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Highlights • A multi-stage robust optimization-based formulation is proposed to model the TCUC problem with uncertainty. • Non-anticipativity of the ED decisions and multi-stage robustness of the UC decisions are guaranteed. • A decomposition framework with implicit decision rules is proposed and the formulation scale is small. • Subproblems in the decomposition framework have a time-decoupled structure and are easy to solve. • A numerical example is given to clarify the difference between two-stage robustness and multi-stage robustness. Abstract With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment problem. Among all methods, two-stage and multi-stage robust optimization-based methods are the most widely adopted ones. In the two-stage methods, non-anticipativity of economic dispatch (ED) decisions are not considered. While in multi-stage methods, explicit decision rules (like affine decision rules) are adopted to guarantee non-anticipativity of ED decisions, the computational burden can be heavy and the optimality of the solution is affected. In this paper, a multi-stage robust TCUC formulation with implicit decision rules is proposed, as well as a decomposition framework to solve it. The solutions are proved to be multi-stage robust and non-anticipativity of ED decisions is guaranteed. Meanwhile, a computationally efficient time-decoupled solution method for the feasibility check subproblems is also proposed, such that the method is suitable for large-scale TCUC problems with uncertain power injections. Numerical tests are conducted on IEEE 118-bus system and Polish 2383-bus system. The proposed method outperforms the multi-stage robust method with explicit decision rules in solution's economic performances, and is more computationally efficient than the all-scenario-feasible method. The effectiveness of time-decoupled solution method is also verified. [ABSTRACT FROM AUTHOR]

Highlights • A hierarchical and fully distributed method based on ADMM is proposed. • Coupling constraints are decoupled by solving dual problem. • The proposed method can be implemented in master-slave distributed and parallel schema. Abstract The mechanism of energy supply has been greatly changed due to the liberalization of electricity, which creates major challenges in power system operations. As such, in this paper, a hierarchical alternating direction method of multipliers (ADMM) approach for the unit commitment (UC) problem is presented, which is proposed to solve the UC problem of each individual unit in parallel. This approach consists of two-layers ADMM. In outer layer, the x -update and v -update steps can be decoupled for each unit and executed in parallel after rearranging and grouping the variables and constraints of the UC mixed integer quadratic programming (MIQP) model according to each unit. The difficulty in this approach is the z-update steps, which couple all units because of system constraints. We used an inner consensus ADMM to solve their Lagrangian dual problems, which are decoupled for each individual unit. Then, the UC problem with a different number of units without transmission constraints is used to test the effectiveness of the algorithm. The simulation results show that the proposed hierarchical ADMM can obtain high-quality solutions in reasonable times and keep the units' information secret. It can also help to obtain a good speedup and is suitable for solving large-scale distributed unit commitment (D-UC) problems. [ABSTRACT FROM AUTHOR]

Highlights • Existing electricity markets, based on energy, are inefficient. • We compare power-based scheduling to the current practice of increasing resolution. • Power-based scheduling results in less reserve activation at equal computation time. • Increasing the resolution requires great computational expense. • We provide a set of market rules to implement and price power-based bids. Abstract Day-ahead electricity markets are inefficient due to their coarse discretisation of time and their representation of electricity production and consumption in energy per time interval. This leads to excessive costs and infeasible schedules in the market clearing results. Some real-world systems have increased the resolution to improve accuracy, but this comes at a high computational cost. We propose an alternative, based on using linear power trajectories in the day-ahead scheduling process, which represent the momentary electricity production. Changing from a traditional energy-based to such a power-based formulation of the scheduling method can reduce cost by several percentage points, leading to a cost reduction of millions of euros in real-world systems on a yearly basis. Attempting to do so by increasing the resolution of the schedule would be accompanied by large increases in computational demands. Furthermore, we provide market design options to implement power-based bidding and pricing in day-ahead electricity markets, showing that pricing and market rules which encompass existing markets are readily available for implementation, and illustrate these with examples. [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]

The penetration of renewable energy resources into the power system is rising prominently worldwide, and is causing increased uncertainty in power system operations. Increasing loads and scarce transmission resources have exacerbated this issue, imposing critical operational challenges, such as congestion issues, on the power system operator (SO). This study proposes a unit commitment that employs dynamic line rating (DLR) to develop a method that enables efficient use of network resources. A mathematical formulation is suggested, based on two-stage stochastic programming, to manage the newly introduced uncertainties related to DLR properly. In addition, we build approximated power-flow equations for the proposed model. The performance of the proposed method is verified using a six-bus system and the modified IEEE 118-bus system integrated with wind power units. The simulation results clearly demonstrate that, with DLR, an SO can significantly reduce the expected operating cost. This advantage stems from the sufficiently effective utilization of the existing transmission line, which leads to the optimal commitment of the generating units and dispatched volume, and efficient use of the harvested wind energy. Moreover, the results, which demonstrate that the expected-energy-not-supplied is markedly reduced by incorporating the DLR, prove that the proposed method is highly reliable. [ABSTRACT FROM AUTHOR]

This paper proposes a new technique to intelligently split busbars within a meshed power system, to facilitate the insertion of series active power flow-controllers into the high voltage transmission systems. Such flow-controllers have historically been placed at system and national boundaries to modulate cross-border flows for regulatory, commercial and security purposes. The present work proposes a new concept for power system control, and embeds series flow-controllers within meshed transmission networks to gauge the extent to which their dispatchable flows can be used to alleviate thermal congestion. To articulate the value that such flexibility might provide, a new simplified unit commitment and dispatch formulation is presented, which integrally uses series flow-controllers to manage congestion and thus reduce operating costs. While both the siting and operation methodologies are shown to be practical, the achieved cost savings are modest at best, even on systems which are weakened to have significant levels of thermal congestion. [ABSTRACT FROM AUTHOR]

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 an integrated framework for operational flexibility assessment in power system planning with a significant share of intermittent renewable energy sources (RES). The framework proposed includes: (i) the formulation of an integrated generation expansion planning (GEP) and unit commitment (UC) model accounting for key short-term technical constraints, (ii) the elaboration of accurate and systematic horizon reduction methods to alleviate the computational burden of the resulting large-sized optimization problems and (iii) the definition of suitable metrics for the operational flexibility assessment of the obtained plans. The framework is applied to a ten year planning horizon of a realistically sized case study representing the national power system of France, under several scenarios of RES penetration levels and carbon limits, spanning levels of up to 50%. The importance of incorporating the detailed short-term constraints within long-term planning models is shown. The results of the assessment show that, under high renewable energy penetration, neglecting the short-term constraints may lead to plans significantly short on flexibility, reaching shortage levels of up to 50% in frequency and several GWs in magnitude. Also, the load not served reaches levels of up to 3% and carbon emission is underestimated by up to 60%. Furthermore, the results highlight the importance of relying on suitable quantitative metrics for operational flexibility assessment in power systems planning rather than solely relying on generic performance measures, such as system costs and mixes of power plants, which are shown not to sufficiently reflect the flexibility levels of the obtained plans. [ABSTRACT FROM AUTHOR]

The variable and intermittent nature of large-scale wind power integration makes day-ahead unit commitment (UC) decision-making difficult. This paper establishes a novel and effective UC model with wind power integration by optimizing the utilization of the forecast error and reserve decision. First, considering the temporal feature of the UC model, a time sequence segment-fitting method (TSFM) for the wind power forecast error is presented, in which the non-parametric fitting method is used to address the ‘fat-tail’ effect of error distribution. Second, according to the probability intervals of the forecast error and characteristic of the reserve, a new reserve decision method is proposed to define three classes of reserve strategies and optimize the capacity for each type of reserve. Third, a UC model with time-varying confidence levels is established by introducing conditional value at risk (CVaR) and chance-constrained programming (CCP), and is linked with the TSFM. This novel model can balance the costs of fuel, various reserves, load shedding risk, and wind curtailment risk, which can improve the economy of the power grid operation. Finally, an improved hybrid particle swarm optimization algorithm with a heuristic searching strategy is applied to solve this multivariate mixed integer non-linear programming problem. The simulation results verify the effectiveness and practicality of the model proposed. [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]

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]

The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the unit commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that restrict their application to real-world systems. This paper demonstrates that, by considering dispatchable wind and a box uncertainty set for wind availability, a fully adaptive two-stage robust UC formulation, which is typically a bi-level problem with outer mixed-integer program (MIP) and inner bilinear program, can be translated into an equivalent single-level MIP. Experiments on the IEEE 118-bus test system show that computation time, wind curtailment, and operational costs can be significantly reduced in the proposed unified stochastic–robust approach compared to both pure stochastic approach and pure robust approach, including budget of uncertainty. [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]

In some highly populated areas of the planet, air quality is an issue. Since power plants in those areas significantly contribute to air pollution due to SO 2 and NO x emissions, it is appropriate to operate such power plants enforcing admissible emission limits. Since emissions directly impact the air quality index, which is highly uncertain 24 h in advance, admissible emission limits should be modeled as stochastic parameters.To represent the stochastic nature of such admissible emission limits, we propose a two-stage stochastic programming model for the commitment of power plants. The first stage represents the day-ahead scheduling, and the second stage represents the real-time power system operation under different weather and thus admissible emission limit conditions. We show the effect of stochastic emission limits on power system operations using a simple example and a 118-node case study. [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 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]

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]

Summary: This paper establishes a probabilistic scenario–based framework for the stochastic dynamic economic emission dispatch with unit commitment (SDEED‐UC) problem, taking into account wind power uncertainty. To solve the stochastic UC problem, this paper presents a probabilistic scenario analysis approach to find the unit scheduling solution considering all the original scenarios under a predetermined probability level. And a reduced scenario set can be obtained by the simultaneous backward method. Consequently, the SDEED problem is decomposed into a number of deterministic multiobjective dispatch problems. For each scenario, an enhanced multiobjective particle swarm optimization (EMOPSO) algorithm integrated with the handling strategy for system operation constraints is proposed to produce the Pareto optimal solutions. Furthermore, the available reserve capacity by the UC solution is verified. The simulation results demonstrate that the proposed probabilistic scenario–based and EMOPSO approach is practicable for solving SDEED‐UC from the perspectives of system operation economy, emission, and reliability simultaneously. [ABSTRACT FROM AUTHOR]

The integration of wind power to the grid is essential to meet the growing power demand and possess a challenge to unit commitment to meet the load demand at low cost for scheduling the generating units. A new imperialistic competitive algorithm (ICA) has been developed for the above mentioned unit commitment problem for solving deterministic and stochastic condition. This imperialistic competitive algorithm has been developed with constraints, including generation limits, start up and shut down cost, minimum up and downtime along with ramp constraint. The ICA has been studied initially on the 10 units 24 hour system and 40 units 24 hour system for the deterministic load. Later, a wind generator has been added to the 10 units 24 hour system with wind data for 24 hours and the results are compared with genetic algorithm (GA), particle swarm optimization (PSO), hybrid particle swarm optimisation (HPSO), shuffled frog leaping algorithm (SFLA), invasive weed optimization (IWO). The comparison result is presented in this paper and it shows that the ICA gives optimized fuel cost of $482246.2 which is less than the LR, GA, BFOA, SFLA, IWO for stochastic unit commitment. [ABSTRACT FROM AUTHOR]

Electric power systems worldwide are receiving an increasing volume of wind power generation (WPG) because of environmental concerns and cost declines associated with technological innovation. To manage the uncertainty of WPG, a system operator must commit sufficient conventional generators to provide an appropriate reserve. At times, frequent start and stop operations are applied to certain generators, which incurs maintenance costs associated with thermal-mechanical fatigue. In this paper, we suggest a comprehensive approach to unit commitment (UC) that considers maintenance cost: the parameters of equivalent start (ES) and equivalent base load hours (EBHs) are adopted in the UC problem to determine optimal generation scheduling. A new formulation for the maintenance cost that can be readily combined with an existing mixed integer linear programming algorithm is presented. The effectiveness of the proposed UC method is verified through simulations based on an IEEE 118-bus test system. The simulation results show that considering maintenance cost in the UC problem effectively restricts frequent start and stop operation scheduling. Furthermore, the operating cost is reduced, the required reserve level is maintained, and the computational time is comparable with that of the conventional UC method. [ABSTRACT FROM AUTHOR]

With increase in power demand, load demand values have also risen to a greater extent. Sometimes, these demands are met with the great difficulties. All these difficulties drive us to seek other alternative ways. One such a way demand response (DR) is considered in this paper, it is a new concept that is introduced in the system in order to reduce peak hour stresses. When implementing the demand response, the main setbacks that arise is the load kickback effect, which the sudden rise in demand during non-peak hours that is caused by the overuse of power by consumers, after their constant reduction of power during peak hours. This paper discusses the various kickback load types, and an effective approach to avoid and tackle kickback effect, by an effective method Cat Swarm Optimization (CSO), which is based on studying the movement of cats. The optimization has been implemented on an IEEE 30 bus and 75 bus Indian utility system, and the results are discussed. [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]

Chronological operation simulation (COS) is an essential tool for planning and analyzing power systems under high penetration of renewable energy. Conventional COS methods heavily depend on the availability of renewable power output data to obtain accurate results, and often require hours or even days of computational time while the sequential simulation could easily get infeasible for power systems with intensive flexibility. To cover the absence of output data for newly proposed wind and solar projects and accelerate the computation speed, this paper proposes a novel COS simulation framework for regional power systems with high penetration of renewable energies using meteorological data. The proposed simulation framework consists of the following three steps: data preparation, modeling and solving, and result output. In the data preparation step, wind, solar power output profiles and heat demands are converted from public accessible meteorological data. Then in the modeling and solving step, a unit commitment based COS model for simulating the hourly operation of power and heat sectors is proposed, and the proposed model is solved with a time domain partitioning (TDP) and a rollback mechanism to accelerate the computation speed as well as avoiding infeasible solutions. The accuracy of the wind and solar power output converted from meteorological data is verified through comparing with measured power output. Moreover, the feasibility and accuracy of utilizing the proposed COS framework to simulate the operation of a real regional power system is also verified through the 2015 annual operation statistics of the Northwest China Grid. [ABSTRACT FROM AUTHOR]

The unit commitment (UC) problem aims to find an optimal schedule of generating units subject to demand and operating constraints for an electricity grid. The majority of existing algorithms for the UC problem rely on solving a series of convex relaxations by means of branch-and-bound and cutting-planning methods. The objective of this paper is to obtain a convex model of polynomial size for practical instances of the UC problem. To this end, we develop a convex conic relaxation of the UC problem, referred to as a strengthened semidefinite program (SDP) relaxation. This approach is based on first deriving certain valid quadratic constraints and then relaxing them to linear matrix inequalities. These valid inequalities are obtained by the multiplication of the linear constraints of the UC problem, such as the flow constraints of two different lines. The performance of the proposed convex relaxation is evaluated on several hard instances of the UC problem. For most of the instances, globally optimal integer solutions are obtained by solving a single convex problem. For the cases where the strengthened SDP does not give rise to a global integer solution, we incorporate other valid inequalities. The major benefit of the proposed method compared to the existing techniques is threefold: (i) the proposed formulation is a single convex model with polynomial size and, hence, its global minimum can be found efficiently using well-established first-and second-order methods by starting from any arbitrary initial state, (ii) unlike heuristic methods and local-search algorithms that return local minima whose closeness to a global solution cannot be measured efficiently, the proposed formulation aims at obtaining global minima, (iii) the proposed convex model can be used in convex-hull pricing to minimize uplift payments made to generating units in energy markets. The proposed technique is extensively tested on IEEE 9-bus, IEEE 14-bus, IEEE 30-bus, IEEE 57-bus, IEEE 118-bus, and IEEE 300-bus systems with different settings and over various time horizons. [ABSTRACT FROM AUTHOR]

In this work, we develop a mathematical model and framework to represent rolling-horizon unit commitment (UC) processes with multiple periodicities. In control center operations, UC is solved repeatedly to adjust device commands based on new information about load, generation availability, renewable energy production, and other aspects of system state as uncertain conditions are realized. We develop a three-level model including 24-h UC, rolling-horizon UC (RHUC), and economic dispatch (ED) and give formulations for the three problems including interdependencies. This framework allows for evaluation of, among other things, different periodicities of the rolling horizon problem and the benefits of more accurate forecasting information. Experimental results are shown for a 6-bus system and a 3012-bus system with wind generation in two wind scenarios. Although the generation costs are very similar, the deviation between RHUC schedules and actual deployment is noted to be superior for a 20-min periodicity compared to a 30-min periodicity. Additionally, less reserve is deployed in the 20-min RHUC case. [ABSTRACT FROM AUTHOR]

For the purposes of lowering environmental emission cost and increasing economic profit, energy efficient combined heat and power (CHP) units can be integrated with conventional separate heat and power production units to meet heat and power demands. The goal of this study is to develop and examine a novel heuristic and deterministic optimization algorithm for solving the profit-based unit commitment (PBUC) problem for a generation company with integrated CHP-thermal-heat only system for (i) satisfying demands for heat and power, (ii) selling spinning reserve for power, (iii) reducing environmental CO 2 emission cost, and (iv) accounting for valve-point effects for steam turbines. For validation, the developed optimization algorithm is applied to power systems examined in other studies for a 24 h operation period, where reduction of 2.54–5.86% in environmental CO 2 emission and improvements of 2.91–5.67% in economic profit are achieved. When environmental CO 2 emission cost and valve-point effects are considered, the utilization of CHP units in an integrated CHP-thermal-heat only system results in environmental CO 2 emission reduction and economic profit improvement by and 29.45 and 15.41%, respectively, as compared with those resulting from operating thermal and heat only units separately. [ABSTRACT FROM AUTHOR]

Until recently, transmission network constraints have been incorporated into the unit commitment (UC) problem (security-constrained UC [SCUC]) using the classical direct current (DC)-based equation. This paper proposes a new formulation to model network constraints in the UC problem by using the power transfer distribution factor (PTDF). The classical formulation uses the binary commitment status, the power generation, and the voltage-phase angles as decision variables. For the proposed formulation, the nodal balance equality constraints are modeled using one equality constraint, and the transmission network constraints have been modeled using the PTDF and the active power generation (decision variables). The main advantage of this formulation is the reduction of decision variables in the operation problem in comparison with the classical DC formulation. Transmission losses, using a piecewise linear approximation, are included in the SCUC problem as well. Both formulations are validated and tested on the Institute of Electrical and Electronics Engineers (IEEE) 14-bus, the IEEE 30-bus, the IEEE 57-bus, and the IEEE 118-bus. The IEEE 14-bus and IEEE 57-bus systems are used to compare the loss and the lossless models. The results show that the PTDF-based formulation, which requires fewer continuous variables and equality constraints than the classical DC formulation, reduces the simulation time without sacrificing optimality. The results also demonstrate the feasibility of the proposed formulation to address the SCUC problem and its potential applicability to medium-scale and large-scale power systems. [ABSTRACT FROM AUTHOR]

This paper proposes an optimal scheduling/allocation of energy and spinning reserves for a wind-thermal power system. There is a considerable need for the renewable energy resources in the modern power system; therefore, in this paper, wind energy generators are used. Here, two different market clearing models are proposed. One model includes reserve offers from the conventional thermal generators, and the other includes reserve offers from both thermal generators, and demand/consumers. The stochastic behavior of wind speed and wind power generation is represented by the Weibull probability density function. The objective function considered in this paper includes cost of energy provided by conventional thermal and wind generators, cost of reserves provided by conventional thermal generators and load demands. It also includes costs due to under-estimation and over-estimation of available wind power generation. Clustered adaptive teaching learning based optimization algorithm is used to solve the proposed optimal scheduling problem for both conventional and wind-thermal power systems considering the provision for spinning reserves. To show the effectiveness and feasibility of the proposed frame work, various case studies are presented for two different test systems. [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]

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]

Optimization of power networks is a rich research area that focuses mainly on efficiently generating and distributing the right amount of power to meet demand requirements across various geographically dispersed regions. The Unit Commitment (UC) problem is one of the critical problems in power network research that involves determining the amount of power that must be produced by each generator in the power network subject to numerous operational constraints. Growth of these networks coupled with increased interconnectivity and cybersecurity measures have created a need for applying decentralized optimization paradigms. In this paper, we develop a novel asynchronous decentralized optimization framework to solve the UC problem. We demonstrate that our asynchronous approach outperforms conventional synchronous approaches, thereby promising greater gains in computational efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a new approach with a three-stage optimization algorithm for the least-cost optimal solution of the unit commitment problem. In the proposed work, the optimal schedule is obtained by optimizing the lambda operator for the states that violate the inequality constraints. The objective of the work is to minimize the fuel cost when subjected to various constraints such as load balance, minimum up/down time, ramp limit, and spinning reserve. This method of committing the units yields the least-cost solution when applied to the IEEE 10-unit systems and 7-unit Indian utility practical systems scheduled for 24 h and the results obtained are compared with the existing methods. [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]

Wind power and photovoltaic power, two types of renewable energy (RE), have made large inroads into the power system. In this paper, we study a unit commitment (UC) problem that considers the uncertainty in RE and pumped hydro-energy storage (PHES). To improve the optimisation performance for this problem, we propose a novel heuristic algorithm called the Binary Artificial Sheep Algorithm (BASA) that is based on the social behaviour of sheep flock. To evaluate the effect of the uncertainty of RE, a scenario evaluation method is defined to assess quantitatively the stability and economy of the UC results with respect to different levels of RE forecasting errors. In addition, we investigate and analyse the effect of PHES on the UC problem. Three UC test systems with different RE and PHES combinations are used to verify the feasibility and effectiveness of the proposed BASA as well as its performance. The proposed BASA performed better than traditional fundamental metaheuristics in solving UC problems. Our results also demonstrated that the equivalent load fluctuation and operating costs of the thermal units will increase significantly with an increase in RE power forecast error, but the PHES can effectively counterbalance this adverse effect. [ABSTRACT FROM AUTHOR]

Due to the increased penetration of intermittent renewables, operating reserves are becoming increasingly important in electricity markets. Coordinating the sizing, allocation and activation of reserves among market zones can decrease operational costs and enhance system reliability. However, network limitations constrain reserve coordination among zones. This paper investigates the value of interzonal coordination of reserve sizing, allocation and activation. A series of three models that simulate unit commitment and dispatch decisions within network-constrained markets simulate the impact of intermarket coordination of each of these sets of decisions. A case study for the Central Western European electricity system indicates that such coordination can lower operational costs and increase system reliability. However, the best performing strategy for the considered case study turns out to be a strategy with coordinated activation but uncoordinated sizing and allocation of reserves due to suboptimal coordination of sizing and allocation with activation. In particular, because transmission constraints are simplified when sizing and allocating reserves, reserves might not actually be deliverable to where renewable output is different from forecast. [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 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 development of advanced metering technologies makes demand response (DR) able to provide fast response services, e.g., primary frequency control. It is recognized that DR can contribute to the primary frequency control like thermal generators. This paper proposes a day-ahead scheduling method that considers DR as a frequency control resource, so that the DR resources can be dispatched properly with other resources. In the proposed method, the objective of frequency control is realized by defining a frequency limit equation under a supposed contingency. The frequency response model is used to model the dynamics of system frequency. The nonlinear frequency limit equation is transformed to a linear arithmetic equation by piecewise linearization, so that the problem can be solved by mixed integer linear programming (MILP). Finally, the proposed method is verified on numerical examples. [ABSTRACT FROM AUTHOR]