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The basic circuit shown in Figure 2.6 is considered here for modeling. The development is based on the fundamental frequency model of UPFC which is presented in Refs. [14] and [15]. The basic concept of UPFC has briefly explained already in this section. Modeling aims to determine the relationship between unified DC bus voltage and injected voltage. A three-phase, PWM controlled voltage source inverter is typically made of six controlled switches (GTO valves with six anti-parallel diodes) switched on and off at very high frequency around 5 kHz. The model considered a stable voltage condition for fundamental frequency voltage sources. One source is connected in parallel while the other connected in a series branch.

The series converters are injecting voltage and hence in the equivalent diagram in Figure 2.7 it is represented with voltage source and modeling is also based on this assumption [16]. The instantaneous power flowing into shunt inverter from AC bus, neglecting transformer losses and assuming balancing conditions with fundamental frequency, can be represented by:

(2.6)

Where,

(2.7a)

Figure 2.7 GUPFC equivalent circuit.

(2.7b)

(2.7c)

(2.7d)

This model consists of two voltage sources. These voltage sources are gained from inverters connected in series and parallel. Hence amplitude modulation factors are used to calculate voltage source magnitudes as:

(2.8)

(2.9)

(2.10)

Where,

k = constant based on type of inverter (for six pulse converter

The power delivered by GUPFC in steady state is given by:

(2.11)

Where,

(2.12a)

(2.12b)

(2.12c)

Using line impedance for calculating voltage as shown in Equation (2.6), Equation (2.11) can be rewritten as:

(2.13)

and

(2.14)

Where,

The resulting equation of GUPFC is considered using Equations (2.10) to (2.14) for finding out factors on which injected power depends. The resulting equation has the form given below:

(2.15)

Equation (2.15) is true only if ash, ase, msh, mse, XT remain constant. It can be seen that series injected power by the GUPFC is controlled by DC voltage (V_dc) and phase angle difference between V₁ and V_se1 (α). This means the sub-system voltage control depends on two quantities (i.e. V_dc and α).