Short-term Hydro-thermal Coordination By Lagrangian Relaxation: A New Algorithm for the Solution of the Dual Problem

For decades, researchers have been studying the unit commitment problem in electrical power generation. To solve this complex, large scale and constrained optimization (primal) problem in a direct manner is not a feasible approach, which is where Lagrangian relaxation comes in as the answer. The dual Lagrangian problem translates a relaxed problem approach, that indirectly leads to solutions of the original (primal) problem. In the coordination problem, a decomposition takes place where the global solution is achieved by coordinating between the respective subproblems solutions. This dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. To tackle, time-consuming tuning tasks  or user related experience, a new adaptative algorithm, is proposed to better adjust the step-size used to update Lagrange multipliers, i.e., avoid the need to pre-select  a set of parameters. A results comparison against a traditionally employed step-size update mechanism, showed that the adaptive algorithm manages to obtain improved performances in terms of the targeted primal problem. Keywords: Hydro-Thermal coordination, Lagrangian relaxation, Lagrangian dual problem, Lagrange multipliers, Subgradient method

Wind Integrated Thermal Unit Commitment Solution Using Grey Wolf Optimizer

The augment of ecological shield and the progressive exhaustion of traditional fossil energy sources have increased the interests in integrating renewable energy sources into existing power system. Wind power is becoming worldwide a significant component of the power generation portfolio. Profuse literature have been reported for the thermal Unit Commitment (UC) solution. In this work, the UC problem has been formulated by integrating wind power generators along with thermal power system. The Wind Generator Integrated UC (WGIUC) problem is more complex in nature, that necessitates a promising optimization tool. Hence, the modern bio-inspired algorithm namely, Grey Wolf Optimization (GWO) algorithm has been chosen as the main optimization tool and real coded scheme has been incorporated to handle the operational constraints. The standard test systems are used to validate the potential of the GWO algorithm. Moreover, the ramp rate limits are also included in the mathematical WGIUC formulation. The simulation results prove that the intended algorithm has the capability of obtaining economical resolutions with good solution quality

The optimal solution for unit commitment problem using binary hybrid grey wolf optimizer

The aim of this work is to solve the unit commitment (UC) problem in power systems by calculating minimum production cost for the power generation and finding the best distribution of the generation among the units (units scheduling) using binary grey wolf optimizer based on particle swarm optimization (BGWOPSO) algorithm. The minimum production cost calculating is based on using the quadratic programming method and represents the global solution that must be arriving by the BGWOPSO algorithm then appearing units status (on or off). The suggested method was applied on “39 bus IEEE test systems”, the simulation results show the effectiveness of the suggested method over other algorithms in terms of minimizing of production cost and suggesting excellent scheduling of units

A Comparative Study of Fuzzy Logic, Genetic Algorithm, and Gradient-Genetic Algorithm Optimization Methods for Solving the Unit Commitment Problem

Due to the continuous increase of the population and the perpetual progress of industry, the energy management presents nowadays a relevant topic that concerns researchers in electrical engineering. Indeed, in order to establish a good exploitation of the electrical grid, it is necessary to solve technical and economic problems. This can only be done through the resolution of the Unit Commitment Problem. Unit Commitment Problem allows optimizing the combination of the production units’ states and determining their production planning, in order to satisfy the expected consumption with minimal cost during a specified period which varies usually from 24 hours to one week. However, each production unit has some constraints that make this problem complex, combinatorial, and nonlinear. This paper presents a comparative study between a strategy based on hybrid gradient-genetic algorithm method and two strategies based on metaheuristic methods, fuzzy logic, and genetic algorithm, in order to predict the combinations and the unit commitment scheduling of each production unit in one side and to minimize the total production cost in the other side. To test the performance of the optimization proposed strategies, strategies have been applied to the IEEE electrical network 14 busses and the obtained results are very promising

Unit commitment by a fast and new analytical non-iterative method using IPPD table and “λ-logic” algorithm

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

A binary symmetric based hybrid meta-heuristic method for solving mixed integer unit commitment problem integrating with significant plug-in electric vehicles

Conventional unit commitment is a mixed integer optimization problem and has long been a key issue for power system operators. The complexity of this problem has increased in recent years given the emergence of new participants such as large penetration of plug-in electric vehicles. In this paper, a new model is established for simultaneously considering the day-ahead hourly based power system scheduling and a significant number of plug-in electric vehicles charging and discharging behaviours. For solving the problem, a novel hybrid mixed coding meta-heuristic algorithm is proposed, where V-shape symmetric transfer functions based binary particle swarm optimization are employed. The impact of transfer functions utilised in binary optimization on solving unit commitment and plug-in electric vehicle integration are investigated in a 10 unit power system with 50,000 plug-in electric vehicles. In addition, two unidirectional modes including grid to vehicle and vehicle to grid, as well as a bi-directional mode combining plug-in electric vehicle charging and discharging are comparatively examined. The numerical results show that the novel symmetric transfer function based optimization algorithm demonstrates competitive performance in reducing the fossil fuel cost and increasing the scheduling flexibility of plug-in electric vehicles in three intelligent scheduling modes

Quantum Inspired Evolutionary Algorithm with a Novel Elitist Local Search Method for Scheduling of Thermal Units

The unit commitment problem is a complex and essential problem in the power generation field, which is solved to obtain the schedule of a large number of generating units to minimize the operating cost and the fulfillment of consumer load demand. The present work solves the unit commitment problem using quantum-inspired evolutionary algorithms with a novel elitist local search method (QIEA-ELS). The proposed algorithm solves the unit commitment problem efficiently and its applicability is verified on various unit test systems. The constraints are satisfied efficiently to find a feasible solution, the novel elitist search method is used to locally explore the search area around the fittest individual to find a better solution in its vicinity in genotype space represent by qubits. The solution of the unit commitment is carried out considering two small population sizes as suggested in earlier work by other authors using QIEA, though it can be extended using larger population size also. The computational time is also reduced by using the suggested method with a novel elitist local search (ELS) method. The results obtained after applying the proposed algorithm are found to better as compared to other well-known solution techniques

Short term complex hydro thermal scheduling using integrated PSO-IBF algorithm

In this article, an integrated evolutionary technique such as particle swarm optimization (PSO) algorithm and improved bacterial foraging algorithm (IBFA) have been developed to provide an optimum solution to the scheduling problem with complex thermal and hydro generating stations. PSO algorithm is framed based on the intelligent behavior of the fish school and a flock of birds and the optimal solution in the multidimensional search region is achieved by assigning a random velocity to each potential solution (called the particle). BFA is designed by following the prey-seeking (chemotactic) nature of E. coli bacteria. This technique is followed in an improved manner to get the convergence rate in dynamic for a hyperspace problem by implementing a chemotactic step in a linearly decreased way instead of the static one. The effectiveness of this integrated algorithm is evaluated by using it in a complex thermal and hydro generating system. In this testing system, multiple numbers of cascaded reservoirs in hydro plants have a time coupling effect and thermal power units have a valve point loading effect. The simulation results indicate its merits by comparing it with other meta-heuristic techniques related to the fuel cost required to generate the thermal power.