Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation

One of the common problems faced by many electric utilities concernes with the uncertainty from both load forecast error and generating unit unavailability. This uncertainty might lead to uneconomic operation if it is not managed properly in the planning stage. This paper explicitly demonstrates how to include the uncertainties to obtain the best operating strategy for any power systems. The uncertainty of the load forecast is handled using decision analysis method, meanwhile the uncertainty of the generating unit is approached by inclusion of risk cost to the total cost. In addition, three spinning reserve strategies based on deterministic criteria are incorporated in the development of scenario. Meanwhile, Mixed Integer Linear Programming method is utilized to generate unit commitment decision in each created scenario. The best strategy which gives the minimum total cost is selected among the developed scenarios. The flowchart of the proposed method is shown in Fig. 1.The proposed method has been implemented to solve a modified IEEE 24-bus system comprising 26 generating units. Three spinning reserve strategies based on deterministic criteria are set for each hour at 8%, 10%, and 12% of the load demand, representing low, medium and high spinning reserve strategy respectively. Meanwhile, the demand uncertainty is modeled by low, medium, and high Fig. 1. Flowchart of the proposed method load level with its associated probability. The load forecast uncertainty is represented by the standard deviation (SD), i.e. x% of the expected values. Sensitivity analysis with respect to the number of unit, expected unserved energy (EUE) price, standard deviation of load forecast, and probability of load level is reported.In the sensitivity analysis of number of unit, the IEEE test system is duplicated to be 26-unit, 78-unit and 130-unit system representing small, medium, and large-scale system. The load forecast error represented by SD is assumed to be 1% of the forecast value in the first hour and linearly increased to 4% in the last hour. The EUE is priced at 2000 $/MWh. The results shows that the generation cost for each scenario is a litlle bit different whereas the risk cost is rather different from each other.The impact of the load forecast error is analyzed through the variation of standard deviation (SD) values. In this analysis, it is supposed that the SD is assumed to be 1% of the forecasted value in the first hour, and is treated as either a constant value for the whole lead time of 24 hours or linearly increased to 2-4% in the last hour. The results show that with higher forecast error, i.e. higher SD, the total cost obtaied from the best strategy tends to decrease. However, as the system becomes larger, lower reserve strategy tends to be more appropiated, since the risk cost contribution to the total cost is relatively small. EUE price is varied to verify its impact on the operating strategy. It can be noticed that if the risk cost is neglected from our consideration, i.e. EUE price is set at zero, the lower spin...

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“…The proposed method has been implemented to solve a modified IEEE 24-bus system (5) comprising 26 generating units as shown in Fig. 4.…”

Section: Numerical Resultsmentioning

confidence: 99%

Short-term Operating Strategy with Consideration of Load Forecast and Generating Unit Uncertainty

Sarjiya

Eua‐arporn

Yokoyama³

2007

IEEJ Trans. PE

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“…These include deterministic, meta-heuristic, and hybrid approaches. Deterministic approaches include the priority list method [4], dynamic programming [5], Lagrangian Relaxation (LR) [6], integer/mixed-integer programming [7], [8], and the branch-andbound methods [9]. Due to the mixed binary and continuous variable nature, of the short term scheduling problem traditional optimization techniques may miss the optimal solution.…”

Section: Unmanaged Short-term Scheduling Of Fcppsmentioning

confidence: 99%

Smart Energy Management of Multiple Full Cell Powered Applications

Alam¹

2007

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DOE Project Officer:Mr. Stephen Waslo Objectives• To demonstrate the most effective design and protection scheme of minigrid power system for multiple fuel cell power plants application • To define the most economical operational schedule for the multiple fuel cell in terms of electrical, thermal and hydrogen production • To lay the bases for generation of hydrogen using the photoelectrochemical solar cells • To develop models for hydrogen production, purification, and storage systems • To demonstrate that smart energy management and control of a fuel cell power sources when subjected to varying demands of electrical and thermal loads together with demand of hydrogen production. Executive SummaryFuel cells, as a distributed energy source, are considered as one of the most promising sources of electrical energy that can meet the increasing demand and environmental constraints. To understand how the fuel cell behaves in a multi-unit generation environment, the research team designed a minigrid system with five fuel cells connected in parallel to feed five different neighborhoods. The thermal power, cogenerated from the fuel cells, is used to feed part of the neighborhood thermal load. In addition, the research team developed smart energy management control software to guarantee that the total power consumption of a typical residential home remains below the available power generated from a fuel cell. Generating hydrogen to feed the fuel cells is one of the main objectives of this project. New materials that help in producing hydrogen from water using sunlight are investigated. Another objective of this research is to investigate the application of small power fuel cells for portable applications. The research team investigated the feasibility of using fuel cells to feed the power to a laptop computer. In addition, using storage devices such as supercapacitor with the fuel cell to meet the sharp change in the laptop computer load is also investigated. Based on the economical analysis of the system and experimental results, we infer that a distributed energy system consisting of multiple fuel cells is a viable and feasible option to supply electrical and thermal power to a minigrid system. OverviewIn this research project the University of South Alabama research team has been investigating smart energy management and control of multiple fuel cell power sources when subjected to varying demands of electrical and thermal loads together with demands of hydrogen production. This research has focused on finding the optimal schedule of the multiple fuel cell power plants in terms of electric, thermal and hydrogen energy. The optimal schedule is expected to yield the lowest operating cost. Our team is also investigating the possibility of generating hydrogen using photoelectrochemical (PEC) solar cells through finding materials for efficient light harvesting photoanodes. The goal is to develop an efficient and cost effective PEC solar cell system for direct electrolysis of water. In addition, models for hydrogen production...

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“…where is the number of buses; is the number of transmission lines; referring to [17] is power transfer distribution factor of bus to line ; ∧ , ∧ , and ∧ represent the generator , wind farm , and load connected to bus , respectively; + and − are the maximum positive and negative power flows of line during period ; w,3 and w,4 are the decision variables of power output of wind farm under the worst-case scenario for the positive and negative transmission flow constraint;…”

Section: Transmission Flow Constraintsmentioning

confidence: 99%

“…where (23) is the objective function of the upper model, where x is the column vector of decision variables composed of the discrete variables , , and , y is the column vector of decision variables composed of the continuous variables , (5) and (7)- (8), Hy ≤ h represents (16), (17), and (22), Ax + By ≤ m represents (3), (9), (18), and (19), Ix + Jy = n represents (2); the extremal problem min y (Cx + Dy) = Ky of the lower model represents (10), (12), (14), and (15), min y (Mx + Ny) ≥ k represents (10)- (13), (20), and (21), F, E, H, A, B, I, J, C, D, K, G, M, N, and Q are the coefficient matrixes, and f, e, h, m, n, v, g, and q are the coefficient column vectors.…”

Section: Construction Of a Single-level And Two-stage Robustmentioning

confidence: 99%

Two‐Stage Robust Security‐Constrained Unit Commitment with Optimizable Interval of Uncertain Wind Power Output

Dayan

Zhang

et al. 2017

Mathematical Problems in Engineering

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Because wind power spillage is barely considered, the existing robust unit commitment cannot accurately analyze the impacts of wind power accommodation on on/off schedules and spinning reserve requirements of conventional generators and cannot consider the network security limits. In this regard, a novel double-level robust security-constrained unit commitment formulation with optimizable interval of uncertain wind power output is firstly proposed in this paper to obtain allowable interval solutions for wind power generation and provide the optimal schedules for conventional generators to cope with the uncertainty in wind power generation. The proposed double-level model is difficult to be solved because of the invalid dual transform in solution process caused by the coupling relation between the discrete and continuous variables. Therefore, a two-stage iterative solution method based on Benders Decomposition is also presented. The proposed double-level model is transformed into a single-level and twostage robust interval unit commitment model by eliminating the coupling relation, and then this two-stage model can be solved by Benders Decomposition iteratively. Simulation studies on a modified IEEE 26-generator reliability test system connected to a wind farm are conducted to verify the effectiveness and advantages of the proposed model and solution method.

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Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation

Cited by 465 publications

References 19 publications

Short-term Operating Strategy with Consideration of Load Forecast and Generating Unit Uncertainty

Short-term Operating Strategy with Consideration of Load Forecast and Generating Unit Uncertainty

Smart Energy Management of Multiple Full Cell Powered Applications

Two‐Stage Robust Security‐Constrained Unit Commitment with Optimizable Interval of Uncertain Wind Power Output

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