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.

On units combination and commitment optimization for electric power production

Electric power system is one of the most important and complex engineering in modern society, supplying main and general power for social production and social life. Meanwhile, since it is a productive system with both high input and output, it has an obvious economic significance to improve its operating efficiency. For an example, an unit is 10 GW scale, if its standard coal consumption can be decreased with 1 g/kW·h, it can save about 5 000 tons standard coal per year. It will be discussed mainly that how to establish optimization model and its numerical algorithm for operating management of the electric power system. The idea on establishing optimization model is how to dispatch work state of units or power plants, so that total cost of fuel consumption for generation is reduced to the minimum. Here the dispatch is to decide which unit or plant to operate, which unit or plant to stop running, how much power should be generated for those operating units or plants at each given time interval.

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.

A Quick Method for Judging the Feasibility of Security-Constrained Unit Commitment Problems within Lagrangian Relaxation Framework

Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to solve the economic dispatch of generation power among all the generating units. The core of the two stages is how to determine the feasibility of SCUC states. The existence of ramp rate constraints and security constraints increases the difficulty of obtaining an analytical necessary and sufficient condition for determining the quasi-feasibility of SCUC states at each scheduling time. However, a numerical necessary and sufficient numerical condition is proposed and proven rigorously based on Benders Decomposition Theorem. Testing numerical example shows the effectiveness and efficiency of the condition.

Lagrangian Relaxation-Based Unit Commitment Considering Fast Response Reserve Constraints

Unit commitment (UC) is to determine the optimal unit status and generation level during each time interval of the scheduled period. The purpose of UC is to minimize the total generation cost while satisfying system demand, reserve requirements, and unit constraints. Among the UC constraints, an adequate provision of reserve is important to ensure the security of power system and the fast-response reserve is essential to bring system frequency back to acceptable level following the loss of an online unit within a few seconds. In this paper, the authors present and solve a UC problem including the frequency-based reserve constraints to determine the optimal FRR requirements and unit MW schedules. The UC problem is solved by using Lagrangian Relaxation-based approach and compared with the actual system schedules. It is observed that favorable reserve and unit MW schedules are obtained by the proposed method while the system security is maintained.

Unit Commitment under the Environment of Wind Power and Large-Scale Bilateral Transactions

Bilateral electric power contract is settled based on contract output curve. This paper considered the bilateral transactions execution, new energy accommodation, power grid security and generation economy, considering the executive priority of different power components to establish a multi-objective coordination unit commitment model. Through an example to verify the effectiveness of the model in promoting wind power consumption, guaranteeing trade execution, and improving power generation efficiency, and analyzed the interactions to each other among the factors of wind power, trading and blocking. According to the results, when wind power causes reverse power flow in the congestion line, it will promote the implementation of contracts, the influence of wind power accommodation to trade execution should be analyzed combined with the grid block, the results can provide reference for wind power planning.

The Linear Formulation of Thermal Unit Commitment Problem with Uncertainties through a Computational Mixed Integer

The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with security due to the new challenges in power system supply. In solar and wind renewable energy, the only partially predictable is the output with very low controllability which creates unit commitment problems in thermal units. In this research paper, a different linear formulation via mixed integer is presented that only requires “binary variables” and restraints concerning earlier stated models. The framework of this model allows precisely the costs of time-dependent startup & intertemporal limitations, for example, minimum up & down times and a ramping limit. To solve the unit commitment problem efficiently, a commercially available linear programming of mixed-integer is applied for sizeable practical scale. The results of the simulation are shown in conclusions.

A Hybrid Unit Commitment Approach Incorporating Modified Priority List with Charged System Search Methods

This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL);however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods.

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.

Optimization of unit commitment based on genetic algorithms

How to solve unit commitment and load dispatch of power system by genetic algorithms is discussed in this paper. A combination encoding scheme of binary encoding and floating number encoding and corresponding genetic operators are developed. Meanwhile a contract mapping genetic algorithm is used to enhance traditional GA’s convergence. The result of a practical example shows that this algorithm is effective.

Binary-Real Coded Genetic Algorithm Based <i>k</i>-Means Clustering for Unit Commitment Problem

This paper presents a new algorithm for solving unit commitment (UC) problems using a binary-real coded genetic algorithm based on k-means clustering technique. UC is a NP-hard nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems, in which some power generating units are to be scheduled in such a way that the forecasted demand is met at minimum production cost over a time horizon. In the proposed algorithm, the algorithm integrates the main features of a binary-real coded genetic algorithm (GA) and k-means clustering technique. The binary coded GA is used to obtain a feasible commitment schedule for each generating unit;while the power amounts generated by committed units are determined by using real coded GA for the feasible commitment obtained in each interval. k-means clustering algorithm divides population into a specific number of subpopulations with dynamic size. In this way, using k-means clustering algorithm allows the use of different GA operators with the whole population and avoids the local problem minima. The effectiveness of the proposed technique is validated on a test power system available in the literature. The proposed algorithm performance is found quite satisfactory in comparison with the previously reported results.

Optimizing Combination of Units Commitment Based on Improved Genetic Algorithms

GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms, such as natural selection, genetic recombination and survival of the fittest. By use of coding betterment, the dynamic changes of the mutation rate and the crossover probability, the dynamic choice of subsistence, the reservation of the optimal fitness value, a modified genetic algorithm for optimizing combination of units in thermal power plants is proposed. And through taking examples, test result are analyzed and compared with results of some different algorithms. Numerical results show available value for the unit commitment problem with examples.

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.

Extended Sequential Truncation Technique for Adaptive Dynamic Programming Based Security-Constrained Unit Commitment with Optimal Power Flow Constraints

Considering the economics and securities for the operation of a power system, this paper presents a new adaptive dynamic programming approach for security-constrained unit commitment (SCUC) problems. In response to the “curse of dimension” problem of dynamic programming, the approach solves the Bellman’s equation of SCUC approximately by solving a sequence of simplified single stage optimization problems. An extended sequential truncation technique is proposed to explore the state space of the approach, which is superior to traditional sequential truncation in daily cost for unit commitment. Different test cases from 30 to 300 buses over a 24 h horizon are analyzed. Extensive numerical comparisons show that the proposed approach is capable of obtaining the optimal unit commitment schedules without any network and bus voltage violations, and minimizing the operation cost as well.

A Literature Review of Stochastic Programming and Unit Commitment

The study of unit commitment (UC) aims to find reasonable schedules for generators to optimize power systems’ operation. Many papers have been published that solve UC through different methods. Articles that systematically summarize UC problems’ progress in order to update researchers interested in this field are needed. Because of its promising performance, stochastic programming (SP) has become increasingly researched. Most papers, however, present SP’s UC solving approaches differently, which masks their relationships and makes it hard for new researchers to quickly obtain a general idea. Therefore, this paper tries to give a structured bibliographic survey of SP’s applications in UC problems.

Cost Effective Operating Strategy for Unit Commitment and Economic Dispatch of Thermal Power Plants with Cubic Cost Functions Using TLBO Algorithm

This paper deals with a Unit Commitment (UC) problem of a power plant aimed to find the optimal scheduling of the generating units involving cubic cost functions. The problem has non convex generator characteristics, which makes it very hard to handle the corresponding mathematical models. However, Teaching Learning Based Optimization (TLBO) has reached a high efficiency, in terms of solution accuracy and computing time for such non convex problems. Hence, TLBO is applied for scheduling of generators with higher order cost characteristics, and turns out to be computationally solvable. In particular, we represent a model that takes into account the accurate higher order generator cost functions along with ramp limits, and turns to be more general and efficient than those available in the literature. The behavior of the model is analyzed through proposed technique on modified IEEE-24 bus system.

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.

Composite Cost Function Based Solution to the Unit Commitment Problem

This paper presents a new approach via composite cost function to solve the unit commitment problem. The unit com-mitment problem involves determining the start-up and shut-down schedules for generating units to meet the fore-casted demand at the minimum cost. The commitment schedule must satisfy the other constraints such as the generating limits, spinning reserve, minimum up and down time, ramp level and individual units. The proposed algorithm gives the committed units and economic load dispatch for each specific hour of operation. Numerical simulations were carried out using three cases: four-generator, seven-generator, and ten-generator thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as Dynamic programming, Branch and bound, Ant colony system, and traditional Tabu search. The result demonstrated the accuracy of the proposed method.

Multi-Area Unit Commitment Using Hybrid Particle Swarm Optimization Technique with Import and Export Constraints

This paper presents a novel approach to solve the Multi-Area unit commitment problem using particle swarm optimization technique. The objective of the multi-area unit commitment problem is to determine the optimal or a near optimal commitment strategy for generating the units. And it is located in multiple areas that are interconnected via tie lines and joint operation of generation resources can result in significant operational cost savings. The dynamic programming method is applied to solve Multi-Area Unit Commitment problem and particle swarm optimization technique is embedded for computing the generation assigned to each area and the power allocated to all committed unit. Particle Swarm Optimization technique is developed to derive its Pareto-optimal solutions. The tie-line transfer limits are considered as a set of constraints during the optimization process to ensure the system security and reliability. Case study of four areas each containing 26 units connected via tie lines has been taken for analysis. Numerical results are shown comparing the cost solutions and computation time obtained by using the Particle Swarm Optimization method is efficient than the conventional Dynamic Programming and Evolutionary Programming Method.

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.