Study on the soft-start process of PSM high voltage power supply for ECRH

The soft-start process of high voltage power supply (HVPS) based on pulse step modulation (PSM) for ECRH on EAST is introduced, which is the first procedure of system operation. The response process is detailed by proposing DC equivalent circuit model, process analysis and performance comparison is given under the conditions of different soft-start resistor parameters, and the theoretical analysis is proved by the simulation package ANSYS Simplorer simulations. The soft-start resistor is designed for the HVPS of 140GHz ECRH system for a smooth charging without overshoot of the capacitor[6], and the final experimental results show that it is in agreement with the theoretical analysis and is stable and reliable to the power devices.


Introduction
The HVPS based on PSM [1] technology has the advantages of fast opening and closing, high reliability and modularization etc., which has been widely used in Tokamak auxiliary heating system. The structure of 140GHz ECRH HVPS system [2,3] is shown in Fig.1, which is composed of 10kV breaker cabinets, 10kV contactor cabinets, multi-winding transformers and rectifying modules.
There are two steps to establish output DC voltage of power supply.
1) The first step is that the filter capacitor of rectifier module is charged by closing breaker and contactor.
2) The second step is that the output DC voltage is built by closing IGBT.
When the HVPS is powered up, to limit the inrush current of transformers and the charging current of capacitor, the series resistor needs to be connected in the 10kVAC side or in the module side. There are almost one hundred of rectifier modules in the HVPS system, so the series resistor [4,5,6] in each module will significantly increase the manufacturing difficulty, volume and cost of modules, therefore the series resistor in 10kVAC side is more economical and feasible [7] . The soft-start includes two processes: insert and removal of the resistor. In the following, the soft-start process will be analyzed theoretically and be verified by ANSYS Simplorer simulation and experimental results.

DC equivalent model of rectifier module
The equivalent circuit with the series resistor which is located in the 10kVAC side is shown in Fig.2. The AC source charges the capacitor through the soft-start resistor, transformer, and three-phase uncontrolled rectifier, and then the DC output of the rectifying module is controlled by the IGBT switch. The process of charging the filter capacitor is called the soft start process. The parameters of each branch are equal, mutual influence can be ignored, and the current and voltage on each branch are approximately equal, so the model in Fig.2 can be simplified as DC equivalent circuit which is shown in Fig.3. The basic parameters of multi-winding transformer are shown in Table 1.  Because the current always flows over two phases, when the filter capacitor is charged, the DC side resistor is two times of it in the AC side. Equivalent inductance:

The analysis of soft-start process
The soft-start process consists of two steps: 1) The first step is that the soft-start resistor is connected into the circuit, the filter capacitor is charged to the first steady state value through the soft-start resistor.
2) The second step is that the soft-start resistor is removed, so the filter capacitor is charged to the second steady state value.

The charging process with the soft-start resistor
The charging equivalent circuit with the soft-start resistor is shown in Fig.4.
And the characteristic equation of transfer When ∆< 0 , the equivalent resistor satisfies R < 2√ L C , the circuit is underdamped. It will cause overshoot of the output voltage. In order to avoid overshoot, ∆ should be more than zero, the equivalent resistor should satisfy R > 2√ L C , so that the circuit is overdamped. Take note of (3), the soft-start resistor can be defined by: If the resistor is large enough to satisfyR ≫ 2√ , the RLC circuit can be equivalent to a RC circuit, U: Input voltage of DC equivalent circuit The peak current of charging is express as follow equation: In order to ensure that the rectifying bridge and capacitor can withstand maximum current, the charging current must be less than 300A, therefore the soft-start resistor should satisfy: According to (5), when N=1, 2 N √ get the maximum 2 √ , so the soft-start resistor satisfy: The circuit is simulated by selecting different softstart resistor, the results are shown in Figure 5. According to the design of the module, the simulation parameters are set as follows: 1) Input voltage of DC equivalent circuit U: 1000V.
3) Filter capacitor C: 10mF.  According to Fig.5 and Table 2, when the soft-start resistor is less than K 2 √ L C which is equal to 124Ω according to the simulation parameters, the circuit is underdamped, the steady voltage of filter capacitor is larger than 1000V, and furthermore, the overshoot voltage is smaller with the increase of the soft start resistor. When the soft-start resistor is larger than K 2 √ L C which is equal to 124Ω, the circuit is over damped, the steady voltage of filter capacitor is about 1000V, and the capacitor is charged without overshoot.

The charging process of removing the softstart resistor
When the filter capacitor is charged to the first steady state value, the voltage is less than the rated value because of soft-start resistor voltage drop, so the softstart resistor must be removed to get the rated value and reduce the power loss. The soft-start resistor is removed by closing S2 in Fig.3, then the capacitor will be charged again to the rated value. The equivalent circuit is shown in Fig.6. The voltage drop of soft-start resistor which is produced by transformer magnetizing current is ∆U = , the excitation can be equivalent to: The time domain expression is established as follow equation. According to (10), the voltage increment of filter capacitor is: The peak current is expressed as follow equation: In order to ensure that the charging current is less than 300A, the soft-start resistor should satisfy: The circuit is simulated by selecting different softstart resistor, the selection of resistor need to guarantee that the circuit is over damped. According to the simulation parameters, the soft-start resistor must be R > 2 √ and the simulation parameters are set as follows: 1) Input voltage of DC equivalent circuit U: 1000V.
3) Filter capacitor C: 10mF.   500  160  943  1050  107   1500  472  837  1150  313 Imax2: Maximum charging current of removing the softstart resistor. U1: The initial voltage of the filter capacitor before removing the soft-start resistor. U2: The steady voltage of the filter capacitor after removing the soft-start resistor. △U: The voltage change of the filter capacitor by removing the soft-start resistor.

Rsoft(Ω)
According to (13), when the soft-start resistor is less than 300 √6 √ , which is equal to 968Ω, the rectifying bridge and capacitor can withstand maximum current 300A. Take note of Table 3, when Rsoft=500 ＜ 968Ω, Imax2=160＜300A, and when R=1500＞968Ω, Imax2=472 ＞300A. According to (12) and Table 3, Imax2 will enlarge with the increase of the soft-start resistor, and according to (11) and Table 3, △U will enlarge with the increase of the soft-start resistor. So in order to reduce voltage fluctuation of filter capacitor, the soft-start resistor should be reduced as far as possible.
According to the analysis, the design of the softstart resistor must meet the following conditions. (1)In order to avoid overshoot, the soft-start resistor must satisfy: (2)In order to ensure that the rectifying bridge and capacitor can withstand the maximum charging current, the soft-start resistor must satisfy:

The resistor design of HVPS for ECRH system
According to the multi-windings transformer parameters in the HVPS for 140GHz ECRH system, the leakage inductance of transformer can be calculated as follow:

＝0.6mH
So the equivalent inductance is: L＝2L1=1.2mH To ensure that the output voltage ripple is less than 1%, the filter capacitor is selected as follow: C＝10mF According to condition (1), in order to avoid voltage overshoot the soft-start resistor must satisfy: According to condition (2), in order to limit the maximum charging current the soft-start resistor must satisfy: Actually the soft-start resistor is designed for 300Ω in the HVPS for ECRH system. Some experiment results are shown in Fig.8 and Fig.9. X-axis: 2s/div Y-axis: 200V/div, 40A/div In Fig.8, the maximum value of charging current with the resistor is 16A and the first steady state voltage is 870V. In Fig.9, the maximum current value of removing the resistor is 110A and the second steady state voltage is about 930V. The voltage change of the capacitor is about 60V.
According to (7) and (12), the calculation for the maximum value of charging current is 11A and 93A for different process. According to (11), the voltage change is 64V. The experimental results are in agreement with the theoretical analysis.

Conclusion
The soft-start process of HVPS based on PSM technology is studied in this paper. A simplified DC equivalent model is proposed, and the transient and steady state responses of the soft-start process are analysed in detail. The qualifications are obtained and proved by simulation results. The soft-start resistor has been designed for the HVPS of the 140GHz ECRH system, and the final experimental results show that it is coincident with the theoretical analysis.