Improved Unit Commitment with Accurate Dynamic Scenarios Clustering Based on Multi-Parametric Programming and Benders Decomposition

Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus system.Numerical results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.

Grid Integration of Wind Generation Considering Remote Wind Farms:Hybrid Markovian and Interval Unit Commitment

Grid integration of wind power is essential to reduce fossil fuel usage but challenging in view of the intermittent nature of wind.Recently,we developed a hybrid Markovian and interval approach for the unit commitment and economic dispatch problem where power generation of conventional units is linked to local wind states to dampen the effects of wind uncertainties.Also,to reduce complexity,extreme and expected states are considered as interval modeling.Although this approach is effective,the fact that major wind farms are often located in remote locations and not accompanied by conventional units leads to conservative results.Furthermore,weights of extreme and expected states in the objective function are difficult to tune,resulting in significant differences between optimization and simulation costs.In this paper,each remote wind farm is paired with a conventional unit to dampen the effects of wind uncertainties without using expensive utility-scaled battery storage,and extra constraints are innovatively established to model pairing.Additionally,proper weights are derived through a novel quadratic fit of cost functions.The problem is solved by using a creative integration of our recent surrogate Lagrangian relaxation and branch-and-cut.Results demonstrate modeling accuracy,computational efficiency,and significant reduction of conservativeness of the previous approach.

Optimal Intelligence Planning of Wind Power Plants and Power System Storage Devices in Power Station Unit Commitment Based

Renewable energy sources(RES)such as wind turbines(WT)and solar cells have attracted the attention of power system operators and users alike,thanks to their lack of environmental pollution,independence of fossil fuels,and meager marginal costs.With the introduction of RES,challenges have faced the unit commitment(UC)problem as a traditional power system optimization problem aiming to minimize total costs by optimally determining units’inputs and outputs,and specifying the optimal generation of each unit.The output power of RES such as WT and solar cells depends on natural factors such as wind speed and solar irradiation that are riddled with uncertainty.As a result,the UC problem in the presence of RES faces uncertainties.The grid consumed load is not always equal to and is randomly different from the predicted values,which also contributes to uncertainty in solving the aforementioned problem.The current study proposes a novel two-stage optimization model with load and wind farm power generation uncertainties for the security-constrained UC to overcome this problem.The new model is adopted to solve the wind-generated power uncertainty,and energy storage systems(ESSs)are included in the problem for further management.The problem is written as an uncertain optimization model which are the stochastic nature with security-constrains which included undispatchable power resources and storage units.To solve the UC programming model,a hybrid honey bee mating and bacterial foraging algorithm is employed to reduce problem complexity and achieve optimal results.

Optimal Unit Commitment with Renewable Energy in Regulated and Deregulated Systems

In this paper, the impact of the wind power generation system on the total cost and profit of the system is studied by using the proposed procedure of binary Sine Cosine (BSC) optimization algorithm with optimal priority list (OPL) algorithm. As well, investigate the advantages of system transformation from a regulated system to a deregulated system and the difference in the objective functions of the two systems. The suggested procedure is carried out in two parallel algorithms;The goal of the first algorithm is to reduce the space of searching by using OPL, while the second algorithm adjusts BSC to get the optimal economic dispatch with minimum operation cost of the unit commitment (UCP) problem in the regulated system. But, in the deregulated system, the second algorithm adopts the BSC technique to find the optimal solution to the profit-based unit commitment problem (PBUCP), through the fast of researching the BSC technique. The proposed procedure is applied to IEEE 10-unit test system integrated with the wind generator system. While the second is an actual system in the Egyptian site at Hurghada. The results of this algorithm are compared with previous literature to illustrate the efficiency and capability of this algorithm. Based on the results obtained in the regulated system, the suggested procedure gives better results than the algorithm in previous literature, saves computational efforts, and increases the efficiency of the output power of each unit in the system and lowers the price of kWh. Besides, in the deregulated system the profit is high and the system is more reliable.

Unit Commitment with Production Cost Uncertainty： A Recourse Programming Method

Many studies have considered the solution of Unit Commitment problems for the management of energy networks. In this field, earlier work addressed the problem in determinist cases and in cases dealing with demand uncertainties. In this paper, the authors develop a method to deal with uncertainties related to the cost function. Indeed, such uncertainties often occur in energy networks （waste incinerator with a priori unknown waste amounts, cogeneration plant with uncertainty of the sold electricity price...）. The corresponding optimization problems are large scale stochastic non-linear mixed integer problems. The developed solution method is a recourse based programming one. The main idea is to consider that amounts of energy to produce can be slightly adapted in real time, whereas the on/off statuses of units have to be decided very early in the management procedure. Results show that the proposed approach remains compatible with existing Unit Commitment programming methods and presents an obvious interest with reasonable computing loads.

An Optimization Approach for Unit Commitment of a Power System Integrated with Renewable Energy Sources： A Case Study of Afghanistan

This paper focused on generation scheduling problem with consideration of wind, solar and PHES （pumped hydro energy storage） system. Wind, solar and PHES are being considered in the NEPS （northeast power system） of Afghanistan to schedule all units power output so as to minimize the total operation cost of thermal units plus aggregate imported power tariffs during the scheduling horizon, subject to the system and unit operation constraints. Apart from determining the optimal output power of each unit, this research also involves in deciding the on/off status of thermal units. In order to find the optimal values of the variables, GA （genetic algorithm） is proposed. The algorithm performs efficiently in various sized thermal power system with equivalent wind, solar and PHES and can produce a high-quality solution. Simulation results reveal that with wind, solar and PHES the system is the most-cost effective than the other combinations.

Stochastic Unit Commitment with High-Penetration Offshore Wind Power Generation in Typhoon Scenarios

To tackle the energy crisis and climate change,wind farms are being heavily invested in across the world.In China's coastal areas,there are abundant wind resources and numerous offshore wind farms are being constructed.The secure operation of these wind farms may suffer from typhoons,and researchers have studied power system operation and resilience enhancement in typhoon scenarios.However,the intricate movement of a typhoon makes it challenging to evaluate its spatial-temporal impacts.Most published papers only consider predefined typhoon trajectories neglecting uncertainties.To address this challenge,this study proposes a stochastic unit commitment model that incorporates high-penetration offshore wind power generation in typhoon scenarios.It adopts a data-driven method to describe the uncertainties of typhoon trajectories and considers the realistic anti-typhoon mode in offshore wind farms.A two-stage stochastic unit commitment model is designed to enhance power system resilience in typhoon scenarios.We formulate the model into a mixed-integer linear programming problem and then solve it based on the computationally-efficient progressive hedging algorithm(PHA).Finally,numerical experiments validate the effectiveness of the proposed method.

Multi-area Frequency-constrained Unit Commitment for Power Systems with High Penetration of Renewable Energy Sources and Induction Machine Load

The increasing penetration of renewable energy sources(RESs)brings great challenges to the frequency security of power systems.The traditional frequency-constrained unit commitment(FCUC)analyzes frequency by simplifying the average system frequency and ignoring numerous induction machines(IMs)in load,which may underestimate the risk and increase the operational cost.In this paper,we consider a multiarea frequency response(MAFR)model to capture the frequency dynamics in the unit scheduling problem,in which regional frequency security and the inertia of IM load are modeled with high-dimension differential algebraic equations.A multi-area FCUC(MFCUC)is formulated as mixed-integer nonlinear programming(MINLP)on the basis of the MAFR model.Then,we develop a multi-direction decomposition algorithm to solve the MFCUC efficiently.The original MINLP is decomposed into a master problem and subproblems.The subproblems check the nonlinear frequency dynamics and generate linear optimization cuts for the master problem to improve the frequency security in its optimal solution.Case studies on the modified IEEE 39-bus system and IEEE 118-bus system show a great reduction in operational costs.Moreover,simulation results verify the ability of the proposed MAFR model to reflect regional frequency security and the available inertia of IMs in unit scheduling.

Low-carbon unit commitment with intensive wind power generation and carbon capture power plant

The paper proposes a stochastic unit commitment(UC)model to realize the low-carbon operation requirement and cope with wind power prediction errors for power systems with intensive wind power and carbon capture power plant(CCPP).A linear re-dispatch strategy is introduced to compensate the wind power deviation from the spot forecast.The robust optimization technique is employed to obtain a reliable commitment plan against all realizations of wind power within the uncertainty set given by probabilistic forecast.The proposed model is validated with IEEE 39-bus system.The advantages of flexible CCPPs are compared to the normal coal-fueled plants and the impacts of robustness controlling are discussed.

Integration of power-to-hydrogen in day-ahead security-constrained unit commitment with high wind penetration

The increasing integration of variable wind generation has aggravated the imbalance between electricity supply and demand. Power-to-hydrogen(P2H) is a promising solution to balance supply and demand in a variable power grid, in which excess wind power is converted into hydrogen via electrolysis and stored for later use. In this study, an energy hub(EH) with both a P2H facility(electrolyzer) and a gas-to-power(G2P) facility(hydrogen gas turbine) is proposed to accommodate a high penetration of wind power. The EH is modeled and integrated into a security-constrained unit commitment(SCUC) problem, and this optimization problem is solved by a mixed-integer linear programming(MILP) method with the Benders decomposition technique. Case studies are presented to validate the proposed model and elaborate on the technological potential of integrating P2H into a power system with a high level of wind penetration(HWP).

Scenario-based Unit Commitment Optimization for Power System with Large-scale Wind Power Participating in Primary Frequency Regulation

Continuous increase of wind power penetration brings high randomness to power system,and also leads to serious shortage of primary frequency regulation(PFR)reserve for power system whose reserve capacity is typically provided by conventional units.Considering large-scale wind power participating in PFR,this paper proposes a unit commitment optimization model with respect to coordination of steady state and transient state.In addition to traditional operation costs,losses of wind farm de-loaded operation,environmental benefits and transient frequency safety costs in high-risk stochastic scenarios are also considered in the model.Besides,the model makes full use of interruptible loads on demand side as one of the PFR reserve sources.A selection method for high-risk scenarios is also proposed to improve the calculation efficiency.Finally,this paper proposes an inner-outer iterative optimization method for the model solution.The method is validated by the New England 10-machine system,and the results show that the optimization model can guarantee both the safety of transient frequency and the economy of system operation.

A solution to the unit commitment problem a review

Unit commitment （UC） is an optimization problem used to determine the operation schedule of the generating units at every hour interval with varying loads under different constraints and environments. Many algorithms have been invented in the past five decades for optimization of the UC problem, but still researchers are working in this field to find new hybrid algorithms to make the problem more realistic. The importance of UC is increasing with the constantly varying demands. There- fore, there is an urgent need in the power sector to keep track of the latest methodologies to further optimize the working criterions of the generating units. This paper focuses on providing a clear review of the latest techniques employed in optimizing UC problems for both stochastic and deterministic loads, which has been acquired from many peer reviewed published papers. It has been divided into many sections which include various constraints based on profit, security, emission and time. It emphasizes not only on deregulated and regulated environments but also on renewable energy and distributed generating systems. In terms of contributions, the detailed analysis of all the UC algorithms has been discussed for the benefit of new researchers interested in working in this field.

A Comprehensive Review of Security-constrained Unit Commitment

Security-constrained unit commitment(SCUC)has been extensively studied as a key decision-making tool to determine optimal power generation schedules in the operation of electricity market.With the development of emerging power grids,fruitful research results on SCUC have been obtained.Therefore,it is essential to review current work and propose future directions for SCUC to meet the needs of developing power systems.In this paper,the basic mathematical model of the standard SCUC is summarized,and the characteristics and application scopes of common solution algorithms are presented.Customized models focusing on diverse mathematical properties are then categorized and the corresponding solving methodologies are discussed.Finally,research trends in the field are prospected based on a summary of the state-of-the-art and latest studies.It is hoped that this paper can be a useful reference to support theoretical research and practical applications of SCUC in the future.

Application of Modified Progressive Hedging for Stochastic Unit Commitment in Electricity-Gas Coupled Systems

The increasing number of gas-fired units has significantly intensified the coupling between electric and gas power networks.Traditionally,nonlinearity and nonconvexity in gas flow equations,together with renewable-induced stochasticity,resulted in a computationally expensive model for unit commitment in electricity-gas coupled integrated energy systems(IES).To accelerate stochastic day-ahead scheduling,we applied and modified Progressive Hedging(PH),a heuristic approach that can be computed in parallel to yield scenario-independent unit commitment.Through early termination and enumeration techniques,the modified PH algorithm saves considerable com,putational time for certain generation cost settings or when the scale of the IES is large.Moreover,an adapted second-order cone relaxation(SOCR)is utilized to tackle the nonconvex gas flow equation.Case studies were performed on the IEEE 24.bus system/Belgium 20-node gas system and the IEEE 118-bus system/Belgium 20-node gas system.The computational efficiency when employing PH is 188 times that of commercial software,and the algorithm even outperforms Benders Decomposition.At the same time,the gap between the PH algorithm and the benchmark is less than 0.01% in both IES systems,which proves that the solutions produced by PH reach acceptable optimality in this stochastic UC problem.

Security region based security-constrained unit commitment

As the issues of security and stability of power systems are becoming increasingly significant,it is necessary to consider the constraints of the static voltage stability and transient stability,which are closely related to the active power dispatch of power systems,in the daily power dispatch,i.e.the unit commitment.However,due to the complexity of these constraints and limitation of the existing analysis methods,there has been no unit commitment model reported so far that can deal with these security constraints.On the other hand,as lack of effective measures to evaluate the security margin of dispatch schemes,it is difficult for power system operators to integrate both the security and economy of power systems in unit commitment.To resolve the above-mentioned issues,a security region based security-constrained unit commitment model is presented in the paper,which gives consideration to both the security and economy of power systems.For the first time,the active power flow constraint,the static voltage stability constraint and the transient stability constraint are taken into account in unit commitment at the same time.The model presented in the paper takes the operating cost,the branch transmission capacity margin,the static voltage stability margin and the transient stability margin as sub-objectives.By adjusting the weighting factors of sub-objectives,it is convenient to adjust the preference on the security and economy of power systems and reach a balance.The IEEE RTS-24 test system is adopted to validate the correctness and the efficiency of the proposed model.

Binary glowworm swarm optimization for unit commitment

This paper proposes a new algorithm—binary glowworm swarm optimization(BGSO)to solve the unit commitment(UC)problem.After a certain quantity of initial feasible solutions is obtained by using the priority list and the decommitment of redundant unit,BGSO is applied to optimize the on/off state of the unit,and the Lambda-iteration method is adopted to solve the economic dispatch problem.In the iterative process,the solutions that do not satisfy all the constraints are adjusted by the correction method.Furthermore,different adjustment techniques such as conversion from cold start to hot start,decommitment of redundant unit,are adopted to avoid falling into local optimal solution and to keep the diversity of the feasible solutions.The proposed BGSO is tested on the power system in the range of 10–140 generating units for a 24-h scheduling period and compared to quantuminspired evolutionary algorithm(QEA),improved binary particle swarm optimization(IBPSO)and mixed integer programming(MIP).Simulated results distinctly show that BGSO is very competent in solving the UC problem in comparison to the previously reported algorithms.

Security Constrained Unit Commitment with Extreme Wind Scenarios

The rapid development of economy and society stimulates the increase of power demand. Wind power has received great attention as a typical renewable energy, and the share of wind power is continually increasing in recent years.However, the high integration of wind power brings challenges to the secure and reliable operation of power grid due to the intermittent characteristic of wind power. In order to solve the operation risk caused by wind power uncertainty, this paper proposes to solve the problem of stochastic security-constrained unit commitment(SCUC) by considering the extreme scenarios of wind power output. Firstly, assuming that the probability density distribution of wind power approximately follows a normal distribution, a great number of scenarios are generated by Monte Carlo(MC) simulation method to capture the stochastic nature of wind power output. Then, the clustering by fast search and find of density peaks(CSFDP) is utilized to separate the generated scenarios into three types: extreme, normal and typical scenarios. The extreme scenarios are identified to determine the on/off statuses of generators, while the typical scenarios are used to solve the day-ahead security-constrained economic dispatch(SCED) problem. The advantage of the proposed method is to ensure the robustness of SCUC solution while reducing the conservativeness of the solution as much as possible.The effectiveness of the proposed method is verified by IEEE test systems.

A Mixed-integer SDP Solution to Distributionally Robust Unit Commitment with Second Order Moment Constraints

A power system unit commitment(UC)problem considering uncertainties of renewable energy sources is investigated in this paper,through a distributionally robust optimization approach.We assume that the first and second order moments of stochastic parameters can be inferred from historical data,and then employed to model the set of probability distributions.The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints,and it can be recast as a mixed-integer semidefinite programming(MI-SDP)with finite constraints.The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation.Based on the verification of strong duality of the semidefinite programming(SDP)problems,we propose a cutting plane algorithm for solving the MI-SDPs;we also introduce an SDP relaxation for the feasibility checking problem,which is an intractable biconvex optimization.Experimental results on the IEEE 6-bus system are presented,showing that without any tuning of parameters,the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general,and our method also enjoys higher reliability of dispatch operation.

A Fast Calculation Method for Long-term Security-constrained Unit Commitment of Large-scale Power Systems with Renewable Energy

With the increase in the penetration rate of renewable energy, the planning and operation of power systems will face huge challenges. To ensure the sufficient utilization of renewable energy, the reasonable arrangement for the long-term power generation plan has become more crucial. Security-constrained unit commitment(SCUC) is a critical technical means to optimize the long-term power generation plan. However, the plentiful power sources and the complex grid structure in largescale power systems will bring great difficulties to long-term SCUC. In this paper, we propose a fast calculation method for long-term SCUC of large-scale power systems with renewable energy. First, a method for unit status reduction based on temporal decomposition is proposed, which will reduce plenty of binary variables and intertemporal constraints in SCUC. Then,an efficient redundant constraint identification(RCI) method is developed to reduce the number of network constraints. Furthermore, a joint accelerated calculation framework for status reduction and RCI is formed, which can reduce the complexity of long-term SCUC while ensuring a high-precision feasible solution. In case studies, numerical results based on two test systems ROTS2017 and NREL-118 are analyzed, which verify the effectiveness and scalability of the proposed calculation method.

Graph Computing Based Security Constrained Unit Commitment in Hydro-thermal Power Systems Incorporating Pumped Hydro Storage

This paper proposes a graph computing based mixed integer programming(MIP)framework for solving the security constrained unit commitment(SCUC)problem in hydro-thermal power systems incorporating pumped hydro storage(PHS).The proposed graph computing-based MIP framework considers the economic operations of thermal units,cascade hydropower stations and PHS stations,as well as their technical impacts towards the network security.First,the hydro-thermal power system data and unit information are stored in a graph structure with nodes and edges,which enables nodal and hierarchical parallel computing for the unit commitment(UC)solution calculation and network security analysis.A MIP model is then formulated to solve the SCUC problem with the mathematical models of thermal units,cascade hydropower stations and PHS stations.In addition,two optimization approaches including convex hull reformulation(CHR)and special ordered set(SOS)methods are introduced for speeding up the MIP calculation procedure.To ensure the system stability under the derived UC solution,a parallelized graph power flow(PGPF)algorithm is proposed for the hydro-thermal power system network security analysis.Finally,case studies of the IEEE 118-bus system and a practical 2749-bus hydro-thermal power system are introduced to demonstrate the feasibility and validity of the proposed graph computing-based MIP framework.