Probabilistic Optimal Power Flow in Correlated Hybrid Wind&amp;#x2013;Photovoltaic Power Systems

Aien, Morteza; Fotuhi‐Firuzabad, Mahmud; Rashidinejad, Masoud

doi:10.1109/tsg.2013.2293352

Cited by 177 publications

(98 citation statements)

References 24 publications

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“…The uncertain PV generation is estimated using the point estimation method [39,40], as follows. Let the expected values, standard deviation and skewness coefficient of each uncertain PV generation (i.e., PV j ) be µ PV j , σ PV j and, λ PV j , respectively, where j = 1, 2, .…”

Section: Point Estimation Methodsmentioning

confidence: 99%

Novel Genetic Algorithm-Based Energy Management in a Factory Power System Considering Uncertain Photovoltaic Energies

Hong

2017

Applied Sciences

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Abstract:The demand response and accommodation of different renewable energy resources are essential factors in a modern smart microgrid. This paper investigates the energy management related to the short-term (24 h) unit commitment and demand response in a factory power system with uncertain photovoltaic power generation. Elastic loads may be activated subject to their operation constraints in a manner determined by the electricity prices while inelastic loads are inflexibly fixed in each hour. The generation of power from photovoltaic arrays is modeled as a Gaussian distribution owing to its uncertainty. This problem is formulated as a stochastic mixed-integer optimization problem and solved using two levels of algorithms: the master level determines the optimal states of the units (e.g., micro-turbine generators) and elastic loads; and the slave level concerns optimal real power scheduling and power purchase/sale from/to the utility, subject to system operating constraints. This paper proposes two novel encoding schemes used in genetic algorithms on the master level; the point estimate method, incorporating the interior point algorithm, is used on the slave level. Various scenarios in a 30-bus factory power system are studied to reveal the applicability of the proposed method.

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Section: Point Estimation Methodsmentioning

confidence: 99%

Novel Genetic Algorithm-Based Energy Management in a Factory Power System Considering Uncertain Photovoltaic Energies

Hong

2017

Applied Sciences

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“…(1), authors in [17] proposed to model the PPF problem assuming that y = f (x), where x is the input variable vector that contains loads, network configuration and powers generated by distributed generation; y is the output vector that includes voltage magnitudes, angles and some powers generated; and f (x) determines the state of the system as a function of the input variables.…”

Section: Bayesian Modeling For Probabilistic Power Flow Problemsmentioning

confidence: 99%

Bayesian Probabilistic Power Flow Analysis Using Jacobian Approximate Bayesian Computation

Zuluaga

Álvarez

2018

IEEE Trans. Power Syst.

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Abstract-A probabilistic power flow (PPF) study is an essential tool for the analysis and planning of a power system when specific variables are considered as random variables with particular probability distributions. The most widely used method for solving the PPF problem is Monte Carlo simulation (MCS). Although MCS is accurate for obtaining the uncertainty of the state variables, it is also computationally expensive, since it relies on repetitive deterministic power flow solutions. In this paper, we introduce a different perspective for the PPF problem. We frame the PPF as a probabilistic inference problem, and instead of repetitively solving optimization problems, we use Bayesian inference for computing posterior distributions over state variables. Additionally, we provide a likelihood-free method based on the Approximate Bayesian Computation philosophy, that incorporates the Jacobian computed from the power flow equations. Results in three different test systems show that the proposed methodologies are competitive alternatives for solving the PPF problem, and in some cases, they allow for reduction in computation time when compared to MCS.

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“…It is assumed that the cut-in, rated and cut-out speeds are 3 m/s, 13 m/s and 25 m/s, respectively. The wind farm power factor is assumed as 0.85 lag [47]. The parameters of the objective functions are taken from MATPOWER files [46].…”

Section: Case Studiesmentioning

confidence: 99%

A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

Deng

Zhang

2017

Energies

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Abstract:The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush-Kuhn-Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish-Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS).

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Probabilistic Optimal Power Flow in Correlated Hybrid Wind–Photovoltaic Power Systems

Cited by 177 publications

References 24 publications

Novel Genetic Algorithm-Based Energy Management in a Factory Power System Considering Uncertain Photovoltaic Energies

Novel Genetic Algorithm-Based Energy Management in a Factory Power System Considering Uncertain Photovoltaic Energies

Bayesian Probabilistic Power Flow Analysis Using Jacobian Approximate Bayesian Computation

A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

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