Two‐stage minimax stochastic unit commitment

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

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.

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.

The authors propose an algorithm to consider the ramp characteristics in starting up and shutting down the generating units as well as increasing and decreasing power generation. They consider the inclusion of ramping constraints in both unit commitment and economic dispatch. Since implementing ramp-rate constraints is a dynamic process, dynamic programming (DP) is a proper tool to treat this problem. To overcome the computational expense which is the main drawback of DP, this study initially employs artificial intelligence techniques to produce a unit commitment schedule which satisfies all system and unit operation constraints except unit ramp-rate limits. Then, a dynamic procedure is used to consider the ramp properties as units are started up and shut down. According to this adjustment, maximum generating capabilities of units will change the unit operation status instead of following a step function. Finally, a dynamic dispatch procedure is adopted to obtain a suitable power allocation which incorporates the unit generating capability information given by unit commitment and unit ramping constraints, as well as the economical considerations. Two examples are presented to demonstrate the efficiency of the method. >

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.

To enhance the resilience of transmission systems with offshore wind farms before the advent of typhoons, a proactive unit commitment scheme is proposed. A novel scenario tree is proposed to quantify the uncertain impacts of typhoons on offshore wind farms, transmission lines, and system states, where the inertia support from offshore wind farms and random system state are in‐cooperated. The frequency security constraint is captured by a multi‐variative piece‐wise linear function, where the frequency nadir are simulated under varying inertia and disturbance combinations. The unit commitment problem is formulated as a two‐stage stochastic optimisation problem with nonlinear recourse. This problem is solved by a multi‐cuts Benders decomposition algorithm with finite iteration convergence property. Simulations are conducted on a modified IEEE‐RTS 79 test system with offshore wind farms. Results verify the effectiveness of the proposed model regarding the load shedding and frequency nadir enhancement.

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.

Full cover charging station location problem with routing

Unit Commitment (UC) problem plays a key role in power systems' operations. Due to the strong modeling capacity of robust optimization to capture various complicated uncertainties in power systems, including those in renewable generation, load realization, demand response, and contingencies, two-stage robust UC has gained intensive attentions from both academic scholars and industry practitioners. However, such tri-level optimization problem is very challenging to solve, considering large-scale real power grids. In this research, we study new computational methods and strategies to address this challenge, including incorporating strong formulations for basic UC model, deriving new valid inequalities considering network constraints, and designing and implementing a decomposition procedure. On large-scale test instances, our solution approach leads to significantly better computational performance, compared to existing formulations or methods.

This chapter describes and formulates three important problems for the economic management of power systems, namely, the Unit Commitment (UC), the Economic Dispatch (ED), and the Network Constrained Unit Commitment (NCUC) problems. The UC problem determines the commitment of generating units with the aim of minimizing operating costs while supplying the demand and meeting technical and security constraints. Then, once the commitment of generating units is decided, the ED problem determines the actual power output of each generating unit that is needed to supply all demands at minimum cost, while complying with the technical constraints of the transmission network. Finally, if both the commitment of generating units and transmission constraints are considered simultaneously, the resulting problem is known as the NCUC problem. These three problems are mostly considered in electricity markets throughout the US.

A rolling-horizon unit commitment framework with flexible periodicity

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

The paper presents a stochastic Hopfield artificial neural network for unit commitment and economic power dispatch. Because of uncertainties in both the system load demand and unit availability, the unit commitment and economic power dispatch problem is stochastic, in this paper we model forced unit outages as independent Markov processes, and load demand as a normal Gaussian random variable. The (0,1) unit commitment-status variables and the hourly unit loading are modelled as sample functions of appropriate random processes. They are solutions of appropriately derived stochastic differential equations which describe the dynamics of a stochastic system for which the operating cost function is a stochastic Lyapunov function. Once the unit commitment and economic power dispatch have been done, the corresponding production costs are computed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A layered matrix encoding cascade genetic algorithm and particle swarm optimization approach (GA-PSO) for unit commitment and economic load dispatch problem in a thermal power system is presented in this paper. The tasks of determining and allocating power generation to different thermal units in a way that the total power production cost is at the minimum subject to equality and inequality constraints makes unit commitment and economic load dispatch challenging. A case study, based on the thermal power generation problem presented in [1], is used to demonstrate the effectiveness of the proposed method in generating a cost-effective power generation schedule. The schedule obtained is compared with that of Linear Programming (LP) as reported in [1]. The results show that the proposed GA-PSO approach outperforms LP in solving the unit commitment and economic load dispatch problem for thermal power generation system in this case study.

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.