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As the level of uncertain renewable capacity increases on power systems worldwide, industrial and academic researchers alike are seeking a scalable, transparent, and effective approach to unit commitment under uncertainty. This paper presents a statistical ranking methodology that allows adaptive robust stochastic unit commitment using a modular structure, with much-needed flexibility. Specifically, this paper describes a bus ranking methodology that identifies the most critical buses based on a worst-case metric. An important innovation is the ability to identify alternative metrics on which to rank the uncertainty set—for example, to minimize economic dispatch cost or ramping needs, to provide a customized robust unit commitment solution. Compared to traditional robust unit commitment models, the proposed model combines statistical tools with analytical framework of power system networks. The resulting formulation is easily implementable and customizable to the needs of the system operator. The method and its applications are validated against other established approaches, showing equivalent solution to the state-of-the-art approach. Case studies were conducted on the IEEE-30, IEEE-118, and the pegase-1354 networks. In addition, the flexibility of bus ranking formulation is illustrated through implementation of alternative definitions of worst-case metrics. Results show that the bus ranking method performs as well as the best of these methods, with the provision of additional flexibility and potential for parallelization. [ABSTRACT FROM AUTHOR]

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper “Large-scale Unit Commitment under uncertainty: a literature survey” that appeared in 4OR 13(2):115-171 (2015); this version has over 170 more citations, most of which appeared in the last 3 years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject. [ABSTRACT FROM AUTHOR]

Unit commitment (UC) is a popular problem in electric power system that aims at minimizing the total cost of power generation in a specific period, by defining an adequate scheduling of the generating units. The UC solution must respect many operational constraints. In the past half century, there was several researches treated the UC problem. Many works have proposed new formulations to the UC problem, others have offered several methodologies and techniques to solve the problem. This paper gives a literature review of UC problem, its mathematical formulation, methods for solving it and Different approaches developed for addressing renewable energy effects and uncertainties. [ABSTRACT FROM AUTHOR]

Recently, there is a growing use of renewable energy in the electricity markets due to governmental subsidy aiming to comply with reduced greenhouse gas emission targets. Jointly with its highly volatile generation it greatly affects the operation planning of power plants, particularly, when addressing the unit commitment problem (UCP). The UCP is imperative in electric power system operations. It seeks an operating policy for a system of generating units over a multi-period finite horizon to meet the demand, subject to equipment and physical constraints. We consider a profit based UCP (PUCP) of an energy producer operating in a deregulated market aiming to maximize its profit facing uncertainty in both market price and wind generation. Here, we employ the robust optimization (RO) methodology which provides a feasible solution for any realization of the uncertain parameters within a bounded set, resulting in a guaranteed value of the objective function. This leads to a model, which is a bilinear mixed integer problem. The method we develop in this paper results in a problem, which is notably as difficult to solve without uncertainty. Furthermore, its resulting policy is more successful in meeting the demand for electricity than that of currently used methods. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven affinely adjustable distributionally robust method for unit commitment considering uncertain load and renewable generation forecasting errors. The proposed formulation minimizes expected total operation costs, including the costs of generation, reserve, wind curtailment, and load shedding, while guaranteeing the system security. Without any presumption about the probability distribution of the uncertainties, the proposed method constructs an ambiguity set of distributions using historical data and immunizes the operation strategies against the worst case distribution in the ambiguity set. The more historical data is available, the smaller the ambiguity set is and the less conservative the solution is. The formulation is finally cast into a mixed integer linear programming whose scale remains unchanged as the amount of historical data increases. Numerical results and Monte Carlo simulations on the 118- and 1888-bus systems demonstrate the favorable features of the proposed method. [ABSTRACT FROM AUTHOR]

Unified Power Flow Controller (UPFC) is recognized as the most powerful flexible AC transmission systems (FACTS) device for power system operation. This paper addresses how UPFC explores the transmission flexibility and facilitates the integration of uncertain and volatile wind power generation. To this end, a comprehensive unit commitment (UC) model with UPFC and uncertain wind power generation is proposed. Then, some metrics are introduced to evaluate the impacts of UPFC on the reliability, security and economy of power system operation. Further, different dispatch strategies of UPFC are compared to provide helpful guidances on making full use of UPFC to hedge against uncertainties. In addition, facing the challenging mixed-integer non-linear non-convex problems, approximate models are proposed to provide a starting point to solve the problems efficiently. All these models are easy to adapt to other types of FACTS devices. Illustrative numerical results are provided. [ABSTRACT FROM AUTHOR]

This paper provides a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case. The proposed reformulation is based on partitioning the sample space of the uncertain factors by clustering the scenarios that approximate their probability distributions. The degree of conservatism of the resulting unit-commitment plan (that is, how close it is to the one provided by a purely robust or stochastic unit-commitment formulation) is controlled by the number of partitions into which the said sample space is split. To efficiently solve the proposed reformulation of the unit-commitment problem under uncertainty, we develop two alternative parallelization and decomposition schemes that rely on a column-and-constraint generation procedure. Finally, we analyze the quality of the solutions provided by this reformulation for a case study based on the IEEE 14-node power system and test the effectiveness of the proposed parallelization and decomposition solution approaches on the larger IEEE 3-Area RTS-96 power system. [ABSTRACT FROM PUBLISHER]

Consider a general security-constrained unit commitment (SCUC) problem for an arbitrary power network. This problem includes discrete variables corresponding to commitment parameters as well as demand and generation constraints, among others. Aside from its nonconvexity, SCUC is a large-scale problem for real-world systems due to the security constraints. The main objective of this paper is to propose an algorithm to eliminate a vast majority of linear security constraints in the high-dimensional mixed-integer SCUC problem in order to arrive at an equivalent reduced-order SCUC problem. To this end, we develop a parallel and computationally cheap algorithm for finding a minimal subset of security constraints whose satisfaction guarantees the satisfaction of all security constraints. The proposed algorithm does not depend on the unknown unit commitment parameters and allows the load forecasts to be imprecise. More specifically, a low-order model of the SCUC problem is found based on the topology of the power system, given lower and upper bounds on nodal power injections (to accommodate uncertainties in loads and generation productions), and the normal and emergency line ratings. This algorithm is tested on several power systems with as many as 5500 buses, for which each set of security constraints with millions of conditions is reduced to a minimal subset with only a few hundred conditions. [ABSTRACT FROM AUTHOR]

We propose a two-stage mixed-integer linear stochastic optimization model to analyze the scheduling of electricity-production units under natural gas-supply uncertainty due to pipeline congestion and natural gas-price variability. The first stage of this stochastic optimization model represents the day-ahead scheduling (i .e., unit commitment) stage, while the second stage represents actual real-time operations through a number of scenarios. We use this model to analyze the effect on unit commitment and dispatch of two types of natural gas-supply conditions. First, we analyze a case involving low-cost natural gas supply with natural gas-transmission issues related to potential gas-pipeline congestion. We then examine a case involving higher-cost natural gas, which is used solely to attain feasibility with fast-ramping events. The first case mimics situations in the ISO New England system, in which relatively low-cost natural gas supply is uncertain in cold-weather conditions due to natural gas-transmission bottlenecks. The second case is reminiscent of situations in the California ISO system, in which relatively expensive but flexible natural gas-fired units need to be used to handle rapid changes in net demand in the early mornings and late afternoons. [ABSTRACT FROM AUTHOR]

The renewable energy sources (RES) integration in the electricity supply utilities can reduce the energy procurement costs as well as the environmental concerns. Wind power is the most popular form of RES which is vastly utilized worldwide. This paper proposes a robust model for unit commitment (UC) problem, minimizing the operating costs considering uncertainty of wind power generation. In order to handle the uncertainties arising from volatile nature of wind power, information gap decision theory (IGDT) is utilized, where risk averse (RA) and opportunity seeker (OS) strategies are developed. RA strategy gives a robust decision making tool for handling the severe uncertainty of wind power, whereas the OS strategy makes benefit of possible uncertainties by adjusting the decision variables in a right way. Besides, the impact of demand flexibility (or demand response) on the operation costs is also investigated. The proposed model is examined on the IEEE 118-bus test system, and its benefits over the existing stochastic programming technique is examined. The obtained results demonstrate the applicability of the proposed method to deal with the UC problem with uncertain wind power generation. It is also observed that demand flexibility has positive impacts in both RA and OS strategies. [ABSTRACT FROM AUTHOR]

This paper addresses two vital issues which are barely discussed in the literature on robust unit commitment (RUC): 1) how much the potential operational loss could be if the realization of uncertainty is beyond the prescribed uncertainty set; 2) how large the prescribed uncertainty set should be when it is used for RUC decision making. In this regard, a robust risk-constrained unit commitment (RRUC) formulation is proposed to cope with large-scale volatile and uncertain wind generation. Differing from existing RUC formulations, the wind generation uncertainty set in RRUC is adjustable via choosing diverse levels of operational risk. By optimizing the uncertainty set, RRUC can allocate operational flexibility of power systems over spatial and temporal domains optimally, reducing operational cost in a risk-constrained manner. Moreover, since impact of wind generation realization out of the prescribed uncertainty set on operational risk is taken into account, RRUC outperforms RUC in the case of rare events. The traditional column and constraint generation (C&CG) and two algorithms based on C&CG are adopted to solve the RRUC. As the proposed algorithms are quite general, they can also apply to other RUC models to improve their computational efficiency. Simulations on a modified IEEE 118-bus system demonstrate the effectiveness and efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

The use of appropriate hourly reserve margins can maintain power system security by balancing supply and demand in the presence of errors in the forecast demand, generation outages, or errors in the forecast of wind power generation. Because the cost of unit commitment increases with larger reserve margins, cost analysis to determine the most economical reserve margin is an important issue in power system operation. Here, we define the "short-term reliability of balance" and describe a method to determine the reserve margin based on the short-term reliability of balance. We describe a case study, in which we calculate the reserve margin using this method with various standards of short-term reliability of balance. A cost analysis is then performed to determine the most economic standard, and a comparison between our method and a conventional method is carried out. The results show that our method with an economic short-term reliability of balance enables more reliable and efficient operation of the power system. Moreover, with an hourly reserve margin, we show that an increase in wind power generation can result in a significant decrease in the operating cost, which makes wind power generation economically viable. [ABSTRACT FROM AUTHOR]

Developing usage of renewable resources, such as wind turbine and photovoltaic units, and their output uncertainty beside the system total load forecasting imprecision leads to the uncertainty of unit commitment solution. This article presents a new fuzzy approach for modeling of these uncertainty sources behavior in a power system including wind turbine, photovoltaic, and thermal units. For the first time, based on Monte Carlo simulation, a new concept called Monte Carlo mismatch index is proposed as a criterion for uncertainty modeling precision, which is used as a fitness function for optimization of the proposed fuzzy system parameters by genetic algorithm. Then this stochastic-optimized fuzzy system is applied for uncertainty modeling. The fuzzy system output is that part of the power system total load, which should be distributed among thermal units. Then, this output is fed to a crisp unit commitment program based on particle swarm optimization. Finally, optimal thermal units generation cost and scheduling is presented and the proposed method performance is compared with other uncertainty modeling methods. [ABSTRACT FROM AUTHOR]

Wind power generation is continuously increasing around the world, but due to uncertainty in wind power generation, the unit commitment problem has become complex. In this paper, scenario generation and reduction techniques are used to consider wind power uncertainty on system operation. Also, a new approach is developed for creating clusters of unit status associated with a probability of occurrence from an initial set of large wind power generation scenarios. And then a model of wind-hydro-thermal coordination problem along with the pumped storage plant is established. Combination of proposed weighted-improved crazy particle swarm optimization along with a pseudo code based algorithm and scenario analysis method is utilized to solve above problem. The effectiveness and feasibility of the proposed method is tested on systems with and without pumped storage plant integration. The results are analyzed in detail, which demonstrate the model and the proposed method is practicable in solving the unit commitment. [ABSTRACT FROM AUTHOR]

A stochastic model for day-ahead Micro-Grid (MG) management is proposed in this paper. The presented model uses probabilistic reconfiguration and Unit Commitment (UC) simultaneously to achieve the optimal set points of the MG’s units besides the MG optimal topology for day-ahead power market. The proposed operation method is employed to maximize MG’s benefit considering load demand and wind power generation uncertainty. MG’s day-ahead benefit is considered as the Objective Function (OF) and Particle Swarm Optimization (PSO) algorithm is used to solve the problem. For modeling uncertainties, some scenarios are generated according to Monte Carlo Simulation (MCS), and MG optimal operation is analyzed under these scenarios. The case study is a typical 10-bus MG, including Wind Turbine (WT), battery, Micro-Turbines (MTs), vital and non-vital loads. This MG is connected to the upstream network in one bus. Finally, the optimal set points of dispatchable units and best topology of MG are determined by scenario aggregation, and these amounts are proposed for the day-ahead operation. In fact, the proposed model is able to minimize the undesirable impact of uncertainties on MG’s benefit by creating different scenarios. [ABSTRACT FROM AUTHOR]

In this paper, a two-stage stochastic unit commitment (UC) model considering flexible scheduling of demand response (DR) is proposed. In the proposed UC model, the DR resources can be scheduled: (1) in the first stage, as resources on a day-ahead basis to integrate the predicted wind fluctuation with lower uncertainty; (2) in the second stage, as resources on an intra-day basis to compensate for the deviation among multiple wind power scenarios considering the coupling relationship of DR on available time and capacity. Simulation results on the Pennsylvania-New Jersey-Maryland (PJM) 5-bus system and IEEE 118-bus system indicate that the proposed model can maximize the DR value with lower cost. Moreover, different types of DR resources may vary in the contract costs (capacity costs), the responsive costs (energy costs), the time of advance notice, and the minimum on-site hours. The responsive cost is considered as the most important factor affecting DR scheduling. In addition, the first-stage DR is dispatched more frequently when transmission constraints congestion occurs. [ABSTRACT FROM AUTHOR]

The integration of wind power requires the power system to be sufficiently flexible to accommodate its forecast errors. In the market clearing process, the scheduling of flexibility relies on the manner in which the wind power uncertainty is addressed in the unit commitment (UC) model. This paper presents a novel risk-based day-ahead unit commitment (RUC) model that considers the risks of the loss of load, wind curtailment and branch overflow caused by wind power uncertainty. These risks are formulated in detail using the probabilistic distributions of wind power probabilistic forecast and are considered in both the objective functions and the constraints. The RUC model is shown to be convex and is transformed into a mixed integer linear programming (MILP) problem using relaxation and piecewise linearization. The proposed RUC model is tested using a three-bus system and an IEEE RTS79 system with wind power integration. The results show that the model can dynamically schedule the spinning reserves and hold the transmission capacity margins according to the uncertainty of the wind power. A comparison between the results of the RUC, a deterministic UC and two scenario-based UC models shows that the risk modeling facilitates a strategic market clearing procedure with a reasonable computational expense. [ABSTRACT FROM PUBLISHER]

Although price responsive demand response has been widely accepted as playing an important role in the reliable and economic operation of power system, the real response from demand side can be highly uncertain due to limited understanding of consumers’ response to pricing signals. To model the behavior of consumers, the price elasticity of demand has been explored and utilized in both research and real practice. However, the price elasticity of demand is not precisely known and may vary greatly with operating conditions and types of customers. To accommodate the uncertainty of demand response, alternative unit commitment methods robust to the uncertainty of the demand response require investigation. In this paper, a robust unit commitment model to minimize the generalized social cost is proposed for the optimal unit commitment decision taking into account uncertainty of the price elasticity of demand. By optimizing the worst case under proper robust level, the unit commitment solution of the proposed model is robust against all possible realizations of the modeled uncertain demand response. Numerical simulations on the IEEE Reliability Test System show the effectiveness of the method. Compared to unit commitment with deterministic price elasticity of demand, the proposed robust model can reduce the average Locational Marginal Prices (LMPs) as well as the price volatility. [ABSTRACT FROM AUTHOR]

To handle significant variability in loads, renewable energy generation, as well as various contingencies, (two-stage) robust optimization method has been adopted to construct unit commitment models and to ensure reliable solutions. In this paper, we further explore and extend the modeling capacity of two-stage robust optimization and present two new robust unit commitment variants: the expanded robust unit commitment and the risk constrained robust unit commitment model. We derive structural properties, demonstrate the connection to the popular scenario based stochastic unit commitment models, and present a customized column-and-constraint generation method. Numerical experiments on those models are performed using practical data sets, which illustrate their modeling strength, economic outcomes, and the algorithm performance in solving those models. [ABSTRACT FROM PUBLISHER]

Optimal operation of power systems with high integration of renewable power sources has become difficult as a consequence of the random nature of some sources like wind energy and photovoltaic energy. Nowadays this problem is solved using the Monte Carlo Simulation (MCS) approach, which allows the consideration of important statistical characteristics of wind and solar power production, such as the correlation between consecutive observations, the diurnal profile of the forecasted power production, and the forecasting error. In this paper, a new model of the unit scheduling of power systems with significant renewable power generation based on the scenario generation/reduction method combined with the priority list (PL) method is proposed that finds the probability distribution function (PDF) of a determined generator be committed or not. This approach allows the recognition of the role of each generation unit on the day-ahead unit commitment (UC) problem with a probabilistic point of view, which is important for acquiring a cost-effective and reliable solution. The capabilities and performance of the proposed approach are illustrated through the analysis of a study case, where the spinning reserve requirements are probabilistically verified with success. [ABSTRACT FROM AUTHOR]

Integrating wind power generation into bulk power grids imposes significant challenging to system operations due to the stochastic variation and limited predictability of wind power generation. One of the key issues is how to optimally schedule various units and determine a proper spinning reserve level to guarantee a reliable operation of the integrated system in a robust and economic manner. In this paper, we propose a two-level unit commitment (TLUC) for power systems facing large uncertainties in the context of adjustable robust optimization. The commitment decision acts as first-stage decisions that need to be robust against uncertainty, whereas the output decision acts as adjustable decisions that is decided after uncertainty is revealed. This decision mechanism naturally decomposes a conventional unit commitment (UC) problem into two levels, the upper level provides unit working status, whereas the lower level checks if there is at least one dispatch solution under uncertainty subject to the status. Unlike conventional UC, where the reserve level is fixed from operating experiences, in TLUC, the reserve level also acts as a decision variable in the upper level that controls the robustness of UC decisions. A heuristic algorithm is developed to solve this TLUC problem, providing the robust UC decision against uncertainty as well as the minimal spinning reserve level required to maintain reliability. Numerical experiments are carried out on the IEEE 39-bus system and large-scale realistic Guangdong power grid in China and demonstrate the effectiveness of our approach. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present a unit commitment problem with uncertain wind power output. The problem is formulated as a chance-constrained two-stage (CCTS) stochastic program. Our model ensures that, with high probability, a large portion of the wind power output at each operating hour will be utilized. The proposed model includes both the two-stage stochastic program and the chance-constrained stochastic program features. These types of problems are challenging and have never been studied together before, even though the algorithms for the two-stage stochastic program and the chance-constrained stochastic program have been recently developed separately. In this paper, a combined sample average approximation (SAA) algorithm is developed to solve the model effectively. The convergence property and the solution validation process of our proposed combined SAA algorithm is discussed and presented in the paper. Finally, computational results indicate that increasing the utilization of wind power output might increase the total power generation cost, and our experiments also verify that the proposed algorithm can solve large-scale power grid optimization problems. [ABSTRACT FROM PUBLISHER]