current lines (HVDC) to increase transmission capacity. These HVDC transmission lines and the flexibility and controllability they offer must be incorporated effectively and safely into the system. In this work, we introduce an optimization tool that addresses both challenges by incorporating the full AC power flow equations, chance constraints to address the uncertainty of renewable infeed, modelling of point-to-point HVDC lines, and optimized corrective control policies to model the generator and HVDC response to uncertainty. The main contributions are twofold. First, we introduce a HVDC line model and the corresponding HVDC participation factors in a chance-constrained AC-OPF framework. Second, we modify an existing algorithm for solving the chance-constrained AC-OPF to allow for optimization of the generation and HVDC participation factors. Using realistic wind forecast data, for 10 and IEEE 39 bus systems with HVDC lines and wind farms, we show that our proposed OPF formulation achieves good in- and out-of-sample performance whereas not considering uncertainty leads to high constraint violation probabilities. In addition, we find that optimizing the participation factors reduces the cost of uncertainty significantly.

Rahul Nellikkath, Andreas Venzke, Mohammad Kazem Bakhshizadeh et al.

A significant increase in renewable energy production is necessary to achieve the UN's net-zero emission targets for 2050. Using power-electronic controllers, such as Phase Locked Loops (PLLs), to keep grid-tied renewable resources in synchronism with the grid can cause fast transient behavior during grid faults leading to instability. However, assessing all the probable scenarios is impractical, so determining the stability boundary or region of attraction (ROA) is necessary. However, using EMT simulations or Reduced-order models (ROMs) to accurately determine the ROA is computationally expensive. Alternatively, Machine Learning (ML) models have been proposed as an efficient method to predict stability. However, traditional ML algorithms require large amounts of labeled data for training, which is computationally expensive. This paper proposes a Physics-Informed Neural Network (PINN) architecture that accurately predicts the nonlinear transient dynamics of a PLL controller under fault with less labeled training data. The proposed PINN algorithm can be incorporated into conventional simulations, accelerating EMT simulations or ROMs by over 100 times. The PINN algorithm's performance is compared against a ROM and an EMT simulation in PSCAD for the CIGRE benchmark model C4.49, demonstrating its ability to accurately approximate trajectories and ROAs of a PLL controller under varying grid impedance.

Andreas Venzke, Guannan Qu, Steven Low et al.

This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on.

Ilgiz Murzakhanov, Andreas Venzke, George S. Misyris et al.

This paper introduces a framework to capture previously intractable optimization constraints and transform them to a mixed-integer linear program, through the use of neural networks. We encode the feasible space of optimization problems characterized by both tractable and intractable constraints, e.g. differential equations, to a neural network. Leveraging an exact mixed-integer reformulation of neural networks, we solve mixed-integer linear programs that accurately approximate solutions to the originally intractable non-linear optimization problem. We apply our methods to the AC optimal power flow problem (AC-OPF), where directly including dynamic security constraints renders the AC-OPF intractable. Our proposed approach has the potential to be significantly more scalable than traditional approaches. We demonstrate our approach for power system operation considering N-1 security and small-signal stability, showing how it can efficiently obtain cost-optimal solutions which at the same time satisfy both static and dynamic security constraints.

George S. Misyris, Andreas Venzke, Spyros Chatzivasileiadis

This paper introduces for the first time, to our knowledge, a framework for physics-informed neural networks in power system applications. Exploiting the underlying physical laws governing power systems, and inspired by recent developments in the field of machine learning, this paper proposes a neural network training procedure that can make use of the wide range of mathematical models describing power system behavior, both in steady-state and in dynamics. Physics-informed neural networks require substantially less training data and can result in simpler neural network structures, while achieving high accuracy. This work unlocks a range of opportunities in power systems, being able to determine dynamic states, such as rotor angles and frequency, and uncertain parameters such as inertia and damping at a fraction of the computational time required by conventional methods. This paper focuses on introducing the framework and showcases its potential using a single-machine infinite bus system as a guiding example. Physics-informed neural networks are shown to accurately determine rotor angle and frequency up to 87 times faster than conventional methods.

Andreas Venzke, Spyros Chatzivasileiadis

This paper presents for the first time, to our knowledge, a framework for verifying neural network behavior in power system applications. Up to this moment, neural networks have been applied in power systems as a black-box; this has presented a major barrier for their adoption in practice. Developing a rigorous framework based on mixed integer linear programming, our methods can determine the range of inputs that neural networks classify as safe or unsafe, and are able to systematically identify adversarial examples. Such methods have the potential to build the missing trust of power system operators on neural networks, and unlock a series of new applications in power systems. This paper presents the framework, methods to assess and improve neural network robustness in power systems, and addresses concerns related to scalability and accuracy. We demonstrate our methods on the IEEE 9-bus, 14-bus, and 162-bus systems, treating both N-1 security and small-signal stability.