Static Stability Analysis And Optimization Control Of Distribution Systems With High DG Penetration

Power distribution systems containing a high penetration of distributed generation (DG) have become the desirable and sustainable implementations of new and renewable energy sources. However, due to the unprecedented increase in energy demand, distribution systems have been driven to operate near their limits, losing their static stability with unacceptable deviations of voltage and frequency, especially under islanded modes without main grid support.In static stability analysis, continuation power flow (CPF) has been widely adopted to calculate the distance between the current equilibrium point and critical operation point which corresponds to the maximum loading point (MLP). When the system reaches its MLP, the Jacobian matrix becomes singular, and consequently, the power flow method will face convergence problems. The CPF method can trace voltage profiles, namely PV curves, by repeatedly computing the equilibrium point using a predictor-corrector scheme after introducing a continuation parameter even when the system Jacobian is ill-conditioned.CPF has been applied to stability analysis of distribution systems. However, since the implementation of high penetration of DGs in distribution systems, conventional CPF needs to be revisited due to:1) the complexity of utility interfaces of DG challenges in obtaining accurate and appropriate representations of components in distribution systems;2) the condition of multiple generations leading to alterations in the scale and direction of power flow, especially when the R/X ratio is high;3) the influence of the intermittency and fluctuation of renewables on the results of CPF by changing the power growth pattern.This paper proposes an improved continuation power flow method for the modelling and stability analysis of distribution systems with a high penetration of distributed generation. This method aims at solving the flaws of conventional CPF in the description of DGs, the allocation of unbalanced power and the consideration of renewables. To precisely indicate the power variations of DGs with respect to terminal voltage and system frequency, the comprehensive static characteristics bus models are introduced into the calculation of the equilibrium point. Then, in the case of multiple generations, the distributed slack bus model based on incremental loss factors (ILFs) is used to allocate unbalanced power, making the results of CPF independent of slack bus selection. In addition, the load growth pattern involving the output characteristics of renewable DGs is reinterpreted as the net load growth pattern to evaluate the effect of intermittency and fluctuation of renewables on the static stability of distribution systems. A detailed solution process of improved CPF is then elaborated. Case studies are presented on the IEEE 33-bus distribution system to illustrate the validity of the improved CPF method, and more simulations on the PG&E 69-bus distribution system using the proposed method are performed to assess the effect of DGs on the static stability of distribution systems.Based on the proposed improved CPF method, an optimization control method for static stability of distribution systems with high DG penetration is presented. This method have described the optimization control problem, and then have calculated the stability critical point and corresponding control sensitivity to form the static stability optimization control model. The detailed algorithm flow for this method is the proposed.