Capturing Power System Dynamics by Physics-Informed Neural Networks and Optimization

This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications. Traditional methods in power systems require the use of a large number of simulations and other heuristics to determine parameters such as the critical clearing time, i.e. the maximum allowable time within which a disturbance must be cleared before the system moves to instability. The work proposed in this paper uses physics-informed neural networks to capture the power system dynamic behavior and, through an exact transformation, converts them to a tractable optimization problem which can be used to determine critical system indices. By converting neural networks to mixed integer linear programs, our framework also allows to adjust the conservativeness of the neural network output with respect to the existing stability boundaries. We demonstrate the performance of our methods on the non-linear dynamics of converter-based generation in response to voltage disturbances.Comment: 6 pages, 5 figures, submitted to the 60th IEEE conference on Decision and Control (CDC), 2021, Austin, Texas, US

Zero-inertia Offshore Grids: N-1 Security and Active Power Sharing

With Denmark dedicated to maintaining its leading position in the integration of massive shares of wind energy, the construction of new offshore energy islands has been recently approved by the Danish government. These new islands will be zero-inertia systems, meaning that no synchronous generation will be installed in the island and that power imbalances will be shared only among converters. To this end, this paper proposes a methodology to calculate and update the frequency droops gains of the offshore converters in compliance with the N-1 security criterion in case of converter outage. The frequency droop gains are calculated solving an optimization problem which takes into consideration the power limitations of the converters as well as the stability of the system. As a consequence, the proposed controller ensures safe operation of off-shore systems in the event of any power imbalance and allows for greater loadability at pre-fault state, as confirmed by the simulation results.Comment: Submitted to "IEEE Transactions on Power Systems" on February 19, 202

Frequency dynamics of the Northern European AC/DC power system: a look-ahead study

peer reviewedIn many power systems, the increased penetration of inverter-based renewable generation will cause a decrease in kinetic energy storage, leading to higher frequency excursions after a power disturbance. This is the case of the future Nordic Power System (NPS). The look-ahead study reported in this paper shows that the chosen units participating in Frequency Containment Reserves (FCR) cannot keep the frequency above the prescribed threshold following the outage of the largest plant. This analysis relies on a detailed model of the Northern European grid. The latter is compared to the classical single-mass equivalent, and the impact of voltage-dependent loads is assessed in some detail. Next, the paper focuses on emergency power control of the HVDC links that connect the NPS to the rest of the European grid, which can supplement or even replace part of the FCR. The proper tuning of that control is discussed. Finally, the analysis is extended to the HVDC links connecting the future North Sea Wind Power Hub under two configurations, namely low and zero inertia. The impact of outages in the latter sub-system is also assessed. The material to simulate the system with industrial software is made publicly available

Frequency dynamics of the Northern European AC/DC power system: a look-ahead study

In many power systems, the increased penetration of inverter-based renewable generation will cause a decrease in kinetic energy storage, leading to higher frequency excursions after a power disturbance. This is the case of the future Nordic Power System (NPS). The look-ahead study reported in this paper shows that the chosen units participating in Frequency Containment Reserves (FCR) cannot keep the frequency above the prescribed threshold following the outage of the largest plant. This analysis relies on a detailed model of the Northern European grid. The latter is compared to the classical single-mass equivalent, and the impact of voltage-dependent loads is assessed in some detail. Next, the paper focuses on emergency power control of the HVDC links that connect the NPS to the rest of the European grid, which can supplement or even replace part of the FCR. The proper tuning of that control is discussed. Finally, the analysis is extended to the HVDC links connecting the future North Sea Wind Power Hub under two configurations, namely low and zero inertia. The impact of outages in the latter sub-system is also assessed. The material to simulate the system with industrial software is made publicly available

North Sea Wind Power Hub: System Configurations, Grid Implementation and Techno-economic Assessment

In 2017, Energinet and TenneT, the Danish and Dutch Transmission System Operators (TSOs), have announced the North Sea Wind Power Hub (NSWPH) project. The project aims at increasing by 36 GW the North Sea offshore wind capacity, with an artificial island collecting all the power produced by wind turbines and several HVDC links transmitting this power to the onshore grids. This project brings together new opportunities and new challenges, both from a technical and economic point of view. In this regard, this paper presents three analyses regarding the design and operation of such an offshore system. First, we perform a techno-economic assessment of different grid configurations for the collection of the power produced by wind farms and its transmission to the hub. In this analysis, two frequencies and two voltage levels for the operation of the offshore grid are investigated. Our findings show that the nominal-frequency high-voltage option is the more suitable, as low-frequency does not bring any advantage and low-voltage would results in higher costs. The second analysis is related to the differences in operating the system with low- or zero-inertia; different dynamic studies are performed for each configuration to identify proper control actions and their stability properties. Comparing the outcomes of the simulations, we observed that voltage and frequency oscillations are better damped in the zero-inertia system; however, the risk of propagating offshore faults in the connected onshore grids is mitigated with the inclusion of the synchronous condensers. Lastly, a comparison of ElectroMagnetic Transient (EMT) and phasor-mode (also known as RMS) models is presented, in order to understand their appropriateness of simulating low- and zero- inertia systems. The results show that phasor approximation modelling can be used, as long as eigen-frequencies in power network are well damped.Comment: Submitted to "CIGRE Technical Exhibition 2020 - Session 48" on January 3, 2020 - Revised on February 15, 2020 - Accepted on June 4, 202

Transient Stability Analysis with Physics-Informed Neural Networks

We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment, the traditionally applied methods either carry a significant computational burden, require model simplifications, or use overly conservative surrogate models. Conventional neural networks can circumvent these limitations but are faced with high demand of high-quality training datasets, while they ignore the underlying governing equations. Physics-informed neural networks are different: they incorporate the power system differential algebraic equations directly into the neural network training and drastically reduce the need for training data. This paper takes a deep dive into the performance of physics-informed neural networks for power system transient stability assessment. Introducing a new neural network training procedure to facilitate a thorough comparison, we explore how physics-informed neural networks compare with conventional differential-algebraic solvers and classical neural networks in terms of computation time, requirements in data, and prediction accuracy. We illustrate the findings on the Kundur two-area system, and assess the opportunities and challenges of physics-informed neural networks to serve as a transient stability analysis tool, highlighting possible pathways to further develop this method.Comment: 9 pages, 8 figures, submitted to IEEE Transactions on Power System

Physics-Informed Neural Networks for Power Systems

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