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Fig. 19.10 Comparison of STATCOM models for the IEEE 14-bus system

19.4.1Detailed Model

The detailed model consists of a series-connected VSC device with a capacitor on the dc side (see Figure 19.11). The model is composed of three parts, namely the dc network, the VSC and the controllers.

+

vdc

−

Fig. 19.11 SSSC scheme

Dc network : The dc side is a parallel RC defined by (17.10) and (17.2). Furthermore, the dc network must contain two nodes, one of which is connected to the ground. The VSC and the RC element are connected in parallel to the dc nodes.

Series-connected VSC model : The equations of the VSC are (17.2), (18.9)- (18.11) and (18.13).

Regulators: The control system is then used for controlling the dc voltage vdc and the active power ph or current flow ih in the ac side. Figure 19.12 depicts the dc voltage control, the active power control and the measurement transfer functions, which are described by the following DAE system:

where all parameters are defined in Table 19.12. Both the firing angle α and the modulating amplitude am undergo windup limiters. The active power signal in the firing angle control diagram can be substituted by the current ih.

Fig. 19.12 SSSC control diagrams

19.4.2Simplified Dynamic Model

Simplified SSSC dynamic models have been proposed in [162, 193, 288] where the SSSC is represented by a series voltage source v¯S , as depicted in Figure 19.13. The voltage v¯S is in quadrature with line current. Thus, the voltage magnitude vS is the only controllable variable. The total active and reactive power flows in a transmission line in series with a SSSC device are:

The SSSC regulator is shown in Figure 19.14. The regulator di erential equations are:

v˙S = (˜vS − vS )/Tr

Table 19.7 defines all parameters of the SSSC simplified dynamic model.

vSmin

Fig. 19.14 SSSC simplified control diagram

Table 19.7 Simplified SSSC model parameters

19.4.3Power Flow Model

The SSSC power flow model is simply obtained based on the power flow model of the VSC device (18.29) and (18.30). In particular, (18.30) are:

The latter condition is satisfied only if the current ise ≤ imaxse .

19.4.4SSSC Initialization

Dynamic SSSC devices can be initialized using a static tie line, similarly to the TCSC devices. The tie line provides the compensated value x˜hk of the

series reactance that leads to the desired active power flow. Then, the SSSC state variable vS can be obtained by solving:

Alternatively, one can use the power flow model described in Subsection 19.4.3.

19.5Unified Power Flow Controller

The Unified Power Flow Controller (UPFC) combines together a shunt and a series VSC with a common capacitor in the dc side. The shunt connection allows regulating the voltage (like a STATCOM) while the series connection allows controlling the power flow (like a SSSC). The UPFC is a very versatile device although it is relatively rare due to its complexity and high cost.

19.5.1Detailed Model

The detailed model consists in a shunt-connected VSC device and a seriesconnected VSC device with a common capacitor in the dc side (see Figure 19.15). The model is composed of four parts, namely the dc network, the shunt VSC, the series VSC and the controllers.

+

vdc

−

Fig. 19.15 UPFC scheme

Dc network : The dc side is a parallel RC defined by (17.10) and (17.2). Furthermore, the dc network must contain two nodes, one of which is

The power flow regulation is a dq control, as shown in Figure 19.17, which allows decoupling the controls of the active and reactive powers [232, 323].

Fig. 19.17 UPFC series dq control diagrams

where the sub-indexes d and q indicate the direct and quadrature components, respectively. For this series branch dq control, the variables am,se, αse and other control parameters are given by the following relations where Ωb is the fundamental frequency base in rad/s and other variables are expressed in per unit: