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# Master of Science Thesis in Electric Power Engineering - page 39 / 114

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### VOLTAGE ORIENTED CONTROL – SIMULATION

• 3.5

• 3.5.1

DC LINK MODEL The DC link voltage is modeled as a pure capacitor. This capacitor is an energy storage where

the stored electrical energy in Joule is 1

2

(3.20)

The time derivative of this stored energy should be equal to the sum of instantaneous grid power and load power [14] .

1 2

(3.21)

As we can see, the previous equation is not linear with respect to Vdc.

Figure 3.15 : Energy transfer

## LINEARIZATION

The design of the voltage controller is facilitated thanks a feedback linearization. The feedback linearization transforms the nonlinear dc voltage dynamics to a equivalent linear system, on which traditional linear controller design can be applied.

.

(3.22)

## Then, equation (3.21) becomes

1 2

(3.23)

which is linear with respect to

. The physical interpretation is that the energy is chosen to

represent the dc link voltage dynamics instead of the voltage itself. Other type of linearization can

be found [14] .

# 3.5.2 Design of voltage controller

Â System transfer function Following [14] and the Internal Model Control method, we can write

1 2

3 2

(3.18)

(3.24)

1

3

2

2

where

is the d current, and the grid voltage

. The coefficient comes from the amplitude

invariant transformation (see section “2.2.2 Mathematical model” about power calculation).

(3.25)

30

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