Line Roald

Coordinated scheduling for interdependent electric power and natural gas infrastructures

The extensive installation of gas-fired power plants in many parts of the world has led electric systems to depend heavily on reliable gas supplies. The use of gas-fired generators for peak load and reserve provision causes high intraday variability in withdrawals from high-pressure gas transmission systems. Such variability can lead to gas price fluctuations and supply disruptions that affect electric generator dispatch, electricity prices, and threaten the security of power systems and gas pipelines. These infrastructures function on vastly different spatio-temporal scales, which prevents current practices for separate operations and market clearing from being coordinated. In this paper, we apply new techniques for control of dynamic gas flows on pipeline networks to examine day-ahead scheduling of electric generator dispatch and gas compressor operation for different levels of integration, spanning from separate forecasting, and simulation to combined optimal control. We formulate multiple coordination scenarios and develop tractable physically accurate computational implementations. These scenarios are compared using an integrated model of test networks for power and gas systems with 24 nodes and 24 pipes, respectively, which are coupled through gas-fired generators. The analysis quantifies the economic efficiency and security benefits of gas-electric coordination and dynamic gas system operation.

Closure of “a unified analysis of security-constrained OPF formulations considering uncertainty, risk, and controllability in single and multi-area systems”

This paper presents a variety of different Security Constrained Optimal Power Flow formulations addressing four power system operation and planning problems: (a) forecast uncertainty of Renewable Energy Sources (RES) in-feed and load, (b) security criteria based on contingency risk, (c) corrective control offered through High Voltage Direct Current (HVDC) lines and flexible demand, (d) operation of multi-area systems with limited data exchange. A comprehensive probabilistic Security Constrained Optimal Power Flow (SCOPF) framework based on scenario-based methodologies is presented. This approach provides a-priori guarantees regarding the probability of the constraint satisfaction. In this paper, we show how HVDC lines, flexible demand, and novel risk-based operational paradigms can be used to handle outage uncertainty and the fluctuating in-feed from RES. Our analysis is extended by introducing a distributed probabilistic SCOPF algorithm for multi-area systems involving different levels of data exchange. The applicability of the methods is demonstrated on the three-area Reliability Test System (RTS-96). Results are compared based on operating costs and maximum wind power penetration.

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.

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.

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.

Optimal power flow with wind power control and limited expected risk of overloads

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 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 optimizing 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 expected 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.

Uncertainty margins for probabilistic AC security assessment

In the past few years, the share of renewable power generation has been growing significantly, leading to increased uncertainties in power system operation. In this paper, the effect of wind in-feed uncertainties on power flow in the AC grid is investigated. The wind power in-feed deviations from initial forecast are modelled as Gaussian random variables. To assess the influence of wind power deviations on power flows, sensitivity factors based on a linearised version of the AC power flow equations are used. These factors are then applied in the calculation of appropriate security margins needed for keeping the system secure in the presence of wind power fluctuations. The modelling methods are implemented on the IEEE RTS96 test system with additional wind power in-feed. Simulation results show that the proposed method based on linearised AC power flow can estimate uncertainty margins for active power more accurately than the DC approximation model, and also provides satisfactory estimation of uncertainty margins for apparent power.

Control policies for operational coordination of electric power and natural gas transmission systems

The abundance of natural gas in the United States and the need for cleaner electric power have prompted widespread installation of gas-fired power plants and caused electric power systems to depend heavily on reliable gas supplies. The use of gas generators for peak load and reserve generation causes high intra-day variability in withdrawals from high pressure gas transmission systems, which leads to gas price fluctuations and supply disruptions that affect electric generator dispatch and threaten the security of both power and gas systems. In this manuscript, we investigate different gas compressor operation policies and their influence on the affected power system. Specifically, we consider constant pressure boost ratios and dynamic adjustment of these ratios to track pressure set-points. We also implement a joint optimization of generator dispatch schedules and gas compressor protocols using a dynamic gas flow model. We develop tractable, physically accurate implementations that are compared using an integrated model of test networks for power and gas systems with 24 and 25 nodes, which are coupled through gas-fired generators. This demonstrates the benefits that can be achieved with globally optimized gas system operations and increased gas-electric coordination.

Joint scheduling of frequency control reserves and energy dispatch for islanded power systems

In this paper, we propose a framework to jointly schedule energy and frequency control reserves in islanded systems, taking into account the system dynamic response. In islanded power systems, the control of system frequency differs considerably comparing to large interconnections, and dynamic models are employed to study the system behaviour. We suggest a way of incorporating relevant aspects of the dynamic response in an optimal power flow formulation, which in addition to including dynamic constraints also accounts for transmission, generation and security constraints. The applicability of the method is demonstrated on the Swiss power system under a special, critical case where the Swiss system is disconnected from the remaining European grid and energy shortage is a concern. We show that the proposed framework can be successfully applied for the operational planning and allows for a secure and reliable power system islanded operation.

Stochastic AC optimal power flow with approximate chance-constraints

With higher shares of fluctuating electricity generation from renewables, new operational planning methods to handle uncertainty from forecast errors and short-term fluctuations are required. In this paper, we formulate a probabilistic AC optimal power flow where the uncertainties are accounted for using chance constraints on line currents and voltage magnitudes. The chance constraints ensure that the probability of limit violations remain small, but require a tractable reformulation. To achieve this, an approximate, analytical reformulation of the chance constraints is developed based on linearization around the expected operating point and the assumption of normally distributed deviations. Further, an iterative solution approach is suggested, which allows for a straightforward adaption of the method based on any existing AC OPF implementation. We evaluate the performance of our method in a case study on the 24-bus IEEE RTS96 system. The proposed algorithm is found to converge fast and substantially reduce constraint violations.