For some industrial applications, The demand for voltage ratings is so high that a single SCR cannot fulfill such requirements. Hence SCRs are connected in series in order to meet the h.v. demand.
String Efficiency=Actual voltage rating of the whole strings/(Individual voltage rating of one SCR x Number of SCR in the string)
Derating factor (DRF)=1-string efficiency
Note: String efficiency is degree of utilization of SCR and Derating factor is a measure of the reliability of string.

Characteristics of SCR

I-V characteristics of both the SCR should be as close as possible. On account of inherent variations in their characteristics, The voltage shared by each SCR my not be equal.
• For SCR1, Leakage resistance, RL1=V1/IO
• For SCR2, Leakage resistance, RL2=V2/IO
• As V2<V1, String efficiency=(V1+V2)/(VX 2)=1/2x(1+V2/V1)

Static Equalization Circuit

A uniform voltage distribution in steady state can be achieved by connecting a suitable resistance across each SCR i.e. each parallel combination has the same resistance as given in Fig. 2.
Now calculating R:
• Consider n thyristors connected in series. Let SCR1 has minimum leakage current Ibmn and each remaining (n-1) SCR have the same leakage current Ibmx>Ibmn. Hence SCR1 will block voltage Vbm (sar) which is more than shared by each of the other (n-1) SCR. From Fig.
• I1=I-Ibmn.................................................(1)
• I2=I-Ibmx.................................................(2)
• VS=I1R+I2R(n-1)
• VS=Vbm+(I-Ibmx)R(n-1)
• VS=Vbm+(I1+Ibmn-Ibmx)R(n-1)
• VS=Vbm+(I1-△Ib)R(n-1)
• VS=Vbm+I1R(n-1)-△IbR(n-1)
• VS=Vbm+Vbm(n-1)-△IbR(n-1)
• VS=Vbm+nVbm-Vbm-△IbR(n-1)
• VS=nVbm-△IbR(n-1)
• △IbR(n-1)=nVbm-VS
• R=(nVbm-VS)/△Ib(n-1)
Note: SCR with lower leakage current blocks more voltage.

Dynamic Equalization Circuit

SCR do not have identical dynamic characteristics, In such case, series connected SCRs will have unequal voltage distribution during the transient conditions of turn-ON, turn-OFF and high frequency operation.
A simple resistor for static voltage equalization cannot maintain equal voltage distribution under transient condition.

• Voltage equalization under these conditions can be achieved by employing shunt capacitors.
• The function of RC and C is to equalize the voltage during dynamic conditions.
• C=(n-1)△Q/(nVbm-VS)
• Where: △Q=Q2-Q1

Reference

• Dr. P. S. Bimbhra, "Power Electronics", Khanna Publishers, Fifth Edition, 2013.