Some uncertainties, such as the uncertain output power of a plug-in electric vehicle (PEV) due to its stochastic charging and discharging schedule, that of a wind generation unit due to the stochastic wind speed, and that of a solar generating source due to the stochastic illumination intensity, volatile fuel prices, and future uncertain load growth could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distribution system planning. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal siting and sizing of DGs. First, a mathematical model of CCP is developed with the minimization of the DGs' investment cost, operating cost, maintenance cost, network loss cost, as well as the capacity adequacy cost as the objective, security limitations as constraints, and the siting and sizing of DGs as optimization variables. Then, a Monte Carlo simulation-embedded genetic-algorithm-based approach is employed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is used to verify the feasibility and effectiveness of the developed model and method, and the test results have demonstrated that the voltage profile and power-supply reliability for customers can be significantly improved and the network loss substantially reduced.

Optimal Siting and Sizing of Distributed Generators in Distribution Systems Considering Uncertainties

CIGRE WG C4.605 : “Modelling and aggregation of loads in flexible power networks”

This paper presents the development of the dynamic equivalent model of an active distributed network (ADN) based on the grey-box approach. The equivalent model of an ADN comprises a converter-connected generator and a composite load model in parallel. The grey-box approach was chosen for model development as it incorporates prior knowledge about the ADN structure into the model, makes the model more physically relevant and intuitive than black-box or white-box models, and potentially improves the accuracy of the model. The dynamic equivalent model is presented in the seventh-order nonlinear state space format. It was initially loosely developed from the algebraic and differential equations describing assumed typical components of an ADN. Various static load models, dynamic load compositions, fault locations and a diverse range of distributed generation types and scenarios are considered in order to establish the generic range of model parameters for an ADN. The model is intended for the use in large power system stability studies.

Generic Model of Active Distribution Network for Large Power System Stability Studies

This paper presents an effective optimization scheme for the measurement-based load modeling based on the sensitivity analysis of composite load model parameters Each parameter of load model has different effects on its dynamic response Moreover, some parameters are insensitive to the change of others To estimate the dynamic interactions between parameters, their sensitivity is analyzed by using the eigenvalues of Hessian matrix used in the optimization algorithm Also, the linear dependence between two load model parameters is then identified by examining the condition number of Jacobian matrix With this parameter analysis, the performance of optimization process for measurement-based composite load modeling is improved by reducing the number of necessary parameters to consider The performance of proposed method is verified with the practical data measured at a feeder in a real substation

Improvement of Composite Load Modeling Based on Parameter Sensitivity and Dependency Analyses

This paper concerns the voltage dependence of composite loads in power systems. Based upon continuous field measurements by automatic monitoring devices, dynamic responses of typical system loads to sudden voltage changes have been obtained. The parameters of a load model have been evaluated from the field data, and their changes in a day and in a year have been presented for typical system loads. A constructive approach to synthesize load characteristics from load components has been discussed by comparing the synthesized load parameters with the measured ones.

Voltage Dependence of Composite Loads in Power Systems

The composite load model with an induction motor in parallel with a static load has been studied and applied in analysis of dynamics of power systems for a long time. However, the load parameters from field tests are still very limited. Based on the theoretical results of identifiability and estimation methodology of load parameters that have been achieved in the previous work, a project of load modelling based on field measurements is described. Eight sets of equipment for load modelling were installed in HeNan Electric Power Grid (HNEPG) Corporation, and the dynamics of the load were recorded and a dynamic index is proposed to evaluate the dynamic characteristics of the data measured. The load models derived from the field measurements are applied to stability analysis of HNEPG. The critical clearing time and power transfer capability analyses illustrate the enhancement of the stability analysis of the power grid using the load parameters derived from the field measurements and show the benefits of application of such model parameters in power system dynamic analysis.

N.-Q. He

Papers

Composite load models based on field measurements and their applications in dynamic analysis