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DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 24.1.2019
Tampere University of Technology

Electrical Energy Engineering

Tuomas Messo Use of own programmable calculator is allowed.

Problem 1 (max 5 points)

Figure 1 shows the control scheme of a grid-connected converter. Answer the following guestions:

a) In which reference frame is the current control implemented in? What is the benefit of using this
reference frame?

b) Justify why the DC voltage can be regulated by changing the value of inductor current d-component.

c) How would you modify the control system if you implemented the current control in the stationary
reference frame?

d) Whyisthe term &,,, multiplied with the inductance value and subseguently multiplied with current
value and then added in the output of the PI-controller? How does this additional signal loop affect the
converter operation during transients?

e) To which voltage does the converter synchronize its output currents into? How can you see this from
the control diagram?

PCC

 

 

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gr

  

 

 

 

N av.ref

 

 

 

 

 

 

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Figure 1: Control system of a grid-connected converter.

Problem 2 (max 5 points)

A voltage-fed inverter is as shown in Figure 2. Define the average model in the dg-domain. Use the average
model to derive the decoupling gains in current control and the grid-voltage feedforward gains. L.e., how should
you modify control inputs to decouple current d and g-components and to reduce the effect of grid voltage
harmonies? Give the appropriate gains. Note that variables c, and €, are now the control variables. (Hint:

Derive the model first assuming d, and d, as inputs, and subseguently add the effect of gains k, and £, ).

i;

   

 

 

 

 

 

 

 

Figure 2: Voltage-fed inverter.

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DEF-34206 Dynamics and Control of Grid-Connected Converters Final exam, 24.1.2019
Tampere University of Technology

Electrical Energy Engineering
Tuomas Messo Use of own programmable calculator is allowed.

Problem 3 (max 5 points)
Transfer function matrix of a grid-connected photovoltaic inverter is given at open-loop in (1).

a) Draw the control block diagrams that represent the inverter output dynamics in dg-domain and include
the output current controllers, sensing gains and PWM modulator gain.

b) Draw a control block diagram where cascaded control scheme is implemented to regulate the PV
voltage. You can assume that DC-side dynamics depend mainly on d-components and that cross-
couplings between d and g-components can be neglected.

c) Use the control block diagram to solve the transfer function of the DC voltage control loop gain.
d) Explain the tuning process of the cascaded control loops.

€) Solve the output admittance g-component from the block diagram. You can assume the output current
g-component is not affected by any of the d-components.

[ [6 6 6 Ge erä
iu |=|GX GX 05 09 03 | a | (1)
i | [ot 62 09 62 o] d,|

KN

Problem 4 (max 5 points)

Three-phase LCL-filter is shown in Figure 3. Solve the average state-space model of the filter in the dg-domain.
You can assume that the three-phase input and output voltages are balanced. The zero component can be
neglected. Draw the electrical circuits of the filter in dg-domain (separately for d and g-components),

 

 

 

 

 

 

 

 

 

 

 

 

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Vaa o hi ta n bin voa
0) N > 1 O
aN Ke].
N +-0 Nr R
Nm L ni n & Noe] V
* JE lc C
Voi I
S

 

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