Last Comments on Control J. McCalley

Modeling of Variable Speed Wind Turbine Aerodynamic model, evaluates the turbine torque as a function of wind speed and turbine angular speed . Pitch system, evaluates the pitch angle dynamics as a function of pitch reference . Mechanical system, evaluates the generator and turbine angular speed as a function of turbine torque and generator torque . Electrical machine and power converters transform the generator torque into a grid current as a function of voltage grid. Control system, evaluates the generator torque, pitch angle and reactive power references as a function of wind speed and grid voltage. Block Scheme of a variable speed wind turbine model

Wind turbine control levels Rotor-side converter (RSC) is controlled so that it provides independent control of Tem and Qs. Level I: Regulates power flow between grid and generator. Level II: Controls the amount of energy extracted from the wind by wind turbine rotor. Level III: Responds to wind-farm or grid-central control commands for MW dispatch, voltage, or frequency control. 3

Basic topology and View of Level 1 Control Below is the basic topology of the basic back-to-back two-level voltage source converter (VSC). 4

Level 1 control DC bus voltage is controlled by grid-side converter (GSC) to a pre-determined value for proper operation of both GSC and RSC. Qg also controlled via GSC. We achieve RSC control objectives by controlling rotor-side voltage. We control rotor voltage to achieve a specified torque and stator reactive power. This (open-loop) control not heavily used for DFIGs 5

Overview of Level 1 Control 6

Grid-side converter 7

Dwell time and switching sequence Modulation index See the next slide, for Table 4-4 8

A larger view 9

PI Controllers Observe the currents idr* and iqr* being supplied as control signals for the target values of torque Te* and stator reactive power Qs*. These target currents are compared to the actual currents, and the difference drives a PI controller which generates the control signals vdr* and vqr*. There are similar controllers for the GSC as well (not shown in this diagram). 10

Comments on PI Controllers PI stands for “proportional plus integral” PI control (also known as lag compensation) provides zero steady-state error to a step input. Since the input is the difference between the target value and the actual value, the PI control forces the target value to equal the actual value in the steady state. The transfer function of the PI controller is given by Block diagram representations can be viewed as follows: idr KP - Σ v'dr idr* + KI/s 11

Comments on PI Controllers idr KP - Σ The corresponding time-domain expression is given by: v'dr idr* + KI/s One reference [1] provides a slightly different control law: From [1], “For this particular case, both PI controllers in (13) have been tuned applying the pole assignment method, in an attempt to reach a critically damped inner loop response with a 40-ms settling time. Furthermore, inclusion of parameter b allows placing independently not only the inner loop poles, but also the unique zero inherent to the PI controller. Particularly, if b is made equal to zero, the PI controller zero is placed at s= -∞, and, as a result, its influence on the closed-loop time response is cancelled out. The point is that the PI controller must be tuned to obtain the desired response. This tuning can be done in time-domain. A procedure for doing it in the z-domain is illustrated in [2]. 12

Comments on PI Controllers A compensation term is added in all of the references, like this: idr KP - Σ v'dr Σ vdr idr* + + KI/s + Compensation term It appears the term is added to diminish coupling between the d-axis quantities and the q-axis quantities. I have not been able to identify a satisfying explanation for it. 13

Some References That Address PI Control Design [1] Arantxa Tapia, Gerardo Tapia, J. Xabier Ostolaza, and José Ramón Sáenz, “Modeling and control of a wind turbine driven doubly fed induction generator,” IEEE Transactions on Energy Conversion, Vol. 18, No. 2, June 2003. [2] P. Pena, J. Clare, and G. Asher, “Doubly fed induction generator using back-to-back PWM converters and its application to variable speed wind energy generation,” IEEE Proc. Electr. Power Applications, Vol 143, No. 3, May 1996. [3] O. Anaya-Lara, N. Jenkins, J. Ekanayake, P. Cartwright, and M. Hughes, “Wind Energy Generation: Modelling and Control,” Wiley 2009, pp. 84-89. [4] G. Abad, J. Lopex, M. Rodriguez, L. Marroyo, and G. Iwanski, “Double fed induction machine: modeling and control for wind energy generation,” Wiley, 2011, pp. 304-311. [5]www.mathworks.com/help/physmod/sps/powersys/ref/windturbinedoublyfedinductiongeneratorphasortype.html 14