Unit commitment in interconnected generating systems using a probabilistic technique

Deterministic methods to evaluate unit commitment and spinning reserve requirements cannot explicitly recognise the stochastic nature of a power system. Probabilistic techniques can, however, be used to incorporate a wide range of stochastic system parameters. The usual techniques of probabilistic unit commitment in an interconnected power system consider the tie-line constraints but not the transmission facilities within the systems. In a real power system, the transmission facilities within the systems have limits and do fail. Units committed from only probabilistic generation studies, therefore, provide optimistic values. In the paper, the usual techniques of unit commitment are extended to calculate a risk value from a composite system point of view. The effect on the risk value of rapid start and hot reserve units are considered.

Low-carbon electric power systems are often characterized by high shares of renewables, such as wind power. The variable nature and limited predictability of some renewables will require novel system operation methods to properly size and cost-efficiently allocate the required reserves. The current state-of-the-art stochastic unit commitment models internalize this sizing and allocation process by considering a set of scenarios representing the stochastic input during the unit commitment optimization. This results in a cost-efficient scheduling of reserves, while maintaining the reliability of the system. However, calculation times are typically high. Therefore, in this paper, we merge a state-of-the-art probabilistic reserve sizing technique and stochastic unit commitment model with a limited number of scenarios in order to reduce the computational cost. Results obtained for a power system with a 30% wind energy penetration show that this hybrid approach allows to approximate the expected operational costs and reliability of the resulting unit commitment of the stochastic model at roughly one thirtieth of the computational cost. The presented hybrid unit commitment model can be used by researchers to assess the impact of uncertainty on power systems or by independent system operators to optimize their unit commitment decisions taking into account the uncertainty in their system.

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.

Researches on the unit commitment with transmission network have been reported recently. However, most of these researches mainly discussed the security constrained unit commitment, while the relationship between unit commitment and transmission losses was not considered. However, from the standpoint of operating reserve for ensuring power supply reliability, a unit commitment considering transmission losses is required. Further, under the deregulation and liberalization of the electric power industry, not only the line's security but also transmission losses are expected to play an important role in calculating the network access charge, and unit commitment taking into account transmission losses is also desired from this viewpoint. In this paper, a unit commitment approach with both transmission losses and line flow constraint is presented. Based on a heuristic iterative optimization method, first, an initial schedule is created by using a successively decommitting unit approach that is proposed in this paper. Then, we determine constraints included in the unit commitment schedule by a heuristic iterative optimization approach, in which an algorithm able to get rid of line overload by DC optimal power flow is developed. Through numerical simulations on two test power systems, the effectiveness of the proposed method is shown. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 142(4): 9–19, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10116

Unit commitment is an efficient method to lower the total cost of the power plant by scheduling units' generation and meeting the constraint condition. However, in practice, few power plants implement the algorithm for fear that the load response in the power plant would not be fast enough to track the unscheduled load demand from the power grid if some units of the power plant are shut down. This paper proposes a new unit commitment method that tries to solve this problem effectively. The proposed method guarantees the desired speed limit by setting the plant-level load tracking speed. In this method a ‘one-at-a-time’ unit commitment is accomplished. The most expensive unit (which is determined by computing its cost) is optimized, the unit commitment schedule is updated, and the load dispatch result is re-computed. The result will be repeatedly optimized until the spinning reserve or load tracking speed is lack. The optimization loop will breaks out as well if the unit schedules of two consecutive iterations over the time period remain unchanged. The test results from 10-machine system shows that the proposed method is easy to understand and quick to solve, and is of practical use.

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.

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.

Unit commitment (UC) plays a key role in power system operation and control. This paper deals with UC problem using hybrid Priority List (PL) method. Evolution Programming (EP), Hybrid Evolution Programming (HEP) and Gbest based Artificial Bee Colony (ABC) optimization algorithms are applied to 10 thermal unit system and are executed to achieve minimum operating cost by optimal scheduling of thermal units over a scheduled period. It is found from the comparison of these three algorithms that the Gbest based Artificial Bee Colony (ABC) yields the best optimum solution.

The authors present a thermal unit commitment method for interconnected multiarea power systems. The method is a natural extension of the commitment utilization factor (CUF)-based single-area unit commitment method. CUF is extended to reflect the impact of multiarea transmission interconnection constraints on the utilization efficiency of committing a candidate unit at a given priority position. The multiarea CUF is used in conjunction with the average full load cost. (AFLC) to efficiently determine the optimal or a near-optimal multiarea priority commitment order. This priority order is then used to generate the multiarea unit commitment schedule. The excellent quality of the results of the CUF-based multiarea method is consistent with that of the previously reported single-area method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A probabilistic technique is presented to evaluate the effect of standby units, interruptible load, postponable outages and margin time on the response well-being of a generation system. The well-being of the system is quantified in terms of system health and margin, in addition to the system risk index. A procedure is presented which utilises a least costly adjustment to determine how far the acceptable load dispatch must be displaced from the most economic one. A given load dispatch is considered to be acceptable if the response criterion is satisfied. Reliable power system operation requires that a generation system has high healthy state probability in both unit commitment and response studies. The concepts of unit commitment and response well-being are described pictorially to make them more understandable.

As an attempt to reduce reliance on fossil fuels to satisfy electricity demand, the penetration of renewable sources like wind or solar power has experienced rapid growth in recent years. Due to their intermittent nature, the exact contribution of renewable sources to electricity supply is at least partly unknown. In order to be able to accommodate this uncertainty in real-time, sufficient capacities in the form of thermal and hydro power plants must be available. On that account, power system operators solve the so-called unit commitment problem after bidding in the day-ahead market closes to derive schedules for their power plants which can ensure system reliability at low costs. In literature, two approaches have mainly been studied in this context: Robust and stochastic unit commitment. Being a worst-case formulation, robust unit commitment puts its focus on reliability. A common drawback of this approach is that it tends to deliver over-conservative schedules. Stochastic unit commitment on the other hand creates more cost-effective schedules by preparing for the expected case, but either fails to guarantee system reliability or puts a high workload on the CPU. The limitations of known formulations have sparked interest in so-called hybrid approaches, which aim at combining the ideas of robust and stochastic unit commitment in a favorable way. This paper reports a novel hybrid approach to solve the unit commitment under uncertainty, which yields both robust and cost-efficient schedules. The new method respects the continuous nature of uncertainties and is thus in particular favorable for applications in power systems with high penetration of volatile renewable sources. By merging the ideas of robust and stochastic unit commitment, the proposed hybrid formulation minimizes the expected worst-case dispatch costs. Our method relies on partitioning the continuous range of the uncertainties into subsets. By means of the number of partitions, the solution can be adjusted between the conservative robust and the cost-efficient stochastic unit commitment in a user-friendly manner. A Benders decomposition algorithm is derived to solve the hybrid unit commitment efficiently. Finally, a case study confirms the superior performance of the proposed method.

This paper focuses on the optimal unit commitment (UC) scheme along with optimal power trading for the Northeast Power System (NEPS) of Afghanistan with a penetration of 230 MW of PV power energy. The NEPS is the biggest power system of Afghanistan fed from three main sources; 1. Afghanistan’s own power generation units (three thermal units and three hydro units); 2. imported power from Tajikistan; 3. imported power from Uzbekistan. PV power forecasting fluctuations have been handled by means of 50 scenarios generated by Latin-hypercube sampling (LHS) after getting the point solar radiation forecast through the neural network (NN) toolbox. To carry out the analysis, we consider three deterministic UC and two stochastic UC cases with a two-stage programming model that indicates the day-ahead UC as the first stage and the intra-day operation of the system as the second stage. A binary-real genetic algorithm is coded in MATLAB software to optimize the proposed cases in terms of thermal units’ operation costs, import power tariffs, as well as from the perspective of the system reliability risks expressed as the reserve and load not served costs. The results indicate that in the deterministic UC models, the risk of reserve and load curtailment does exist. The stochastic UC approaches including the optimal power trading are superior to the deterministic ones. Moreover, the scheduled UC costs and reserves are different from the actual ones.

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.

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

Unit commitment (UC) is a problem to economically determine the commitment status and generation level for each thermal unit during each time interval of the scheduled periods. The purpose of UC is to minimize the total generation cost while satisfying system demand, reserve requirements, and other unit constraints. The combined-cycled units have been increasingly installed throughout the world because of their high efficiency and fast response. However, the combined-cycle units usually have multiple operating configurations. The multi-configuration characteristic causes that the UC problem is more complex and difficult to be solved. In this paper, the authors present a simplified combined-cycled unit model to efficiently solve the related mixed integer linear programming-based UC problem. By simulating two test systems, results show that the proposed model is effective to reduce the complexity of problem with losing little solution accuracy.