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DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 29.11.2017
Tampere University of Technology

Electrical Energy Engineering

Tuomas Messo Use of own programmable calculator is allowed.

Problem 1 (max 6 points)
Transfer function matrix of a grid-connected battery-interfacing inverter is given at open-loop in (1) and at
closed-loop in (2). What transfer function should be analyzed in the following cases described below.
a) The discharging current of the battery i,,, is controlled using DC-current feedback and the controller
transfer function should be designed. DC-side dynamics are assumed to be dominated by d-components
(real power).

b) Current control is implemented in dg-domain. Crossover freguency and phase margin of the AC-
current control should be evaluated. It is assumed that PI-controlled parameters are already selected,
i.e., controller transfer function is known.

c) Control design is already finished and the effect of grid voltage harmonies on the generated output
currents should be analyzed.

d) Control bandwidth of the AC-current control should be determined.

e) Output admittance d-component should be re-shaped to have higher magnitude at the fifth harmonic.
Changing the size of passive components is not allowed.

Vat [ia
hm] [Gu Ga Cs Gu Gy] hu] [61 G G Gu Gi] %
ia |=| Gn Gn Ox Gn Osl|m|(D) Nin -|6a Cn Ga Gu Gl) tu |
ia] 161 Gn G x G5l/ di ia] 16 Oo Ga Gu Gyli Ki
|4. i

Problem 2 (max 6 points)
Control block diagram of a phase-locked-loop is as shown in Figure 1. The feedforward term o, is a constant
which improves start-up. The Park's transformation can be linearized as ” = v, where %, denotes the

ideal grid voltage g-component.

 

 

 

 

Figure 1: Phase-locked-loop.

a) Draw the linearized control block diagram and define control loop gain of the PLL.

b) Solve transfer function from the reference input 9; to the controlled variable ”

in dg-domain.

€) The transfer function from reference to the controlled variable can be written as a second-order
system as in (3). 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 (4).

G = (2öm,s+0,')/(s* + 20,5+0,?) (3)

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DEE-34206 Dynamics and Control of Grid-Connected Converters Final exam, 29.11.2017
Tampere University of Technology

Electrical Energy Engineering

Tuomas Messo Use of own programmable calculator is allowed.

6, C-Klf+1) N

s

Problem 3 (max 6 points)
Figure 2 shows a simple power electronics -based power system. Answer the following guestions:

a) Which converter is responsible of freguency control of the AC line? Justify how you determine this
from the figure.

b) What variables are controlled using cascaded control scheme?

e) Which converter is responsible of regulating the RMS value of AC voltage? Justify based on Figure 2.

d) How can you decide the minimum voltage of the DC voltage source? (short answer please, no
eguations needed)

e) Consider you need to define an open-loop small-signal model for the load converter. What are the
output variables of the small-signal model? Justify their selection.

  
 

Ac Interface

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i
'
Zaayse i

     
  

 

 

 

 

 

 

 

 

 

 

o i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      
     

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

;
i Current Current ibe) |!
i |/a |] Connor conuoter | || ||

i
i W TT 7 tol !
| E vosge |]!
| can Controller |* |
| BI Gnmle Y5CConrll i

 

 

 

Figure 2: Control system of a power-electronics based AC system.
Problem 4 (max 6 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. Draw the electrical circuits of the
filter in dg-domain (separately for d and g-components).

 

    

 

 

= 7 (Pasn Vina Vina Vea Vea)?

 

 

 

 

 

2 Iliaassa saa)?

Figure 3: Three-phase LCL-type filter. d
= (Pas Vea: Voa Vaa Von)?

 

 

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DEF-34206 Dynamics and Control of Grid-Connected Converters Final exam, 29.11.2017

Tampere University of Technology
Electrical Energy Engineering

Tuomas Messo Use of own programmable calculator is allowed.

Problem 5 (max 6 points)
Grid voltage in unbalanced condition is given in stationary frame according to (5).

a) How is the grid voltage seen in the dg-domain? Give the amplitude and freguencies of different

components.

b) A three-phase inverter is connected to the unbalanced grid defined in (5). The fundamental freguency
of the grid is 50 Hz. A conventional SRF-PLL is used according Figure 1. How much does the PLL
loop gain attenuate the effect of unbalance when it is as shown in Figure 4?

c) How does the unbalance affect power guality of the inverter?

d) What can you do to mitigate the effect of unbalance even more?

= 230." 4100-e 5)

 

Bode Diagram

Magnitude (dB)
p v &
5 o 8 &

ei
83

S
a

Phase (deg)

 

10? 10! 10? 105
Freguency (Hz)

Figure 4: Control loop gain of the PLL in Problem 5.

 

Eguations...
yt ylä mie
e” = cos(x)-— jsin(x)

T

T*".[k k kj" =[0 0 4]

 

 

 

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