Hydrothermal scheduling by augmented Lagrangian: consideration of transmission constraints and pumped-storage units

Al-Agtash, Salem

doi:10.1109/59.962422

Cited by 67 publications

(16 citation statements)

References 16 publications

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“…Consequently, direct application of the standard Lagrangian relaxation technique will not be effective. The augmented Lagrangian [15]- [18] as opposed to the standard Lagrangian is thus used to overcome the linearity difficulty [19] and [20], while the surrogate optimization framework of [14] will be used to handle the inseparability difficulty.…”

Section: Solution Methodologymentioning

confidence: 99%

“…To solve , in view that there is no cross product term of MCPs for different hours and MCP-offer constraints have been relaxed, MCPs for different hours can be solved independently for a given set of . Therefore, by collecting all terms involving from (11) while keeping all other variables at their latest available values, MCP subproblems are formed, one for each (17) Similar to (13) for offer subproblems, a good direction for multiplier updating can be obtained if the following condition is satisfied for MCPs (18) To solve (17), note that consists of a linear term and multiple quadratic terms depending on the magnitude of of individual offers. If is positive, then the maximum term is a quadratic function of .…”

Section: Formulating and Solving Mcp Subproblemsmentioning

confidence: 99%

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Payment Cost Minimization Auction for Deregulated Electricity Markets Using Surrogate Optimization

Luh

Blankson

Chen

et al. 2006

IEEE Trans. Power Syst.

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Abstract-Deregulated electricity markets use an auction mechanism to select offers and their power levels for energy and ancillary services. A settlement mechanism is then used to determine the payments resulting from the selected offers. Currently, most independent system operators (ISOs) in the United States use an auction mechanism that minimizes the total offer costs but determine payment costs using a settlement mechanism that pays uniform market clearing prices (MCPs) to all selected offers. Under this setup, the auction and settlement mechanisms are inconsistent since minimized costs are different from payment costs. Illustrative examples in the literature have shown that for a given set of offers, if an auction mechanism that directly minimizes the payment costs is used, then payment costs can be significantly reduced as compared to minimizing offer costs. This observation has led to discussions among stakeholders and policymakers in the electricity markets as to which of the two auction mechanisms is more appropriate for ISOs to use. While methods for minimizing offer costs abound, limited approaches for minimization of payment costs have been reported. This paper presents an effective method for directly minimizing payment costs. In view of the specific features of the problem including the nonseparability of its objective function, the discontinuity of offer curves, and the maximum term in defining MCPs, our key idea is to use augmented Lagrangian relaxation and to form and solve offer and MCP subproblems by using the surrogate optimization framework. Numerical testing results demonstrate that the method is effective, and the resulting payment costs are significantly lower than what are obtained by minimizing the offer costs for a given set of offers.Index Terms-Augmented Lagrangian relaxation, deregulated electricity markets, market clearing price (MCP), offer cost minimization, payment cost minimization, surrogate optimization.

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Section: Solution Methodologymentioning

confidence: 99%

Section: Formulating and Solving Mcp Subproblemsmentioning

confidence: 99%

Payment Cost Minimization Auction for Deregulated Electricity Markets Using Surrogate Optimization

Luh

Blankson

Chen

et al. 2006

IEEE Trans. Power Syst.

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“…Dynamic optimal power flow (DOPF) is an extension of dynamic economic dispatch (DED) [1,2] and generation resource schedules (RS) [3][4][5][6][7]. DED and RS aim to determine the startup/shutdown and optimal dispatch scheme for various types of power plants accounting for dynamic (time-related) constraints.…”

Section: Introductionmentioning

confidence: 99%

Solving long time‐horizon dynamic optimal power flow of large‐scale power grids with direct solution method

Qin

Hou

et al. 2014

IET Generation, Transmission & Distribution

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Dynamic optimal power flow (DOPF) is an extension of optimal power flow for the optimal generation dispatch in a given time-horizon. The dynamic constraints bring tremendous numerical difficulties in solving this model. With particular attention to handle dynamic constraints, an efficient method has been presented for directly solving the large-scale DOPF Karush-Kuhn-Tucker (KKT) system arising from the primal-dual interior point method. First, the reduced KKT system is derived, showing that dynamic constraints lead to non-zeros in off-diagonal parts in the coefficient of KKT system. Then, the efficiency of the algorithm is improved by two measures: (i) to utilise the Cholesky factorisation algorithm, a constant diagonal perturbation is introduced in the positive-indefinite KKT coefficient and (ii) efficient reordering algorithms are identified and integrated in the sparse direct solver to improve the efficiency. Case studies on the IEEE 118-bus system over 24-96 time intervals are presented. These case studies show that the proposed method has a significant speed-up than decomposed interior point methods. The proposed method has also been successfully applied in Chinese realistic large-scale power grids. Two realistic case studies are reported. Both realistic cases have over 100 000 decision variables. NomenclatureF DOPF objective function f t generation cost at the tth time interval N t number of time intervals K number of blocks of dynamic constraints N d number of dynamic constraints N ineq number of inequality constraints in each time interval N eq number of equality constraints in each time interval N g number of generators N number of variables in each time interval L Lagrangian function μ barrier parameter ε convergence criteria a, b, c arrays of generation cost coefficients of all generators P gt , Q gt arrays of active and reactive power generation of generators at the tth time interval P lt , Q lt arrays of active and reactive load demands at the tth time interval V t ,V t arrays of complex bus voltage and its conjugation of all buses at the tth time interval Y conjugation of nodal admittance matrix S bt array of apparent power of branches at the tth time interval P g , P g , Q g , Q g arrays of lower and upper bound of active output of generators, lower and upper bound of reactive output of generators S b , S b arrays of lower and upper bound of apparent power of branches V , V arrays of lower and upper bound of all buses' voltages R, R arrays of lower and upper bound of generators' ramping rates C, C arrays of lower and upper bound of generators' generation contracts x t array of variables at the tth time interval x array of variables of the whole time-horizon www.ietdl.org & The Institution of Engineering and Technology 2014 h t , g tArrays of equality constraints and inequality constraints at the tth time interval g, g arrays of lower and upper bound of inequality constraints g d , g d arrays of lower and upper bound of dynamic constraints l t , u t arrays of lower and upper slack variables of ineq...

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“…This is unacceptable for system operators. For such a complicated optimization problem, a commonly used way is to decompose the original problem into several easily solved subproblems [18][19][20][21] according to the characteristics of the considered hydropower system. This method is also employed in the study.…”

Section: Introductionmentioning

confidence: 99%

Peak Operation of Cascaded Hydropower Plants Serving Multiple Provinces

et al. 2015

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Abstract:The bulk hydropower transmission via trans-provincial and trans-regional power networks in China provides great operational flexibility to dispatch power resources between multiple power grids. This is very beneficial to alleviate the tremendous peak load pressure of most provincial power grids. This study places the focus on peak operations of cascaded hydropower plants serving multiple provinces under a regional connected AC/DC network. The objective is to respond to peak loads of multiple provincial power grids simultaneously. A two-stage search method is developed for this problem. In the first stage, a load reconstruction strategy is proposed to combine multiple load curves of power grids into a total load curve. The purpose is to deal with different load features in load magnitudes, peaks and valleys. A mutative-scale optimization method is then used to determine the generation schedules of hydropower plants. In the second stage, an exterior point search method is established to allocate the generation among multiple receiving power grids. This method produces an initial solution using the load shedding algorithm, and further improves it by iteratively coordinating the generation among different power grids. The proposed method was implemented to the operations of cascaded hydropower plants on Xin-Fu River and another on Hongshui River. The optimization OPEN ACCESSEnergies 2015, 8 11296 results in two cases satisfied the peak demands of receiving provincial power grids. Moreover, the maximum load difference between peak and valley decreased 12.67% and 11.32% in Shanghai Power Grid (SHPG) and Zhejiang Power Grid (ZJPG), exceeding by 4.85% and 6.72% those of the current operational method, respectively. The advantage of the proposed method in alleviating peak-shaving pressure is demonstrated.

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Hydrothermal scheduling by augmented Lagrangian: consideration of transmission constraints and pumped-storage units

Cited by 67 publications

References 16 publications

Payment Cost Minimization Auction for Deregulated Electricity Markets Using Surrogate Optimization

Payment Cost Minimization Auction for Deregulated Electricity Markets Using Surrogate Optimization

Solving long time‐horizon dynamic optimal power flow of large‐scale power grids with direct solution method

Peak Operation of Cascaded Hydropower Plants Serving Multiple Provinces

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