International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
June 2013, pp.
ISSN: 2088-8708
Predictive Power Control of Grid and Rotor Side converters in Doubly Fed Induction Generators Based Wind Turbine Abdelmalek Boulahia*.
Mehdi Adel*.
Benalla Hocine* * Department of Electrical Engineering.
Montoury Constantine University.
ALGERIA
Article Info
ABSTRACT
Article history:
This paper presents a new control scheme for grid and rotor side for doubly fed induction generator (DFIG) using model based predictive control.
The control strategy minimizes quality functions, which represent the desired behavior of the converter.
The technique developed uses predictive direct power control to control the rotor and grid side converter.
The main advantages of this method are no need of linear controllers, coordinates transformations or modulators for converter and inverter.
Simulation results demonstrate robust, precise, and fast dynamic behavior of system.
Received Feb 11, 2013 Revised Apr 10, 2013 Accepted May 14, 2013 Keyword:
Predictive direct power control PWM converter Double fed induction generator Wind turbine Copyright A 2013Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Abdelmalek Boulahia.
Departement of Electrical Engineering.
Montoury Constantine University.
ALGERIA Email: boulahiamalek@yahoo.
INTRODUCTION
Doubly-fed induction generator (DFIG) wind turbines with converters rated at about 25Ae30% of the generator rating are becoming increasingly popular.
DFIG-based wind turbines offer variable s peed operation, four-quadrant active and reactive power capabilities, lower converter cost, and reduced power loss compared to wind turbines using fixed s peed induction generators or fully-fed synchronous generators with full-sized converters.
One of the most conventional control methods for DFIG is vector control in which rotor currents are decupled into stator active power .
r torqu.
and reactive power .
r flu.
and these two currents are controlled in the reference frame fixed to stator flux .
r voltag.
In this method accurate value of machine parameters such as resistances and inductances are required and nonlinear operation of converter for tuning current controllers is not considered.
So performance of vector control method is affected by changing machine parameters and operation condition.
Direct torque control (DTC) of induction machine drives was developed in the mid 1980s.
DTC is based on decoupled torque and flux control which have very fast and precise dynamic without using inner control loop.
the control of DFIG in which the rotor flux is estimated and an optimal switching table is used based on rotor flux position, based on DTC strategy, direct power control (DPC) is developed to control the DFIG.
But the problem with this method is that variation of Grid side converter (GSC) is used to maintain DC link voltage at desired reference level for all operation conditions of DFIG.
In .
, .
conventional voltage-oriented control (VOC) is used to control GSC.
In this method two decoupled current control loops are used to control DC voltage and reactive power which result in complex algorithm and dependency of system response on system parameters and operation condition.
Because of dependence of rotor active power on generator speed, it has fast dynamic and in order to have constant DC voltage the GSC must transmit the active power between rotor and grid with a fast response.
Journal homepage: http://iaesjournal.
com/online/index.
php/IJECE ISSN:2088-8708 The model predictive control is similar to (DTC for rotor side and DPC for grid sid.
only in that they both select one and only one voltage vector, but the basic principle in selecting voltage vector is very The DTC (DPC) uses a heuristic switching table to obtain the vector, which is determined when the difference between preferences and estimations occurs.
On the contrary, the model predictive, predicts the evolutions of torque .
ctive powe.
and flux .
eactive powe.
over the next several periods for each possible voltage vector, and then selects the one minimizing the errors between the references and estimations.
As a result, better performance can be anticipated for Predictive control.
It can be said that the voltage vector obtained from Predictive Control is more accurate and effective in controlling the torque .
ctive powe.
and rotor flux .
eactive powe.
than its counterpart obtained from DTC (DPC).
The key technology of Predictive Control lies in the definition of cost function, which is usually related to the control objectives.
GRID SIDE PREDICTIVE POWER CONTROL
The whole diagram of the predictive direct power control of grid side is illustrated in Figure 1.
Figure 1.
Schematic of the original predictive DPC control strategy of grid side PWM converter.
The input filter model can be described by the following continuous-time equations:
= o Oe u Oe o WhereRg and Lg are the filter resistance and inductance, respectively, and eg is the grid voltage.
vi converter voltage applying a sampling periods, the derivative form di/dt can be approximated by:
u OOue OAO = e s Replacing .
and shifting the discrete time one step forward, the relation between the discrete-time variables can be described as:
o ( .
= Ie s Ue s Ie s o o 1 Oe u ( .
Equation .
is used to obtain predictions for the future value of the input current ig .
for each voltage vector v.
generated by valid switching states.
IJECE Vol.
No.
June 2013: 287Ae293
IJECE
ISSN: 2088-8708
Considering the input voltage and current vectors in orthogonal coordinates, the predicted instantaneous input active and reactive power can be expressed by equations:
o 1 = o 1 oI ( .
o 1 = o 1 oI ( .
Where ig.
is the predicted input current vector, for a given voltage vector generated by the rectifier vi .
For a small sampling time, with respect to the grid fundamental frequency, it can be assumed that:
o ( .
OO o () .
The cost function ggsummarizes the desired behavior of the rectifier: minimize the reactive powerQgand control the active power Pg to be equal to reference value Pg*.
o = ( oO Oe o ( .
oO Oe o ( .
) .
u OO .
A , , , , , .
WhereQgO andPg* are the required active and reactive input power, and Qg and Pg are the predicted active and reactive input power, which depend on the conduction state.
As sinusoidal input currents, in phase with the supply line voltages, are required, the reactive input power referencemust be zero.
On the other hand, the DC link voltage is regulated by controlling the input power Pg*required by the load.
ROTOR SIDEPREDICTIVE POWER CONTROL
The whole diagram of the predictive control in this paper is illustrated in Figure 2.
Figure 2.
Schematic of the original predictive DPC control strategy of rotor side PWM converter.
Dynamic equations that describe the behavior of an induction machine are widely studied .
, .
, .
the stator and rotor voltage equations in fixed rotor coordinates can be presented as:
u = u u
O O
Where Rs andRr are the stator and rotor resistances.
Os and Or are the stator and rotor fluxes and Os is the stator angular frequency.
All variables are considered in rotor reference frame.
The stator and rotor fluxes are related with the stator and rotor currents by:
Predictive Power Control of Grid and Rotor Side converters in Doubly Fed.
(Abdelmalek Boulahi.
ISSN:2088-8708 O = u Ou = u u u Where vs, vr, is, ir.
Os, and Or are the stator voltage, rotorvoltage, stator current, rotor current, stator flux linkage and rotor flux linkage, respectively.
Rs.
Rr.
Ls.
L rand L mare the stator resistance, rotor resistance, stator inductance, rotor inductance and mutual inductance, respectively.
The stator active and reactive power can be calculated from the stator voltage and currents as:
= I I
= OI I
Substituting .
, .
, .
, the active and reactive power can also be expressed in terms of stator flux and rotor flux as:
Ou O
= O
= u Ou Oe O Ou O Where O1 is the synchronous speed, = 1/( u Oe ) The presented continuous-time model of the induction machine describes the behavior of the machineAos variables.
Discrete-time equations are derived from this model, in order to obtain active and reactive power predictions for the next sampling interval, where k represent the present sampling instant.
Discrete-time transformation is computed simply by sampling signals and considering a first-order approximation for first derivative forms.
The discrete-time equation for stator and rotor flux prediction, obtained from the presented model, is:
O 1 = O [ Oe O u O ()] .
Ou 1 = Ou .
u u ] .
Where.
Ts is the sampling time.
Using equations .
, the discrete-time prediction of the active and reactive power can be computed as:
Ou 1 O
= O
1 = u Ou Oe O Ou 1 O Equation .
are used to obtain predictions of active and reactive power for each of the 8 valid switching combinations.
Each switching state produce a possible v.
to be applied to the rotor in the nextsampling instant.
That voltage will depend on the switching state to be selected and on the input voltages, as presented in .
Every possible switching state will produce a given value for v.
that will change the machineAos predictions according to equation .
The key technology of predictive direct power control lies in the definition of cost function, which is usually related to the control objectives.
For DFIG used in wind energy applications, the torque .
or-responding to active powe.
and rotor flux .
orresponding to reactive powe.
are of concern.
The cost function will be defined in such a way that active and reactive power at the endof the control period is as close as possible to the commanding value.
Specifically, the cost function is defined as:
= | O Oe 1 | |O Oe 1 | u OO .
A , , , , , .
IJECE Vol.
No.
June 2013: 287Ae293
IJECE
ISSN: 2088-8708
It should be noted that when a null vector is selected, the specific state (V0orV.
will be determined on the principle of minimal switching commutations, which is related to the switching states of the old voltage vector.
SIMULATION RESULTS
To validate the proposed PDPC strategy, simulations using Matlab/Simulink are carried out.
The system and machine parameters are listed in Table.
Table 1.
Parameters of simulation of DFIG Rated Power Stator voltage 6mE Lls Llr Pole paires 9mE DC link voltage DC linkcapacitor Gridside inductance Generator Converter Ir(A ) Is (A ) Is (A ) Ir(A ) The rotor speed is operating at 100red/s.
The active power steps from zero to 1 MW .
at t=0.
5 s and then steps from 1MW to -1 MW at t=0.
55 s .
The reactive power is kept constant at zero, as shown in Figure 5.
P s (W ) & Q s (V A R ) P s (W )& Q s (V A R ) U d c (V ) U dc (V ) t(S) t(S) Figure 3.
Responses rotor and stator current, active and reactive power.
DC link voltage.
m= 100rad/.
Figure 4.
Responses rotor and stator current, active and reactive power.
DC link voltage .
m= 200rad/.
The harmonic spectra of stator and rotor currents under the steady state condition of 1 MW and subsynchronous speed are shown in Figure 6 and 7.
The THD is calculated up to 5000 Hz harmonics.
Predictive Power Control of Grid and Rotor Side converters in Doubly Fed.
(Abdelmalek Boulahi.
ISSN:2088-8708 Ir(A) Is(A) wm.
Ps(W)& Qs(VAR) Udc(V) t(S) Figure 5.
Responses rotor and stator current, active and reactive power.
DC link voltage with rotor speed varying from 100 rad/s to 180 rad/s Ir(A ) Time .
Fundamental .
= 859.
THD= 1.
M a g (% o f F u n d a m e n t a .
Frequency (H.
Figure 6.
Harmonic spectrum of stator current M ag (% of F undam enta.
I s (A ) Time .
Fundamental .
= 1093 .
THD= 1.
Frequency (H.
Figure 7.
Harmonic spectrum of rotor current
CONCLUSION
Based on simulation results, it can be concluded that applied Predictive DPC strategy to control the DFIG has fast, precise and quicker response and better steady state performance.
In addition stator and rotor currents have a low THD.
In order to control DC link voltage.
Predictive DPC strategy is used which has fast and robust performance and maintain the DC voltage at desired reference level, in all operation conditions.
As a consequence, predictive control is a very promising alternative for the future of power electronics.
REFERENCES