Unit Commitment solution using an optimized genetic system

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. >

This paper studies how to sample load more realistically and efficiently for security constraint unit commitment (SCUC) problems in order to achieve a high degree of robustness of the unit commitment (UC) solution. For example, given the UC solution, 95% of load profiles can be supplied. Principal component analysis (PCA) is introduced to find a clear feature of the historical load in two-dimensional space rather than the original high-dimensional load space, whose feature is hard to capture. Kernel density estimation (KDE) with Gaussian kernel is applied to form the probability density function (PDF), from which hourly load profiles are sampled. The load profiles based on sparse sampling are used to find the UC solution with high robustness while the load profiles based on dense sampling are used to verify the robustness of the obtained UC solution.

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 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.

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.

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.

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.

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.

A novel projected two-binary-variable formulation for unit commitment in power systems

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.

Unified solution of a non-convex SCUC problem using combination of modified Branch-and-Bound method with Quadratic Programming

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.

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.