In this paper we investigate how the equilibrium characteristics of conventional power systems may change with an increase in wind penetration. We first derive a differentialalgebraic model of a power system network consisting of synchronous generators, loads and a wind power plant modeled by a wind turbine and a doubly-fed induction generator (DFIG). The models of these three components are coupled via nonlinear power flow equations. In contrast to the traditional approach for solving the power flows via iterative methods that often lead to only local solutions, we apply a recently developed parameter-homotopy based numerical continuation algorithm to compute all possible solutions. The method solves the power flow equations over multiple values of the wind penetration level with far less computational effort instead of solving them at each value individually. We observe that depending on the penetration limit and the setpoint value for the magnitude of the wind bus voltage, the system may exhibit several undesired or even unstable equilibria. We illustrate these results through a detailed simulation of a 5-machine power system model with wind injection, and highlight how the solutions may be helpful for small-signal stability assessment.Index Terms-wind power system, power flow solutions, nonlinear equations, homotopy, small-signal stability
In this paper, we present a homotopy based numerical continuation algorithm to efficiently compute all feasible equilibria of a complex power system model. The dynamic characteristics of conventional power systems are undergoing a sea change due to the impact of large-scale integration of renewables, storage elements, new type of loads etc. Several parameters of these components affect the power system operation leading to multiple feasible equilibria which may be intractable by the traditional load flow techniques. In contrast, our algorithm finds all the feasible solutions over a certain parameter space. We illustrate the results through the simulation of a 5-machine power system model with wind, storage elements, and dynamic loads. We observed that the wind velocity and the reference to the wind bus voltage strongly affect the number and the stability of the system equilibria. Knowledge of these equilibria can benefit small-signal stability assessment and system level planning.
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