A CCS model to be considered must be defined. A basic MATLAB/Simulink CCS model is presented in Figure 1 and Figure 2 presents a basic simplified CCS.

In a multiple CCS, each CCS can be represented using a simplified equivalent circuit model as presented in Figure 2 with:

Given:

$V_T=V_{in}\times \frac{C_1}{C_1+C_2}$

$V_{out}=V_T-V_L$

where:

A model representation of multiple CCS is given in Figure 3 , which is the combination of a number of CCS. This basic model is used as the basis for modelling. However, any number of CCS can be incorporated into the system.

Assume a transmission line of length $L_t$ with N CCSs placed at distances, $d_1,d_2,\cdots ,d_N$ from the source.

For each CCS:

$Z_{line,i}=R_{line,i}+X_{line,i}$

where:

$R_{line,i}$ is the resistance of the line segment up to CCS i.

$X_{line,i}$ is the reactance of the line segment up to CCS i.

$V_i=V_{in}-I_i\times Z_{line,i}$

The current drawn by the CCS i is:

$I_i=\frac{V_T}{Z_{CCS,i}}$

where:

$Z_{CCS,i}=R_{CCS,i}+j{X}_{CCS,i}$ is the impedance of the CCS i including its internal elements.

$Q_{total}={\displaystyle {\sum }_{i-1}^N{Q}_{CCS,i}}$

$V_{line}=f\left(d_i,Z_{line,i},Z_{CCS,i},V_{in}\right)$

$I_{line,i}=\frac{V_i}{Z_{line,i}}$

$P_i=V_i\times I_i\times \text{cos}\left({\theta }_i\right)$

$Q_i=V_i\times I_i\times \text{sin}\left({\theta }_i\right)$

where ${\theta }_i$ is the phase angle between voltage and current.

The three following simple steps can be used during simulation, vis.:

MATLAB can be used to simulate a number of parameters that may be required. Example of a MATLAB code used to simulate the voltage drop across the transmission line with three CCS units placed 300 km apart, each with a load of 80 kW at 11 kV is given by:

The experimental data used, selected purely on the limited available resources, is presented in Table 4 .

The result of the simulation is presented in Table 5 where the measurements were taken from the points as demonstrated in Figure 4 .

A verification approach was used using different parameters of the CCS where the supply voltage was selected as 230 kVrms and the downstream load was 100 kW, with the three identical CCS. The focus was on the supply voltage interference when the CCSs were connected to it. The results are presented in Figures 5-9 .

From both the modelled results and the tested results, it shows that when the CCSs are switched into the system, there is no notable interference on the supply voltage, which could imply system instability is a real life setting if there was any observed interference and drastic changes in the tested voltage at different points.

The parameters selected for the model, were based on a typical transmission network voltage of 230 kVrms, while the prototypes were built for the laboratory available 230 Vrms system. The distances for the prototypes were represented by the resistances. These values were arbitrarily selected to observe the system behaviour in the event of distance changes. The observed reactive power fluctuations from Figures 4-8 , can be attributed to switching transients as they are present only after a CCS is switched either ON or OFF. The test on the prototypes did not consider any power flow, its main focus was the behaviour of the supply voltage as the results in Table 5 show that the supply voltage magnitude was not affected by the switching ON of the CCSs.