Effects of ramp-rate limits on unit commitment and economic dispatch

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

In this paper, a hybrid multiobjective improved bacterial foraging algorithm with fuzzy dominance sorting FSIBF is proposed and used to solve environmental friendly economic load dispatch problem. The fuzzy dominance-based sorting procedure is used to select the non-dominated solutions in the Pareto front. The proposed algorithm is applied to nonlinear constrained multiobjective environmental friendly economic load dispatch problem. In the proposed work, we have considered the standard IEEE 30-bus six-generator test system with fuel cost and emission as two conflicting objectives to be optimised simultaneously satisfying the system's operational constraints. The constraints imposed from the operation point of view are the limits on generator real power and reactive power outputs, bus voltages and power flow in the transmission lines. The proposed work also includes the effect of having non-smooth cost characteristics of the thermal generators which arises because of the valve point loading effect. The practical generator constraints such as ramp rate limits and prohibited operating zones are also incorporated in this work suitably.

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

A fuzzy optimization-based approach to large scale thermal unit commitment

Evaluating the impact of sub-hourly unit commitment method on spinning reserve in presence of intermittent generators

This paper presents a trustworthy unit commitment study to schedule both Renewable Energy Resources (RERs) with conventional power plants to potentially decarbonize the electrical network. The study has employed a system with three IEEE thermal (coal-fired) power plants as dispatchable distributed generators, one wind plant, one solar plant as stochastic distributed generators, and Plug-in Electric Vehicles (PEVs) which can work either loads or generators based on their charging schedule. This paper investigates the unit commitment scheduling objective to minimize the Combined Economic Emission Dispatch (CEED). To reduce combined emission costs, integrating more renewable energy resources (RER) and PEVs, there is an essential need to decarbonize the existing system. Decarbonizing the system means reducing the percentage of CO2 emissions. The uncertain behavior of wind and solar energies causes imbalance penalty costs. PEVs are proposed to overcome the intermittent nature of wind and solar energies. It is important to optimally integrate and schedule stochastic resources including the wind and solar energies, and PEVs charge and discharge processes with dispatched resources; the three IEEE thermal (coal-fired) power plants. The Water Cycle Optimization Algorithm (WCOA) is an efficient and intelligent meta-heuristic technique employed to solve the economically emission dispatch problem for both scheduling dispatchable and stochastic resources. The goal of this study is to obtain the solution for unit commitment to minimize the combined cost function including CO2 emission costs applying the Water Cycle Optimization Algorithm (WCOA). To validate the WCOA technique, the results are compared with the results obtained from applying the Dynamic Programming (DP) algorithm, which is considered as a conventional numerical technique, and with the Genetic Algorithm (GA) as a meta-heuristic technique.

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

There is increasing evidence of shortage of ramping resources in the real-time operation of power systems. To explain and remedy this problem systematically, in this paper we take a novel look at the way the day-ahead unit commitment (UC) problem represents the information about load, generation and ramping constraints. We specifically investigate the approximation error made in mapping of the original problem, that would decide the continuous-time generation and ramping trajectories of the committed generating units, onto the discrete-time problem that is solved in practice. We first show that current practice amounts to approximating the trajectories with linear splines. We then offer a different representation through cubic splines that provides physically feasible schedules and increases the accuracy of the continuous-time generation and ramping trajectories by capturing sub-hourly variations and ramping of load in the day-ahead power system operation. The corresponding day-ahead UC model is formulated as an instance of mixed-integer linear programming (MILP), with the same number of binary variables as the traditional UC formulation. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of events of ramping scarcity in the real-time operations.

Many different methods have been presented to solve unit commitment (UC) problem in literature with different advantages and disadvantages. The need for multiple runs, huge computational burden and time, and poor convergence are some of the disadvantages, where are especially considerable in large scale systems. In this paper, a new analytical and non-iterative method is presented to solve UC problem. In the proposed method, improved pre-prepared power demand (IPPD) table is used to solve UC problem, and then analytical “λ-logic” algorithm is used to solve economic dispatch (ED) sub-problem. The analytical and non-iterative nature of the mentioned methods results in simplification of the UC problem solution. Obtaining minimum cost in very small time with only one run is the major advantage of the proposed method. The proposed method has been tested on 10 unit and 40-100 unit systems with consideration of different constraints, such as: power generation limit of units, reserve constraints, minimum up and down times of generating units. Comparing the simulation results of the proposed method with other methods in literature shows that in large scale systems, the proposed method achieves minimum operational cost within minimum computational time.

The medium and long-term operation of the unit is an important part of the operation of the power energy system. With the development of IES, the coupling of various energy forms such as electricity, heat and natural gas has been continuously strengthened. When a CHP unit or a gas unit is shut down, its impact will involve a variety of energy systems. Therefore, It is of great significance to formulate a reasonable annual unit combination plan and a coordinated optimization plan for the maintenance plan. First of all, starting from the coupling mechanism of the power supply, heating and gas supply of the unit, consider the relationship between each system and equipment. On this basis, taking into account the system operation constraints, unit maintenance constraints and unit operation constraints, a combined dispatch model of IES unit combination and maintenance plan including power-to-gas (P2G) and electric boiler equipment are proposed. The accuracy and effectiveness of the proposed model are verified through simulation analysis of a numerical example. The calculation example results show that the overall arrangement of the unit maintenance plan and the unit combination plan in the integrated energy system can improve the operating economy of the system; the introduction of coupling equipment such as P2G and electric boilers can effectively improve the new energy consumption rate and reduce the system operating cost.

This chapter describes and formulates three important problems for the economic management of power systems, namely, the Unit Commitment (UC), the Economic Dispatch (ED), and the Network Constrained Unit Commitment (NCUC) problems. The UC problem determines the commitment of generating units with the aim of minimizing operating costs while supplying the demand and meeting technical and security constraints. Then, once the commitment of generating units is decided, the ED problem determines the actual power output of each generating unit that is needed to supply all demands at minimum cost, while complying with the technical constraints of the transmission network. Finally, if both the commitment of generating units and transmission constraints are considered simultaneously, the resulting problem is known as the NCUC problem. These three problems are mostly considered in electricity markets throughout the US.

The study proposes a stochastic optimisation approach based on discrete scenarios and the minimax criterion to deal with demand uncertainty in the two-stage unit commitment problem. To avoid making an over-conservative decision, the approach is designed to assign a probability-based weight to each demand scenario and provide a unit commitment schedule that minimises the maximum possible-weighted generation cost. Unit commitment is determined in the first stage and the economic dispatch under the scenario that corresponds to the maximum possible-weighted generation cost is determined in the second stage. The problem is formulated as a type of min–max–min mixed integer programming model. By introducing an auxiliary variable, the model is further transformed into a minimisation problem. A Benders decomposition algorithm is developed to solve the problem. The Benders master problem determines the unit commitment decision, while the Benders subproblem determines the dispatch decision. Multiple Benders feasibility cuts are constructed when the Benders subproblem is infeasible. Valid inequalities are derived to improve the lower bound provided by the Benders master problem. Numerical results show the performance of the algorithm.

The paper presents a stochastic Hopfield artificial neural network for unit commitment and economic power dispatch. Because of uncertainties in both the system load demand and unit availability, the unit commitment and economic power dispatch problem is stochastic, in this paper we model forced unit outages as independent Markov processes, and load demand as a normal Gaussian random variable. The (0,1) unit commitment-status variables and the hourly unit loading are modelled as sample functions of appropriate random processes. They are solutions of appropriately derived stochastic differential equations which describe the dynamics of a stochastic system for which the operating cost function is a stochastic Lyapunov function. Once the unit commitment and economic power dispatch have been done, the corresponding production costs are computed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A layered matrix encoding cascade genetic algorithm and particle swarm optimization approach (GA-PSO) for unit commitment and economic load dispatch problem in a thermal power system is presented in this paper. The tasks of determining and allocating power generation to different thermal units in a way that the total power production cost is at the minimum subject to equality and inequality constraints makes unit commitment and economic load dispatch challenging. A case study, based on the thermal power generation problem presented in [1], is used to demonstrate the effectiveness of the proposed method in generating a cost-effective power generation schedule. The schedule obtained is compared with that of Linear Programming (LP) as reported in [1]. The results show that the proposed GA-PSO approach outperforms LP in solving the unit commitment and economic load dispatch problem for thermal power generation system in this case study.

A rolling-horizon unit commitment framework with flexible periodicity