Unit Commitment Algorithm Research Articles

Value of stochastic reserve policies in low-carbon power systems

The intermittent nature of wind power and the high ratings of next-generation nuclear units mean that low-carbon power systems will have high short-term reserve requirements, if these requirements are determined using current methods. Meanwhile, the flexible fossil-fuel generators, which have been the traditional providers of reserve services, will run much less frequently. A fundamental review of the reserve requirement is therefore needed if power systems are to absorb high wind penetrations in an efficient manner. A fast Stochastic Unit Commitment algorithm is presented, which accounts for the uncertainties in demand, wind power and thermal generator outages, and schedules both frequency response (primary reserve) and longer-term reserves considering the costs and benefits of their provision. It is shown through multi-year simulations that stochastic scheduling can have substantial benefits at high wind penetrations, in terms of wind curtailment and efficient running of the flexible generators. Under the assumptions made, the cost reduction, compared with system operation under current reserve requirements, is about 4 per cent at a 50 per cent penetration.

An Advanced Quantum-Inspired Evolutionary Algorithm for Unit Commitment

Based on a quantum-inspired evolutionary algorithm for unit commitment, this paper proposed ways to advance the efficiency and robustness of the algorithm so that its capacity for application in large-scale unit commitment problems can be significantly enhanced. The paper develops an advanced quantum-inspired evolutionary unit commitment algorithm by developing a new initialization method based on unit priority list and a special Q-bit expression for ensuring diversity in the initial search area for improving the efficiency of solution searching. Different techniques such as multi-observation, single-search, and group-search are also proposed for incorporation in the advanced algorithm. The advanced algorithm is tested and compared with the earlier quantum-inspired evolutionary algorithm and a number of known methods through its applications to test systems with up to 100 generator units for a 24-h scheduling horizon.

Influence of feasibility constrains on the bidding strategy selection in a day-ahead electricity market session

Large part of liberalized electricity markets, including the Italian one, features an auction mechanism, called day-ahead energy market, which matches producers’ and buyers’ simple bids, consisting of energy quantity and price pairs. The match is achieved by a merit-order economic dispatch procedure independently applied for each of the hours of the following day. Power plants operation should, however, take into account several technical constraints, such as maximum and minimum production bounds, ramp constraints and minimum up and downs times, as well as no-load and startup costs. The presence of these constraints forces to adjust the scheduling provided by the market in order to obtain a feasible scheduling. The paper presents an analysis of the possibility and the limits of taking into account the power plants technical constraints in the bidding strategy selection procedure of generating companies (Gencos). The analysis is carried out by using a computer procedure based both on a simple static game-theory approach and on a cost-minimization unit-commitment algorithm. For illustrative purposes, we present the results obtained for a system with three Gencos, each owning several power plants, trying to model the bidding behaviour of every generator in the system. This approach, although complex from the computational point of view, allows an analysis of both price and quantity bidding strategies and appears to be applicable to markets having different rules and features.

A dynamic regrouping based sequential dynamic programming algorithm for unit commitment of combined heat and power systems

This paper addresses the unit commitment (UC) in multi-period combined heat and power (CHP) production planning under the deregulated power market. In CHP plants (units), generation of heat and power follows joint characteristics, which implies that it is difficult to determine the relative cost efficiency of the plants. We introduce in this paper the DRDP-RSC algorithm, which is a dynamic regrouping based dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units, sequential commitment of units in small groups. Relaxed states of the plants are used to reduce the dimension of the UC problem and dynamic regrouping is used to improve the solution quality. Numerical results based on real-life data sets show that this algorithm is efficient and optimal or near-optimal solutions with very small optimality gap are obtained.

Power generation scheduling algorithm using dynamic programming

Power generation scheduling is a constrained optimization problem whose solution determines the set of generating units, among those owned by the electric utility, that should be connected to the grid at any hourly interval over a period of time, lasting from a day to a week, such that an objective function–usually, cost of operation–, is minimized. The actual power generation allocated to each committed unit is typically determined by an economic dispatch to meet the actual system load demand that may deviate from the forecasted one. Dynamic programming is considered an effective solution technique in power systems, not only because scheduling is naturally a sequential decision process, but also because formulation of the unit commitment problem results in a non-linear, non-convex, time dependent, and mix-integer problem that is not easily amenable to other solution techniques. Although dynamic programming-based solution algorithms provide optimal commitment schedules, execution time and memory requirements are affected by the “curse of dimensionality,” that is by the number of unit combinations to be considered in the solution process. In dynamic programming-based power scheduling algorithms, thousands of hourly economic dispatches must be performed to consider every possible unit combination over all the stages of the optimization interval. If the unit commitment problem is constrained to observe a minimum system spinning reserve and an economic dispatch of a combination of units does not comply with this requirement, necessary and sufficient conditions have been established to guarantee that the dispatch of these units will meet the constraint. However, these conditions can only be checked for feasibility after a dispatch is performed. In this paper, we present necessary and sufficient conditions for the feasibility of unit combinations that can be checked off-line — that is, before the start of the unit commitment algorithm, and thus before any economic dispatches are performed, thereby rendering a very efficient unit scheduling algorithm in terms of computer memory and execution time. Moreover, these feasibility conditions are independent of the problem formulation and thus can easily be applied to other unit commitment algorithms. Examples are provided to illustrate the efficiency attainable by the implementation of these conditions.

A variant of the dynamic programming algorithm for unit commitment of combined heat and power systems

Abstract The paper addresses the unit commitment in multi-period combined heat and power (CHP) production planning under the deregulated power market. In CHP plants (units), generation of heat and power follows joint characteristics, which means that production planning must be done in coordination. We introduce in this paper the DP-RSC1 algorithm, which is a variant of the dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units and sequential commitment of units one by one . The time complexity of DP-RSC1 is proportional to the number of generating units in the system, the number of periods over the planning horizon and the time for solving a single-period economic dispatch problem. We have compared the DP-RSC1 algorithm with realistic power plants against the unit decommitment algorithm and the traditional priority listing method. The results show that the DP-RSC1 algorithm gives somewhat more accurate results (0.08–0.5% on average, maximum 10% for the individual sub-case) and executes 3–5 times faster on average than the unit decommitment algorithm. It is not surprising that the solution quality of the DP-RSC1 algorithm is much better than that of the priority listing method.

Security-Constrained Unit Commitment With Volatile Wind Power Generation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a security-constrained unit commitment (SCUC) algorithm which takes into account the intermittency and volatility of wind power generation. The UC problem is solved in the master problem with the forecasted intermittent wind power generation. Next, possible scenarios are simulated for representing the wind power volatility. The initial dispatch is checked in the subproblem and generation redispatch is considered for satisfying the hourly volatility of wind power in simulated scenarios. If the redispatch fails to mitigate violations, Benders cuts are created and added to the master problem to revise the commitment solution. The iterative process between the commitment problem and the feasibility check subproblem will continue until simulated wind power scenarios can be accommodated by redispatch. Numerical simulations indicate the effectiveness of the proposed SCUC algorithm for managing the security of power system operation by taking into account the intermittency and volatility of wind power generation. </para>

Dynamic double-population particle swarm optimization algorithm for power system unit commitment

Dynamic Double-population Particle Swarm Optimization (DDPSO) algorithm was presented to solve the problem that the standard PSO algorithm easily fell into a locally optimized point, where the population was divided into two sub-populations varying with their own evolutionary learning strategies and exchanging between them. The algorithm had been applied to power system Unit Commitment (UC). The DDPSO particle consisted of a two-dimensional real number matrix representing the generation schedule. According to the proposed coding manner, the DDPSO algorithm could directly solve UC. Simulation results show that the proposed method performs better in term of precision and convergence property.

An improved particle swarm optimization algorithm for unit commitment

This paper presents an improved particle swarm optimization algorithm (IPSO) for power system unit commitment. IPSO is an extension of the standard particle swarm optimization algorithm (PSO) which uses more particles’ information to control the mutation operation, and is similar to the social society in that a group of leaders could make better decisions. The convergence property of the proposed IPSO method is analyzed using standard results from the dynamic system theory and some guidelines are derived for proper algorithm parameter selection. A new adaptive strategy for choosing parameters is also proposed to assure convergence of IPSO method, and the proposed algorithm adopts the orthogonal design to generate initial population that are scattered uniformly over feasible solution space. Furthermore, this method combines relaxation technique to zero-one variable and penalty function method to transform the problem to a nonlinear continuous variable optimization one by taking into account more constraints. The feasibility of the proposed method is demonstrated from 10 to 100 unit systems, and the test results are compared with those obtained by Evolutionary Programming (EP) and Genetic Algorithm (GA) in terms of solution quality and convergence properties. The simulation results show that the proposed method is capable of obtaining higher quality solutions.

Using chaos search immune genetic and fuzzy system for short-term unit commitment algorithm

This paper presents a hybrid chaos search (CS) immune algorithm (IA)/genetic algorithm (GA) and fuzzy system (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shut-down 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 chaos search and the fuzzy system approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20 and 30 thermal unit power systems over a 24 h 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). A comparison with an IGA combined with the chaos search and FS was carried out. The results show that the chaos search and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.

Simulated annealing with local search-a hybrid algorithm for unit commitment

A hybrid algorithm has been developed for the solution of the unit commitment problem. This hybrid technique uses simulated annealing as the main algorithm. At each temperature, fresh solutions are generated randomly, and with a high likelihood of being feasible. Local search is made in the neighborhood of the best solution, using a heuristic decommitment technique. The hybrid algorithm is robust and has improved convergence, compared with earlier algorithms. The results obtained in system studies indicate its potential for solving the unit commitment problem.

Simulated Annealing with Local Search: A Hybrid Algorithm for Unit Commitment

Simulated Annealing with Local Search: A Hybrid Algorithm for Unit Commitment

Cutting plane methods for Lagrangian relaxation‐based unit commitment algorithm

AbstractIn this paper, we study cutting plane methods for a Lagrangian relaxation‐based unit commitment algorithm. In the algorithm, nondifferentiable optimization methods can be applied to optimize the dual function, and a subgradient method which needs parameter tuning and has some drawbacks such as computational inefficiency and oscillating behavior is commonly used. The cutting plane method and the central cutting plane method are applied to the algorithm and implemented using reoptimization techniques. A numerical example shows that both methods are accelerated by the reoptimization techniques and have good convergence without parameter tuning. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 141(3): 17–29, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10066

Cooperative coevolutionary algorithm for unit commitment

This paper presents a new cooperative coevolutionary algorithm (CCA) for power system unit commitment. CCA is an extension of the traditional genetic algorithm (GA) which appears to have considerable potential for formulating and solving more complex problems by explicitly modeling the coevolution of cooperating species. This method combines the basic ideas of Lagrangian relaxation technique (LR) and GA to form a two-level approach. The first level uses a subgradient-based stochastic optimization method to optimize Lagrangian multipliers. The second level uses GA to solve the individual unit commitment sub-problems. CCA can manage more complicated time-dependent constraints than conventional LR. Simulation results show that CCA has a good convergent property and a significant speedup over traditional GAs and can obtain high quality solutions. The "curse of dimensionality" is surmounted, and the computational burden is almost linear with the problem scale.

Cooperative Coevolutionary Algorithm for Unit Commitment

This paper presents a new cooperative coevolutionary algorithm (CCA) for power system unit commitment. CCA is an extension of the traditional genetic algorithm (GA) which appears to have considerable potential for formulating and solving more complex problems by explicitly modeling the coevolution of cooperating species. This method combines the basic ideas of Lagrangian relaxation technique (LR) and GA to form a two-level approach. The first level uses a subgradient-based stochastic optimization method to optimize Lagrangian multipliers. The second level uses GA to solve the individual unit commitment sub-problems. CCA can manage more complicated time-dependent constraints than conventional LR. Simulation results show that CCA has a good convergent property and a significant speedup over traditional GAs and can obtain high quality solutions. The curse of dimensionality is surmounted, and the computational burden is almost linear with the problem scale.

A practical algorithm for unit commitment based on unit decommitment ranking

AbstractThis paper presents a practical algorithm for solving Unit Commitment (UC) problems with network constraints represented in Optimal Power Flow (OPF). The proposed algorithm is based on Successive Approximation Dynamic Programming (SADP) according to a Unit Decommitment Ranking (UDR) which is a priority list for unit decommitment procedure. The UDR can be determined by Dynamic Programming (DP) according to the information of OPF consisting of a set of Lagrange multipliers (dual variables). Since the set of Lagrange multipliers represents the relationship between the optimal value of objective function and OPF constraints, the proposed algorithm can determine power system resource scheduling in consideration of network constraints, such as line flow and voltage constraints. The feasibility and effectiveness of the proposed algorithm are demonstrated on a modified IEEE Reliability Test System. © 2001 Scripta Technica, Electr Eng Jpn, 138(2): 1–13, 2002

Knowledge-based genetic algorithm for unit commitment

A genetic algorithm (GA) augmented with knowledge-based methods has been developed for solving the unit commitment economic dispatch problem. The GA evolves a population of binary strings which represent commitment schedules. The initial population of schedules is chosen using a method based on elicited scheduling knowledge. A fast rule-based dispatch method is then used to evaluate candidate solutions. The knowledge-based genetic algorithm is applied to a test system of ten thermal units over 24-hour time intervals, including minimum on/off times and ramp rates, and achieves lower cost solutions than Lagrangian relaxation in comparable computational time.

切除平面法を用いたラグランジュ緩和法による発電機起動停止計画について

切除平面法を用いたラグランジュ緩和法による発電機起動停止計画について

A new economic dispatch algorithm considering any higher order generation cost functions

In this paper, a new Economic Dispatch (ED) algorithm for Unit Commitment (UC) is proposed to improve both the accuracy of the final solution and the calculation speed of ED. By using the inverse incremental cost functions, ED can be transformed into a simple optimization problem associated with an nth order polynomial equation. The proposed method remarkably reduces the computation time with adaptability to any higher order generation cost functions. The proposed method is tested with sample systems, which shows that the proposed algorithm yields more accurate and economical generation scheduling results with a high computation speed.

A profit-based unit commitment GA for the competitive environment

As the electrical industry restructures, many of the traditional algorithms for controlling generating units need modification or replacement, previously utilized to schedule generation units in a manner that minimizes costs while meeting all demand, the unit commitment (UC) algorithm must be updated. A UC algorithm that maximizes profit will play an essential role in developing successful bidding strategies for the competitive generator. Simply bidding to win contracts is insufficient; bidding strategies must result in contracts that, on average, cover the total generation costs. No longer guaranteed to be the only electricity supplier, a generation company's share of the demand will be more difficult to predict than in the past. Removing the obligation to serve softens the demand constraint. In this paper the authors provide a price/profit-based UC formulation which considers the softer demand constraint and allocates fixed and transitional costs to the scheduled hours. The authors describe a genetic algorithm solution to this new UC problem and present results for an illustrative example.