Solving the unit commitment problem in large systems using hybrid PSO algorithms

In this paper, an probability offset BPSO (binary particle swarm) method is proposed to solve the unit commitment problems in power systems with wind farms. Firstly, the initial unit commitment is determined by the prioritization method, and according to this result, the range of an optimization window is determined, and the BPSO is used to solve the solution in this range. During each iteration, the heuristic adjustment strategy enables the particles in each generation to meet the constraints. On the issue of economic load distribution, the classical Lagrange multiplication method combined with the dichotomy method is used to solve the problem, which greatly improves the efficiency of the solution. Finally, the results obtained are compared with those obtained by other algorithms, which proves that the proposed method has strong superiority and practicability.

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

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

Guest Editorial: Situational awareness of integrated energy systems

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.

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.

Unit Commitment is one of the most complex and difficult optimization problem in power systems. The objective of the optimal commitment is to determine the on/off states of the units in the system to meet the load demand and spinning reserve requirements at each time period, such that the overall cost of generation is minimized, while satisfying the various operational constraints. This paper presents the application of an improved genetic algorithm (GA) with crossover, mutation, and advanced operators such as repair and swap mutation to determine the commitment order of the thermal units in power generation. The proposed GA has been successfully applied to 10 and 26 generating-unit systems. Robustness of the proposed GA is demonstrated by comparison to the dynamic programming algorithm. The comparison results show the effectiveness of the proposed GA in solving the unit commitment problem with sufficient accuracy and low computational time.

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.

Unit Commitment (UC) is an essential decision taken by ISO to ensure reliable and economic operation of the power system. Renewable energy penetration is increasing in a power system due its inexhaustive and environment friendly nature. Renewable energy poses some challenges to the present power systems due to its high uncertainty. In addition to this, the impact of contingencies on the power system also cannot be ignored. Both renewable energy and contingencies make the power system more prone to uncertain behaviour which can affect the economics as well as reliability of the power system. In this paper, UC is solved using deterministic and stochastic approaches. Deterministic UC considers forecasted wind data and Stochastic UC considers uncertain scenarios of the wind. Practically the power system is more prone to uncertainty because of renewable energy penetration and contingencies. Thus, this paper discusses how a UC decision varies as more uncertainties arises. Mixed Integer Linear Programming (MILP) is used for obtaining the UC decision results for IEEE 30-bus system. The results of UC, power dispatch and generation costs obtained with the two approaches have been compared.

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

Nowadays, in power systems, we still lack the existence of standardized test systems that can be used to benchmark the performance and solution quality of proposed optimization techniques. Several authors report that the electric load pattern is very complex. It is therefore necessary to develop new methods for design of test cases for economic analysis in power systems. Therefore, we compared two methods to generate test systems: time series model and a method simulating stable random variables based on the use of Chambers-Mallows-Stuck. This paper describes a method for simulating stable random variables in the generation of test systems for economic analysis in power systems. A study focused on generating test electrical systems through stable distribution to model for unit commitment problem in electrical power systems. Usually, the instances of test systems in unit commitment are generated using normal distribution, but the behavior of electrical demand does not follow a normal distribution; in this work, simulation data are based on a new method. For empirical analysis, we used three original systems to obtain the demand behavior and thermal production costs. Numerical results illustrate the applicability of the proposed method by solving several unit commitment problems directly and through the Lagrangian relaxation of the original problem. All Rights Reserved © 2015 Universidad Nacional Autonoma de Mexico, Centro de Ciencias Aplicadas y Desarrollo Tecnologico. This is an open access item distributed under the Creative Commons CC License BY-NC-ND 4.0.

The principle of power determined by heat and the anti-peak-regulation characteristics of wind power output cause the difficulty of peak regulation in the power grid along with the production of the abandon wind. By analyzing the topological differences between power system and thermal system, establishing positive and negative spinning reserve constraints of the district heating network, and considering both the hot and the cold start-up cost of the units as well as the thermoelectric coupling of the CHP units, a unit commitment model of wind power accommodation in combined heat and power system— whose objective function is to minimize the total coal consumption and environmental cost of the units—is presented in this paper. In this model, unit commitment and optimized dispatch are combined, the electric load is shared by all the units, and the heat load is balanced by the local CHP plants respectively. Finally, the optimization results show that while meeting power and heat load demand, the model of this paper can timely start up or shut down units according to load change and spinning reserve demand, reduce total minimum technical output of operating units, and further improve wind power accommodation rate.

Operation of a large power system with maintaining proper power quality is always been a difficult task. It becomes more difficult to maintain the power quality when rapid expansion of previously designed power system occurred. To redesign of such a power system is not feasible and also cost effective. To improve the quality of power of such a large system, conventional methods of compensation can be used. In this paper a power system of 419 buses is analyzed. It is found that 76 buses have under voltage problem. Conventional shunt compensation method is used by connecting capacitor in parallel to the bus. After compensation the system is simulated again and found that the under voltage problem of this large power system is removed. Power factor of the system is also improved.

Unit Commitment is usually formulated as a Mixed Binary Linear Programming (MBLP) problem. When considering a large number of units, state-of-the-art methods such as branch-and-cut may experience difficulties. To address this, an important but much overlooked direction is formulation transformation since if the problem constraints can be transformed to directly delineate the convex hull in the data pre-processing stage, then a solution can be obtained by using linear programming methods without combinatorial difficulties. In the literature, a few tightened formulations for single units with constant ramp rates were reported without presenting how they were derived. In this paper, a systematic approach is developed to tighten formulations in the data pre-processing stage. The idea is to derive vertices of the convex hull without binary requirements. From them, vertices of the original convex hull can be innovatively obtained. These vertices are converted to tightened constraints, which are then parameterized based on unit parameters for general use, tremendously reducing online computational requirements. By analyzing short-time horizons, e.g., two or three hours, tightened formulations for single units with constant and generation-dependent ramp rates are obtained, beyond what is in the literature. Results based on the IEEE 118-bus and Polish 2383-bus systems demonstrate computational efficiency and solution quality benefits of formulation tightening. The approach is general and has great potential for tightening complicated MBLP problems in power systems and beyond.

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.