Probabilistic load flow in systems with high wind power penetration

This paper proposes a method for solving a probabilistic load flows that takes into account the uncertainties of wind generation, but also of load and conventional systems. The method uses a combination of methods including cumulant, point estimate and convolution. Cornish Fisher expansion series are also used to find the CDF. The method is of especial application to estimate active power flows through lines

On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source

In this paper, we develop an explicit formula allowing to compute the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source. We derive efficient algorithms allowing to deal both with low or high complexity patterns and either homogeneous or heterogenous Markov models. We then apply these results to the distribution of DNA patterns in genomic sequences where we show that moment-based developments (namely: Edgeworth's expansion and Gram-Charlier type B series) allow to improve the reliability of common asymptotic approximations like Gaussian or Poisson approximations

Probabilistic load flow with wind production uncertainty using cumulants and Cornish–Fisher expansion

This paper proposes a method for probabilistic load flow in networks with wind generation, where the uncertainty of the production is non-Gaussian. The method is based on the properties of the cumulants of the probability density functions (PDF) and the Cornish–Fisher expansion, which is more suitable for non-Gaussian PDF than other approaches, such as Gram–Charlier series. The paper includes examples and comparisons between different methods proposed in literature.Publicad

Probabilistic Load Flow Solution Considering Optimal Allocation of SVC in Radial Distribution System

This paper proposes a solution procedure for probabilistic load flow problem considering the optimal allocation of Static Var Compensator (SVC) in radial distribution systems. Pareto Envelope-based Selection Algorithm II (PESA-II) with fuzzy logic decision maker is developed to determine the optimal location and size of SVC based on the minimum total power losses and Voltage Deviation (VD). Combined cumulants and gram-chalier expansion are used for solving the probabilistic load flow problem. The proposed algorithm is tested on 33-bus and 69-bus distribution systems. The developed algorithm gives an acceptable solution with low number of iterations and less computation cost compared with the Monte Carlo method

Improving the Reliability of an Electric Power System by Biomass-Fueled Gas Engine

This paper shows a practice to raise the reliability of an electric power system by the installation of distributed generation, taking gasified biomass as fuel. To calculate the reliability index, a probabilistic load flow was used. This index is determined as the fault probability of the system. The resolution of this probabilistic load flow combines the method of cumulants and Gram–Charlier expansion. To achieve the reliability index, simulating a number of contingencies is required; the greater the number of simulated contingencies, the higher the accuracy of the index obtained. This probabilistic technique uses the random variables as starting information, so the two generators and loads are simulated as random variables. The generators of this distributed generation are biomass-fueled gas engines, commonly found in Spain. The simulations carried out on the IEEE 14-bus Test System, including three biomass generators, show that the inclusion of this type of generation improves the overall reliability indices of the electrical syste

Energy Losses and Voltage Stability Study in Distribution Network with Distributed Generation

With the distributed generation technology widely applied, some system problems such as overvoltages and undervoltages are gradually remarkable, which are caused by distributed generations like wind energy system (WES) and photovoltaic system (PVS) because of their probabilistic output power which relied on natural conditions. Since the impacts of WES and PVS are important in the distribution system voltage quality, we study these in this paper using new models with the probability density function of node voltage and the cumulative distribution function of total losses. We apply these models to solve the IEEE33 distribution system to be chosen in IEEE standard database. We compare our method with the Monte Carlo simulation method in three different cases, respectively. In the three cases, these results not only can provide the important reference information for the next stage optimization design, system reliability, and safety analysis but also can reduce amount of calculation

Development of a forward/backward power flow algorithm in distribution systems based on probabilistic technique using normal distribution

There are always some uncertainties in prediction and estimation of distribution systems loads. These uncertainties impose some undesirable impacts and deviations on power flow of the system which may cause reduction in accuracy of the results obtained by system analysis. Thus, probabilistic analysis of distribution system is very important. This paper proposes a probabilistic power flow technique by applying a normal probabilistic distribution in seven standard deviations on forward-backward algorithm. The losses and voltage of IEEE 33-bus test distribution network is investigated by our new algorithm and the results are compared with the conventional algorithm i.e., based on deterministic methods

Unscented Transformation-based Probabilistic Optimal Power Flow

Renewable energy-based generation causes uncertainties in power system operation and planning due to its stochastic nature. The load uncertainties combined with the increasing penetration of renewable energy-based generation lead to more complicated power system operations. In power system operation, optimal power flow (OPF) is a widely-used tool in Energy Management System (EMS), for scheduling power generation of power plants, to operate the power system with least cost of generation and to ensure the security and reliability of power transmission grids. On the other hand, in order to deal with the stochastic variables (e.g., renewable energy-based generation and load uncertainties), probabilistic optimal power flow (POPF) has been instituted. This thesis introduces a new Unscented Transformation (UT)-based POPF algorithm. UT-based OPF has a key advantage in handling the correlated random variables, and has become an open research area. Integrated wind power and independent or correlated loads are represented using a Gaussian probability distribution function (PDF). The UT is utilized to generate the sigma points that represent the PDF with a limited number of points. The generated sigma points are then used in the deterministic OPF algorithm. The statistical characteristics (i.e. means and variances) of the UT-based POPF solutions are calculated according to the inputs and their corresponding weights. Different UT methods with their corresponding sigma point selection processes are evaluated and compared with Monte Carlo Simulation (MCS) as the solution benchmark. In the thesis, Locational Marginal Price (LMP) in the transmission network is evaluated as the output of the UT-based POPF. The proposed algorithm is successfully verified on the standard IEEE 30- and 118-bus power transmission systems with wind power generation and unspecified loads. These two test cases represent a portion of American Electric Power (AEP) transmission grid