Thermal unit commitment solution using an improved Lagrangian Relaxation

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.

This paper addresses the unit commitment problem of thermal units. This optimization problem is large-scale, combinatorial, mixed-integer, and nonlinear. Exact solution techniques to solve it are not currently available. This paper proposes a novel repair genetic algorithm conducted through heuristics to achieve a near optimal solution to this problem. This optimization technique is directly parallelizable. Three different parallel approaches have been developed. The modeling framework provided by genetic algorithms is less restrictive than the frameworks provided by other approaches such as dynamic programming or Lagrangian relaxation. A state-of-the-art Lagrangian relaxation algorithm is used to appraise the behavior of the proposed parallel genetic algorithm. The computing time requirement to solve problems of realistic size is moderate. The developed genetic algorithm has been successfully applied to realistic case studies.

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 paper presents a new approach to solving the short-term unit commitment problem in utility system using an evolutionary programming based tabu search method. The objective of this paper is to find the generation scheduling such that the total operating cost can be minimized, when subjected to a variety of constraints. This also means that it is desirable to find the optimal generating unit commitment in the power system for the next H hours. Evolutionary programming, which happens to be a global optimization technique for solving unit commitment problem, operates on a system, which is designed to encode each unit's operating schedule with regard to its minimum up/down time. The best population is selected by evolutionary strategy. A 66-bus utility power system with twelve generating units in India demonstrates the effectiveness of the proposed approach. Numerical results are shown comparing the cost solutions and computation time obtained by using the evolutionary programming method and other conventional methods like dynamic programming, Lagrangian relaxation and tabu search in reaching proper unit commitment.

An optimal solution to the unit commitment (UC) and economic load dispatch (ELD) problems lead to remarkable saving in the power system operational cost. UC and ELD main problems are to find the maximum profit and fast computation simulation time for the scheduling program. Lagrangian relaxation (LR) has become one of the best solution methods in solving the UC and ELD problems. The approach is claimed to be more efficient and easier than other methods in solving large-scale problems. When applying LR, the dual function needed to be updated at the higher level. Lately, bundling method (BM) is one of the best solution methods to Lagrangian dual problem. This paper presents LR technique, BM and interior point method for solving the UC and ELD problems. It will also explore the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

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.

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.

This paper proposes an innovative genetic algorithm (GA) approach to solve the thermal unit commitment (UC) problem in power generation industry through a constraint satisfaction technique. Due to a large variety of constraints to be satisfied, the solution space of the UC problem is highly nonconvex, and therefore the UC problem can not be solved efficiently by the standard GA. To effectively deal with the constraints of the problem and greatly reduce the search space of the GA, the minimum up- and down-time constraints are embedded in the binary strings that are coded to represent the on-off states of the generating units. The violations of the other constraints are handled by integrating penalty factors into the cost function. Numerical results on the practical Taiwan Power (Taipower) system of 38 thermal units over a 24-hour period show that the features of easy implementation, fast convergence, and highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach. >

Sub-hourly Unit Commitment (UC) problems have been suggested as a way to improve power system efficiency. Such problems, however, are much more difficult than hourly UC problems. This is not just because of the increased number of period to consider, but also because of much reduced unit ramping capabilities leading to more complicated convex hulls. As a result, state-of-the-art and practice methods such as branch-and-cut suffer from poor performance. In this paper, our recent Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) method, which overcame major difficulties of standard Lagrangian Relaxation, is enhanced by synergistically incorporating the concept of Ordinal Optimization (OO). By using OO, solving subproblems becomes much faster. Testing of Midcontinent ISO (MISO)’s problem with 15 minutes as the time interval over 36 hours involving about 1,100 units and 15000 virtuals demonstrates that the new method obtains near-optimal solutions efficiently and significantly outperforms branch-and-cut.

To solve joint optimization scheduling problem of thermal power plants based on the electricity market, the constraints and characteristics of optimal operation of thermal power plants are analyzed. From the perspective of economics and environmental science, we propose and establish an electricity market based joint optimization scheduling model of thermal power plants. Mutation particle swarm optimization algorithm (MPSO) is proposed to solve the model. Using an authentication instance, we compare and analyze the performances of the MPSO method and the mixed integer programming (MIP) method in solving the model. Further, considering a commonly used system, we show the efficiency of the MPSO method in solving the model; we apply two case studies to illustrate the performance of the MPSO method in solving the thermal unit commitment (UC) problem. To demonstrate the effectiveness of the MPSO method in solving the UC problem, we use MPSO method, PSO-LR (Lagrangian relaxation) [H. H. Balci and J. Valenzuela, Int. J. Appl. Math. Comput. Sci. 14(3), 411–421 (1989)], improved PSO [B. Zhao et al., Elect. Power Energy Syst. 28, 482–490 (2006)], mimetic algorithm [J. Valenzuela and A. Smith, J. Heuristics 8(2), 173–195 (2002)], adaptive LR [W. Ongsakul and N. Petcharaks, IEEE Trans. Power Syst. 19(1), 620–628 (2004)], stochastic priority list (PL) [T. Senjyu et al., Electr. Power Syst. Res. 76, 283–292 (2006)], PL based evolutionary algorithm [D. Srinivasan and J. Chazelas, in International Conference on Power System Technology (2004), Vol. 90, pp. 1746–1751], enhanced adaptive LR [W. Ongsakul and N. Petcharaks, IEEE Trans. Power Syst. 19(1), 620–628 (2004)], mixed-integer linear programming (MILP) [M. Carrin and J. M. Arroyo, IEEE Trans. Power Syst. 21(1), 321–332 (2006)], MILP [G. Morales-Espana et al., IEEE Trans. Power Syst. 28, 4897 (2013)], NBD [T. Niknam et al., Appl. Energy 86, 1667–1674 (2009)], generalized new benders decomposition approach (NBD) [S. Rahimi et al., World Appl. Sci. J. 6(12), 1665–1672 (2009)], LR and genetic algorithm[C. P. Cheng et al., IEEE Trans. Power Syst. 15(2), 707–714 (2000)], and seeded memetic algorithm (SMA) [J. Valenzuela and A. Smith, J. Heuristics 8(2), 173–195 (2002)] to solve the UC problem, simulation results are compared with the ones obtained by other methods. It is shown that the optimal operation model is right, the MPSO method is better than MIP method in solving the model, and they have universality. The effectiveness of the MPSO method in solving the UC problem is better than other methods. The MPSO method has better solutions in comparison with other methods, especially for systems with a large number of units.

This paper considers the characteristics of hybrid flow shop with energy saving. First of all, established the model of hybrid flow shop with energy saving problem. Then Lagrangian relaxation was proposed to solve the energy scheduling problem in hybrid flow shop. Lagrangian relaxation algorithm introduced precedence constraints into the objective function, and the original problem was decomposed into a series of parallel machine sub-problems. A dynamic programming algorithm was then designed to solve these sub-problems. The method of updating of multiples was sub-gradient algorithm. Lastly, a two stage heuristic approach was constructed to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.

Generation Scheduling problem by Intelligent Genetic Algorithm

The optimal scheduling of power units to meet the estimated demand is called the unit commitment problem. Of the available methods for this problem, those using Lagrangean relaxation seem most promising. A description is given of the thermal unit commitment problem. Also given is a short survey of Lagrangean duality including some new techniques, which are applied to the unit commitment problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents an application of combined Lagrangian relaxation (LR) method and particle swarm optimization (PSO) technique for the Unit Commitment (UC) problem. This hybrid technique uses LR as the main algorithm. The LR method provides a fast solution, but it may suffer from numerical convergence and solution quality problem. The proposed algorithm uses PSO to update the Lagrangian multipliers and improve the performance of LR method. In this paper, ramp rate limit is also considered besides taking minimum up time and minimum down time of thermal units. The proposed method is implemented for solving two examples of UC test problems. The study results have shown that the approach developed is feasible and efficient.

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.