Grid-Side Converter Control

The field oriented control method, although originally developed for motor control applications, can also be used to enable the grid-side converter to control the flow of active and reactive power. When used in this way it is referred to as vector control. A schematic of the grid-side converter is given in Figure 2.12.

Figure 2.12: Grid side converter arrangement.

From Figure 2.12 the grid voltages can be expressed as follows:

(2.27) (2.28) (2.29)

These equations in the , reference frame are given as follows (Pena, Clare & Asher, 1996):

(2.30)

(2.31)

where is the synchronous frequency, and are the grid voltages in the , reference

frame, and are the converter voltages in the , reference frame and and

are the grid currents in the , reference frame. and are the inductance and

resistance between the converter and grid. All parameters of the grid-side converter are in Appendix A4.

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If the converter is lossless then a power balance relationship between the power stored in the DC link and the power flowing to the grid can be given as:

(2.32)

The current flowing in the DC link can be given as:

(2.33)

where is the DC link capacitance, is the DC link voltage, and are the DC link

current and the load current as shown in Figure 2.12.

If the -axis is assumed to be aligned with the grid voltage vector and the -axis leads the -axis by 90 degrees then . Therefore, independent control of the active and reactive power can be achieved by controlling the and -axis currents as shown by equations (2.34) and (2.35) (Chinchilla, Arnaltes & Burgos, 2006).

(2.34)

(2.35)

It is clear from equations (2.34) and (2.35) that the active power can be controlled solely by the -axis current and the reactive power can be controlled solely by the -axis current. The phasor diagram for the field oriented control scheme of the grid-side converter is shown in Figure 2.13, where it is seen that the grid voltage vector contains only a -axis component.

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The vector control strategy implemented on the grid-side converter controls the active power flow into the grid, via regulation of the DC link voltage, using the -axis current. The reactive power flow is controlled using the -axis current as given by equation (2.35).

Figure 2.14 shows the vector control scheme for the grid-side converter. Two control loops are used to control the active and reactive power. A cascaded control loop is used to control the active power flow to the grid, whereby the outer voltage control loop sets the -axis current reference of the inner loop. The reactive power is regulated by setting a -axis current reference In some cases the grid operator may require the turbine to supply reactive power compensation (Michalke, Hansen, 2009). However, under normal operation the converter will transfer all the active power generated by the TST to the grid; therefore, in this case the -axis current reference is set to zero. Figure 2.14 shows the situation under normal conditions where the turbine is operating at unity power factor.

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The values for the -axis and -axis currents and voltages are obtained from the measured three phase values using the transformation given by:

(2.36)

where is the grid phase angleobtained using a phase locked loop (PLL). The PLL was

implemented using a standard block from the SimPowerSystems library in Simulink®_{. The -axis}

and -axis current loops are identical, with each loop generating a voltage reference as described by equations(2.37) and (2.38).

(2.37)

+ (2.38)

and are the proportional and integral gains of the respective PI controllers, is the - axis current error and is the -axis current error . To decouple the voltages and allow for independent control of the active and reactive power decoupling terms, and , are included in both equation (2.37) and (2.38). Feed- forward voltage terms are also added to each voltage reference. Decoupling and voltage feed-forward are commonly used and are known to improve the transient response of the system (Blaabjerg et al, 2006; Twining & Holmes, 2003)

Finally the -axis and -axis voltages are transformed back to a-b-c reference voltages using the transformation of (2.39). The grid phase angle is used to ensure

synchronisation. The reference voltages are then used to generate the PWM signals for the grid- side converter. (2.39)

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Grid-Side Controller Design – Current Loop

The block diagram for the inner current control loop of the grid-side converter has the same structure as the inner current loop for the generator-side converter (Figure 2.10). The transfer functions are given as follows:

(2.40) (2.41) (2.42) All parameters for the converter and grid connection are in Appendix A4. The controller was designed using the same procedure as that used for the generator-side converter. The following criteria were specified before designing the controller:

 Closed loop response should have zero steady state error.

 Maximum overshoot of the step response should be limited to less than 5%.

 The bandwidth should be high enough to ensure that the inner current loop is decoupled from the outer voltage control loop. Thus a minimum bandwidth of 250 Hz was specified.

Once again a damping ratio of 0.69 was chosen to ensure an overshoot of less than 5%, the resulting transfer function of the PI controller was

(2.43) From the frequency response curves of Figure 2.15 (a) it is clear that the controller gives a good response. The phase margin is 78 degrees and the overshoot is well within the 5% limit. This is reflected in the step response of Figure 2.15 (b). The system achieves a bandwidth of 248Hz leading to a settling time of 40 ms which can be seen in the step response of Figure 2.15 (b). It should be noted that the control parameters used for the -axis current loop are also applicable to the -axis.

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Figure 2.15: (a) Bode plot showing frequency response of the grid-side current control loop

in closed loop and open loop (b) Grid-side current control loop step response. Grid-Side Controller Design – Voltage Loop

The outer voltage control loop generates the current reference for the inner current loop (Figure 2.16). The inner loop must be faster to ensure that there is no interaction with the outer voltage loop. As a rule of thumb the bandwidth of the inner loop should be 5-20 times faster than that of the outer loop (Liserre, Blaabjerg & Aquila, 2007). If this is the case then, for the purposes of tuning the outer loop, the inner loop can be approximated as a unity gain.

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The dynamics of the plant, relating the DC link voltage to the -axis current , can be

derived from equations (2.32) - (2.34) giving:

(2.44)

The minimum DC link voltage required is determined by the grid side voltage and the amplitude modulation ratio of the converter as (Mohan, Undeland & Robbins, 2002):

_(2.45)

where is the amplitude modulation ratio, is the peak grid phase voltage. Rearranging (2.45) the peak value of the fundamental voltage component in one inverter leg is given by:

(2.46) Since the reference frame is oriented along the grid voltage = 0 and the grid voltage vector is:

(2.47) therefore the following is true:

(2.48)

By substituting (2.48) into (2.44) it is possible to express the DC link voltage as:

(2.49)

Using (2.49) a Laplace domain transfer function relating the -axis current to the DC link voltage , can be given as:

(2.50)

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 Closed loop response should have zero steady state error.

 Maximum overshoot of the step response should be limited to less than 5%.  The bandwidth should be 20 times lower than that of the inner current loop. The resulting transfer function of the PI controller is:

(2.51)

The frequency response curves of Figure 2.17 (a) show that the controller gives a good response that meets the design criteria. The phase margin is 78 degrees and the overshoot is within the 5% limit. This is reflected in the step response of Figure 2.17 (b). The system achieves a bandwidth of 12.3Hz, which is approximately 20 times slower than that of the inner current loop (Figure 2.15 (a))

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The parameters for the current and DC-voltage controllers of the grid-side converter are summarised in Table 2.2.

Controller

1.01 70

1.01 70

9.4 140

Table 2-2: PI controller parameters for the grid side converter