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The computational efficiency of large-scale unit commitment (UC) is still a critical issue in power system and electricity market operations. To reduce the computation time of UC, relaxation-based neighborhood search (RBNS) and improved relaxation inducement (IRI) are proposed in this article. RBNS explores the neighborhood of the linear program (LP) relaxation optimal solution for a high-quality feasible solution. A new distance function, termed relaxation distance (RD), is proposed to measure the distance between the current solution and the tendency of the LP relaxation optimal solution. RBNS can substantially reduce the optimization space, and thus improve the efficiency. IRI has been developed to effectively induce binary variables towards the tendency of the relaxed solution. In contrast to a conventional relaxation inducement method, the binary variables are symmetrically and bi-directionally induced. The ratio between the inducing functions and the original objective function is optimized. IRI can induce more binary variables to integrality, and fewer binary variables need to be branched. Therefore, the size of the branch-and-bound tree can be reduced significantly. Modified IEEE-300 bus system and Polish 2746 bus system are used to demonstrate the effectiveness and performance of the proposed RBNS and IRI methods. [ABSTRACT FROM AUTHOR]

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]

This paper explores how enhanced flexibility through lower minimum load levels (also called “turndown” limits) for coal- and natural-gas-fired power plants can impact operations and profitability. Using soft-linked capacity planning and unit commitment models, this research examines the economic value of this flexibility and variation across different regions, generation asset types, and market environments (e.g., level of renewable deployment). Model results suggest that lower minimum loads are most valuable for mid-merit units with intermediate capacity factors, policy conditions that rearrange the merit order (e.g., carbon pricing), regions and scenarios without seasonal layup of assets, and units that are more flexible than generators with otherwise similar characteristics. Lower minimum loads can increase operating hours, increase net revenues, and decrease startups and long-run maintenance costs. The scenarios in this analysis show that plant flexibility affects operations more than annual profitability, which may have a higher system value for integrating renewables than a private value for the flexible unit. For many plants, the modest changes in net revenues with lower minimums mean that the focus will likely be on making operational modifications to increase flexibility rather than on capital investments. Additionally, this analysis quantifies how revenues from ancillary services markets can boost the value of lower minimum loads, especially for efficient natural gas units, but total market size and depth are uncertain. [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]

This paper aims at providing a novel techno-economic flexibility index to quantify the relative flexibility of different conventional generation technologies. The proposed measure takes into account a comprehensive set of technical flexibility characteristics of generation units including minimum stable generation level, operating range, minimum up/down times, and ramp up/down capability. The impact of various technical parameters on the flexibility restriction is determined based on the additional costs imposed to the system operator in order to satisfy that constraint. Afterward, the calculated flexibility index is incorporated into day-ahead market clearing procedure as a new objective function beside operation cost using a multiobjective decision-making approach. Simulation results show that the need of different flexibility levels changes the optimal generation dispatch and results in different operation costs. Furthermore, the impact of two emerging flexible options, i.e., bulk energy storages and a typical demand response program in the flexibility contribution of other generation technologies is also investigated. The results reveal that the integration of emerging flexible options frequently changes the flexibility share of conventional units and can provide the required flexibility level at a lower cost. [ABSTRACT FROM AUTHOR]

Clustered unit commitment (CUC) formulations have been proposed to provide accurate and fast approximations to the unit commitment (UC) problem. In these formulations, identical or similar plants are grouped into clusters. This way, the binary commitment variables of all the plants within a cluster can be replaced by a single integer variable. This approach has recently been mainly used for tractably integrating flexibility constraints in generation expansion planning problems. However, a thorough general validation is still missing. In addition, these formulations do not provide commitment schedules on a plant-by-plant level and hence cannot be used directly for operating actual systems or markets. A first contribution of this paper is to show that errors can be introduced both due to the problem formulation and the grouping of nonidentical units. A case study is presented in which these errors are quantified under different conditions. Overall, the error in approximating the total cost does not exceed 0.06%. A second contribution of this paper is the development of a hybrid approach, which sequentially uses a CUC and a traditional UC model. This approach allows to reduce the computational cost of solving the UC problem while providing a guaranteed feasible and near-optimal solution. [ABSTRACT FROM AUTHOR]

Part one of this two-part paper presents new models for evaluating flexible resources in two-settlement electricity markets (day-ahead and real-time) with uncertain net loads (demand minus wind). Physical resources include wind together with fast- and slow-start demand response and thermal generators. We also model financial participants (virtual bidders). Wind is stochastic, represented by a set of scenarios. The two-settlement system is modeled as a two-stage process in which the first stage involves unit commitment and tentative scheduling, while the second stage adjusts flexible resources to resolve imbalances. The value of various flexible resources is evaluated through four two-settlement models: 1) an equilibrium model in which each player independently schedules its generation or purchases to maximize expected profit; 2) a benchmark (expected system cost minimization); 3) a sequential equilibrium model in which the independent system operator first optimizes against a deterministic wind power forecast; and 4) an extended sequential equilibrium model with self-scheduling by profit-maximizing slow-start generators. A tight convexified unit commitment allows for demonstration of certain equivalencies of the four models. We show how virtual bidding enhances market performance, since, together with self-scheduling by slow-start generators, it can help a deterministic day-ahead market to choose the most efficient unit commitment. [ABSTRACT FROM PUBLISHER]

In Part II of this paper, we present formulations for three two-settlement market models: Baseline cost-minimization (\textitStoch- \textitOpt); and two sequential market models in which an independent system operator (ISO) runs real-time (RT) balancing markets after making day-ahead (DA) generating unit commitment decisions based upon deterministic wind forecasts, while virtual bidders arbitrage the two markets ( ${{\textit{Seq}}}$ and ${{\textit{Seq}}}$- ${{SS}}$). The latter two models differ in terms of whether some slow-start generators can self-schedule in the DA market while anticipating probabilities of RT prices. Models in ${{\textit{Seq}}}$ and ${{\textit{Seq}}}$- ${{SS}}$ build on components of the two-settlement equilibrium model ( \textitStoch- ${{MP}}$) defined in Part I of this paper [J. Kazempour and B. F. Hobbs, “Value of flexible resources, virtual bidding, and self-scheduling in two-settlement electricity markets with wind generation - Part I: Principles and competitive model,” IEEE Trans. Power Syst., vol. 33, no. 1, pp. 749–759, Jan. 2018]. We then provide numerical results for all four models. A simple single-node case illustrates the economic impacts of flexibility, virtual bidding, and self-schedules, and is followed by a larger case study based on the 24-node IEEE reliability test system. Their results confirm that flexible resources, including fast-start generators and demand response, can reduce expected costs in a sequential two-settlement market. In addition, virtual bidders can also improve the functioning of sequential markets. In some circumstances, virtual bidders (together with self-scheduling by slow-start generators) enable deterministic ISO DA markets to obtain the least (expected) cost unit commitments. [ABSTRACT FROM AUTHOR]

Combined heat and power (CHP) systems offer additional advantage and flexibility for addressing power grid balance resulting from large-scale introduction of intermittent renewable energy sources (RES) in contrast to power-only systems. The dependence between heat and power production in the CHP plant can be utilized to adjust power production level to accommodate more RES. Furthermore, electricity can be transformed into heat by electric heater and heat pump to avoid starting up heat led CHP plants when RES production is abundant. This paper focuses on solving efficiently unit commitment of the interconnected multi-site CHP system without considering RES. A relaxed on/off state based dynamic programming applying sequential commitment scheme in conjunction with dynamic regrouping is used to coordinate heat and power production in each site (region) as well as power transmission across sites. Computational experiments for real-life daily scheduling demonstrate that our method generates solutions much more quickly than a standard high-performance optimizer (CPLEX) with comparable solution quality, and lays foundation for the future handling of uncertainties of intermittent RES. [ABSTRACT FROM PUBLISHER]

This paper proposes a distributionally robust optimization approach for the contingency-constrained unit commitment problem. In our approach, we consider a case where the true probability distribution of contingencies is ambiguous, i.e., difficult to accurately estimate. Instead of assigning a (fixed) probability estimate for each contingency scenario, we consider a set of contingency probability distributions (termed the ambiguity set) based on the $N-k$ security criterion and moment information. Our approach considers all possible distributions in the ambiguity set, and is hence distributionally robust. Meanwhile, as this approach utilizes moment information, it can benefit from available data and become less conservative than the robust optimization approaches. We derive an equivalent reformulation and study a Benders’ decomposition algorithm for solving the model. Furthermore, we extend the model to incorporate wind power uncertainty. The case studies on a 6-Bus system and the IEEE 118-Bus system demonstrate that the proposed approach provides less conservative unit commitment decisions as compared with the robust optimization approach. [ABSTRACT FROM PUBLISHER]

Short-term hydro-generation planning can be efficiently modeled as a mixed integer linear program (MILP). Depending on the size of the system and the time horizon, the resulting MILP may be too large to be solved in reasonable time with commercial solvers. This paper presents a three-phase approach based on price decomposition that yields quickly near-optimal solutions to large-scale real-world instances. For any partition of the production system into subsystems, the first phase solves a linear program to estimate the marginal cost of electricity in each subsystem. The second phase solves local MILPs corresponding to each subsystem, and gives a solution that is almost feasible. The final phase slightly perturbs the solution to obtain a feasible solution that is proven to be near-optimal. Our method is tested on real instances corresponding to Hydro-Québec's production system. [ABSTRACT FROM PUBLISHER]

In this paper, we present the state-transition formulation for the unit commitment (UC) problem. This formulation uses new decision variables that capture the state transitions of the generators, instead of their on/off statuses. We show that this new approach produces a formulation which naturally includes valid inequalities, commonly used to strengthen other formulations. We demonstrate the performance of the state-transition formulation and observe that it leads to improved solution times especially in longer time-horizon instances. As an important consequence, the new formulation allows us to solve realistic instances in less than 12 minutes on an ordinary desktop PC, leading to a speed-up of a factor of almost two, in comparison to the nearest contender. Finally, we demonstrate the value of considering longer planning horizons in UC problems. [ABSTRACT FROM PUBLISHER]

Security-constrained unit commitment (SCUC) problem is one of the necessary tools for system operators to make operational planning and real-time operation. The internalization of transmission network and security constraints (e.g., N-1 criterion) could lead to different decisions in the generation dispatch. However, the computational burden of this problem is challenging mainly due to its inherent large problem size. Therefore, this paper proposes an N-1 security constrained formulation based on the line outage distribution factors (LODF) instead of the one based on injection sensitivity factors (ISF). This formulation is at the same time more compact than analogous formulations for contingency constraints; hence, it presents a lower computational burden. The computational efficiency of the proposed formulation is shown by solving the SCUC of the IEEE 118 bus system with LODF and ISF. Additionally, an iterative methodology for filtering the active N-1 congestion constraints is detailed, and its implementation for large-scale systems is described. The results show that the proposed filter reduces the computational time by approximately 70% in comparison to the complete formulation of N-1 constraints in SCUC. [ABSTRACT FROM PUBLISHER]

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]

Presents the table of contents for this issue of the publication. [ABSTRACT FROM AUTHOR]

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]

This paper investigates the impact of plug-in electric vehicle (EV) integration on the power systems scheduling and energy cost. An intermediary entity, the EV aggregator, participates in the market on behalf of the EV owners by optimally self-scheduling under the price-taking approach. Through detailed rolling simulations for a year and different EVs’ penetration scenarios at a large insular power system, this work highlights the different impact of direct and smart charging on power system scheduling and energy costs, the limitations of the price-taking approach, which is widely used in self-scheduling models, and the difference in system value and market value that smart charging adoption creates in restructured markets under the marginal pricing rule. [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]

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]

This paper discusses the modeling and analysis of a carbon capture technology-based resource scheduling/unit commitment (UC) methodology in carbon/emission-constrained environment. In carbon markets, the overall generation from conventional/fossil-fueled thermal plants is constrained over the total cost which is the sum of generation, capture cost/emission avoidance cost. Therefore, in this paper, generalized/uniform performance indices affecting the UC schedule are derived. Also, a commitment/scheduling methodology based on capture and fuel cost is devised rather than the existing penalty cost methodology as in the modernized markets everything was dealt in monetary value. Furthermore, the impact of type of resource used, i.e., coal rank is also considered to evaluate the sensitivity of scheduling decisions and financial influence of carbon capture technology. Along with performance indices, correction factors are also proposed to justify the effect of resource/coal rank in the process of optimal generation allocation. The effect of correction factors and type of coal is observed to be predominant at lower capture efficiencies compared to higher capture efficiency. The effectiveness of the proposed method over the penalty method is reflected in reduced generation cost and emission avoidance cost when compared to the penalty-based methodology. [ABSTRACT FROM AUTHOR]

System operators maintain sufficient reserve in power systems in order to respond to generation and transmission contingencies. Traditionally, the reserve requirements have been determined using deterministic criteria (e.g., $N - 1$). These amounts of reserve allocate sufficient spare generation capacity and transmission margins to protect the system against any contingency of magnitude lower or equal to the chosen criterion. However, these criteria ignore the probability of individual contingencies as well as energy redistribution and transmission limitations in post-contingency states. In this paper, we propose to optimize the amount, location, and chronological procurement of the reserve in a given power system using probabilistic criteria. The proposed approach factors the probability of individual contingencies in a cost/benefit analysis, which balances the pre-contingency operating costs against the post-contingency cost of interruptions. The effectiveness of the proposed approach is demonstrated using a modified IEEE Reliability Test System. [ABSTRACT FROM AUTHOR]

As part of the day-ahead market clearing process, MISO solves one of the most challenging Security Constrained Unit Commitment (SCUC) models. With footprint expansions and increased activity from financial traders, the day-ahead market unit commitment encounters significant performance challenges from time to time. This paper reviews MISO's day-ahead market clearing process and identifies the factors contributing to these performance challenges. It then shares techniques that have been developed to overcome these challenges. Three alternative backup solving approaches were developed. An incremental solving algorithm is proposed to better handle the iterative market clearing process and to perform solution polishing and commitment reason identification. Numerical results based on MISO data are presented. [ABSTRACT FROM PUBLISHER]

There is increasing evidence of shortage of ramping resources in the real-time operation of power systems. To explain and remedy this problem systematically, in this paper we take a novel look at the way the day-ahead unit commitment (UC) problem represents the information about load, generation and ramping constraints. We specifically investigate the approximation error made in mapping of the original problem, that would decide the continuous-time generation and ramping trajectories of the committed generating units, onto the discrete-time problem that is solved in practice. We first show that current practice amounts to approximating the trajectories with linear splines. We then offer a different representation through cubic splines that provides physically feasible schedules and increases the accuracy of the continuous-time generation and ramping trajectories by capturing sub-hourly variations and ramping of load in the day-ahead power system operation. The corresponding day-ahead UC model is formulated as an instance of mixed-integer linear programming (MILP), with the same number of binary variables as the traditional UC formulation. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of events of ramping scarcity in the real-time operations. [ABSTRACT FROM PUBLISHER]

This paper addresses the challenge of scheduling a large population of electric water heaters (EWHs) by incorporating a physically-based aggregate model of the population into the day-ahead unit commitment (UC). This goal has been accomplished via several innovations: (i) consideration of a large controllable temperature range over which random distributions of heaters can take many different shapes; (ii) modeling the random nature of the heater population and its dynamics via histograms and their transition equations; (iii) for varying levels of energy stored in the EWH population, finding the specific shapes of stationary EWH histograms that have minimum overlaps with the uncontrollable temperature zones; (iv) from such histograms, computing the bounds on the number of heaters that can be turned on/off in terms of the energy stored in the population; (v) incorporating the aggregate EWH power consumed and energy stored and their constraints into a modified UC; (vi) developing a scheme whereby individual EWHs self-dispatch to meet the scheduled histograms along with their aggregate energy and power levels. Numerical simulations illustrate the applicability and benefits of the approach, which, with minor extensions, can be extended to other forms of electric loads with energy storage such as space heating and cooling systems and electric vehicles. [ABSTRACT FROM PUBLISHER]

The significant growth in gas-fired units worldwide has increased the grade of interdependency between power and natural gas networks. Since these units are usually required to ramp up during the peak and backup intermittent renewable generation and contingencies, the power system tends to demand more flexibility and reliability from the gas system. This paper contributes with a novel mixed-integer linear programing (MILP) formulation that couples power and gas networks taking into account the gas traveling velocity and compressibility. As a result, the model accounts for the gas adequacy needed to assure the power system reliability in the short term. The robustness of the MILP formulation allows guaranteeing global optimality within predefined tolerances. Case studies integrate the IEEE 24-bus system and Belgian high-calorific gas network for validating the formulation. [ABSTRACT FROM PUBLISHER]

We use a unit commitment (UC) model to quantify the operational impacts of subsidizing wind generation when energy prices are negative. Such prices occur increasingly often in U.S. and European Union (EU) markets. Subsidies such as production tax credits, feed-in tariffs, and renewable energy credits motivate renewable generators to submit negative price offers; this lessened flexibility increases system operation and management costs and, in some cases, \CO2 emissions when energy prices are negative. Our simulations of large negative bids can also be interpreted as representing EU policies of granting wind absolute dispatch priority. Applications to four hypothetical systems with high wind penetration and distinct generation mixes quantify the UC and dispatch effects of negative bids. Larger negative bids lead to less wind spillage (reducing the 2.8% average curtailment under $0 bids to 1.0%), more conventional plant startups, higher system costs, and, in many cases, higher total CO2 emissions (by up to 2%). In some systems, wind power's effective incremental emissions are as high as coal's. This impact depends strongly on generation mix, carbon price, and the size of the negative bids. In general, there can be significant economic and, often, environmental benefits to reforming renewable support policies to encourage flexibility in operations. [ABSTRACT FROM PUBLISHER]

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]

This paper presents a novel method to solve the unit commitment (UC) problem by solving a sequence of increasingly tight continuous relaxations based on the techniques of reformulation and lift-and-project (L&P). After projecting the power output of unit onto [0, 1], the continuous relaxation of the UC problem can be tightened with the reformulation techniques. Then, a tighter model which is called L&P-TMIP is established by strengthening the continuous relaxation of the feasible region of the tight UC problem iteratively using L&P. High-quality suboptimal solutions can be obtained from the solutions of the relaxation for this tight model. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the proposed tight relaxation method is competitive with general-purpose mixed integer programming solvers based methods for large-scale UC problems due to the excellent performance and the good quality of the solutions it generates. [ABSTRACT FROM PUBLISHER]

Reserve requirements promote reliability by ensuring resources are available to rebalance the power system following random disturbances. However, reliability is not guaranteed when dispatch is limited by transmission constraints. In this work, we propose a modified form of reserve requirement that identifies response sets for distinct contingency scenarios. The approach disqualifies reserve from counting towards a particular scenario if transmission constraints are likely to render that reserve undeliverable. A decomposition algorithm for security-constrained unit commitment dynamically updates the response sets to address changing conditions. Testing on the RTS 96 test case demonstrates the approach applied in tandem with existing reserve policies to avoid situations where reserve is not deliverable due to transmission constraints. Operational implications of the proposed method are discussed. [ABSTRACT FROM PUBLISHER]

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]

The ability of load to respond to short-term variations in electricity prices plays an increasingly important role in balancing short-term supply and demand, especially during peak periods and in dealing with fluctuations in renewable energy supplies. However, price responsive load has not been included in standard models for defining the optimal scheduling of generation units in short-term. Here, elasticities are included to adjust the demand profile in response to price changes, including cross-price elasticities that account for load shifts among hours. The resulting peak reductions and valley fill alter the optimal unit commitment. Enhancing demand response also increases the amount of wind power that can be economically injected. Further, wind power uncertainty can be managed at a lower cost by adjusting electricity consumption in case of wind forecast errors, which is another way in which demand response facilitates the integration of intermittent renewables. [ABSTRACT FROM AUTHOR]

This paper proposes a new separable model for the unit commitment (UC) problem and three deterministic global optimization methods for it ensuring convergence to the global optimum within a desired tolerance. By decomposing a multivariate function into several univariate functions, a tighter outer approximation methodology that can be used to improve the outer approximations of several classical convex programming techniques is presented. Based on the idea of the outer approximation (OA) method and the proposed separable model, an outer-inner approximation (OIA) approach is also presented to solve this new formulation of UC problem. In this OIA approach, the UC problem is decomposed into a tighter outer approximation subproblem and an inner approximation subproblem, where the former leads to a better lower bound than the OA method, and the later provides a better upper bound. The simulation results for systems of up to 100 units with 24 h are compared with those of previously published methods, which show that the OIA approach is very promising due to the excellent performance. The proposed approaches are also applied to the large-scale systems of up to 1000 units with 24 h, and systems of up to 100 units with 96 h and 168 h. [ABSTRACT FROM AUTHOR]

The purpose of unit commitment (UC) for electric utilities is to determine the optimal thermal unit on/off statuses and their MW generations over the scheduled time horizon. The UC problem is formulated to minimize the total generation cost, while the load demand, reserve requirements, and unit constraints are satisfied. Among the UC constraints, an adequate provision of reserve is important to ensure the security of the power system and the frequency-regulating reserve is essential to bring the system frequency back to acceptable level following the loss of a sizable online unit within seconds. In this paper, the authors present and solve a mixed-integer linear programming (MILP)-based UC problem including the frequency-regulating reserve (FRR) constraints to determine the optimal FRR requirements and unit MW schedules for an isolated power system. Simulation results are then compared with those obtained by Lagrangian relaxation-based approach and by the current Taipower operation practice. It is observed that favorable reserve and unit MW schedules are obtained by the proposed method while the system security is maintained. [ABSTRACT FROM PUBLISHER]

Obtaining high-quality feasible solution is the core and the major difficulty in solving security-constrained unit commitment (SCUC) problems. This paper presents a systematic method for constructing feasible solutions to SCUC problem based on a group of analytical feasibility conditions. The feasibility check is performed based on the analytical necessary conditions such that most of infeasible UC states can be identified without solving LP problem. If a UC state is infeasible, it is adjusted with the possibly minimal operating cost increase based on the cost information. This UC adjusting issue is formulated as a zero-one programming problem and a branch and bound (B&B) method is established based on these feasibility conditions. Numerical testing is performed for a 31-bus system, an IEEE 24-bus system, and an IEEE 118-bus system. The testing results suggest that over 95% of infeasible UC states are identified by the analytical necessary conditions. The near-optimal feasible schedules for SCUC problem can be obtained efficiently by the proposed method. The feasible schedules obtained are compared with those obtained from mixed integer programming-based method in the IEEE 118-bus system. It is shown that the new method can produce competitive results in terms of solution quality and computational efficiency. [ABSTRACT FROM PUBLISHER]

This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times. [ABSTRACT FROM PUBLISHER]

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]

This paper presents a new approach via a new evolutionary algorithm known as imperialistic competition algorithm (ICA) to solve the unit commitment (UC) problem. In ICA the initial population individuals (countries) are in two types: imperialists and colonies that all together form some empires. Imperialistic competitions among these empires converge to a state in which there exists only one empire. In the proposed ICA for the UC problem, the scheduling variables are coded as integers; therefore, the minimum up/down-time constraints can be handled directly. A new method for initializing the countries is proposed. To verify the performance of the proposed algorithm, it is applied to systems with number of generating units in range of 10 up to 100 in one-day scheduling period. [ABSTRACT FROM PUBLISHER]

This letter introduces a deterministic global optimization methods for unit commitment (UC) problem based on outer approximation method (OAM). The proposed Multi-cuts OAM (MCs-OAM) decomposes the UC problem into a mixed integer linear programming (MILP) master problem and several nonlinear programming (NLP) subproblems, whereas only one NLP in classic OAM. After elaborately designing the terminating criterion for solving the bigger but tighter MILP master problems, MCs-OAM can obtained higher quality solutions with fewer main iterations and less total CPU times, although solving more NLPs consumes more CPU times than OAM. The numerical results on 42 test systems of up to 200 units show that the MCs-OAM is very promising for large scale UC problems because that it can obtain high-quality solutions in reasonable time. [ABSTRACT FROM AUTHOR]