Simulation and the monte carlo method

Monte Carlo simulation method combined with simple random sampling (SRS) suffers from long computation time and heavy computer storage requirement when used in probabilistic load flow (PLF) evaluation and other power system probabilistic analyses. This paper proposes the use of an efficient sampling method, Latin hypercube sampling (LHS) combined with Cholesky decomposition method (LHS-CD), into Monte Carlo simulation for solving the PLF problems. The LHS-CD sampling method is investigated using IEEE 14-bus and 118-bus systems. The method is compared with SRS and LHS only with random permutation (LHS-RP). LHS-CD is found to be robust and flexible and has the potential to be applied in many power system probabilistic problems.

Probabilistic Load Flow Evaluation With Hybrid Latin Hypercube Sampling and Cholesky Decomposition

The penetration of renewable distributed generation (DG) sources has been increased in active distribution networks due to their unique advantages. However, non-dispatchable DGs such as wind turbines raise the risk of distribution networks. Such a problem could be eliminated using the proper application of energy storage units. In this paper, optimal planning of batteries in the distribution grid is presented. The optimal planning determines the location, capacity and power rating of batteries while minimizing the cost objective function subject to technical constraints. The optimal long-term planning is based on the short-term optimal power flow considering the uncertainties. The point estimate method (PEM) is employed for probabilistic optimal power flow. The batteries are scheduled optimally for several purposes to maximize the benefits. A hybrid Tabu search/particle swarm optimization (TS/PSO) algorithm is used to solve the problem. The numerical studies on a 21-node distribution system show the advantages of the proposed methodology. The proposed approach can also be applied to the realistic sized networks when some sensitive nodes are considered as candidate locations for installing the storage units.

Optimal Storage Planning in Active Distribution Network Considering Uncertainty of Wind Power Distributed Generation

A probabilistic power flow model that takes into account spatially correlated power sources and loads is proposed. It is particularly appropriate to assess the impact of intermittent generators such as wind power ones on a power network. The proposed model is solved using an extended point estimate method that accounts for dependencies among the input random variables (i.e. loads and power sources). The proposed probabilistic power flow model is illustrated through 24-bus and 118-bus case studies. Finally, conclusions are duly drawn.

Probabilistic power flow with correlated wind sources

A hybrid of ant colony optimization and artificial bee colony algorithm for probabilistic optimal placement and sizing of distributed energy resources

This paper analyzes the behavior of Hong's point estimate methods to account for uncertainties on the probabilistic power flow problem. This uncertainty may arise from different sources as load demand or generation unit outages. Point estimate methods constitute a remarkable tool to handle stochastic power system problems because good results can be achieved by using the same routines as those corresponding to deterministic problems, while keeping low the computational burden. In previous works related to power systems, only the two-point estimate method has been considered. In this paper, four different Hong's point estimate schemes are presented and tested on the probabilistic power flow problem. Binomial and normal distributions are used to model input random variables. Results for two different case studies, based on the IEEE 14-bus and IEEE 118-bus test systems, respectively, are presented and compared against those obtained from the Monte Carlo simulation. Particularly, this paper shows that the use of the scheme provides the best performance when a high number of random variables, both continuous and discrete, are considered.

J.M. Morales

Papers

Point Estimate Schemes to Solve the Probabilistic Power Flow