Simulation of wind power plant with double-fed machine when operating in autonomous system in parallel with synchronous commensurable power generator

. Autonomous system, containing synchronous generators in a classic design, driven by either diesel or gas turbine, which operates in parallel with a wind power plant (WPP) containing an asynchronous double-fed machine (ADFM) through external network, is considered in the paper. At the same time, the power transmission scheme and the corresponding equivalent circuit are also drawn up. The equations of the synchronous generator and the external network are written in the axes rotating at the speed of the synchronous generator rotor, and the equations of the WPP’s generator in the axes rotating at the speed of its rotor. By means of "docking" equations a digital model of the entire system is compiled with the external network parameters and loads on the side of the synchronous generator and WPP’s asynchronous generator, which are represented by constant-conductivity shunts. Static and dynamic characteristics of the system are calculated.


Introduction
Autonomous commensurable power systems of are widely used in various sectors of national economy. When using wind power plants in the autonomous power supply system, naturally in places with high wind power potential, the problem of studying the conditions of parallel operation arises, when the output power of wind power plants changes depending on the wind speed value. Such systems can be used in regions without centralized power supply -mountainous villages, oil production platforms ("Oil rocks" type), etc.

Materials and methods
The electricity transmission diagram is presented in Fig.  1. Here synchronous generator SG, generator voltage of which is about 10.5 kV, feeds the load 1 from generator buses. Further, the step-up transformer Tr1 through the high-voltage power line L1 and the transformer Tr2 feeds the load 2, at which the asynchronous generator ADFM WPP also operates. This scheme, of course, cannot be the only one -Tr1 and Tr2 may be absent, power takeoff may be in different places of the line L1, etc. But this scheme corresponds to the semantic content of the question under study, i.e., when the output power of the WPP's asynchronous generator changes depending on the wind speed, the power distribution on load 2 will change -when the output power of the WPP decreases, the main synchronous generator will be loaded, and when it increases-vise versa [1,2,3,4,5].
The equivalent circuit of the power transmission scheme, presented in Fig.1, is shown in Fig. 2.
Currents in nodes 1 and 2 are respectively as follows: Current balance: taking into account the last expression, the voltages of synchronous and asynchronous generators will be written as: Then, substituting the load current values from equations (2) into the expression (3), we get:
Grouping members, we obtain: At last, the last equations can be written in the following form: Solving together the equations of the system (7), we get:  (8) For simplicity of further transformations these equations can be represented as: Now we write down the equations of the external network in the axes d, q, rotating at the speed of the synchronous machine rotor [0, 0]. At the same time we superpose the q axis with the real numbers axis, and the d axis with the imaginary numbers axis. Then the voltages and currents of generators can be written in the following form: Exactly the same representation is made for the external axis parameters: Substituting the values of the relationships (10) and (11) in equations (9), and making the corresponding multiplication, we obtain for the synchronous generator: and for asynchronous generator: In equations (12) and (13): Accordingly, the components of the asynchronous generator voltage in the axes rotating at the speed of the WPP's asynchronous generator rotor can be represented as follows: Thus, taking into account the above, the equations of the synchronous generator in the axes d, q, rotating at the speed of its rotor [8,9], are represented in the form:

Results and discussion
To study the adequacy of the presented equations (16) and (17), the parameters of the elements and the coefficients of the equations were calculated. a) As a synchronous generator, a generator of the FWTG type (forced water turbo-generator) -100-2 [12] with parameters: Pl =100 MW; ULn=10.5 kV; cosφ=0.85 (sinφ=0.527); η=0.983.
As a result of the calculations, the generator parameters are determined in relative units: f) Generator made on the basis of double-fed machine, which, of course, is an asynchronous machine with a phase rotor, is accepted as WPP's asynchronous generator [0, 0]. The power of one generator is assumed to be equal to Pl =20 MW, which is equivalent to 10 WPPs, each of which has the power of 2 MW.
Thus, parameters of equivalent generator of WPS in relative units at Zbaz=4.5 Ohm are equal to:

Conclusions
Dynamic characteristics have represented the discrete change process of the voltage and part of the current of the rotor, at which the speed of the WPP shaft changes within ± 22 %.
Model of operation of WPP with a double-fed machine in parallel with a synchronous generator is proposed. At the same time, the WPP power is assumed to be about 20% of the synchronous generator power.