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Nuclear power plants are commonly operated in a “baseload” mode at maximum rated capacity whenever online. However, nuclear power plants are technically capable of flexible operation, including changing power output over time (ramping or load following) and providing frequency regulation and operating reserves. At the same time, flexibility is becoming more valuable as many regions transition to low-carbon power systems with higher shares of variable renewable energy sources such as wind or solar power. We present a novel mixed integer linear programming formulation to more accurately represent the distinct technical operating constraints of nuclear power stations, including impacts of xenon transients in the reactor core and changing core reactivity over the fuel irradiation cycle. This novel representation of nuclear flexibility is integrated into a unit commitment and economic dispatch model for the power system. In a case study using representative utility data from the Southwest United States, we investigate the potential impacts of flexible nuclear operations in a power system with significant solar and wind energy penetration. We find that flexible nuclear operation lowers power system operating costs, increases reactor owner revenues, and substantially reduces curtailment of renewables. [ABSTRACT FROM AUTHOR]

Short term probabilistic load forecasting is essential for any power generating utility. This paper discusses an application of partially linear additive quantile regression models for predicting short term electricity demand during the peak demand hours (i.e. from 18:00 to 20:00) using South African data for January 2009 to June 2012. Additionally the bounded variable mixed integer linear programming technique is used on the forecasts obtained in order to find an optimal number of units to commit (switch on or off. Variable selection is done using the least absolute shrinkage and selection operator. Results from the unit commitment problem show that it is very costly to use gas fired generating units. These were not selected as part of the optimal solution. It is shown that the optimal solutions based on median forecasts ( Q 0.5 quantile forecasts) are the same as those from the 99th quantile forecasts except for generating unit g 8 c , which is a coal fired unit. This shows that for any increase in demand above the median quantile forecasts it will be economical to increase the generation of electricity from generating unit g 8 c . The main contribution of this study is in the use of nonlinear trend variables and the combining of forecasting with the unit commitment problem. The study should be useful to system operators in power utility companies in the unit commitment scheduling and dispatching of electricity at a minimal cost particularly during the peak period when the grid is constrained due to increased demand for electricity. [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]

After restructuring the power systems, demand response programs form the main part of consumption management programs. This is because these programs are by nature particularly suitable for adapting to the new structure in power system management. These programs are considered as a suitable solution for solving some problems in power system restructuring. Unit commitment (UC) programs are used for power production with minimum cost. In this paper, after presenting an overview of demand response methods, a mechanism is proposed for simultaneous execution of the UC program, emergency demand response programs and interruptible/curtailable loads. The proposed mechanism, in addition to decreasing the payment costs, ensures a at load curve and increases system reliability. [ABSTRACT FROM AUTHOR]

Energy Management System (EMS) applications of modern power networks like microgrids have to respond to a number of stringent challenges due to current energy revolution. Optimal resource dispatch tasks must be handled with specific regard to the addition of new resource types and the adoption of novel modeling considerations. In addition, due to the comprehensive changes concerning the multi cell grid structure, new policies should be fulfilled via microgrids’ EMS. At the same time achieving a variety of (conflicting) goals in different microgrids requires a universal and a multi criteria optimization tool. Few of recent works in this area have considered the different perspectives of network operation with high amount of constraints and decision criteria. In this paper two dispatch-optimizers for a centralized EMS (CEMS) as a universal tool are introduced. An improved real-coded genetic algorithm and an enhanced mixed integer linear programming (MILP) based method have been developed to schedule the unit commitment and economic dispatch of microgrid units. In the proposed methods, network restrictions like voltages and equipment loadings and unit constraints have been considered. The adopted genetic algorithm features a highly flexible set of sub-functions, intelligent convergence behavior, as well as diversified searching approaches and penalty methods for constraint violations. Moreover, a novel method has been introduced to deal with the limitations of the MILP algorithm for handling the non-linear network topology constraints. A new aging model of a Lithium-Ion battery based on an event-driven aging behavior has been introduced. Ultimately, the developed GA-based and MILP-based optimizers have been applied to a test microgrid model under different operation policies, and the functionality of each method has been evaluated and compared together. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for solving Security Constrained Unit Commitment (SCUC) problems based on the application of several linear approximation techniques. Model considers thermal units, transmission constraints, and Pumped Storage Units (PSUs), which are important in power systems during peak and off-peak demand periods. Particularly, the proposed MILP model takes into account the hydraulic heads of PSUs for generating and pumping modes through linear methods of operation point selection. Therefore, a more realistic model is presented in comparison with other models available in the literature. To verify the effectiveness of the proposed approach, a modified IEEE 31-bus power system with two PSUs is tested. Our results indicate that the implementation of PSUs can achieve production cost savings compared with power systems in which thermal generation supplies the entire electricity demand. For improving the power system operations and maintenance, different indicators obtained from results are reported in graphs. This information is useful to identify the most critical parts of the systems and make recommendations for corrective or future actions. [ABSTRACT FROM AUTHOR]

Unit commitment is a traditional mixed-integer non-convex problem and remains a key optimisation task in power system scheduling. The high penetration of intermittent renewable generations such as wind and solar as well as mass roll-out of plug-in electric vehicles (PEVs) impose significant challenges to the traditional unit commitment problem, not only by significantly increasing the complexity of the problem in terms of the dimension and constraints, but also dramatically change the problem formulation. In this paper, a new hybrid unit commitment problem considering renewable generation scenarios and charging and discharging management of plug-in electric vehicles is first formulated. To effectively solve the problem, a novel parallel-series hybrid meta-heuristic optimisation method is then proposed, which combines a hybrid topology binary particle swarm optimisation, the self-adaptive differential evolution algorithm and a lambda iteration method, to simultaneously and intelligently determine the binary on/off status of each thermal unit, the generation power of online units, as well as the demand side management of plug-in electric vehicles. The proposed parallel-series hybrid method is first assessed on a 10-unit benchmark, and then on a case where renewable generation and smart PEV management are integrated. Numerical results confirm the superiority of the proposed new algorithm in comparison with some popular meta-heuristic approaches. [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]

Unit commitment, one of the significant tasks in power system operations, faces new challenges as the system uncertainty increases dramatically due to the integration of time-varying resources, such as wind. To address these challenges, we propose the formulation and solution of a generalized unit commitment problem for a system with integrated wind resources. Given the prespecified interval information acquired from real central wind forecasting system for uncertainty representation of nodal wind injections with their correlation information, the proposed unit commitment problem solution is computationally tractable and robust against all uncertain wind power injection realizations. We provide a solution approach to tackle this problem with complex mathematical basics and illustrate the capabilities of the proposed mixed integer solution approach on the large-scale power system of the Northwest China Grid. The numerical results demonstrate that the approach is realistic and not overly conservative in terms of the resulting dispatch cost outcomes. [ABSTRACT FROM AUTHOR]

The thermal unit commitment (UC) problem in power systems can usually be formulated as a mixed-integer quadratic programming (MIQP) problem, which is an NP-hard problem for practical-scale systems and thus is difficult to solve efficiently. In this paper, by projecting the unit generation level onto the interval [ 0 , 1 ] and using reformulation techniques, a novel two-binary-variable (2-bin) MIQP formulation for the UC problem is proposed. The proposed 2-bin formulation is more compact than the state-of-the-art one-binary-variable (1-bin) and three-binary-variable (3-bin) formulations. Moreover, the 2-bin formulation is tighter than the 1-bin and 3-bin formulations in terms of the quadratic cost function, and it is tighter than the 1-bin formulation in terms of linear constraints. The proposed model was tested on 73 instances, including 43 realistic instances and 30 8-unit-based instances, over a scheduling period of 24 h for systems ranging from 10 to 1040 generating units. The simulation results show that our proposed MIQP UC formulation is the tightest and most compact model and can be solved most efficiently. After introducing a sequence of piecewise perspective cuts to approximate the quadratic operational cost function, the three UC MIQP formulations can be approximated by three corresponding mixed-integer linear programming (MILP) formulations. Our experiments show that the proposed 2-bin MILP formulation also performs the best in terms of solution times. [ABSTRACT FROM AUTHOR]

Environmental concerns combined with the liberalisation of the energy markets has led to the emergence of small to medium-scale decentralised generation equipment embedded within transmission and distribution networks. Commonly, such plant is operated by small to medium private enterprises and dispatched independently from centralised resources. The liberalisation of energy markets has also brought about the rise of variable wholesale electricity markets, in the form of the spot (day-ahead) market and the balancing (intra-day) markets across the EU and beyond. As such, there is much interest in how decentralised generation equipment can be most profitably operated in this context. This paper focuses on short-term forecasting of both heat and electrical loads, along with unit commitment scheduling and economic dispatch optimisation, for a small/medium scale decentralised combined heat and power (CHP) plant. In the work presented the plant is assumed to be equipped with local heat and electricity storage and operating in the presence of fluctuating wholesale energy prices and local loads. The approach adopted builds on recent research employing Mixed Integer Linear Programming (MILP) models and non-linear boiler efficiency curves, and extends this work into a rolling horizon context. Results are presented which demonstrate the efficiency of the proposed approach and investigate the sensitivity of the results with respect to CHP model accuracy and load prediction accuracy. The results indicated that profit is much more sensitive to the accuracy of load predictions than indicated by previous work in the area. The findings also challenge those of recent work in the field, which suggest that a strategy of interacting with the spot (day-ahead) market only is the most profitable for small/medium scale decentralised energy producers. The results presented in this paper indicate that when load prediction inaccuracies are also considered in the CHP optimisation framework, a strategy interacting with both the spot (day-ahead) market and the balancing (intra-day) market is significantly more profitable than a strategy interacting with the spot market only. [ABSTRACT FROM AUTHOR]

This paper has proposed a novel Hybrid modified Genetic – Imperialist Competitive Algorithm (HGICA) for solving thermal Unit Commitment Problem (UCP). The UCP is a mixed integer problem with many equality and inequality constraints like the minimum down and minimum up time, spinning reserve, and ramp rate so need to a complex optimization process. In this paper the constraint handling of the problem is realized without any penalizing of solutions so a wide range of feasible solutions will be available for final optimum response. The proposed modified genetic is a novel method which has better performance than its original version and helps ICA to find more optimized responses and escape for local minimum areas easily. The main advantages of HGICA are good quality of the solution and high computational speed, which make it a suitable method for solving optimization problems. This method is carried out for three case studies including 10 and 20 units systems to efficiency of it be proved. Also the obtained results is compared to other optimization methods represented in literature for different scenarios. [ABSTRACT FROM AUTHOR]

Symmetry is a natural phenomenon that appears when an electric system has identical generating units. As a core function in any electricity market, the unit commitment algorithm solves a very large-scale mixed-integer based optimization problem. In this work, the symmetric properties that exist in a competitive electricity market are exploited in improving the performance of its unit commitment solutions. A static symmetry removal strategy based on hierarchical constraints is proposed. They establish priorities for the unit status variables. Extensive numerical examples are illustrated using a real-world, large-scale electricity market. Two available commercial solvers are used to compare the performance of each solver with and without our proposed method. Results show that there are opportunities to improve the unit commitment solutions if the symmetric properties of the market system are properly exploited. [ABSTRACT FROM AUTHOR]

This paper presents a generic Mixed Integer Linear Programming (MILP) model that integrates a Mid-term Energy Planning (MEP) model, which implements generation and transmission system planning at a yearly level, with a Unit Commitment (UC) model, which performs the simulation of the Day-Ahead Electricity Market. The applicability of the proposed model is illustrated in a case study of the Greek interconnected power system. The aim is to evaluate a critical project in the Ten Year Network Development Plan (TYNDP) of the Independent Power Transmission System Operator S.A. (ADMIE), namely the electric interconnection of the Crete Island with the mainland electric system. The proposed modeling framework identifies the implementation (or not) of the interconnection of the Crete Island with the mainland electric system, as well as the optimum interconnection capacity. It also quantifies the effects on the Day-Ahead electricity market and on the energy mix. The paper demonstrates that the model can provide useful insights into the strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level, by providing the optimal energy roadmap and management, as well as clear price signals on critical energy projects under real operating and design constraints. [ABSTRACT FROM AUTHOR]

A coupled optimization of the electricity and gas systems is presented in this paper. The electricity problem involves a unit commitment with co-optimization of energy and reserves under a power pool, considering all system operational and unit technical constraints. The gas problem involves a medium-scale highly non-convex and non-linear problem structure, which is modeled as a Mixed Integer Non-Linear Programming model. The decomposition of the overall problem is based on the Augmented Lagrangian method. An iterative process is implemented, coordinating the two interdependent systems using an alternating minimization method, in which the Lagrange multipliers are updated using the subgradient method. The gas problem is solved in two phases in order to avoid numerical instabilities; first, the direction of flow is defined, and then the gas flow is derived in the second phase. The solution algorithm is evaluated using the Greek power and gas system, comprising thirteen gas-fired units and fifty-three gas network nodes. The test results indicate the strong interdependence of the two systems, and demonstrate the efficiency of the presented algorithm in coordinating them. [ABSTRACT FROM AUTHOR]

The unit commitment problem (UCP) is a nonlinear, mixed-integer, constraint optimization problem and is considered a complex problem in electrical power systems. It is the combination of two interlinked subproblems, namely the generator scheduling problem and the generation allocation problem. In large systems, the UCP turns out to be increasingly complicated due to the large number of possible ON and OFF combinations of units in the power system over a scheduling time horizon. Due to the insufficiency of conventional approaches in handling large systems, numerous metaheuristic techniques are being developed for solving this problem. The genetic algorithm (GA) is one of these metaheuristic methods. In this study, an attempt is made to solve the unit commitment problem using the GA with ring crossover and swap mutation operators. One half of the initial population is intelligently generated by focusing on load curve to obtain better convergence. Lambda iteration is used to solve the generation allocation subproblem. Tests are carried out on systems with up to 100 generators over a time horizon of 24 h. Test outcomes demonstrate the proficiency of the presented scheme when compared with previously used techniques. [ABSTRACT FROM AUTHOR]

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 attempts to provide an optimum loading schedule of power generating units with the least cost by solving a unit commitment (UC) problem and to present good estimates of cost differences when UC problem is not applied. UC is a fundamental optimization problem of power generation systems which determines the optimum schedule of generating units which minimizes generation costs. However, for small power generation firms which are situated in developing countries, UC-based problems are poorly understood if not implemented and the scheduling of generating units is based on some methodologies which may provide results that are not optimal. Thus, a case study in a small power generation firm in central Philippines is carried out to elucidate these objectives. The case requires a solution of the mixed-integer nonlinear programming (MINLP) problem. Results show that the proposed UC-based problem yields optimal costs and the cost disparity from the current scheduling scheme is approximately at 27% which may be considered as potential cost savings. This shows that UC-based problem provides a reliable platform in achieving minimal generation costs. These results are significant to decision-makers particularly in small power generation firms and to engineering practitioners in the Philippines and in some developing countries as these provide an overview of the disparity of cost figures of not implementing UC. [ABSTRACT FROM AUTHOR]

When operating a compressor station, given its mass flow rate, inlet pressure and temperature, and discharge pressure, dispatchers need to decide which compressors to run and at what flow rates, i.e., the operating scheme of the station, to cut its energy costs. This paper addresses this problem under unsteady states. This means that at least one of the four given operating parameters is time-dependent, and therefore so is the operating scheme. The key constraints of the problem are the minimum uptime and downtime of each compressor, which interconnect the operating schemes at each time step and complicate the problem. The energy cost of a compressor unit is almost a linear function of its flow rate for a given inlet pressure, inlet temperature, and discharge pressure. Therefore, the optimization problem was formulated as a mixed integer linear programming (MILP) model, which was solved by CPLEX. The optimal operating schemes given by CPLEX were simulated to reevaluate the objective function, and the error of the linearized energy cost model was shown to be within 5%. The recalculated objective function values were 0.22%–1.18% higher than those of the true optimum. However, the MILP method was 0.49–64.95 times faster than the dynamic programming approach yielding global optimal solutions. [ABSTRACT FROM AUTHOR]

This paper addresses the study of symmetry in Unit Commitment (UC) problems solved by Mixed Integer Linear Programming (MILP) formulations, and using Linear Programming based Branch & Bound MILP solvers. We propose three sets of symmetry breaking constraints for UC MILP formulations exhibiting symmetry, and its impact on three UC MILP models are studied. The case studies involve the solution of 24 instances by three widely used models in the literature, with and without symmetry breaking constraints. The results show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed. The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers. [ABSTRACT FROM AUTHOR]

This work presents a generic mixed integer linear programming (MILP) model that integrates the unit commitment problem (UCP), i.e., daily energy planning with the long-term generation expansion planning (GEP) framework. Typical daily constraints at an hourly level such as start-up and shut-down related decisions (start-up type, minimum up and down time, synchronization, soak and desynchronization time constraints), ramping limits, system reserve requirements are combined with representative yearly constraints such as power capacity additions, power generation bounds of each unit, peak reserve requirements, and energy policy issues (renewables penetration limits, CO 2 emissions cap and pricing). For modelling purposes, a representative day (24 h) of each month over a number of years has been employed in order to determine the optimal capacity additions, electricity market clearing prices, and daily operational planning of the studied power system. The model has been tested on an illustrative case study of the Greek power system. Our approach aims to provide useful insight into strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level by providing the optimal energy roadmap under real operating and design constraints. [ABSTRACT FROM AUTHOR]

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]

This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are (1) generation limits and (2) minimum up and down times. Apart from this, the startup and shutdown processes are also modeled, using (3) startup and shutdown power trajectories for slow-start units, and (4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, power schedules are used to represent the staircase energy schedule; however, this simplification leads to infeasible energy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-based UC formulation drawing a clear distinction between power and energy. The proposed constraints can be used as the core of any power-based UC formulation, thus tightening the final mixed-integer programming UC problem. We provide evidence that dramatic improvements in computational time are obtained by solving different case studies, for self-UC and network-constrained UC problems. [ABSTRACT FROM AUTHOR]

Demand response (DR) has recently become an important resource in both system operation and market operation. The focus of this paper is to investigate and quantify the cost impact of various demand response modelings on unit commitment and dispatch in a day-ahead market regime. We have used mixed integer programming unit commitment model, in the market operation framework. Day-ahead market is modeled with a typical test system. Our research results show that DR can exert downward pressure on electricity prices, causing significant implications on social welfare. Results from this work will help policy makers, resource planners, and market designers to make more informed decisions with the goal of better accommodating more demand response resources in the future. [ABSTRACT FROM AUTHOR]

The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. 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 projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. [ABSTRACT FROM AUTHOR]

This paper presents an improved priority list and neighborhood search (IPL-NS) method for ramp rate constrained unit commitment (RUC). The IPL-NS consists of two steps. At the first step, an IPL based on a mixed integer linear programming (MILP) formulation for UC is proposed to get unit status for UC without ramp rate constraints. At the second step, a neighborhood search (NS) algorithm based on three neighborhoods is produced to get unit status for RUC. The IPL-NS approach is applied to solve several popular test systems of up to 1000 units and the simulation results confirm the superiority of the proposed method. At the same time, the numerical results show that the proposed IPL can commit the most economic unit first much better than other existing PL methods. The results also indicate that the presented NS can handle the ramp rate constraints efficiently. [ABSTRACT FROM AUTHOR]

The past decade has seen advances in general methods for symmetry breaking in mixed-integer linear programming. These methods are advantageous for general problems with general symmetry groups. Some important classes of mixed integer linear programming problems, such as bin packing and graph coloring, contain highly structured symmetry groups. This observation has motivated the development of problem-specific techniques. In this paper we show how to strengthen orbital branching in order to exploit special structures in a problem's symmetry group. The proposed technique, to which we refer as modified orbital branching, is able to solve problems with structured symmetry groups more efficiently. One class of problems for which this technique is effective is when the solution variables can be expressed as 0/1 matrices where the problem's symmetry group contains all permutations of the columns. We use the unit commitment problem, an important problem in power systems, to demonstrate the strength of modified orbital branching. [ABSTRACT FROM AUTHOR]

As renewable energy becomes more prevalent in transmission and distribution systems, it is vital to understand the uncertainty and variability that accompany these resources. Microgrids have the potential to mitigate the effects of resource uncertainty. With the ability to exist in either an islanded mode or maintain connections with the main-grid, a microgrid can increase reliability, defer T&D infrastructure and effectively utilize demand response. This study presents a co-optimization framework for a microgrid with solar photovoltaic generation, emergency generation, and transmission switching. Today, unit commitment (UC) models ensure reliability with deterministic criteria, which are either insufficient to ensure reliability or can degrade economic efficiency for a microgrid that has a large penetration of variable renewable resources. A stochastic mixed integer program for day-ahead UC is proposed to account for uncertainty inherent in PV generation. The model incorporates the ability to trade energy and ancillary services with the main-grid, including the designation of firm and non-firm imports, which captures the ability to allow for reserve sharing between the two systems. In order to manage the computational complexities, Benders’ decomposition is applied. The commitment schedule is validated with solar scenario analysis, i.e., Monte-Carlo simulations are conducted to test the proposed dispatch solution. [ABSTRACT FROM AUTHOR]

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]

Highlights: [•] The combinatorial complexity of unit commitment problem was greatly reduced. [•] Time dependent costs and constraints of thermal generators are not linearized. [•] Achieved near optimal unit commitment schedule which is better than MILP solution. [Copyright &y& Elsevier]

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]

Abstract: Fully EVs (electric vehicles) and PHEVs (plug-in hybrid electric vehicles) have attracted much attention in recent years. Towards an increasing share of EVs, their economic feasibility and impact on the electricity distribution have been studied in detail. However, little has been achieved in investigating the impact on the electricity generation systems. This paper presents a MILP (mixed-integer linear programming) unit commitment model with focus on the effect of EVs on the generation side. The most important advantage of the proposed method is the ability to solve systems with a very large number of EVs. The algorithm is demonstrated on a benchmark system, which has been widely used in the literature and has been used here for all scenarios. It is demonstrated that optimized charging (centrally controlled) is cheaper and allows for higher EV penetration, compared to random charging. Simulations were also run for two scenarios based on the advancement in the charging infrastructure: (1) perfect infrastructure, with opportunity for charging everywhere and (2) moderate infrastructure, where charging is possible only at the owners' homes. In both cases the generation cost increases by 1% for every 10% of additional EV penetration, the modest infrastructure case being slightly more expensive. [Copyright &y& Elsevier]

Highlights: [•] Symmetry breaking method is applied to MILP based UC problems with identical units. [•] Elements that generate symmetry in UC are identified. [•] The B&C algorithm under the presence of symmetry is evaluated. [•] Addition of constraints to set generator status variable priorities is proposed. [•] Results show that this method leads to a substantial reduction in computation cost. [Copyright &y& Elsevier]

Highlights: [•] Increasing renewables reduce “residual demand” to be met by conventional power plants. [•] MILP faces computational difficulties for low load UC problems. [•] New EPL method is developed specifically for low load UC. [•] The EPL method proves to be fast, accurate and close to optimal. [ABSTRACT FROM AUTHOR]

We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, and emissions costs. A constraint set balances the load, imposes requirements on the way in which generators and storage devices operate, and tracks reserve requirements. We capture cost functions with piecewise-linear and (concave) nonlinear constructs. We strengthen the formulation via cut addition. We then describe an underestimation approach to obtain an initial feasible solution to our model. Finally, we constitute a Benders' master problem from the scheduling variables and a subset of those variables associated with the nonlinear constructs; the subproblem contains the storage and reserve requirement quantities, and power from generators with convex (linear) emissions curves. We demonstrate that our strengthening techniques and Benders' Decomposition approach solve our mixed integer, nonlinear version of the unit commitment model more quickly than standard global optimization algorithms. We present numerical results based on a subset of the Colorado power system that provide insights regarding storage, renewable generators, and emissions. [ABSTRACT FROM AUTHOR]

Abstract: One of the main needs that power system operators around the world have is to solve complex Unit Commitment models for large-scale power systems in an acceptable computation time. This Paper presents an alternative Heuristic algorithm that successfully addresses this need. The Heuristic algorithm makes use of various optimization techniques such as Mixed Integer Linear Programming (MILP), Quadratic Programming (QP), Quadratically Constrained Programming (QCP), and Dynamic Programming (DP). CPLEX 12.2 is used as the main optimization engine for MILP, QP, and QCP. DP is an in-house algorithm used to obtain the commitment of Combined Cycle Plants (CCPs) when represented with the component-based model. This Heuristic algorithm combines the global optimality capabilities of MI (L) P formulations with the highly detailed models available for CCPs using LR–DP formulations. The Heuristic algorithm introduced in this Paper is capable of solving up to 1-week scenarios with a 1-hour time window for the complex Mexican Power System. [Copyright &y& Elsevier]

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]

The perspective reformulation has been recently proposed for constructing tight relaxations of the unit commitment (UC) problem with quadratic cost functions. In this case, it has been shown that the perspective reformulation can be cast as a second-order cone program. Conic quadratic programming is based on interior-point methods and does not benefit from the warm-start capabilities of the simplex method available in commercial mixed-integer linear programming software. It is known that the perspective formulation can be approximated with arbitrary accuracy by dynamically adding gradient-type inequalities. This study presents a higher dimensional polyhedral approximation of the perspective reformulation. The proposed approximation is not based on gradient information and can be easily implemented in a modelling language; in addition, it requires defining additional variables and constraints whose number grows moderately with increasing levels of accuracy. Extensive numerical comparisons show that the polyhedral approximation of the perspective reformulation yields a tight UC formulation, which is competitive with currently known ones. [ABSTRACT FROM AUTHOR]

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]

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]

This study proposes a mixed-integer linear programming (MILP) model to figure out the transmission-constrained direct current (DC)-based unit commitment (UC) problem using the generalized generation distribution factors (GGDF) for modeling the transmission network constraints. The UC problem has been reformulated using these linear distribution factors without sacrificing optimality. Several test power systems (PJM 5-bus, IEEE-24, and 118-bus) have been used to validate the introduced formulation. Results demonstrate that the proposed approach is more compact and less computationally burdensome than the classical DC-based formulation, which is commonly employed in the technical literature to carry out the transmission network constraints. Therefore, there is a potential applicability of the accomplished methodology to carry out the UC problem applied to medium and large-scale electrical power systems. [ABSTRACT FROM AUTHOR]