Xu Andy Sun

Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.

Adaptive Robust Optimization With Dynamic Uncertainty Sets for Multi-Period Economic Dispatch Under Significant Wind

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in todays power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.

Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow

It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate the situation where generation lower bounds are present. We show that even for a 2-bus 1-generator system, the SDP relaxation can have all possible approximation outcomes, that is 1) SDP relaxation may be exact, 2) SDP relaxation may be inexact, or 3) SDP relaxation may be feasible while the optimal power flow (OPF) instance may be infeasible. We provide a complete characterization of when these three approximation outcomes occur and an analytical expression of the resulting optimality gap for this 2-bus system. In order to facilitate further research, we design a library of instances over radial networks in which the SDP relaxation has positive optimality gap. Finally, we propose valid inequalities and variable bound tightening techniques that significantly improve the computational performance of a global optimization solver. Our work demonstrates the need of developing efficient global optimization methods for the solution of OPF even in the simple but fundamental case of radial networks.

Multistage Robust Unit Commitment With Dynamic Uncertainty Sets and Energy Storage

The deep penetration of wind and solar power is a critical component of the future power grid. However, the intermittency and stochasticity of these renewable resources bring significant challenges to the reliable and economic operation of power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the unit commitment (UC) problem, which models the sequential nature of the dispatch process and utilizes a new type of dynamic uncertainty sets to capture the temporal and spatial correlations of wind and solar power. The model also considers the operation of energy storage devices. We propose a simplified and effective affine policy for dispatch decisions, and develop an efficient algorithmic framework using a combination of constraint generation and duality-based reformulation with various improvements. Extensive computational experiments show that the proposed method can efficiently solve multistage robust UC problems on the Polish 2736-bus system under high dimensional uncertainty of 60 wind farms and 30 solar farms. The computational results also suggest that the proposed model leads to significant benefits in both costs and reliability over robust models with traditional uncertainty sets as well as deterministic models with reserve rules.

A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching

It is well known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the United States should “encourage, as appropriate, the deployment of advanced transmission technologies” including “optimized transmission line configurations.” As such, many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems such as contingency correction, real-time dispatch, and transmission expansion. The mathematical theory of the DC-OTS problem is ...

Minimal Impact Corrective Actions in Security-Constrained Optimal Power Flow Via Sparsity Regularization

This paper proposes a new formulation for the corrective security-constrained optimal power flow (SCOPF) problem with DC power flow constraints. The goal is to produce a generation schedule which has a minimal number of post-contingency corrections as well as a minimal amount of total MW rescheduled. In other words, the new SCOPF model effectively clears contingencies with corrective actions that have a minimal impact on system operations. The proposed SCOPF model utilizes sparse optimization techniques to achieve computational tractability for large-scale power systems. We also propose two efficient decomposition algorithms. Extensive computational experiments show the advantage of the proposed model and algorithms on several standard IEEE test systems and large-scale real-world power systems.

Sensor-Driven Condition-Based Generator Maintenance Scheduling—Part II: Incorporating Operations

A framework for sensor driven condition based generator maintenance scheduling was proposed in Part I of this paper. In Part II, we extend the previous model by incorporating the unit commitment and dispatch into the optimal maintenance scheduling problem. We reformulate this extended maintenance scheduling problem as a two-stage mixed integer program. We use this reformulation to construct an algorithm that obtains the global optimal solution to the proposed generator maintenance problem. Finally, we test and analyze the proposed model through extensive experiments conducted on IEEE-118 bus system. For every experiment, we present a benchmark analysis against the maintenance models used in current industry practice and power systems literature. Experimental results indicate that the proposed maintenance schedules provide considerable improvements in both cost and reliability.

Integrated Predictive Analytics and Optimization for Opportunistic Maintenance and Operations in Wind Farms

This paper proposes an integrated framework for wind farm maintenance that combines i) predictive analytics methodology that uses real-time sensor data to predict future degradation and remaining lifetime of wind turbines, with ii) a novel optimization model that transforms these predictions into profit-optimal maintenance and operational decisions for wind farms. To date, most applications of predictive analytics focus on single turbine systems. In contrast, this paper provides a seamless integration of the predictive analytics with decision making for a fleet of wind turbines. Operational decisions identify the dispatch profiles. Maintenance decisions consider the tradeoff between sensor-driven optimal maintenance schedule, and the significant cost reductions arising from grouping the wind turbine maintenances together—a concept called opportunistic maintenance. We focus on two types of wind turbines. For the operational wind turbines, we find an optimal fleet-level condition-based maintenance schedule driven by the sensor data. For the failed wind turbines, we identify the optimal time to conduct corrective maintenance to start producing electricity. The economic and stochastic dependence between operations and maintenance decisions are also considered. Experiments conducted on i) a 100-turbine wind farm case, and ii) a 200-turbine multiple wind farms case demonstrate the advantages of our proposal over traditional policies.

The Adaptive Robust Multi-Period Alternating Current Optimal Power Flow Problem

This paper jointly addresses two major challenges in power system operations: 1) dealing with non-convexity in the power flow equations, and 2) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period AC optimal power flow problem (AC-OPF) with detailed modeling considerations, such as reactive capability curves of conventional and renewable generators and transmission constraints. This paper then applies strong second-order cone programming (SOCP)-based convex relaxations of AC-OPF combined with the use of an alternating direction method to identify worst-case uncertainty realizations, and also presents a speed-up technique based on screening transmission line constraints. Extensive computational experiments show that the solution method is efficient and that the robust AC OPF model has significant advantages both from the economic and reliability standpoints as compared to a deterministic AC-OPF model.