21.1 Introduction

Conventional dc power supplies operate at a given dc output voltage into a constant or near constant load. However, pulse loads such as lasers, fiashlamps, railguns, and radar require short but intense bursts of energy. Typically, this energy is stored in a capacitor and then released into the load. The rate at which the capacitor is charged and discharged is called the repetition rate, T, and may vary from 0.01 Hz for large capacitor banks to a few kHz for certain lasers. Recharging the capacitor voltage to a specified voltage is tasked to a capacitor charging power supply (CCPS). The role of power electronics devices, topologies, and charging strategies for capacitor charging applications is presented in this chapter.

Figure 21.1 shows the voltage across the energy storage capacitor connected to the output of a CCPS. This figure shows that the CCPS has three modes of operation. The first mode is the charging mode in which the capacitor is charged from an initial voltage of zero to a specified final voltage. The duration of the charging mode is determined by the capacitance of the energy storage capacitor and the rate at which the CCPS delivers energy. The next mode of operation is the refresh mode, which can be considered a “standby mode,” where the stored energy is simply maintained. When the output voltage drops below a predetermined value, the CCPS should turn on and deliver the energy necessary to compensate for capacitor leakage. Since energy is lost during the refresh mode, the duration of the refresh mode should be as brief as possible. Issues that lead to nonzero refresh times include safety margins for worst-case charging and discharging mode times and SOA requirements of switching devices. The final mode of operation is the discharge mode in which the load is actively discharging the capacitor. The CCPS does not supply any energy to the load in this mode. The amount of time the CCPS remains in this mode is determined by how quickly the load can discharge the capacitor.

FIGURE 21.1 Three modes of operation of a capacitor charging power supply.

The instantaneous output power for a CCPS varies over a wide range in comparison to a conventional dc power supply that supplies a near-constant power to its load. This is shown in Fig. 21.2; the output power for the pulsed power load is drawn as linear for illustration purposes only. The charging mode is characterized by high peak power. At the beginning of this mode, the output power is zero (i.e. there is no voltage present but current is flowing). Thus, the load capacitor is equivalent to a short circuit. In addition, at the end of the charging mode, the output power is again zero (i.e. there is an output voltage present but no current is flowing). Now, the load capacitor is equivalent to an open circuit. The refresh mode is typically a low-power mode because the current required to compensate for capacitor leakage is small. The CCPS does not supply any power during the discharge mode when the energy storage capacitor is being discharged by the pulsed load.

FIGURE 21.2 Power requirements for pulsed power and constant power loads.

The average output power for a CCPS depends on the discharge mode energy and the repetition rate of the load. It is maximum when the energy storage capacitor is discharged at the end of the charging mode (large voltage and current), which corresponds to operation without a refresh mode. Because the CCPS power is not constant, the rating of a CCPS is often given in kJ/s instead of kW. The kJ/s rating can be written as

where W_load is the energy delivered to the load per charging cycle and T is the repetition rate. In the optimum case with no refresh and instantaneous discharge, the kj/s rating is limited to how fast a particular capacitor can be charged by its specified voltage.

21.2 High-Voltage DC Power Supply with Charging Resistor

In this technique, the energy storage capacitor is charged by a high-voltage dc power supply through a charging resistor as shown in Fig. 21.3. The charging mode ends when the capacitor voltage equals the output voltage of the power supply. The capacitor is continually refreshed by the power supply. During the discharge mode, the charging resistor isolates the power supply from the pulse load. The advantages of this technique are its simplicity, reliability, and low cost.

FIGURE 21.3 High-voltage dc power supply and charging resistor.

The major disadvantage of this technique is its poor efficiency In the charging mode, the energy dissipated in the charging resistor is equal to the energy stored in the capacitor in the ideal case; therefore, the maximum efficiency is 50%. As a result, this technique is utilized only in applications where the charge rate is low, i.e. 200 J/s. Another disadvantage of this technique is related to the charging time, which is determined by the RC time constant. Some laser applications require that the output voltage be within 0.1% of a target voltage. For this technique, more than five time constants are required for the capacitor voltage to meet this voltage specification.

21.3 Resonance Charging

The basic resonance-charging technique is shown in Fig. 21.4. An ac input voltage is stepped up with a transformer, rectified, and filtered with capacitor C₂ to produce a high dc voltage V₀. In this circuit, C₂ is much greater than C₁. Thyristor T₁ is gated and current flows through the inductor and diode D₁ is transferring energy from C₂ to C₁. The voltage v(t) and current i (t) are described by the following equations assuming that C₂ C₁. The charge time, t_c, for this circuit can be calculated by finding the time at which the current, described by Eq. (21.2), reaches zero and is given below. The voltage v(t) has a value of 2 V₀ at the end of the charging mode.

(21.1)

(21.2)

(21.3)

(21.4)

FIGURE 21.4 Resonance charging.

Even though this technique is simple and efficient, it is not without its limitations. A high-voltage capacitor with a large capacitance value is needed for C₂, which increases the cost. A single thyristor is shown in Fig. 21.4. Multiple thyristors connected in series or a thyratron may be required depending on the voltage level. The repetition rate of the pulse load should be such that C₁ is fully charged and i(t) has reached zero before the load discharges to prevent latch up of T₁. It is not possible for this circuit to operate in the refresh mode because of the switch characteristics. Therefore, v(t) will drift due to capacitor leakage. The charge time is a function of the circuit parameters and will drift as they change with temperature or due to aging.

Because all of the energy stored in C₁ is transmitted from C₂ in a single pulse, it can be difficult to achieve precise voltage regulation with the resonance-charging technique. However, regulation can be improved with the addition of a de-queing circuit as shown in Fig. 21.5. The voltage v(t) is monitored with a sensing network. Before v(t) reaches the desired level, thyristor T₂ is fired, which terminates the charging mode. The remaining energy stored in the inductor is dissipated in R. The addition of the de-queing circuit reduces the circuit efficiency and increases the circuit complexity and cost but still does not enable a refresh mode to compensate for capacitor leakage.

FIGURE 21.5 Resonance charging with de-queing.

Boost charging, a variation on the resonance-charging technique, is shown in Fig. 21.6 [1]. An extra switch is added to the circuit of Fig. 21.4, allowing energy to be stored in both C₂ and L. This can be modeled as an increase in the voltage gain of the CCPS. With switches S₁ and S₂ closed, the current i(t) is given by

(21.5)

FIGURE 21.6 Boost charging.

When t = t_on, S₂ is opened, and the current is now described by

(21.6)

where

(21.7)

is the inductor current initial value at t_0n. The voltage v(t) is then

(21.8)

The time required for the current to reach zero and for the voltage v (t) to reach its peak value can be calculated from

(21.9)

This is also the charge time, t_c, or the length of the charging mode. Note from equation (21.9) that the charge time depends on t_on which is the on-time of switch S₂. In addition, the peak capacitor voltage is a function of t_on. The peak capacitor voltage is limited to 2V₀ without S₂; voltage gains as high as 20 are possible with the addition of S₂ [1].

The switching elements in Figs. 21.4 and 21.5 are realized with thyristors. Simple switches are shown for the boost-charging technique in Fig. 21.6. Switch S₁ could be implemented with a thyristor. The boost capability provided by switch S2 is best realized with a gate-controlled semiconductor device such as a GTO or an IGBT.

21.4 Switching Converters

The poor efficiency when charging a capacitor through a resistor from a high-voltage power supply limits its application to low charging rates. In the resonance-charging concepts, the energy is transferred to the load capacitor in a single pulse, and it is not possible to compensate for capacitor leakage. Energy storage capacitors may be charged utilizing the same power electronic technology that has been applied in switching converters for constant power loads. Instead of charging the energy storage capacitor with a single pulse, switching converters can charge the capacitor with a series of pulses or pulse train. The peak current is reduced when charging with a series of pulses, thus improving the efficiency of the charging process. In addition, soft-switching techniques maybe used in the switching converter to increase the efficiency. The regulation of the output voltage is also improved with the pulse train because the energy is passed to the energy storage capacitor as small packets. Common control techniques such as pulse-width modulation can be used to control the size of the energy packet. This capability to control the size of the energy packet permits the CCPS to operate in the refresh mode and compensate for capacitor leakage. As a result, the CCPS may operate over a broad range of load repetition rates and still maintain tight output voltage regulation during refresh mode. During the refresh mode, energy lost due to capacitor leakage may be replaced in a burst fashion [2] or in a continuous fashion similar to trickle charging a battery [3].

In the switching converter, semiconductor switches may be operated on the lower side of the transformer permitting the use of MOSFETs or IGBTs in the CCPS. Because the CCPS begins the charging mode with a short circuit across its output, the switching converter must be capable of operating under this severe load condition. This may require the implementation of a current limiting scheme in the converter control circuit.

One switching converter as shown in Fig. 21.7 consists of a resonant converter. Note that the MOSFETs and resonant components L_r and C_r are connected on the low-voltage side of the transformer. Only the rectifier diodes and energy storage capacitor must have high voltage ratings. When the output rectifier is conducting, the energy storage capacitor C₁ is connected in series with the resonant capacitor C_r. For a transformer turns ratio of 1:N, reflecting C₁ through the transfomer yields a capacitance of N² C₁. Since N is typically large, this reflected capacitance is much larger than C_r, thus the resonant frequency, which is defined in Eq. (21.10), is not affected by C₁. For high-voltage, high-frequency operation, the leakage inductance of the transformer maybe utilized as L_r. Thus, the resonant frequency can be expressed as

(21.10)

FIGURE 21.7 Series resonant converter.

One characteristic of this converter, which makes it attractive for capacitor charging, is the ability to operate under the short-circuit conditions present at the beginning of the charging mode. The voltage across C₁ is zero at the beginning of this mode. The current in the switches is limited by the input voltage and impedance Z₀ as is defined in Eq. (21.11).

(21.11)

Another method for current limiting is to vary the ratio of f_s, the switching frequency of the MOSFETs, and the resonant frequency, f_r, which is ω_τ/2π. This effectively controls the flow of energy from the source to C₁. The ratio f_s f_r may be set to a low value at the beginning of the charging mode and increased toward unity as the voltage across C₁ increases. This limits the current when the voltage across C₁ is low and allows increased energy transfer as the voltage approaches the target voltage. The disadvantage of this approach is that variable frequency operation complicates device and component selection and degrades EMI/EMC performance of the CCPS.

The flyback converter, shown in Fig. 21.8, also may be utilized for capacitor-charging applications [4, 5]. When the MOSFET is turned on, current increases in the primary winding, storing energy in the magnetic field. When it reaches a specified level, the MOSFET is turned off and the energy is transferred from the magnetic field to C₁. This energy transfer is terminated when the MOSFET is turned on again.

FIGURE 21.8 Flyback converter.

In cases where precise output regulation is not required and the packet energy is low, the diode in Fig. 21.8 can be replaced with a Zener diode with a Zener voltage of

where V_o,nom is the nominal value of Vo [6]. Once V_o,nom is reached, the next energy packet will force the diode into a brief period of breakdown with the excess energy partially recycled to the input circuit. If the packet energy is small enough, the breakdown is not destructive and V_? is limited to

where V_?,ω is the small excess voltage caused by the last energy packet.

Sokal and Redl [7] have investigated different control schemes for charging capacitors using the flyback converter. Their recommendation is to charge C₁ with current pulses that are nearly flat-topped. This strategy results in higher average current for a given peak current. The capacitor is charged faster because the charge delivered to it during a pulse is directly proportional to the average current. This desired pulse shape is achieved by turning on the MOSFET to terminate the transfer of energy to C₁ soon after the MOSFET is turned off, which increases the switching frequency. When the primary current rises to a preset minimum level, the MOSFET is again turned off. This switching strategy is essentially hysteretic current mode control, in which the switch current is limited between two preset bounds.

Another converter for capacitor-charging applications is the Ward converter [8–10] shown in Fig. 21.9. When the MOSFET is turned on, energy is stored in the inductor and capacitor C_a transfers energy into the energy storage capacitor C₁ and capacitor C_b. The energy stored in the inductor is transferred to C_a when the MOSFET is turned off. The leakage inductance of the transformer and C_a resonate producing a sinusoidal current that flows in the primary winding of the transformer and the MOSFET. When the primary current reaches zero and starts negative, the diode turns on, which allows the MOSFET to be turned off efficiently at zero current.

FIGURE 21.9 Ward converter.

In some converter operating conditions, the voltage across C_a is very small because most of the energy has been transferred from C_a to C₁. The energy stored in C_a may be too small to ensure zero-current turn off of the MOSFET. In this case, the energy stored in C_b, helps to ensure that the amplitude of the current is large enough for zero-current turn off of this device.

REFERENCES

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2. Lippincott AC, Nelms RM. A capacitor-charging power supply using a series-resonant topology, constant on-time/variable frequency control, and zero current switching. IEEE Trans. Industrial Electronics. December 1991; vol. 38(no. 6):438–447.

3. Strickland BE, Garbi M, Cathell F, Eckhouse S, Nelms M. 2 kJ/sec 25-kV high-frequency capacitor-charging power supply using MOSFET switches,”. Proc. 1990 Nineteenth Power Modulator Symposium. June 1990; 531–534.

4. Newsom RL, Dillard WC, Nelms RM. Digital power-factor correction for a capacitor-charging power supply. IEEE Trans. Industrial Electronics. October 2002; vol. 49(no. 5):1146–1153.

5. Dawson FP, Dewan SB. A subresonant flyback converter for capacitor charging,”. Proc. Second Annual IEEE Applied Power Electronics Conf.. March 1987; 274–283.

6. Dillard WC, Nelms RM. A digitally-controlled, low-cost driver for piezoceramic flight control surfaces in small unmanned air-craft and munitions,”. Seventeenth Annual Applied Power Electronics Conf. Exposition. 2002; 1154–1160 [APEC ’ 02].

7. Sokal NO, Redl R. Control algorithms and circuit designs for optimally flyback-charging an energy-storage capacitor (e.g. for flash lamp or defibrillator),”. IEEE Trans. Power Electronics. September 1997; vol. 12(no. 5):885–894.

8. M.A.V. Ward, DC to DC Converter Current Pump,” U.S. Patent Number 4,868,730, September 1989.

9. Chryssis GC. High-Frequency Switching Power Supplies: Theory and Design. New York: McGraw-Hill Publishing; 1989.

10. Nelms RM, Schatz JE. A capacitor charging power supply utilizing a ward converter. IEEE Trans. Industrial Electronics. October 1992; vol. 39(no. 5):421–428.