Applications of the genetic algorithm to the unit commitment problem in power generation industry

This paper presents a hybrid immune algorithm (IA)/genetic algorithm (GA) and fuzzy system (FS) method (IGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shutdown schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve and individual units. First, we combined the IA and GA, then we added the fuzzy system approach. This hybrid system was used to solve the UC problems. Numerical simulations were carried out using three cases; ten, twenty and thirty thermal unit power systems over a 24 hrs period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional tabu search (TTS). The result demonstrated the accuracy of the proposed CIGAFS approach.

This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. In the UC problem, the goal is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, the solution must satisfy a set of technological and operational constraints. The algorithm developed is a hybrid biased random key genetic algorithm (HBRKGA). It uses random keys to encode the solutions and introduces bias both in the parent selection procedure and in the crossover strategy. To intensify the search close to good solutions, the GA is hybridized with local search. Tests have been performed on benchmark large-scale power systems. The computational results demonstrate that the HBRKGA is effective and efficient. In addition, it is also shown that it improves the solutions obtained by current state-of-the-art methodologies.

This paper presents a new approach for the large scale unit commitment problem. The unit commitment (UC) problem plays a major role in the power system since the improvement of commitment schedule results in the reduction of operating cost. However, the unit commitment problem is one of the most difficult optimization problems in the power system, because this problem has many constraints. Moreover search space is vast. To overcome these problems, a new genetic operator based on unit characteristic classification and unit integration technique are proposed. The proposed algorithm was tested on a reported UC problem. From simulation results, better solutions are obtained in comparison with previously reported results. Numerical results for a system up to 100 units are compared to previously reported results.

This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited. This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility. UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space. Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations. To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.

This paper presents an algorithm for integrating and managing electrochemical energy storage systems (ESSs) on unit commitment (UC) problem. As some elements required for integrating electrochemical ESS, such as the power converter, have non-linear characteristics, its corresponding linear modeling could be difficult to be developed and included on the UC problem, which could lead to unfeasible solutions or unexpected results. In order to incorporate full models of ESS and its interface with the power system, in this paper an algorithm to incorporate electrochemical ESS management on the UC problem is presented. An insular power system of 10-units is analyzed, and conclusions are duly drawn.

In this paper, Security Constrained Unit Commitment (SCUC) problem with combined Thermal- Solar generating units is solved using Artificial Bee Colony (ABC) algorithm. SCUC problem aims to obtain minimum generation cost while satisfying the system, network and security constraints. The SCUC problem is divided into Unit Commitment Problem (UCP) which is considered as the master problem and Security Constrained Economic Dispatch (SCED) is considered as the sub problem. Here, both thermal and solar generations are considered in UCP and SCED solutions. Binary Coded ABC Algorithm is used to solve the UCP and Real Coded ABC Algorithm is used for solving the SCED problem. The constraints such as spinning reserves, hourly load demands, ramp up/ramp down limits of generators, minimum up/down limits, line flow and voltage limits are considered in the problem formulation. Beta distribution function is employed to forecast the solar power generation in different seasons. The comparison is carried out with and without incorporating solar generation. The proposed method is validated on a 6 bus system and a South Indian 86 bus utility.

Objectives: The main objective of this paper is to solve the Cost Based Unit Commitment (CBIC) problem considering Renewable Energy Sources (RES) and Plug-in Electric vehicles (PEVs). The proposed problem minimizes the total operating of the interconnected system. Methods: A novel and recently developed successful optimization tool of Cat and Mouse Based Optimizer (CMBO) is proposed for optimal solution of Cost Based UC problem. The proposed CMBO approach is having two groups such as Cat group and Mice group for searching the global optimal solution with less computational time. It contains two phases like Cat’s movement towards Mice and Mice escape to a safe place is effectively updating the new position of Cat and Mice to easily reaching the best solutions. The control parameter of CMBO is number of agents is 50, number of variables is 10 and maximum number of iteration is 500. MATLAB 14.0 platform is utilized for the projected problem. Findings: The method tested on standard IEEE-39 bus system (10 generators and 24 hour) with an equivalent PEV and Wind farm. The CMBO approach minimize the total operating cost with various test cases. The outcomes such as UC schedule, Real power output of thermal, wind and PEV units, fuel cost, startup cost and total operating cost of the interconnected system are numerically and graphically reported. The total operating cost is 4.11 % minimized when compared with base case approach and 0.73 % reduced than the other existing method viz. Parallel UCs-RP method. Novelty: The CMBO is recently developed powerful optimizer and parameter free algorithm, so easily reaches the global optimal solutions. The obtained simulated results are compared with other mathematical and intelligent computational approaches for proving the efficiency and performance of the proposed CNBO technique. Keywords: Unit Commitment, Plug­in Electric Vehicles, Renewable Energy Sources, Cost minimization, Cat and Mouse Based Optimizer

This paper presents the solving unit commitment (UC) problem using Modified Subgradient Method (MSG) method combined with Simulated Annealing (SA) algorithm. UC problem is one of the important power system engineering hard-solving problems. The Lagrangian relaxation (LR) based methods are commonly used to solve the UC problem. The main disadvantage of this group of methods is the difference between the dual and the primal solution which gives some significant problems on the quality of the feasible solution. In this paper, MSG method which does not require any convexity and differentiability assumptions is used for solving the UC problem. MSG method depending on the initial value reaches zero duality gap. SA algorithm is used in order to assign the appropriate initial value for MSG method. The major advantage of the proposed approach is that it guarantees the zero duality gap independently from the size of the problem. In order to show the advantages of this proposed approach, the four-unit Tuncbilek thermal plant and ten-unit thermal plant which is usually used in literature are chosen as test systems. Penalty function (PF) method is also used to compare with our proposed method in terms of total cost and UC schedule.

Study on unit commitment problem considering pumped storage and renewable energy via a novel binary artificial sheep algorithm

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.

This paper presents centralized control for a wind farm using model predictive control (MPC) method. In order to solve intra-day unit commitment (UC) problem, the UC problem is solved by using the MPC method with short-term wind power forecasting. We introduce a new dynamics model for the UC with some constraints to utilize the benefits of the MPC method. The objective function considering the operation and maintenance costs is formulated by adding a new variable in order to average the operating time of each wind turbine (WT) within the whole time. The proposed method could solve the UC problems on-line using the prediction time horizon that could be selected flexibly considering time horizon based on wind power forecasting errors. From the simulation study using 10 WTs, we observed that the proposed dynamics model of UC effectively provided the optimal solution to each scenario. Numerical study will validate that the proposed method can be applied to solving the UC problem of a large scale wind farm by aggregating WTs.

The unit commitment(UC) problem is a critical problem in economic dispatch of power system, and it is the key to planning for short-term power generation. Its economic benefit is generally greater than the benefit of economic distribution of load. However, unit commitment is a high-dimensional, nonconvex, discrete, nonlinear mixed integer optimization problem, and is difficult to find the optimal theoretical solution. Therefore, people have been actively studying to solve this problem. Social learning particle swarm optimizer is a recent proposed metaheuristic algorithm specialized in solving the high-dimensional problem. In this paper, a novel binary social learning particle swarm optimizer (BSLPSO) is proposed for solving the UC problem associated with lambda iteration method. In order to verify the effectiveness of the algorithm for UC problem, a comprehensive numerical study of 10 to 100 units has been conducted, and compared with other related algorithms. The result shows that this algorithm performs well in UC problem and is better than other algorithms.

In traditional electricity market unit commitment (UC) is done only for the reduction of operating cost. In the deregulated electricity market, for a secure and economical hourly generation schedule of the day ahead market, independent system operator (ISO) executes the security constrained unit commitment (SCUC) problem. The objective of the paper is to develop scheduling algorithm using hybrid particle swarm optimization (PSO) for electric generation that accounts directly for system security requirements. The proposed SCUC formulation includes constraints, such as hourly power demand, system reserves, ramp up/down limits, minimum ON/OFF duration limits. The innovation of our approach is to capture the system security requirements within a network flow sub-problem that is solved in conjunction with the unit commitment problem. To solve such SCUC model, a binary coded particle swarm optimization (BPSO) is used for unit commitment master problem and real coded particle swarm optimization (RPSO) is used for the economic dispatch sub-problem. The effectiveness of the suggested method to solve the SCUC problem is validated on different test systems.

The unit commitment operation in power systems is a complex, non-linear, constrained optimization problem. The commitment and de-commitment decision presents a binary problem which needs discrete/binary optimization approaches. This paper presents a binary bat search algorithm (BBSA) to solve unit commitment (UC) problem. The bat search algorithm belongs to a meta heuristic class of optimization approaches inspired by natural echolocation behavior of bats. In order to solve binary UC problem, the real valued bat search process is mapped to binary search space using sigmoidal transformation function. The BBSA is then applied to test system with 10 thermal units. The effectiveness of the BBSA is verified against system dimension using test systems upto 100 units. Extensive numerical experiments are performed to test the effectiveness of BBSA and statistical analysis of simulation results are presented. The simulation results are presented, discussed and compared to various existing classical and heuristic approaches. The same demonstrate the superior performance of BBSA approach in solving UC problem.