Point Estimate Method Addressing Correlated Wind Power for Probabilistic Optimal Power Flow

Saunders, Chris

doi:10.1109/tpwrs.2013.2288701

Cited by 128 publications

(54 citation statements)

References 30 publications

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“…In existing literature, traditional formulations of the OPF problem has been extended to account for variable and partly-predictable nature of the wind power generation [3], [16]- [18]. These papers capture the intermittent nature of wind power generation using different probabilistic techniques and determine a robust operating point of the conventional generating units to meet a constant demand.…”

Section: A Literature Reviewmentioning

confidence: 99%

An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty

Bukhsh

Zhang

Pinson

2016

IEEE Trans. Smart Grid

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Abstract-Renewable energy sources such as wind and solar have received much attention in recent years, and large amount of renewable generation is being integrated to the electricity networks. A fundamental challenge in a power system operation is to handle the intermittent nature of the renewable generation. In this paper we present a stochastic programming approach to solve a multiperiod optimal power flow problem under renewable generation uncertainty. The proposed approach consists of two stages. In the first stage, operating points for the conventional power plants are determined. The second stage realizes generation from the renewable resources and optimally accommodates it by relying on the demand-side flexibilities and limited available flexibilities from the conventional generating units. The proposed model is illustrated on a 4-bus and a 39-bus system. Numerical results show that with small flexibility on the demand-side substantial benefits in terms of re-dispatch costs can be achieved. The proposed approach is tested on all standard IEEE test cases upto 300 buses for a wide variety of scenarios.Index Terms-Demand response; optimal power flow; power system modelling; linear stochastic programming; smart grids; uncertainty; wind energy. NOMENCLATURE Sets BBuses, indexed by b. T Discrete set of time intervals, indexed by t . Parameters b lSusceptance of line l .τ l Off-nominal tap ratio of line l .Min., max. real power outputs of conventional generator g .Real power demand of load d .Cost function for generator g . Cost of renewable generation spillage.Min., max. load flexibility of demand atMin., max. change in operating point ofMin., max. regulation of generator g .Downward, upward regulation cost for generator g .Cost of decreasing, increasing demand in the time period t . P max lMax power flow capacity of line l . Variables pReal power output of generator g .

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Section: A Literature Reviewmentioning

confidence: 99%

An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty

Bukhsh

Zhang

Pinson

2016

IEEE Trans. Smart Grid

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“…The output power of a wind farm depends on the output power of each wind turbine unit. The power generated by the wind turbine unit changes with the wind speed, and the relationship between the generated power of the wind turbine unit and the wind speed can be expressed as

P_{Wg} = ({, \begin{matrix} 0, v \leq v_{in} \\ a + italicbv, v_{in} \leq v \leq v_{r} \\ P_{r}, v_{r} \leq v \leq v_{out} \\ 0, v > v_{out} \end{matrix})

where v is the wind speed; v in is the cut‐in wind speed and v out is the cut‐out wind speed; v r is the rated wind speed; P r is the rated output power of the wind turbine unit; P Wg is the actual output power of the wind turbine unit; and

a = \frac{P_{r} v_{in}}{v_{in} - v_{r}}

and

b = \frac{P_{r}}{v_{r} - v_{in}}

are constants. It is necessary to note that in this paper the output power of the wind turbine is a linear function of wind speed in the wind turbine model (2).…”

Section: Mixed Probabilistic and Interval Optimal Power Flow Modelmentioning

confidence: 99%

“…For the optimal power flow (OPF) problem, there have been many studies on power system uncertain OPF model and solution method considering uncertainties in wind power . Probabilistic optimal power flow (POPF) models considering wind power integration have been considered in , the probability distribution of the objective or unknown variables of OPF has been obtained, and many methods such as analytical method, Latin hypercube sampling, point estimate method of 2 n or 2 n + 1 sampling strategy have been proposed to solve it. The proposed methods could achieve great improvement in efficiency compared with Monte Carlo (MC) sampling.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed methods could achieve great improvement in efficiency compared with Monte Carlo (MC) sampling. Meanwhile, in order to deal with the correlation of wind speed for wind farms, satisfactory results have been achieved by combining orthogonal transformation and polynomial transform techniques with the above methods in . The stochastic OPF model is established by interpreting the restrictions of uncertain factors impacting on the constraint conditions as chance constraints, and an optimal power solution satisfying the chance constraints has been obtained in .…”

Section: Introductionmentioning

confidence: 99%

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Mixed probabilistic and interval optimal power flow considering uncertain wind power and dispatchable load

Guo

Gong

Bao

2017

IEEJ Transactions Elec Engng

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Considering uncertain wind power and dispatchable load, a mixed probabilistic and interval optimal power flow model is proposed, and Monte Carlo sampling and affine arithmetic method are used to solve it. First, an uncertain optimal power flow model with mixed probabilistic variables and interval variables is established by expressing the uncertain dispatchable load as the interval model and the uncertain wind speed and node load as the probabilistic model. Then Monte Carlo sampling is used to sample the probabilistic variables in the proposed model. By this way, the mixed probabilistic and interval optimal power flow can be transformed into interval optimal power flow with sampling points, and the interval optimal power flow of each sampling point can be solved by the affine arithmetic method. Finally, a maximum probability density function and a minimum probability density function are synthesized based on the interval extremum of unknown variables in optimal power flow for each sampling point. The numerical results obtained by the IEEE-118 and IEEE-300 bus systems show that the mixed probabilistic and interval optimal power flow model has the merits of handling the problem including both probabilistic variables and interval variables at the same time, obtaining the probabilistic interval of optimal power flow with any value and learning the maximum probability and minimum probability of the power system's possible operating status. The proposed algorithm has the advantage of high solution efficiency.

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“…[26] traditional 2m þ 1 PEM extended by using a transformation to handle correlated RVs with arbitrary distributions in POPF problem. In [27], a method is proposed for incorporati2m þ 1 ng the effects of spatially and temporally correlated input RVs within the point estimate method for POPF simulation. This method is used to solve multi-period POPF including correlation among time intervals of wind power generation.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties

et al. 2016

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a b s t r a c tIncreasing penetration of wind power in power systems causes difficulties in system planning due to the uncertainty and non dispatchability of the wind power. The important issue, in addition to uncertain nature of the wind speed, is that the wind speeds in neighbor locations are not independent and are in contrast, highly correlated. For accurate planning, it is necessary to consider this correlation in optimization planning of the power system. With respect to this point, this paper presents a probabilistic multiobjective optimal power flow (MO-OPF) considering the correlation in wind speed and the load. This paper utilizes a point estimate method (PEM) which uses Nataf transformation. In reality, the joint probability density function (PDF) of wind speed related to different places is not available but marginal PDF and the correlation matrix is available in most cases, which satisfy the service condition of Nataf transformation. In this paper biogeography based optimization (BBO) algorithm, which is a powerful optimization algorithm in solving problems including both continuous and discrete variables, is utilized in order to solve probabilistic MO-OPF problem. In order to demonstrate performance of the method, IEEE 30-bus standard test case with integration of two wind farms is examined. Then the obtained results are compared with the Monte Carlo simulation (MCS) results. The comparison indicates high accuracy of the proposed method.

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Point Estimate Method Addressing Correlated Wind Power for Probabilistic Optimal Power Flow

Cited by 128 publications

References 30 publications

An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty

An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty

Mixed probabilistic and interval optimal power flow considering uncertain wind power and dispatchable load

Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties

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