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DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 20.12.2016
Tampere University of Technology

Electrical Engineering

Tuomas Messo Use of own programmable calculator is allowed.

Problem 1 (max 8 points)
Power stage of a voltage-fed inverter with output-current control is as shown in Figure 1.
5 i : 357 Sja
a) Develop the inverter average model in dg-domain at open-loop, 6) = 35% (iu) +5% (ia) =
b) Draw the eguivalent linear circuit in dg-domain (DC input port and two AC output ports).

c) How do you have to modify the duty ratio d and g-components (how to define xa and xg ) to make the
inverter output currents independent of the grid voltage d and g-components? Justify the result using
the average model.

d) How do you realize decoupling of the current d and g-components? Use the average model to obtain
necessary control laws / scaling coefficients. Correct answers earn points only if you can justify them
using the average model.

 

 

 

 

Figure 1: Voltage-fed inverter with output-current control.

Problem 2 (max 4 points)

Instantaneous apparent power can be defined as the product of voltage space-vector and the complex-conjugate
of current space-vector in the stationary reference frame as in (1).

a) Define real and imaginary power in the synchronous reference frame, i.e., in the dg-domain. The space
vector is assumed to rotate at the fundamental grid freguency 07. (Useful formulas: eaten.

(x) N (x): E! ; T =1 )

b) Explain based on the previous result how the real and imaginary power produced by three-phase
inverter can be controlled independently.

S= (i) (0)

Problem 3 (max 6 points)
The control block diagram of the phase-locked-loop is as shown in Figure 3. The feedforward term &, isa

constant which improves the start-up. The Parks transformation can be linearized as ' = v, —V;0 where 5,
2 p a g d a

denotes the ideal grid voltage g-component.
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DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 20.12.2016
Tampere University of Technology

Electrical Engineering

Tuomas Messo Use of own programmable calculator is allowed.

 

Figure 3: Phase-locked-loop.

a) Drawthe linearized control block diagram and give the control loop gain of the PLL.
b) Solve transfer function from the reference input to the controlled variable % in dg-domain.
c) Thetransfer function from reference to the controlled variable can be written as a second-order

system as in (2). Find out the damping ratio £ and natural freguency &, in terms of controller
parameters. You can assume that the controller transfer function is as given in (3).

G=(20,s+0" )/(s? +20,s+0,”) (2)

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Problem 4 (max 6 points)
Give short answers to following guestions.
1. Whatis the main benefit of implementing current control in dg-domain?
Why do you need to solve steady-state operating point? |
Can you stabilize a converter which has an unstable pole in its control dynamics? How?
Give a short definition of cascaded control scheme?

How does phase-locked-loop affect the output impedance of a three-phase inverter?

au s E N

How does grid-voltage feedforward affect the output impedance of a three-phase inverter?

Problem 5 (max 6 points)

Three-phase LCL-filter is shown in Figure 4. 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. Draw the electrical circuits of the

filter in dg-domain (separately for d and g-components), (== E1. +) (19 [k k Kl = [0 o 4f') =

 

 

TT (Paso int Vina YC4Y6a)?

 

 

= nan taa)?

Figure 4: Three-phase LCL-type filter. d.
—i3= fPus>YcaYca 1o4:%04)?