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.

A Data-driven Variable Reduction Approach for Transmission-constrained Unit Commitment of Large-scale Systems

This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(MILP)are popular approaches to solving TCUC.However,with many binary unit commitment variables,LR suffers from slow convergence and MILP presents heavy computation burden.The proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems.A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible(ASF)approaches,which is then leveraged to efficiently solve new TCUC instances online.On/off statuses of considerable units can be fixed in the online calculation according to the database,which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances.A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables,which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure changes.Numerical tests illustrate the efficiency of the proposed approach.

Stochastic Security-constrained Unit Commitment Considering Electric Vehicles, Energy Storage Systems, and Flexible Loads with Renewable Energy Resources

In this paper, a new formulation for modeling the problem of stochastic security-constrained unit commitment along with optimal charging and discharging of large-scale electric vehicles, energy storage systems, and flexible loads with renewable energy resources is presented. The uncertainty of renewable energy resources is considered as a scenario-based model. In this paper, a multi-objective function which considers the reduction of operation cost, no-load and startup/shutdown costs, unserved load cost, load shifting, carbon emission, optimal charging and discharging of energy storage systems, and power curtailment of renewable energy resources is considered. The proposed formulation is a mixed-integer linear programming(MILP) model, of which the optimal global solution is guaranteed by commercial solvers. To validate the proposed formulation, several cases and networks are considered for analysis, and the results demonstrate the efficiency.

Data-driven Convexification for Frequency Nadir Constraint of Unit Commitment

The increasing penetration of the renewable energy sources brings new challenges to the frequency security of power systems. In order to guarantee the system frequency security, frequency constraints are incorporated into unit commitment(UC) models. Due to the non-convex form of the frequency nadir constraint which makes the frequency constrained UC(FCUC) intractable, this letter proposes a revised support vector machine(SVM) based system parameter separating plane method to convexify it. Based on this data-driven convexification method, we obtain a tractable FCUC model which is formulated as a mixed-integer quadratic programming(MIQP) problem. Case studies indicate that the proposed method can obtain less conservative solution than the existing methods with higher efficiency.

Frequency-constrained Unit Commitments with Linear Rules Extracted from Simulation Results Considering Regulations from Battery Storage

Heavy renewable penetrations and high-voltage cross-regional transmission systems reduce the inertia and critical frequency stability of power systems after disturbances.Therefore,the power system operators should ensure the frequency nadirs after possible disturbances are within the set restriction,e.g.,0.20 Hz.Traditional methods utilize linearized and simplified control models to quantify the frequency nadirs and achieve frequency-constrained unit commitments(FCUCs).However,the simplified models are hard to depict the frequency responses of practical units after disturbances.Also,they usually neglect the regulations from battery storage.This paper achieves FCUCs with linear rules extracted from massive simulation results.We simulate the frequency responses on typical thermal-hydro-storage systems under diverse unit online conditions.Then,we extract the rules of frequency nadirs after disturbances merely with linear support vector machine to evaluate the frequency stability of power systems.The algorithm holds a high accuracy in a wide range of frequency restrictions.Finally,we apply the rules to three typical cases to show the influences of frequency constraints on unit commitments.

Day-ahead Network-constrained Unit Commitment Considering Distributional Robustness and Intraday Discreteness:A Sparse Solution Approach

Quick-start generation units are critical devices and flexible resources to ensure a high penetration level of renewable energy in power systems.By considering the wind uncertainty and both binary and continuous decisions of quickstart generation units within the intraday dispatch,we develop a Wasserstein-metric-based distributionally robust optimization model for the day-ahead network-constrained unit commitment(NCUC)problem with mixed-integer recourse.We propose two feasible frameworks for solving the optimization problem.One approximates the continuous support of random wind power with a finite number of events,and the other leverages the extremal distributions instead.Both solution frameworks rely on the classic nested column-and-constraint generation(C&CG)method.It is shown that due to the sparsity of L_(1)-norm Wasserstein metric,the continuous support of wind power generation could be represented by a discrete one with a small number of events,and the rendered extremal distributions are sparse as well.With this reduction,the distributionally robust NCUC model with complicated mixed-integer recourse problems can be efficiently handled by both solution frameworks.Numerical studies are carried out,demonstrating that the model considering quick-start generation units ensures unit commitment(UC)schedules to be more robust and cost-effective,and the distributionally robust optimization method captures the wind uncertainty well in terms of out-of-sample tests.

A Polynomial-Time Algorithm with Tight Error Bounds for Single-Period Unit Commitment Problem

This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and proven to be NP-hard.Tight theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are provided.Computational results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.

Hierarchical Frequency-dependent Chance Constrained Unit Commitment for Bulk AC/DC Hybrid Power Systems with Wind Power Generation

As the steady-state frequency of an actual power system decreases from its nominal value,the composite load of the system generally responds positively to lower power consumption,and vice versa.It is believed that this load frequency damping(LFD)effect will be artificially enhanced,i.e.,sensitivities of loads with respect to operational frequency will increase,in future power systems.Thus,for wind-integrated power systems,this paper proposes a frequency-dependent chance constrained unit commitment(FDCCUC)model that employs the operational frequency as a dispatching variable so that the LFD effect-based load power can act as a supplemental reserve.Because the frequency deviation is safely restricted,this low-cost reserve can be sufficiently exerted to upgrade the wind power accommodation capability of a power system that is normally confined by an inadequate reserve to cope with uncertain wind power forecasting error.Moreover,when the FDCCUC model is applied to a bulk AC/DC hybrid power system consisting of several independently operated regional AC grids interconnected by DC tie-lines,a hierarchically implemented searching algorithm is proposed to protect private scheduling information of the regional AC grids.Simulations on a 2-area 6-bus system and a 3-area 354-bus system verify the effectiveness of the FDCCUC model and hierarchical searching algorithm.

An Efficient Method for Identifying the Inactive Transmission Constraints in a Network-Constrained Unit Commitment

Network-constrained unit commitment(NCUC)is one of the most widely used applications in power system and electricity market operations.According to empirical evidence,some of the transmission constraints in a NCUC are inactive.Identifying and eliminating these inactive constraints can improve the efficiency.In this paper,an efficient method is first proposed for identifying the inactive transmission constraints.The physical and economic insights of NCUC are carefully considered and utilized.Both the generating costs and power transfer distribution factor(PTDF)are considered.Not only redundant constraints but also non-binding constraints can be identified via the proposed method.An acceleration method that combines relaxation-based neighborhood search and improved relaxation inducement is proposed for further reducing the computation time.The case study shows that the proposed method can significantly reduce the number of transmission constraints and substantially improve the efficiency of NCUC without impacting the optimality.

Fast Solution Method for the Large-scale Unit Commitment Problem with Long-term Storage

Long-term storage(LTS)can provide various services to address seasonal fluctuations in variable renewable energy by reducing energy curtailment.However,long-term unit commitment(UC)with LTS involves mixed-integer programming with large-scale coupling constraints between consecutive intervals(state-of-charge(SOC)constraint of LTS,ramping rate,and minimum up/down time constraints of thermal units),resulting in a significant computational burden.Herein,an iterative-based fast solution method is proposed to solve the long-term UC with LTS.First,the UC with coupling constraints is split into several sub problems that can be solved in parallel.Second,the solutions of the sub problems are adjusted to obtain a feasible solution that satisfies the coupling constraints.Third,a decoupling method for long-term time-series coupling constraints is proposed to determine the global optimization of the SOC of the LTS.The price-arbitrage model of the LTS determines the SOC boundary of the LTS for each sub problem.Finally,the sub problem with the SOC boundary of the LTS is iteratively solved independently.The proposed method was verified using a modified IEEE 24-bus system.The results showed that the computation time of the unit combination problem can be reduced by 97.8%,with a relative error of 3.62%.

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.