Stability Analysis and Design of Frequency- and Voltage-stabilized Power Supply

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Abstract: The composition principle of voltage and frequency constant (CVCF) power supply is systematically introduced, the factors affecting the frequency stability, phase stability and amplitude stability of CVCF are analyzed, and the system design method of CVCF is introduced.

Keywords: CVCF frequency stability amplitude stability phase stability system design

Analysis and Design on the Stability of CVCF

Abstract:This paper introduces the structure and the principle of CVCF. It analyzes systematically factors which affect the frequency stability and the scope stability and the phase stability of CVCF, and expounds static and dynamic design methods.

Keywords:CVCF Frequency stability Scope stability Phase stability System design

AC frequency-stabilized power supply is widely used as an excitation source or information source in the electronics and electromechanical industries, especially in the manufacture of precision machining machinery, semiconductor processing equipment, adjustment of AC instruments, measurement of magnetic materials and other test systems, due to its high amplitude and frequency stability, small waveform distortion and large output power. It can also replace traditional motor-generator sets and be used in aerospace, navigation and precision machining industries.

1 Working Principle

AC frequency-stabilized power supplies can be divided into waveform-controlled and inverter-type power supplies according to their working modes. The waveform-controlled type uses the sine wave signal output by the signal source as a reference, uses a linear amplifier for power amplification, and connects to the load through a linear transformer with a high coupling degree. This type of frequency-stabilized power supply has low waveform distortion and high stability. The main circuit structure of the inverter type and the waveform-controlled type is basically the same, except that a switching inverter is used to replace the linear amplifier. Through the sine wave pulse width modulation technology (SPWM), the power electronic devices in the main circuit work in the switching state of the super-audio range, output a sine wave pulse width modulation wave, and then restore it to a sine wave through a filter circuit. This type of frequency-stabilized power supply has high efficiency and no noise. However, due to the switching state, there is a certain switching interference, the waveform distortion is large, and its application range is subject to certain restrictions. At present, waveform-controlled frequency-stabilized power supplies are generally used as test excitation sources, and inverter-type power supplies are used as high-power drive power supplies.

According to the number of phases of the output AC power supply, the frequency-stabilized power supply can be divided into single-phase, two-phase orthogonal and three-phase symmetrical types. The frequency-stabilized voltage source with a single output does not require a phase-shifting adjustment circuit because the phase shift between each phase is constant. When the output physical quantity requires both a voltage loop and a current loop, and the phase difference between the voltage and current is required to be both adjustable and stable to adapt to different loads, the corresponding frequency-stabilized voltage/current-stabilized power supply should include voltage and current output loops. Its structure is shown in Figure 1.

(a) Single-phase CVCF

(b) Two-phase orthogonal CVCF (c) Three-phase symmetrical CVCF

Figure 1 CVCF principle block diagram

The amplitude stabilization principle of the frequency-stabilized voltage power supply depends on the amplitude-stabilized amplifier circuit shown in Figure 2. The precision rectifier circuit samples the AC voltage output by the frequency-stabilized voltage source, and transforms it into a DC voltage Uf whose amplitude is proportional to the output AC quantity after rectification. The amplitude-stabilized amplifier circuit uses this Uf as the amplitude feedback voltage, and compares it with the reference source Uj, and takes its deviation Uj-Uf for integral amplification to change the gain of the variable gain amplifier. When the sine wave output by the signal source with stable frequency and amplitude passes through the variable gain amplifier, since its gain depends on the deviation, the amplitude of the signal input to the power amplifier changes, thereby automatically adjusting its output amplitude. If the output amplitude Uo of the voltage-stabilized source decreases due to some reason, the amplitude feedback voltage Uf after precision rectification also decreases, which increases the deviation of the comparator. After integral amplification, the gain of the variable gain amplifier is increased, thereby increasing the input signal of the power amplifier and increasing the output amplitude Uo of the frequency-stabilized voltage source, so as to achieve the purpose of amplitude stability.

The waveform feedback loop samples the output of the frequency-stabilized voltage source and feeds it back to the input of the power amplifier in the form of negative feedback, so that the net input signal of the power amplifier is the deviation between the input signal and the feedback signal. This strong negative feedback is used to reduce the nonlinear distortion of the power amplifier and make the output waveform of the frequency-stabilized voltage source as close to the output waveform of the signal source as possible.

Figure 2 Block diagram of amplitude stabilization principle

Stability analysis of 2CVCF

2.1 Frequency Stability Analysis of CVCF

The frequency stability of CVCF depends largely on the oscillator. Therefore, designing an oscillator that meets the requirements is one of the keys to CVCF.

First, for any oscillator, without considering the resistance R, its oscillation frequency can be expressed by the general expression

If L and C change by △L and △C respectively due to external conditions, the frequency offset is △f==-(f△C/C+f△L/L)/2

The relative change in frequency is

△f/f=-(△C/C+△L/L)/2(1)

The change in inductance △L depends on factors such as changes in temperature and humidity and mechanical vibration. The change in capacitance △C is not only related to changes in humidity and temperature, but also to factors such as the circuit's stray distributed capacitance, load capacitance, and component aging failure.

Secondly, the active load of the oscillation circuit will affect the quality factor Q of the resonant circuit, thereby affecting the stability of the oscillation frequency. Generally speaking, the higher the Q value, the better the frequency stability, and vice versa. The quality factor Q of the resonant circuit is:

Q = ωoL/R = 1/(ωoRC) (2)

It can be seen that the change of the active load R of the oscillation circuit will affect the Q value, and then affect the frequency stability. The active load R of the resonant circuit often depends on factors such as the resistance of the wire, high-frequency skin effect, hysteresis of the magnetic core, eddy current loss and load resistance.

Thirdly, the internal phase shift of the circuit elements will also affect the frequency stability. For example, due to the existence of junction capacitance and the diffusion time of minority carriers in the base region of the transistor, the collector current always lags behind the change of the base input voltage, that is, there is a phase shift angle φ between them. This additional phase shift φ cannot be considered in the oscillator, thus increasing the total phase shift. In addition, this phase shift φ also changes with the changes in power supply voltage and temperature, which may cause the frequency of the resonant circuit to deviate.

2.2 Analysis of the amplitude stability of CVCF

If the closed loop formed by the power amplifier, drive circuit and waveform feedback circuit is regarded as the waveform link of CVCF, then the amplitude stabilization amplifier circuit of CVCF is a single closed loop system.

For the amplitude-stabilized amplifier circuit, its static structure is shown in Figure 3: K1 is the gain of the waveform link, α is the precision rectification coefficient, un is the given reference voltage, and K2 is the gain of the variable gain amplifier, so the static characteristic equation of the system is:

uO=K1unui/(1+αK1ui)(3)

When 1+αK1ui≤1, uo≈un/α

CVCF achieves output amplitude regulation by changing a given reference voltage, so the stability of the given reference voltage and precision rectifier circuit will directly affect the stability of the CVCF output amplitude.

The voltage regulation block diagram of a single closed-loop control system is shown in Figure 4. In this closed-loop system, the transfer function of the integral amplifier is K2/Tos. When un is constant and the precision rectifier feedback coefficient is α, the basic equation of the feedback system is

△uo/uo=K1(△ui/ui-αK2△uo/T0suo)

After sorting, we get

△uo/uo=(K1△ui/ui)/(1+αK1K2/T0s)(4)

Because 1+αK1K2/T0s1, the dynamic approximate expression of the output amplitude stability and transient response of the amplitude stabilization circuit of CVCF is △uo/uo≈T0s△ui/αK2ui.

2.3 Phase shift stability analysis of CVCF

Figure 3 Single closed loop system static structure diagram Figure 4 Voltage regulation rate block diagram

The active phase shift circuit shown in Figure 5 is often used in CVCF.

U+=(1/jωC)Ui/(R2+1/jωC)

U-=(UiRf+UoR1)/(R1+Rf)

Figure 5 Active filter circuit

Figure 6 Closed-loop system structure diagram

Because U+=U-, so

(UiRf+UoR1)/(R1+Rf)

=(1/jωC)Ui/(R2+1/jωC)

Among them φ=φ1+φ2=tg-1ωCR2Rf/R1+tg-1ωCR2

If R1=R2=Rf=R, then K=1

φ=2tg-1ωCR

△φ=2(ωR△C+ωC△R)/[1+(ωCR)2

It can be seen that the stability of the phase shift angle φ is affected by the changes in the capacitor C and the resistor R in the phase shift circuit, both of which are affected by environmental factors. At the same time, the failure of the capacitor C, the reduction in capacity, and the change in the junction capacitance of the internal semiconductor components due to the aging of the integrated circuit have a great impact on the long-term stability and short-term stability indicators of the phase shift.

3. System Design Method of CVCF

Before designing CVCF, the technical indicators required by the system must be clarified, and the static and dynamic design of the system must be carried out according to these indicators, so as to clarify the main technical indicators that each unit circuit should achieve, reasonably analyze and select the type of each unit circuit, and then perform parameter calculation to determine the circuit parameters. It is also necessary to reasonably design various protection circuits according to the working characteristics of the circuit.

3.1 Static Design

As for the amplitude stabilization system, the block diagram of the CVCF amplitude closed-loop system is shown in Figure 6.

Comparison link △u=un-uf

Multiplication output u1=△uui=ui(un-uf)

Amplifier u2 = K1u1 = K1(un-uf)ui

Power amplification u0=K2u2=K1K2(un-uf)ui

Feedback circuit uf=αun

Therefore, the static characteristic equation is: u0=Kunui/(1+αKui) (7)

Where K=K1K2. Its static structure diagram is shown in Figure 7. According to the static characteristic equation and the technical index requirements of the system, the technical index of each unit circuit can be determined. If the amplitude stability index △uo/uo of the system is clear, the stability index △un/un of the given reference voltage un can be calculated according to the characteristic equation:

△un/un=(αK1K2ui+1)△un/K1K2uiun (8)

When αK1K2ui+11, △un/un=α△uo/uo

The technical requirements for the remaining unit circuits can be determined in the same way.

Figure 7 Static structure diagram

3.2 Dynamic Design

Static design does not consider the delay of each unit circuit. In fact, each unit circuit may have a delay, which will affect the dynamic performance of the system and may cause system oscillation.

In the amplitude closed-loop system, the power amplifier has the largest delay. When the total delay including the driving circuit is Ts, the transfer function of the power amplifier is:

K2/(1+Tss)(9)

The transfer function of the integral multiplier is:

ui(1+Ts)/Ts(10)

Because the feedback circuit has a filtering link, its transfer function is α/(1+Tns)

When small time constants are ignored, the dynamic structure of the system is obtained, as shown in Figure 8.

Figure 8 Dynamic structure diagram

When analyzing and designing the system, let T = Ts, and choose the integral multiplier transfer function as ui(1 + Ts)/Ts. Then the corrected system open-loop transfer function is

K′/s(Tns+1)=αK1K2ui/Ts(Tns+1)(11)

So K′=αK1K2ui/T. Since TSs+1≈TSs, the transfer function of the integral multiplier is selected as ui(1+Ts)/Ts, then the corrected open-loop transfer function is:

K′(1+Ts)/s2(Tns+1)(12)

The system open-loop gain can be determined based on the final calibration of the system.

3.3 Protection Design

The output power of CVCF is generally hundreds to thousands of watts, which makes the current passing through the power device very large. In actual design, multiple power devices are often used in parallel. In the parallel process, in addition to considering current sharing,

Figure 5 Active filter circuit

Figure 6 Closed-loop system structure diagram

Figure 7 Static structure diagram

Figure 8 Dynamic structure diagram

In addition to the measures, sufficient current reserve should be considered. In addition, the over-current protection, over-voltage protection, di/dt limiting protection and du/dt limiting protection of the device should also be considered.

For CVCF, the interface problem of the above protection needs attention, because CVCF is actually an AC-DC-AC current converter, which undergoes two processes: rectification and inversion. When a certain device is damaged during the inversion process and an overcurrent occurs, it will inevitably cause an overcurrent during the voltage stabilization process, causing damage to the rectifier and voltage stabilization device, and then causing overcurrent in the power grid. In order to improve the reliability of the system and prevent accidents from expanding, various protections are often applied to the rectifier and voltage stabilization circuit in the design of CVCF. Once a fault occurs in the inverter part, the DC regulated power supply of the main circuit is automatically shut down and various alarm signals are provided.

Reference address:Stability Analysis and Design of Frequency- and Voltage-stabilized Power Supply

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