Polynomial loss models for economic dispatch and error estimation

Jiang, Anning; Ertem, S.

doi:10.1109/59.466490

Cited by 16 publications

(7 citation statements)

References 5 publications

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“…Omitting the square root in the following relation : ( ) (1) P loss a a a aggregates P φ = ∑ ∈ requires the unrealistic assumption that the system losses are a separable function of the bus power injections. As shown in [2], polynomial loss models interpolating the points of load flow solutions suffer a high order error at other operating points : the polynomial coefficients deviate significantly from one base case to another. This suggests the use of functions φ a , quadratic on each interval [P a k , P a k+1 ], which respect : where lf k denotes the k'th load flow solution, so that, the vector of real powers at aggregates is equal to P .…”

Section: Polynomial Loss Modelsmentioning

confidence: 98%

“…However the short term forecasts require the identification of transmission loss coefficients from active generation measurements covering a wide operation range of the EHV/HV network. This paper combines the idea of piece-wise analytical loss model [2] and a parameter state estimation, the goal is an improvement of empirical equivalent hours loss factors [3,4] when the transmission losses depends significantly on generation schedules and wheeling. The practical use of the polynomial loss models is limited by the topology changes which affect the "commons" defined as the sets of contiguous busses supplied by the same generators [5].…”

Section: Polynomial Loss Modelsmentioning

confidence: 99%

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Estimation of transmission loss coefficients from measurements

Fliscounakis¹,

Lafeuillade²,

Limousin³

2005

2005 IEEE Russia Power Tech

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The French system's losses rise nearly up to 12 TWh per year, attributed to the Joule effect. Therefore, the purchase of losses is of high importance from both a technical and an economic point of view, as they are valued up to several hundreds MEuros per year. The problem addressed in this paper is the calculation of transmission loss coefficients when the only information available are active injections measurements and active balance sheets.Index Terms-power losses, transmission loss coefficients, weighted least absolute value estimation I. CONTEXTAs the French TSO, and according to French Law, RTE has to compensate for electrical losses on the EHV and HV networks (especially the current squared resistive losses ). These losses amount to around 12 TWh per year. In order to do this, in France, RTE buys from various sources (from the yearly horizon to D-2) the volume corresponding to the predicted losses. The challenge, therefore, is to secure predictions for these losses for the year down to 2 days. The functional analysis of theses questions is presented in [11]. We focus here on the detailed presentation of one of the models, which can be used for losses estimations (and then predictions). II. POLYNOMIAL LOSS MODELSWhen the network topology is perfectly known and remains constant, the transmission losses can be evaluated efficiently as a quadratic function of generating units through a set of ``A coefficients``. Nanda and all showed that these ``A-coefficients'' are robust and don't have to be re-evaluated, even for large changes in loading pattern of the system [1]. This approach requires a representative snapshot of system operating conditions used as a reference base case and a perturbation technique of the power generation at every plant bus. However the short term forecasts require the identification of transmission loss coefficients from active generation measurements covering a wide operation range of the EHV/HV network. This paper combines the idea of piece-wise analytical loss model [2] and a parameter state estimation, the goal is an improvement of empirical equivalent hours loss factors [3,4] when the transmission losses depends significantly on generation schedules and wheeling. The practical use of the polynomial loss models is limited by the topology changes which affect the "commons" defined as the sets of contiguous busses supplied by the same generators [5]. A consequence is, for example, that the branch power losses cannot be approximated by one set of ``A-coefficients`` when the time sample topologies do not share the same "connection key" which is simply composed of the numbers of generators connected on each plant of primary importance. This fact leads us to approximate the square root of global losses as the sum of piece-wise polynomial function of the active power generation at every aggregate. A generating plant having identical generating units acts as an aggregate. The net MW interchange can be thought of as power flowing into or out of the network from an aggregate of the tie lines....

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Section: Polynomial Loss Modelsmentioning

confidence: 98%

Section: Polynomial Loss Modelsmentioning

confidence: 99%

Estimation of transmission loss coefficients from measurements

Fliscounakis¹,

Lafeuillade²,

Limousin³

2005

2005 IEEE Russia Power Tech

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“…The main drawback of this method is that it enlarges the dimension of the system and hence the problem. Other conventional methods usually consider a slack bus to which all losses are allocated [14]. However, all generators are supposed to participate in supplying the losses.…”

Section: A Modeling Lossesmentioning

confidence: 99%

“…Under the dc approximation, and in the p.u. system, the losses in a transmission line whose resistance is can be expressed by (14) [18]: (14) The above equation is a quadratic function, but can be expressed with a piecewise linear model. If a linear model consisting of line pieces is assumed between and the equation of line piece can be formulated by (15) (see Fig.…”

Section: A Modeling Lossesmentioning

confidence: 99%

Transmission Network Planning Under Security and Environmental Constraints

Kazerooni

Mutale

2010

IEEE Trans. Power Syst.

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This paper explores the impact of CO 2 emission trading on capacity planning of electric power transmission systems. Two different models for annual emission costs are assumed. The CO 2 emission price is modeled as a probability density function in the transmission network planning problem.The Monte Carlo technique is deployed to simulate the CO 2 emission price volatility. The transmission network planning problem is formulated as a mixed-integer optimization whose objective is to minimize the sum of annual generator operating costs and annuitized transmission investment costs over different demand levels subject to N-1 network security constraints as well as operating limits on system components. The overall problem is formulated within the framework of a linear dc optimal power flow incorporating binary decision variables to model the lumpy nature of transmission investment. A linear model of losses is also proposed and included in the dc power flow model. The proposed approach can be used to determine the most probable optimal transmission capacity. The methodology is demonstrated through case studies simulated on the IEEE 24-bus network.

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“…Eventually, the base case value is subtracted from the new value to obtain the incremental loss and incremental power outputs, i.e., ∆P L and ∆P G . The computing procedure of loss coefficients mentioned above can be represented by Equations (12)- (15).…”

Section: Tl Formula Considering Real Power Outputmentioning

confidence: 99%

Derivation and Application of a New Transmission Loss Formula for Power System Economic Dispatch

et al. 2018

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Abstract:The expression and calculation of transmission loss (TL) play key roles for solving the power system economic dispatch (ED) problem. ED including TL must compute the total TL and incremental transmission loss (ITL) by executing power flow equations. However, solving the power flow equations is time-consuming and may result in divergence by the iteration procedure. This approach is unsuitable for real-time ED in practical power systems. To avoid solving nonlinear power flow equations, most power companies continue to adopt the TL formula in ED. Traditional loss formulas are composed of network parameters and in terms of the generator's real power outputs. These formulas are derived by several assumptions, but these basic assumptions sacrifice accuracy. In this study, a new expression for the loss formula is proposed to improve the shortcomings of traditional loss formulas. The coefficients in the new loss formula can be obtained by recording the power losses according to varying real and reactive power outputs without any assumptions. The simultaneous equations of the second-order expansion of the Taylor series are then established. Finally, the corresponding coefficients can be calculated by solving the simultaneous equations. These new coefficients can be used in optimal real and reactive power dispatch problems. The proposed approach is tested by IEEE 14-bus and 30-bus systems, and the results are compared with those obtained from the traditional B coefficient method and the load flow method. The numerical results show that the proposed new loss formula for ED can hold high accuracy for different loading conditions and is very suitable for real-time applications.

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Polynomial loss models for economic dispatch and error estimation

Cited by 16 publications

References 5 publications

Estimation of transmission loss coefficients from measurements

Estimation of transmission loss coefficients from measurements

Transmission Network Planning Under Security and Environmental Constraints

Derivation and Application of a New Transmission Loss Formula for Power System Economic Dispatch

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