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.