Maria Vrakopoulou

A Probabilistic Framework for Reserve Scheduling and

We propose a probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation. We also identify a reserve strategy according to which we deploy the reserves in real-time operation, which serves as a corrective control action. To achieve this, we formulate a stochastic optimization program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines and the generation limits. To incorporate a reserve decision scheme, we take into account the steady-state behavior of the secondary frequency controller and, hence, consider the deployed reserves to be a linear function of the total generation-load mismatch. The overall problem results in a chance constrained bilinear program. To achieve tractability, we propose a convex reformulation and a heuristic algorithm, whereas to deal with the chance constraint we use a scenario-based-approach and an approach that considers only the quantiles of the stationary distribution of the wind power error. To quantify the effectiveness of the proposed methodologies and compare them in terms of cost and performance, we use the IEEE 30-bus network and carry out Monte Carlo simulations, corresponding to different wind power realizations generated by a Markov chain-based model.

{\rm N}-1

This paper presents new results on the applications of reachability methods and computational tools to a two-area power system in the case of a cyber attack. In the VIKING research project a novel concept to assess the vulnerabilities introduced by the interaction between the IT infrastructure and power systems is proposed. Here we develop a new framework and define a systematic methodology, based on reachability, for identifying the impact that an intrusion might have in the Automatic Generation Control loop, which regulates the frequency and the power exchange between the controlled areas. The numerical results reveal the weaknesses of the system and indicate possible policies that an attacker could use to disturb it.

Security Assessment of Systems With High Wind Power Penetration

We propose a novel framework for designing an N-1 secure generation day-ahead dispatch for power systems with a high penetration of fluctuating power sources, e.g., wind or PV power. To achieve this, we integrate the security constraints in a DC optimal power flow optimization and formulate a stochastic program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines and the generation limits. To solve the resulting problem numerically, we transform the initial problem to a tractable one by using the so-called scenario approach, which is based on sampling the uncertain parameter while keeping the desired probabilistic guarantees. To generate wind power scenarios a Markov chain-based model is employed. To illustrate the effectiveness of the proposed technique we apply it to the IEEE 30-bus network, and compare it with the solution of a deterministic variant of the problem, where the operator determines a secure generation dispatch based only on the available wind power forecast. A Monte Carlo simulation study is conducted to collect statistical results regarding the performance of our method.

Cyber attack in a two-area power system: Impact identification using reachability

This paper develops methodologies to robustly destabilize a two-area power system in the case of a cyber attack in the Automatic Generation Control (AGC). In earlier work reachability methods were used to establish conditions under which an attacker can cause undesirable behavior by interrupting the AGC signals and introducing an appropriate fake signal. In this paper we investigate how to robustify this approach to deal with practical situations where the attacker only has partial information about the parameters of the power system and the values of its states. We first propose an open loop procedure, based on Markov Chain Monte Carlo optimization, to identify an optimal attack signal. Motivated by the fact that the results are very sensitive to parameter uncertainty, we develop a systematic algorithm, based on feedback linearization, to construct a feedback policy that an intruder may use to disrupt the network. The numerical simulations demonstrate the effectiveness of the resulting policy, as well as its robustness with respect to modeling uncertainty and imperfect state information.

Probabilistic Guarantees for the N-1 Security of Systems with Wind Power Generation

Demand response (DR) can provide reserves in power systems but a fundamental challenge is that the amount of capacity available from DR is time-varying and uncertain. We propose a stochastic optimal power flow (OPF) formulation that handles uncertain energy from wind and uncertain reserves provided by DR. To handle the uncertainty, we formulate chance constraints and use a scenario based methodology to solve the stochastic OPF problem. This technique allows us to provide a-priori guarantees regarding the probability of constraint satisfaction. Additionally, we devise a strategy for the reserves, provided either by the generators or the loads, that could be deployed in real time operation. To evaluate the effectiveness of our methodology, we carry out a simulation based analysis on the IEEE 30-bus network. Our case studies show that optimizing over the reserves provided by DR, even though they are uncertain, results in lower total cost compared to the case where only generation side reserves are taken into account. We also carry out a Monte Carlo analysis to empirically estimate the probability of constraint satisfaction and demonstrate that it is within the theoretical limits.

A robust policy for Automatic Generation Control cyber attack in two area power network

This paper presents an emergency control strategy, which serves to counteract a cascading disturbance in a large power system that would eventually lead to a blackout. The strategy is composed of two parts: after a disturbance, a real-time controlled islanding algorithm based on slow coherency of synchronous generators and k-means clustering splits the system into autonomously operating parts. The imbalances between load and generation are then accounted for by generator tripping in the generation-rich islands and a novel type of under-frequency load shedding in the load-rich islands, if the available primary control reserves are insufficient or too slow to stabilize the frequency. As opposed to the under-frequency relays in substations which are often used nowadays, the system considered here utilizes a “smart home” communication and control infrastructure for assigning frequency thresholds to individual appliances owned by consumers. Pervasive availability of this infrastructure is assumed. The strategy is evaluated in time-domain simulations using the IEEE 118-bus system.

Stochastic Optimal Power Flow with Uncertain Reserves from Demand Response

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.

Mitigation of cascading failures by real-time controlled islanding and graceful load shedding

We propose a probabilistic framework for designing an N-1 secure dispatch for systems with fluctuating power sources. This could be used in various optimal power flow related applications, however in this work, we demonstrate our approach for a day-ahead planning problem. We extend our earlier work on probabilistic N-1 security, to incorporate recent results on convex AC optimal power flow relaxations. The problem is formulated as a chance constrained convex program; to deal with the chance constraint we follow an algorithm based on a combination of randomized and robust optimization. We also enhance the controllability of the system by introducing a corrective scheme that imposes post-contingency control of the Automatic Voltage Regulation (AVR) set-point. This scheme allows us to inherit a priori probabilistic guarantees regarding the satisfaction of the system constraints, unlike the base case where the AVR set-points are constant. To illustrate the performance of the proposed security-constrained AC optimal power flow we compare it against a DC power flow based formulation using Monte Carlo simulations, and show that it results to lower operational cost compared to the case where the AVR set-points are constant.

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

This article consists of two parts: a theoretical part concerned with fault detection schemes, and an application part dealing with cyber security of power systems. In the first part, we develop a tractable approach to design a robust residual generator to detect and isolate faults in high dimensional nonlinear systems. Previous approaches on fault detection and isolation problems are either confined to linear systems or they are only applicable to low dimensional dynamics with more specific structures. In contrast, we propose a novel methodology to robustify a linear residual generator for a nonlinear system in the presence of certain disturbance signatures. To this end, we formulate the problem into the framework of quadratic programming which enables us to solve relatively high dimensional systems. In the second part, the application is motivated by the emerging problem of cyber security in power networks. We provide description of a multi-machine power system that represents a two-area power system, and we model a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system. The algorithm developed in the first part is finally used to diagnose such an intrusion before the functionality of the power system is disrupted.

Probabilistic security-constrained AC optimal power flow

As power systems are operated closer to their technical limits, dynamic thermal line rating (DLR) can be used to enable additional dispatching flexibility. DLR is used to dynamically adapt the ampacity of the conductors, i.e. the maximum allowed amount of current a conductor can carry without overheating, according to the meteorological conditions. This paper proposes a probabilistic N-1 security assessment method that incorporates DLR in a probabilistic constraint. To model the probability distributions of certain meteorological values we use a copula approach. We calculate the distribution of the ampacity based on the distributions of the meteorological quantities using a model of the thermal behaviour of the line and given weather forecasts. From the resulting distribution, uncertainty realizations are sampled which are needed for a scenario based methodology which is used to deal with the developed chance constraint program.