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DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 1.2.2017
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 dg-domain output-current control is as shown in Figure 1.
a) Develop the inverter average model in dg-domain at open-loop, (5 = ETA (14) + : d, (ä J) 3

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 (by adding xa and x; ) to make the
inverter output currents independent of the grid voltage d and g-components? 1.e., how to implement
grid voltage feedforward?

d) How do you realize decoupling of the current d and g-components? Use the average model to obtain
necessary control laws / scaling coefficients.

 

 

 

 

 

 

 

 

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 o. .

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

s=v".(i*) (1)

Problem 3 (max 6 points)
Control block diagram of a phase-locked-loop is as shown in Figure 2. The feedforward term &, isa constant

which improves start-up. The Park's transformation can be linearized as % =v, -V,0 where %, denotes the

ideal grid voltage g-component.

 

 

Figure 2: Phase-locked-loop.

 
 

DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 1.2.2017
Tampere University of Technology

Electrical Engineering

Tuomas Messo Use of own programmable calculator is allowed.

a) Draw the linearized control block diagram and define control loop gain of the PLL.
b) Solve transfer function from the reference input v” to the controlled variable v; 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" +220,5+0,") (2)

G. -CDKGN (3)
Problem 4 (max 6 points)
Give short answers to following guestions.
1. Whatis the main benefit of implementing current control in dg-domain?
How can one implement current control of three-phase inverter outside dg-domain?
Why do you need to solve steady-state operating point?
Can you stabilize converter which has a RHP-pole in its control dynamics? How?

Give short definition of a cascaded control scheme?

N Uu = » N

How should the PLL bandwidth be selected when grid voltages are unbalanced? *

Problem 5 (max 6 points)

Figure 3 shows current control loop gain with a simple unity-gain integrator as the controller (4). Comment on
the stability and expected performance of the current control. Propose a controller transfer function to increase
stability margins and explain how to select controller parameters (poles/zeros/gains). The control loop gain
should have a crossover freguency around few kilohertz. You don't need to give specific values for controller
parameters. You may sketch bode diagrams to justify the tuning process.

: an = Garda” 4)

Bode Diagram

Magnitude (dB).

 

Figure 3: Current control loop gain.