arXiv subjects

Line Roald

Publications and source records attributed to Line Roald.

51 records · Page 3Linked to original sources

arXiv2020

PowerModelsRestoration.jl: An Open-Source Framework for Exploring Power Network Restoration Algorithms

With the escalating frequency of extreme grid disturbances, such as natural disasters, comes an increasing need for efficient recovery plans. Algorithms for optimal power restoration play an important role in developing such plans, but also give rise to challenging mixed-integer nonlinear optimization problems, where tractable solution methods are not yet available. To assist in research on such solution methods, this work proposes PowerModelsRestoration, a flexible, open-source software framework for rapidly designing and testing power restoration algorithms. PowerModelsRestoration constructs a mathematical modeling layer for formalizing core restoration tasks that can be combined to develop complex workflows and high performance heuristics. The efficacy of the proposed framework is demonstrated by proof-of-concept studies on three established cases from the literature, focusing on single-phase positive sequence network models. The results demonstrate that PowerModelsRestoration reproduces the established literature, and for the first time provide an analysis of restoration with nonlinear power flow models, which have not been previously considered.

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arXiv2019

Chance-Constrained AC Optimal Power Flow Integrating HVDC Lines and Controllability

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.

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arXiv2019

Cloud-AC-OPF: Model Reduction Technique for Multi-Scenario Optimal Power Flow via Chance-Constrained Optimization

Many practical planning and operational applications in power systems require simultaneous consideration of a large number of operating conditions or Multi-Scenario AC-Optimal Power Flow (MS-AC-OPF) solution. However, when the number of exogenously prescribed conditions is large, solving the problem as a collection of single AC-OPFs may be time-consuming or simply intractable computationally. In this paper, we suggest a model reduction approach, coined Cloud-AC-OPF, which replaces a collection of samples by their compact representation in terms of mean and standard deviation. Instead of determining an optimal generation dispatch for each sample individually, we parametrize the generation dispatch as an affine function. The Cloud-AC-OPF is mathematically similar to a generalized Chance-Constrained AC-OPF (CC-AC-OPF) of the type recently discussed in the literature, but conceptually different as it discusses applications to long-term planning. We further propose a tractable formulation and implementation, and illustrate our construction on the example of 30-bus IEEE model.

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arXiv2019

Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained AC optimal power flow problem, which guarantees that generation, power flows and voltages remain within their bounds with a pre-defined probability. We then propose an accurate, yet tractable analytical reformulation of the chance constraints. The reformulation maintains the full, non-linear AC power flow equations for the forecasted operating point, and models the impact of uncertainty through a linearization around this point. We discuss different solution algorithms, including one-shot optimization with and without recourse, and an iterative algorithm which enables scalable implementations. We further discuss how more general chance constraint reformulations can be incorporated within the iterative solution algorithm. In a case study based on four different IEEE systems, we compare the performance of the solution algorithms, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in- and out-of-sample tests, and that the analytical approach outperforms two alternative, sample based chance constraint reformulations.

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arXiv2019

Implied Constraint Satisfaction in Power System Optimization: The Impacts of Load Variations

In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has far-reaching implications not only for power system optimization, but also for the practical long-term planning, operation, and control of the system. We formalize this empirical observation for problems involving the DC power flow equations. We use a two-step constraint screening approach to identify constraints whose satisfaction is implied by other constraints in the problem, and can therefore be removed from the problem. For the first screening step, we derive analytical bounds that quickly identify redundancies in the flow limits on parallel lines. The second screening step uses optimization-based constraint screening, where we solve a (relaxed) optimization problem for each constraint to identify redundancies. Different from existing methods, we specifically focus our approach on large ranges of load variation such that the results are valid for long periods of time, thus justifying the computational overhead required for the screening method. Numerical results for a wide variety of standard test cases show that even with load variations up to +/- 100% of nominal loading, we are able to eliminate a significant fraction of the flow constraints. This large reduction in constraints may enable a range of possible applications. As one illustrative example, we demonstrate the computational improvements for the unit commitment problem obtained as a result of the reduced number of constraints.

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arXiv2019

Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets

In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly modified input parameters, often under tight latency requirements. We consider the problem of using the information available through this repeated solution process to directly learn a model of the optimal solution as a function of the input parameters, thus reducing the need to solve computationally expensive large-scale parametric programs in real time. Our proposed method is based on learning relevant sets of active constraints, from which the optimal solution can be obtained efficiently. Using active sets as features preserves information about the physics of the system, enables interpretable models, accounts for relevant safety constraints, and is easy to represent and encode. However, the total number of active sets is also very large, as it grows exponentially with system size. The key contribution of this paper is a streaming algorithm that learns the relevant active sets from training samples consisting of the input parameters and the corresponding optimal solution, without any assumptions on the problem structure. The algorithm comes with theoretical performance guarantees, and is known to converge fast for problem instances with a small number of relevant active sets. It can thus be used to establish the practicability of the learning method. Through extensive experiments on the Optimal Power Flow problem, we observe that often only a few active sets are relevant in practice, suggesting that the active sets is the appropriate level of abstraction for a learning algorithm to target.

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arXiv2018

Chance Constraints for Improving the Security of AC Optimal Power Flow

This paper presents a scalable method for improving the solutions of AC Optimal Power Flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The focus of the paper is on providing solutions that are more robust to short-term deviations, and which optimize both the initial operating point and a parametrized response policy for control during fluctuations. We formulate this as a chance-constrained optimization problem. To obtain a tractable representation of the chance constraints, we introduce a number of modelling assumptions and leverage recent theoretical results to reformulate the problem as a convex, second-order cone program, which is efficiently solvable even for large instances. Our experiments demonstrate that the proposed procedure improves the feasibility and cost performance of the OPF solution, while the additional computation time is on the same magnitude as a single deterministic AC OPF calculation.

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arXiv2018

Convex Relaxations in Power System Optimization: A Brief Introduction

Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power flow equations. The aim of the videos is to provide the high level ideas of convex relaxations and their applications in power system optimization, and could be used as a starting point for researchers who want to study, use or develop new convex relaxations for use in their own research. The videos do not aim to provide an in-depth tutorial about specific convex relaxations, but rather focus on ideas that are common to all convex relaxations of the AC optimal power flow problem.

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arXiv2018

Chance-Constrained Optimization for Non-Linear Network Flow Problems

Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety and feasibility, especially in the face of uncertainty regarding the system model. To address this problem, we formulate a Chance Constrained Optimal Physical Network Flow (CC-OPNF) problem that attempts to optimize the system while satisfying safety limits with a high probability. However, the non-linear equality constraints representing the network physics introduce modelling and optimization challenges which make the chance constraints numerically intractable in their original form. The main contribution of the paper is to present a method to obtain tractable polynomial approximations to the chance constraints using Semidefinite Programming (SDP). The method uses a combination of existing semi-algebraic techniques for projection and volume computation in combination with novel set manipulations to provide conservative inner approximations to the chance constraints. In addition, we develop a new two-step procedure to improve computational speed. While the method is applicable to general physical network flow problems with polynomial constraints, we use the AC optimal power flow problem for electric grids as an example to demonstrate the method numerically.

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arXiv2017

Fast and Robust Determination of Power System Emergency Control Actions

This paper outlines an optimization framework for choosing fast and reliable control actions in a transmission grid emergency situation. We consider contractual load shedding and generation re-dispatch as exemplary emergency actions. To achieve computational efficiency and scalability, this novel formulation of the robust corrective action optimization is stated in terms of voltages and currents, as opposed to standard formulation in terms of power flows and voltages. The current-voltage formulation is natural for expressing voltage and thermal transmission line constraints, and its major advantage is in the linearity of the power flow equations. The complexity of the current-voltage formulation, which is mainly related to the transformation of voltages and currents into active and reactive power injections, can be largely avoided by stating the cost function directly in terms of currents and using linearized or robust estimates for load and generation constraints. The paper considers five different optimization problem formulations, including the full current-voltage formulation, as well as two convex and two linear approximation to the problem. In a case study on an illustrative case study for the IEEE RTS96 system, we demonstrate pros and cons of the different formulations based on simulations for both normal and contingency operation.

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arXiv2016

Corrective Control to Handle Forecast Uncertainty: A Chance Constrained Optimal Power Flow

Higher shares of electricity generation from renewable energy sources and market liberalization is increasing uncertainty in power systems operation. At the same time, operation is becoming more flexible with improved control systems and new technology such as phase shifting transformers (PSTs) and high voltage direct current connections (HVDC). Previous studies have shown that the use of corrective control in response to outages contributes to a reduction in operating cost, while maintaining N-1 security. In this work, we propose a method to extend the use of corrective control of PSTs and HVDCs to react to uncertainty. We characterize the uncertainty as continuous random variables, and define the corrective control actions through affine control policies. This allows us to efficiently model control reactions to a large number of uncertainty sources. The control policies are then included in a chance constrained optimal power flow formulation, which guarantees that the system constraints are enforced with a desired probability. By applying an analytical reformulation of the chance constraints, we obtain a second-order cone problem for which we develop an efficient solution algorithm. In a case study for the IEEE 118 bus system, we show that corrective control for uncertainty leads to a decrease in operational cost, while maintaining system security. Further, we demonstrate the scalability of the method by solving the problem for the IEEE 300 bus and the Polish system test cases.

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arXiv2016

Unit Commitment with N-1 Security and Wind Uncertainty

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch. In particular, uncontrollable wind generation increases the risk of random component failures. To address these questions, we present an N-1 Security and Chance-Constrained Unit Commitment (SCCUC) that includes the modeling of generation reserves that respond to wind fluctuations and tertiary reserves to account for single component outages. The basic formulation is reformulated as a mixed-integer second-order cone problem to limit the probability of failure. We develop three different algorithms to solve the problem to optimality and present a detailed case study on the IEEE RTS-96 single area system. The case study assesses the economic impacts due to contingencies and various degrees of wind power penetration into the system and also corroborates the effectiveness of the algorithms.

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arXiv2016

Chance Constrained Optimal Power Flow with Curtailment and Reserves from Wind Power Plants

Over the past years, the share of electricity production from wind power plants has increased to significant levels in several power systems across Europe and the United States. In order to cope with the fluctuating and partially unpredictable nature of renewable energy sources, transmission system operators (TSOs) have responded by increasing their reserve capacity requirements and by requiring wind power plants to be capable of providing reserves or following active power set-point signals. This paper addresses the issue of efficiently incorporating these new types of wind power control in the day-ahead operational planning. We review the technical requirements the wind power plants must fulfill, and propose a mathematical framework for modeling wind power control. The framework is based on an optimal power flow formulation with weighted chance constraints, which accounts for the uncertainty of wind power forecasts and allows us to limit the risk of constraint violations. In a case study based on the IEEE 118 bus system, we use the developed method to assess the effectiveness of different types of wind power control in terms of operational cost, system security and wind power curtailment.

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arXiv2015

Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints

The growing amount of fluctuating renewable infeeds and market liberalization increases uncertainty in power system operation. To capture the influence of fluctuations in operational planning, we model the forecast errors of the uncertain in-feeds as random variables and formulate a security constrained optimal power flow using chance constraints. The chance constraints limit the probability of violations of technical constraints, such as generation and transmission limits, but require a tractable reformulation. In this paper, we discuss different analytical reformulations of the chance constraints, based on a given set of assumptions concerning the forecast error distributions. In particular, we discuss reformulations that do not assume a normal distribution, and admit an analytical reformulation given only a mean vector and covariance matrix. We illustrate our method with a case study of the IEEE 118 bus system, based on real data from the European system. The different reformulations are compared in terms of both achieved empirical violation probability and operational cost, which allows us to provide a suggestion for the most appropriate reformulation in an optimal power flow setting. For a large number of uncertainty sources, it is observed that the distributions of the line flows and generator outputs can be close to normal, even though the power injections are not normally distributed.

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arXiv2015

Optimal Power Flow with Weighted Chance Constraints and General Policies for Generation Control

Due to the increasing amount of electricity generated from renewable sources, uncertainty in power system operation will grow. This has implications for tools such as Optimal Power Flow (OPF), an optimization problem widely used in power system operations and planning, which should be adjusted to account for this uncertainty. One way to handle the uncertainty is to formulate a Chance Constrained OPF (CC-OPF) which limits the probability of constraint violation to a predefined value. However, existing CC-OPF formulations and solutions are not immune to drawbacks. On one hand, they only consider affine policies for generation control, which are not always realistic and may be sub-optimal. On the other hand, the standard CC-OPF formulations do not distinguish between large and small violations, although those might carry significantly different risk. In this paper, we introduce the Weighted CC-OPF (WCC-OPF) that can handle general control policies while preserving convexity and allowing for efficient computation. The weighted chance constraints account for the size of violations through a weighting function, which assigns a higher risk to a higher overloads. We prove that the problem remains convex for any convex weighting function, and for very general generation control policies. In a case study, we compare the performance of the new WCC-OPF and the standard CC-OPF and demonstrate that WCC-OPF effectively reduces the number of severe overloads. Furthermore, we compare an affine generation control policy with a more general policy, and show that the additional flexibility allow for a lower cost while maintaining the same level of risk.

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