An Application of Interval Analysis and Optimization to Electric Energy Markets

Sarić, Andrija T.; Stanković, A.M.

doi:10.1109/tpwrs.2006.874539

Cited by 58 publications

(44 citation statements)

References 13 publications

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“…Additionally, it implies that the worst realization of uncertainty sets should be satisfied. The maximum and minimum power of a transmission line can be achieved only when the nodal injection uncertainty reaches its upper or lower bounds [10]. If one nodal injection uncertainty of bus i is DP i 2 ½DP i ; D P i , the maximum contribution of it to transmission constraints for transmission line l will be on the bound of the uncertainty set, depending on the sign of u l;i .…”

Section: Constraintsmentioning

confidence: 99%

“…However, the signs of the variables u l;i and u l;f are unknown and they depend on the balance mechanism for injection uncertainties, to be exact, the participation factors of conventional units shown in (21). Therefore, all possible combinations of signs of u l;i and u l;n should be considered to immunize all possible scenario realizations under interval uncertainties [10]. Thus the number of transmission constraints will be doubled for one more nodal injection uncertainty.…”

Section: Constraintsmentioning

confidence: 99%

“…Some use advanced mathematical techniques to model the uncertainties, including probabilistic distribution [6,7], fuzzy arithmetic [8,9] and interval arithmetic [10,11]. The former two descriptions require the knowledge of membership functions or probability distribution whereas the uncertainties can be easily described by interval arithmetic with upper and lower bounds, which coincides with the available load or wind power forecast methods [12,13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Frequency aware robust economic dispatch

Sun

Han

Zhang

et al. 2016

J. Mod. Power Syst. Clean Energy

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This paper proposes a novel frequency aware robust economic dispatch (FARED) approach to exploit the synergistic capability of accommodating uncertain loads and renewable generation by accounting for both the frequency regulation effect and optimal participation mechanism of secondary regulation reserves for conventional units in response to uncertainties in the robust optimization counterpart of security constrained economic dispatch. The FARED is formulated as a robust optimization problem. In this formulation the allowable frequency deviation and the possible load or renewable generation curtailments are expressed in terms of variable uncertainty sets. The variables in the formulation are described as interval variables and treated in affine form. In order to improve the computational tractability, the dominant constraints which can be the candidates of tight transmission constraints are determined by complementarity constraints. Then the robust optimization problem is simplified to a bilinear programming problem based on duality theory. Finally, the effectiveness and efficiency of the proposed method are illustrated based on several study cases.

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Section: Constraintsmentioning

confidence: 99%

Section: Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frequency aware robust economic dispatch

Sun

Han

Zhang

et al. 2016

J. Mod. Power Syst. Clean Energy

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“…In [15], an automatic contingency selection approach was proposed, based on DC power flow calculations using affine arithmetic and considering load and generation uncertainties. Interval algorithms including interval matrices [16][17][18], interval models [19], and interval optimization algorithms [20] have presented, and applied in various power system applications [21][22][23][24][25][26]. In [27], the interval entropy (IE) method was applied in financial engineering analysis to assess the predictability of finance markets; it has potential for power system applications.…”

Section: Introductionmentioning

confidence: 99%

Hybrid interval AHP-entropy method for electricity user evaluation in smart electricity utilization

Wang

Cai

et al. 2017

J. Mod. Power Syst. Clean Energy

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Smart electricity utilization (SEU) is one of the most important components in a smart grid. It is crucial to evaluate efficiency, safety, and demand response capability of electricity users to achieve the smart use of electricity. The analytic hierarchy process (AHP) uses subjective criteria to determine index weights in multi-criteria decisionmaking problems, while the entropy method provides objectivity in determining index weights. Taking into account the uncertainty of expert scoring and user data, a hybrid interval analytic hierarchy process (IAHP) and interval entropy (IE) method is proposed for electricity user evaluation (EUE). Specifically, in the proposed method, electricity users are evaluated in terms of energy efficiency, safety monitoring, and demand response. The weights of EUE indices are calculated under uncertainty. The proposed approach derives subjective weights of EUE indices by the IAHP with expert scoring as input data, and determines objective weights of EUE indices by the IE method with user data as inputs. In order to obtain the optimal combined index weights, the two weights are normalized by a selected weight factor. Numerical case studies illustrate the effectiveness and advantages of the proposed approach, which combines subjective and objective information to derive the optimal combined index weights.

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“…Widespread applications of interval arithmetic (IA) have appeared in recent years [9][10][11][12][13][14][15]. The uncertainty is an acute problem in power systems because of the complexity of power systems, so several interval arithmetic-based methods have been proposed for solving power system problems [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Power system transient stability simulation under uncertainty based on Taylor model arithmetic

Wang

Zheng

Wang

2009

Front. Electr. Electron. Eng. China

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The Taylor model arithmetic is introduced to deal with uncertainty. The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model (TM). Thus, time domain simulation under uncertainty is transformed to the integration of TM-based differential equations. In this paper, the Taylor series method is employed to compute differential equations; moreover, power system time domain simulation under uncertainty based on Taylor model method is presented. This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation. It is computationally fast compared with the Monte Carlo method, which is another technique for uncertainty analysis. The proposed method has been tested on the 39-bus New England system. The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.

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An Application of Interval Analysis and Optimization to Electric Energy Markets

Cited by 58 publications

References 13 publications

Frequency aware robust economic dispatch

Frequency aware robust economic dispatch

Hybrid interval AHP-entropy method for electricity user evaluation in smart electricity utilization

Power system transient stability simulation under uncertainty based on Taylor model arithmetic

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