6.7 Dual Vector Voltage Control Strategy (AC link)
6.7.1 Sequence Decomposition
An unbalanced three phase voltage and current can be decomposed into two sets of components based on the instantaneous symmetrical components theory [169]. The positive and negative sequence components can be implemented using a band pass filter as described in [170].
6.7.2 Sequence Transformation
The AC voltage and current signals are measured and decomposed into symmetrical components to identify the positive and negative sequence components. The voltage and current measurements are projected onto the synchronous reference frame (SRF) at the fundamental frequency. The positive reference frame rotates in a counter clockwise, therefore the voltage and current are rotated in a positive SRF using positive fundamental frequency. The negative reference frame rotates in a clockwise direction, therefore the voltage and current are rotated in a negative SRF using negative fundamental frequency as shown in Figure 6.7. A phase locked loop (PLL) is used to extract the fundamental frequency () and phase angle (/) from the reference sinusoidal voltage signal (,-.
6.7.3 Voltage Loop
The dynamics of the AC link voltage is defined in (6.2) as a space phasor expressed at the primary side of the transformer
S âL 8 â â( *6.2-
where â, â and â( are the AC link voltage at the primary side of the transformer, current before the filter capacitance, and current after the filter capacitance in space phasor form. Using Park’s transformation technique, the space phasor is transformed into the SRF as shown in (6.3).
ãS
> 8 XSY, G ( S> 8 X, SYG , (,
*6.3-_
where subscript ‘L’ defines the positive ‘5’ and negative ‘6’ sequence components. Therefore, (6.3) can be expressed for both positive and negative sequence components. A feed-forward scheme in the voltage loop is employed to eliminate the coupling between the axis voltages as shown in Figure 6.7. The currents are also measured and feed-forwarded to mitigate the impact of the load dynamics on the AC link voltage. Therefore, (6.3) can be expressed as in (6.4),
ä 8 S åæç XSY,G ( , 8 SåèçG XSYG (, *6.4-_ where Såéç
is the result of controller output, XSYêG (ê is the feedforward term
and ë 8 , . The right hand terms in (6.4) provides the reference current (ê. - for the inner current loop, thus (6.4) can be written as
. 8 ì XSY,G ( *6.5-
,. 8 ì, G XSYG (, *6.6-
where ì and ì, are the PI controller outputs of the voltage error. Therefore, the reference current for the inner current loop is determined by the PI controller and feed- forward terms in the outer voltage loop.
6.7.4 Current Loop
The inverter AC side terminal voltage (,,) in the frame is defined in (6.7).
ã 8 R F
> J QG R,G &
, 8 R F> J Q, , RG &, *6.7-_
The inverter terminal voltage (&,,) is controlled in the - frame by the pulse width modulating signals of the inverter, as defined in (6.8)
ã& 8
2 &, 82 ,
Substituting (6.8) in (6.7) allows the current controller to be expressed as (6.9). ã R F > J G Q 8 R,G2 R F> J G Q, , 8 RG 2 , _ *6.9-
The terms at the right hand side of (6.9) are the feed-forward terms, which are implemented in vector current control to decouple the dynamics of - axes currents, mitigate the dynamic effect of DC voltage variations, and react rapidly to mitigate any changes in AC link voltage. Therefore, (6.9) can be reduced to a first order system using the feed-forward scheme as shown in (6.10).
ãR F
> J G Q 8 í R F> J G Q, , 8 í,
_ *6.10-
The outputs of the PI controllers (í and í,) are used in the current loop allowing the modulating signals ( and ,) to be determined by substituting (6.10) in (6.9).
ä 8
;
åæî*í R,G -
, 8å;æî*í,G RG ,-_ *6.11-
Hence, the vector outer voltage loop and inner current loop can be separately implemented with regards to positive and negative SRF using (6.5), (6.6) and (6.11), as shown in Figure 6.7.
6.7.5 Sequence Composition
The modulating signal (,- of positive and negative sequence components are composed in the frame as shown in (6.12).
ß 8 G '
, 8 ,G ,' _ *6.12-
The modulating signal is transformed into the ‘abc’ form so that the pulse width modulating (PWM) technique can be employed to regulate the amplitude and frequency of the AC link voltage at their respective reference levels irrespective of balanced or unbalanced loads.
6.7.6 Proportional-Integral (PI) Controller
The positive sequence - voltages and currents appear as DC quantities in the positive sequence reference frame. Similarly, the negative sequence - voltages and currents appear as DC quantities in the negative sequence reference frame. Therefore, the PI controller is implemented to regulate the voltage and current as per their reference values in the respective rotating reference frame. The integral part of PI controller takes care of zero steady state error; however, the frequency response analysis technique [171] is used to enhance the stability of the closed loop system. In this application, ideally a high bandwidth is required to have fast dynamics and attenuation of harmonic distortion. However, the bandwidth must be considerably smaller than the switching frequency of 10 kHz [172]. Therefore, the PI controllers are designed with the bandwidth 1/8 times of the switching frequency with a phase margin 53° for inner current loop and 66.7° for outer voltage loop.
6.8 Experimental Validation
An experimental investigation is performed to validate the effectiveness of the proposed control strategy for a hybrid system consisting of a wind source, battery energy storage and loads. The experimental setup is shown in Figure 6.8. An induction motor drives the PMSG generator with control to emulate the wind turbine as a wind turbine simulator (WTS). This WTS emulates the static and dynamic behavior of a real wind turbine installed at the campus. A lead acid battery is used as the energy storage device. A DC- DC converter and an inverter are also designed and fabricated to support this experiment. The Texas Instrument (TI) controller and National Instrument (NI) LabVIEW controller are used to control the DC-DC converter and the WTS, respectively. The data is collected through the dSPACE control desk using a step size of 58 µsec and down-sampled by a factor of 5. The system parameters are given in Appendix A.
Figure 6.8: Experimental configuration of the hybrid system
The following facts need to be considered for the experimental results.
(1) The experiment is performed over a short duration; therefore, the state of charge (SOC) of the battery does not change drastically;
(2) The DLV is the same for all sources and load connected to the DC link; therefore, the flow of current determines the power output and is used as an equivalent term for analysis; and
(3) Some of the experimental results were observed to contain measurement and machine noises, particularly when the wind source was activated.