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This paper proposes a novel robust unit commitment (UC) framework with data-driven disjunctive uncertainty sets for volatile wind power outputs, assisted by machine learning techniques. To flexibly identify the uncertainty space based on wind power forecast error data with disjunctive structures, the uncertainty data are grouped using K-means and density-based spatial clustering of applications with noise following the optimal cluster number determined by the Calinski-Harabasz index. The disjunctive uncertainty sets are constructed accordingly as the union of multiple basic uncertainty sets, including conventional box and budget uncertainty sets, and data-driven uncertainty sets using Dirichlet process mixture model, principal component analysis coupled with kernel density estimation, and support vector clustering. The problem is formulated into a two- stage adaptive robust UC model with data-driven disjunctive uncertainty sets and with a multi-level optimization structure. To facilitate the solution process, a tailored decomposition-based optimization algorithm is developed. The effectiveness of the proposed framework is illustrated using an application on the IEEE 39-bus system. The proposed approach can reduce the price of robustness by 8-38 % compared to the conventional “one-set-fits- all” approaches. Benchmarking with stochastic programming indicates that the proposed framework can achieve the same or better economic performance with over 30 % less computational time. [ABSTRACT FROM AUTHOR]

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

Conventional thermal power system-based units and its participation schedule known as unit commitment problem (UCP) is a significant and stimulating undertaking of allocating generated power among the dedicated units subject to numerous restrictions above a scheduled time prospect to obtain the slightest generation cost. This problem becomes further more complex by increasing the size of the power system. Since unit commitment problem is link optimization problem as it has both binary and continuous variable that is why it is most challenging problem to solve. In this paper, a recently invented optimizer sine–cosine is used to solve unit commitment problem. Sine cosine algorithm (SCA) is an innovative population centered optimization algorithm that has been used for solving the unit commitment optimization problems bounded by some constraints centered on the concept of a mathematical model of the sine and cosine functions. This paper offers the solution of unit commitment optimization problems of the electric power system by using the SCA, as UCP is linked optimization as it has both binary and continuous variables, the strategy adopted to tackle both variables is different. In this paper, proposed sine cosine algorithm searches allocation of generators (units that participate in generation to take upload) and once units are decided, allocation of generations (economic load dispatch) is done by mixed integer quadratic programming. The feasibility and efficacy of operation of SCA algorithm are verified for small- and medium-power systems, in which results for 4 unit, 5 unit, 6 unit, 7 unit, 10 units, 19 unit, 20 unit and 40 units are evaluated. The 10 generating units are evaluated with 5% and 10% spinning reserve. The results obviously show that the suggested method gives the superior type of solutions as compared to other algorithms. [ABSTRACT FROM AUTHOR]

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]

This study proposes a data-driven distributionally robust framework for unit commitment based on Wasserstein metric considering the wind power generation forecasting errors. The objective of the constructed model is to minimise the expected operating cost, including the generating cost, start-up and shut-down costs, and also the reserve cost, which overcomes the shortcomings of the conventional model without optimising the reserve capacity. What is more important, different from the conventional robust optimisation methods, wind power big data is fully utilised in this model to construct the ambiguity set without any presumption about its probability distribution. This is realised by Wasserstein ball with an empirical distribution as the centre. Thus, the proposed robust model is actually data-driven and can immunise the solutions against the worst-case distribution in the ambiguity set. In addition, the scale of the historical data is very critical for this method, the larger the scale is, the smaller the ambiguity set is and the less conservative the result is. Numerical results and Monte Carlo simulations on a real 75-bus system demonstrate the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Abstract Historically, energy system tools were predominantly proprietary and not shared with others. In recent years, there has been an increase in developing open source tools by international research and development organizations. More than half of the open energy modeling (openmod) initiative listed tools are based on the freely available scripting language Python. Previous comparisons of energy and power system modeling tools focused on comparisons such as which tool category (e.g. optimization, simulation) or energy demand (e.g. electricity, cooling, and heating) can be considered. Until now, the assessment of incorporated functions such as unit commitment (UC) or optimum power flow (OPF) has been ignored. Therefore, this work assesses 31 mostly open source tools based on 81 functions for their maturity. The result shows that available open source tools such as Switch, TEMOA, OSeMOSYS, and pyPSA are mature enough based on a function comparison with commercial or proprietary tools for serious use. Nevertheless, future commercial, as well as open source energy system analysis tools, have to consider more functions such as the impact of ambient air conditions and part-load behavior to allow better assessments of including high shares or renewable energy sources and other flexibility measures in existing and new energy systems. Highlights • overview about history within Open Source energy model development; • assessment of 81 modeling details; • detailed analysis of 31 energy models (mainly open source); • identifies area of further research requirements; • supports to achieve an unbiased decision process to select the 'best' suitable model; [ABSTRACT FROM AUTHOR]

Highlights • Novel formulation of unit commitment model for large-scale power system simulation. • Validated with standard test system and applied to real regional systems in China. • Increase the computational speed by more than 20,000 times with ∼1% error. • Can be applied to planning issues, e.g. optimal sizing of wind, solar and hydro. Abstract Deploying high penetration of variable renewables represents a critical pathway for decarbonizing the power sector. Hydro power (including pumped-hydro), batteries, and fast responding thermal units are essential in providing system flexibility at elevated renewable penetration. How to quantify the merit of flexibility from these sources in accommodating variable renewables, and to evaluate the operational costs considering system flexibility constraints have been central challenges for future power system planning. This paper presents an improved linear formulation of the unit commitment model adopting unit grouping techniques to expedite evaluation of the curtailment of renewables and operational costs for large-scale power systems. All decision variables in this formulation are continuous, and all chronological constraints are formulated subsequently. Tested based on actual data from a regional power system in China, the computational speed of the model is more than 20,000 times faster than the rigorous unit commitment model, with less than 1% difference in results. Hourly simulation for an entire year takes less than 3 min. The results demonstrate strong potential to apply the proposed model to long term planning related issues, such as flexibility assessment, wind curtailment analysis, and operational cost evaluation, which could set a methodological foundation for evaluating the optimal combination of wind, solar and hydro investments. [ABSTRACT FROM AUTHOR]

In this paper, we consider a long-term unit commitment problem with thermal and renewable energy sources, where system operating costs have to be minimized. The problem is enhanced by adding pumped storages, where water is stored in reservoirs, being turbinated or pumped up if it is beneficial in terms of reducing the operating costs. We present a tight mixed-integer linear programming model with a redefinition of decision variables and a reformulation of constraints, e.g., for the spinning reserve. The model serves as a basis for a new decomposition method, where fix-and-optimize schemes are used. In particular, a time-oriented, a unit-oriented, and a generic fix-and-optimize procedure are presented. A computational performance analysis shows that the mixed-integer linear model is efficient in supporting the solution process for small- and medium-scale instances. Furthermore, the fix-and-optimize procedures are able to tackle even large-scale instances. Particularly, problem instances with real-world energy demands, power plant-specific characteristics, and a one-year planning horizon with hourly time steps are solved to near-optimality in reasonable time. [ABSTRACT FROM AUTHOR]

This article analyzes how the Unit Commitment Problem (UCP) complexity evolves with respect to the number n of units and T of time periods. A classical reduction from the knapsack problem shows that the UCP is NP-hard in the ordinary sense even for T=1. The main result of this article is that the UCP is strongly NP-hard. When the constraints are restricted to minimum up and down times, the UCP is shown to be polynomial for a fixed n. When either a unitary cost or amount of power is considered, the UCP is polynomial for T=1 and strongly NP-hard for arbitrary T. The pricing subproblem commonly used in a UCP decomposition scheme is also shown to be strongly NP-hard for a subset of units. [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]

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

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

Power grid resilience has been a major concern as extreme weather events become more frequent recently. Particularly, wind power generation has constituted a significant body of generation portfolio worldwide. Under stormy weather conditions, wind power generation would be curtailed due to the over-speed protection of wind turbines. Subsequently, the sharply reduced generation resources would significantly endanger the reliability of power supply. In this study, the authors propose to apply the risk-limiting methodology to improve the efficient utilisation of wind power prior to reluctant wind curtailment on the advent of wind stormy events. The proposed method integrates three programs, namely, day-ahead unit commitment (UC), hourly-ahead UC, and real-time load shedding into one single model along with risk-limiting constraints. The first program provides the baseline of hourly dispatch; whereas, the latter two programs serve as recourse means while wind stormy event unfolds. The proposed model is cast into a multi-stage mixed-integer linear programming model and solved by commercial solvers. Illustrative examples demonstrate that the proposed method can reduce the total dispatch cost over the time-horizon including the wind stormy event, by postponing the timing of proactively starting quick-start generating units and shedding loads, in contrast to conventional two-stage stochastic dispatch methods. [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]

Inclusion of renewable energy resources with existing conventional generation resources summons revisit to optimization methods used in the field of generation scheduling. The Unit Commitment problem in itself is a highly convoluted problem governed by complex time varying constraints. It gets even more complicated when additional constraints are added due to inclusion of renewable generation backed up by battery storage system. An effort has been made in this paper to improve the model for solving the Unit Commitment problem of conventional thermal generation in conjunction with renewable energy based generation system with storage. A hybrid artificial intelligence based multiple stage solution methodology is envisaged to provide a techno-economical optimal solution to the problem. The proposed methodology provides economically better solution to the Unit Commitment problem of ten thermal generators when integrated with battery supported wind and solar generation. The overall operational cost gets reduced due to integration of renewable resources which gets further reduced by incorporating battery with a novel optimized charge/discharge scheduling technique. [ABSTRACT FROM AUTHOR]

This paper proposes a new model for the Turkish Day Ahead Electricity Market including network equations. The existing one does not implicitly consider the power flow limitations, and these are considered separately that might result with a suboptimal day-ahead schedule. The dc network equations are added to the model, which is used to determine the Day Ahead System Sell and Buy Decisions and System Marginal Price in day-ahead planning. The impact of integration of network equations is exhibited using a small 6-bus network, mid-sized Turkish northwest sub-system, and full Turkish electric power system. [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]

In this work, we have undertaken a dual-mode combined heat and power unit commitment model to address the optimum generation scheduling of the committed unit. The model formulation includes the backpressure and an extraction mode of cogeneration unit, which is having a diverse feasible operating region of operation. In backpressure mode, the energy generated from the combined heat and power unit depends on a fixed ratio of power and heat, while in extraction mode, this ratio is relatively relaxed that provides system flexibility as compared to other. Owing to the dynamic features of different generating units as well as combination of binary and continuous decision variables, the problem becomes mixed-integer nondeterministic polynomial hard optimization problem, hence an integrated optimization technique has been applied. The integrated optimization technique is a combination of binary successive approximation technique and civilized swarm optimization technique. The binary successive approximation as a local search technique is used to update the unit status, iteratively and global search technique ‘civilized swarm optimization’ are applied to search optimal generation schedule from the committed units. In order to measure the impact of a dual-mode combined heat and power unit on optimum generation scheduling and system flexibility, four test systems have been undertaken. It has been observed from results that total operating cost of the system during extraction mode of combined heat and power unit is less as compared to backpressure mode. It is also evident from the results, that system provides diverse flexibility in terms of power and heat capability, during the extraction and backpressure mode of operation. [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]

In this paper, a method to review the role of renewable energy as an energy producer in scheduling a problem unit commitment is presented. Today, renewable energy sources, due to the lack of environmental pollution, and consequently a very low marginal cost, have been receiving considerable attention in power systems. The correct management of the unit commitment (UC) is a controversial and important issue in the power production unit, which requires suitable scheduled hours to obtain a minimum cost. This study was conducted to investigate the presence of electric vehicles and photovoltaic sources in UC and their impact to reduce production costs and improve load profiles. To achieve the optimum solution, a meta-heuristic Cuckoo search algorithm with high convergence speed is used to solve the UC problem. An IEEE 10-unit test system is employed to investigate the impacts of PEVs and PV on generation scheduling. Since the PV system is associated with uncertainty, in this study, the Uncertainty problem has been modeled using an iterative algorithm randomly with the allocation of density functions that fits the solar radiation. So, the used stochastic Monte Carlo optimization algorithm is capable of handling uncertain outputs of solar power. The simulation results show the effectiveness of the proposed method in reducing production costs and improving load profiles. [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]

This paper presents a new network‐constrained hydrothermal unit commitment (NCHTUC) model that considers nonlinear hydro generation functions and AC power flow constraints. In addition, the proposed NCHTUC includes dynamic water balance equations of cascaded hydro plants. To cope with the large‐scale and mixed‐integer nonlinear nature of the model, a new hybrid computational strategy consisting of generalized Benders decomposition and optimality condition decomposition is proposed. By using this method, the NCHTUC problem is decomposed into a master problem, a hydro plant subproblem, and a thermal plant subproblem with independent OPF (optimal power flow) solutions for each time period. In order to verify the effectiveness of the proposed model and decomposition strategy, numerical tests are performed on three test systems of up to 703 buses over a 24‐h horizon. Test results indicate that the developed methodology has excellent convergence and is capable of solving large‐scale NCHTUC problems without loss of accuracy. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [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]

Isolated power systems present high levels of Renewable Energy Sources (RES) curtailment as intermittency and isolation impose challenging difficulties regarding the integration of this energy into the electrical grid. The recent developments in electrical vehicles have decreased the kWh cost of lithium-ion batteries below a threshold value that was previously prohibitive for grid-scale applications. Therefore, the integration of RES considering the installation of a Battery Energy Storage System (BESS) into an isolated power grid is an up-to-date research topic and is assessed in this paper. The BESS is inserted into the Unit Commitment and Economic Dispatch (UC + ED) platform and regarded as another dispatchable generator. To keeps the costs down, the BESS is mainly used to provide a portion of the spinning reserve needs and secondly to alleviate the load of the thermal generators, using the free modules. The BESS configurations that maximises the economic viability and minimises the RES curtailment are presented. The results suggest that the investment in this technology may be profitable and considerably decreases the levels of RES curtailment. [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]

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]

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]

The unit commitment problem belongs to the class of complex large scale, hard bound and constrained optimization problem involving operational planning of power system generation assets. This paper presents a heuristic binary approach to solve unit commitment problem (UC). The proposed approach applies Binary Grey Wolf Optimizer (BGWO) to determine the commitment schedule of UC problem. The grey wolf optimizer belongs to the class of bio-inspired heuristic optimization approaches and mimics the hierarchical and hunting principles of grey wolves. The binarization of GWO is owing to the UC problem characteristic binary/discrete search space. The binary string representation of BGWO is analogous to the commitment and de-committed status of thermal units constrained by minimum up/down times. Two models of Binary Grey Wolf Optimizer are presented to solve UC problem. The first approach includes upfront binarization of wolf update process towards the global best solution (s) followed by crossover operation. While, the second approach estimates continuous valued update of wolves towards global best solution(s) followed by sigmoid transformation. The Lambda-Iteration method to solve the convex economic load dispatch (ELD) problem. The constraint handling is carried out using the heuristic adjustment procedure. The BGWO models are experimented extensively using various well known illustrations from literature. In addition, the numerical experiments are also carried out for different circumstances of power system operation. The solution quality of BGWO are compared to existing classical as well as heuristic approaches to solve UC problem. The simulation results demonstrate the superior performance of BGWO in solving UC problem for small, medium and large scale systems successfully compared to other well established heuristic and binary approaches. [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]

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

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

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

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

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]