Issues Regarding the Modeling and Simulation of Wind Energy Conversion System’s Components Iosif Szeidert 1, Octavian Prostean1, Ioan Filip1, Cristian Vasar1, Lucian Mihet-Popa2
1
Politehnica University from Timisoara, Department of Automation and Applied Informatics
[email protected],
[email protected],
[email protected],
[email protected], 1 Politehnica University from Timisoara, Department of Machines and Electrical Drives,
[email protected]
Abstract- The wind energy conversion system’s (WECS) analysis requires the priory knowledge’s regarding the mathematical models for all component subsystems. The paper highlights some contributions to the preset values establishing strategies and models of certain components: rotation speed and voltage preset values establishing strategies, a simplified wind turbine model (fixed blade turbine), the squirrel cage/wound rotor asynchronous machine’s mathematical model (the Park equations), specific to current frequency converter supplier use, frequency inverters’ model. The elaborated models are used in the WECS analysis in its specific steady state / transient regimes as well for the controllers’ design and implementation.
I. INTRODUCTION There are known, presently, a large number of structure variants for asynchronous machine field-oriented control. The considerations presented in the paper are valid for the most structures. In the following, for presentation reasons there will be considered only the case of the induction machine air-gap magnetic field-oriented control system structure (figure 1). The structure is identical as in the case of electrical drives, in which appear: transducers /estimators, controllers and the F. Blaschke field-oriented method specific calculator blocks (phase number transformers TS, TS-1, field orientation block FOB and its elements, phase analyzer PHA, axes transformers AT, AT-1), frequency converters, excepting the PRESET TURBINE - GENERATOR ROTOR SPEED CALCULATOR, PRESET VOLTAGE CALCULATOR and WIND TURBINEINDUCTION GENERATOR GROUP. [2] There are studied the specific windmill’s control systems components.
II. MATHEMATICAL MODELS OF THE WIND ENERGY CONVERSION SYSTEM’S COMPONENTS
A. Preset Turbine-Generator Rotor Speed Calculator There is known that for each wind speed an optimum rotation turbine speed is imposed. Based on original turbine mathematical model, thus a sensor less rotation speed determination strategy can be elaborated; correspondingly a rotation speed calculation method was proposed [1][5][6].
Figure 1. Asynchronous machine air-gap magnetic field-oriented conrol system structure.
B. Preset Generator Voltage Calculator In the case of the variable speed asynchronous machine, optimum operation may be assured [3] if
U =UN.
f fN
M MN
(1)
(in the case of neglecting the issue of magnetic saturation).
In the case of coupled generator machines with ventilators 2 2 and wind turbines, having M ≡ n ≡ f the relation (1) can be rewritten
0
1
Vcc
f U = U N ( )2 fN
f fN
Sb
0 1
Sc
Ra La
Ub
Rb Lb
Uc
Rc Lc
0
(2)
This fact must be considered for variable speed induction generator windmills. As a simplification, in the technical literature, there is assumed that the voltage is:
U =UN.
Ua
Sa
1
PWM
Figure 2. Converter (inverter-side) simplified switching model. COMP
u*2
(3)
+
Sa
C. Frequency Converter Models -
There are different frequency converters: thyristor, transistor, cycle-converter, intermediate direct current circuit, matrix (one of the latest trends). The modern implementations are based on IGBT transistor PWM converters with direct current intermediate circuit. The most models may be considered for the three-phase inverters of considered converters. A very simple model may be the device with three static switches, one for each phase. The IGBT commutation times are neglected. The simplified scheme of inverter is presented in figure 2. Regarding the figure 2, the inverter’s mathematical model is:
ulv GTLV
Figure 3. PWM electric scheme.
1 u a = Vcc (2S a − S b − S c ) 3 1 u b = Vcc (− S a + 2 S b − S c ) 3
(4)
Figure 4. The HEXATRONIC Company converter test setup (voltage and current waveforms).
1 u c = Vcc (− S a − S b − S c ) 3 Where: S i (i = a, b, c) are control signals delivered by the PWM circuit, that have the values 0 or 1, depending on the fact that switch element is “on” or “off”. There was also elaborated a Spice program for the frequency converter (figure 2) and for the PWM generator (figure 3). The simulation results concludes that for small load (current) the distortion of current wave is greater as in the case of a higher value load. The Canadian HEXATRONIC Inc., Toronto research partner in the domain of frequency converters, at his converter test stand: · Input DC Voltage (buck): 460 VDC · Nominal current: 10 ADC · Output voltage: 208 VAC, at low load current of 3 [A] AC, obtained [7], for the inverter, the current and voltage waveforms shown in figure 4 with a satisfactory current harmonic distortion factor THD of 5.23% (considering the IEEE 519 harmonic distortion standard requirements for considered load conditions: THD
