Optimizing the Operation Mode of an Autonomous Wind Power Plant with a Distributed Generation System

Abstract

The article considers physical interactions and a mathematical model of a wind power plant consisting of separate wind turbines distributed over a large area, which generate electric energy to common buses and from them to a transformer and load. Induction generators are used as electromechanical converters, which differ from synchronous ones in having a simple design and featuring better operational reliability. In view of distributed location of wind turbines, each of them generally operates under different wind conditions; in addition, their interaction depends both on the length of cable routes to the busbars and on the parameters of transformers. Owing to these circumstances, it is of interest to study parallel operation of distributed induction generators and the possibility to optimize the wind power plant operation mode to ensure the required quality of the generated electricity in terms of power supply frequency and voltage. The operation mode of such wind power plant – taking as an example two induction generators operating in parallel on a common resistive-inductive load – is represented by a complex T-shaped equivalent circuit, the mathematical description of which is given by nonlinear complex homogeneous equations for nodal potentials. The magnetization inductances are nonlinear functions of the EMFs, which are analytically approximated by an inverse trigonometric function. The mechanical equilibrium equations include the wind turbine torques, the electromagnetic moments of generators, the rotating parts inertia moments, and resistance and friction moments. It should be noted that with a given wind turbine size, its torque depends on the angular rotation speed, wind velocity and blade angle, and is approximated by spline functions of the load impedance and wind turbine rotation speeds. The operating mode analysis is based on the numerical calculation of non-trivial solutions of nonlinear complex equations for the potentials of the equivalent circuit nodes, load voltage and frequency, and their subsequent approximation as a function of rotation speeds and load impedance at fixed values of load inductance, capacitances, ballast conductivity, and other parameters. On the example of a calculation performed for typical parameters of a small-capacity wind power plant with a real difference of wind velocities for individual wind turbines and variable load impedance, it is shown that by changing the blade angle alone, it is not possible to stabilize the voltage parameters on the load, while by simultaneously changing the capacitive and ballast conductivities, the frequency and voltage can be stabilized at the specified levels. In particular, with increasing the wind turbine rotation speeds, the capacitive and ballast conductivity should be increased, and with an increase in load resistance, the ballast conductivity should also increase, and capacitive conductivity should decrease. As a subsequent development of this method, ways to stabilize the operation of such wind power plant with an arbitrary number of generators can be analyzed.