Research on Input LC Filter of Three-phase Uncontrolled Rectifier

1 Introduction

With the continuous advancement of related technologies, AC-DC-AC inverter technology has made great progress, and inverter-motor transmission systems are widely used in various industries. Due to the limitations of single-phase power supply, currently large-power variable-frequency air conditioners and other electrical appliances are all powered by three-phase AC power supply. Since the front-stage AC-DC converter of the traditional AC-DC-AC inverter is an uncontrolled diode rectifier bridge, it is well known that as long as the uncontrolled rectifier bridge is used for the three-phase power supply system, the back stage is any circuit type. For the power grid, the traditional AC-DC-AC inverter is a non-linear load, that is, the grid-side current contains a large amount of low-order and high-order harmonic currents, resulting in a decrease in input power factor and an increase in current THD, which does not meet the harmonic current emission limit standards: IEC61000-3-2 and IEC61000-3-12. The harm of harmonic current is self-evident, so harmonic current suppression measures must be taken. For the traditional three-phase power supply AC-DC-AC-converter system, in addition to improving the input current waveform and reducing the fundamental power factor angle, another important goal is to maintain the hardness of the DC voltage relative to the load, that is, to have a higher load regulation rate, a higher average value and a lower ripple voltage peak-to-peak value, so as to increase the constant torque range of the subsequent inverter-motor system and improve the output power level.

So far, there are a lot of filtering principles and filtering methods, and the analysis of harmonic sources is also quite in-depth. Common methods include passive filtering, active filtering and hybrid filtering, which can be divided into tuned filters, high-pass filtering methods, various active power filter methods, various three-phase controlled rectifiers, various passive power filters, and so on. For active filtering or correction technology, although the filtering or correction effect is good, the technology is complex and the cost is high. It is not suitable for promotion and application in some occasions and certain stages. Passive filtering technology is the earliest developed and has a good effect in suppressing equipment harmonics. A good passive filtering method can not only suppress harmonic currents, but also has a reactive power compensation effect. It is understood that commercial variable frequency air conditioners powered by three-phase AC voltage have not yet adopted three-phase active PFC, and still use LCL filtering method. All production models are exported to European countries. For three-phase AC-DC inverters, a large number of different passive filtering technologies have emerged, such as single-stage LC filters, multi-stage LC filters, filters with multiple third harmonic injections, transformer coupling filters, inductive coupling filters, etc. This paper aims to conduct theoretical analysis, simulation analysis and experimental testing on a cost-effective single-stage LC filter-rectifier bridge-resistance load system, determine the optimal LC filter design method, and solve several key problems of the single-stage LC filter, such as the DC voltage boost principle and the optimal input line voltage waveform of the rectifier bridge, laying the foundation for the application of single-stage LC filters in nonlinear loads such as rectifier bridges.

2 Key issues of three-phase LC filter-uncontrolled rectifier bridge system

2.1 Harmonic source and characteristic issues

The harmonic source types of nonlinear loads can be roughly divided into three types: harmonic voltage source, harmonic current source and mixed harmonic source. For thyristor rectifiers, matrix rectifiers and current source PWM rectifiers, since the output DC side is connected to a smoothing reactor with a large inductance, the harmonic current source characteristics are presented on the grid side. The stronger the inductance and the larger the load, the more significant the harmonic current source characteristics are, and parallel compensation before the rectifier bridge is required. For three-phase uncontrolled rectifiers and voltage source rectifiers, since the output DC side is connected to a filter electrolytic capacitor with a large capacitance, the harmonic voltage source characteristics are presented on the grid side. The stronger the capacitance and the larger the load, the more significant the harmonic voltage source characteristics are, and the higher the peak current is, and series compensation before the rectifier bridge is required. For the DC side of the three-phase uncontrolled rectifier with a larger power output, an LC filter is generally connected. The role of the reactor is to smooth the DC side current. For a non-infinite power supply system, when the inductance is insufficient, the harmonic source characteristics are between the harmonic current source and the harmonic voltage source characteristics.

After the filter inductor is connected in series to the power supply line, the three-phase uncontrolled rectifier bridge-electrolytic capacitor-load system with harmonic voltage source characteristics has the harmonic current source characteristics. The higher the frequency of the harmonic current, the more conducive it is to suppress it. The larger the inductance, the more it reflects the current harmonic source characteristics. Therefore, it is possible to consider connecting capacitors in parallel between lines to bypass the harmonic current generated. The higher the frequency of the harmonic current, the more conducive it is to bypass it. It can be considered that the harmonic equivalent circuit of the single-stage LC filter-three-phase uncontrolled rectifier bridge-electrolytic capacitor-load system has a mixed harmonic source characteristic, and its equivalent circuit should be a combination of harmonic current source and harmonic voltage source, which is in line with Norton's theorem, as shown in Figure 1.

Figure 1 Single-stage LC filter-three-phase uncontrolled rectifier bridge-electrolytic capacitor-load system harmonic equivalent circuit

For the uncontrolled rectifier bridge harmonic source characteristics, when the distributed inductive reactance of the power grid is ignored, the typical relationship between the input phase voltage, line voltage, phase current and DC voltage is shown in Figure 2 (a). The THD of the input current is very large and the sinusoidal degree is not high, which does not meet the harmonic current emission limit standards: IEC61000-3-2 and IEC61000-3-12. Therefore, appropriate passive filtering measures must be taken to improve the displacement factor and waveform factor of the grid-side current. Among the many passive filtering schemes, the single-stage input LC filter is a simple, low-cost and good filtering measure. Through reasonable parameter configuration, an input power factor close to 1 can be obtained. At this time, the relationship between the input phase voltage, line voltage, phase current and DC voltage is shown in Figure 2 (b).

(a) No input filter

(b) Single-stage LC input filter

Figure 2 Relationship between input phase voltage, line voltage, phase current and DC voltage

Figure 2 is derived from a single-stage LC filter-three-phase rectifier circuit with filter inductor L=25mh, filter capacitor C=35mf (Y connection), electrolytic capacitor 680mf, and resistive load 45w. As can be seen from Figure 2b), the grid-side current is basically synchronized with the grid-side phase voltage, the waveforms are basically consistent, and the grid-side power factor is close to 1. It can also be seen that the waveforms of the phase voltage and line voltage on the input side of the rectifier bridge are distorted, and their phases lag behind the corresponding grid-side phase voltage and line voltage, and their amplitudes are also much higher than the corresponding grid-side phase voltage and line voltage amplitudes, which directly leads to an increase in the average value of the DC side voltage of the rectifier bridge, and the ripple peak-to-peak value is also suppressed, which leads to several key issues of the single-stage LC filter-rectifier circuit: equivalent harmonic source problem, LC optimal parameter configuration problem, rectifier optimal line voltage waveform problem, DC voltage increase and DC ripple voltage reduction problem, etc.

2.2 Optimal filtering effect problem

After using a single-stage LC filter, the grid side cannot obtain a unity power factor. The reason is: if the input current waveform is a sinusoidal current synchronized with the phase voltage, the terminal voltage of the filter inductor is a sinusoidal voltage leading the phase current by 90°, the phase voltage before the bridge is the sum of the grid phase voltage and the inductor terminal voltage, the line voltage before the bridge will also be a sinusoidal voltage waveform, the phase current before the bridge will also be a current pulse state, the conduction angle of the diode is less than 120°, and it returns to the state without LC filter. These situations are not consistent with the actual situation.

In order to reasonably configure the L and C parameters and obtain a high input power factor, it is necessary to establish the loop voltage and node current equations of the single-stage LC filter-three-phase rectifier bridge-electrolytic capacitor-load system, and set the input current characteristic indicators, such as the given allowable displacement angle θ1, THD and harmonic current limit. Under the premise of setting the rated output power, the method of using MATLAB or other simulation platforms, numerical calculation and scanning of L and C parameters, to determine the parameters of the inductor and capacitor can be given, and multiple sets of solutions that meet the conditions can be obtained. Among these solutions, try to choose the solution with balanced parameter configuration and the solution with small LC product, so that it is easy to design and manufacture the device and control the cost, volume and weight. Under the premise of ensuring that the harmonic current standard is met with a margin, the LC product can be greatly reduced by appropriately adjusting the size of the displacement angle θ1 and the degree of lead and lag, and appropriately increasing the THD of the grid current. Set

the rated load to 7.5kw. After numerical calculation and scanning of the l and c parameters, it is found that when l=25mh and c=105mf (δ connection), the displacement angle θ1=2°, thd=5.0%, and the input power factor λ=0.99. It is believed that the l and c parameters at this time are a set of filter parameters that can obtain the best filtering effect.

First, establish the node current and loop voltage equations of the rectifier circuit. According to the different front-line voltages of the bridge and the conduction law of the rectifier bridge diode, divide it into 6 intervals, draw the equivalent circuit, see Figure 3, and establish the relevant equations.

Figure 3 Equivalent circuit of different diode conduction intervals

In Figure 3, dh and dl represent a group of diodes that are turned on at the same time, dh is the upper diode, dl is the lower diode, and ux and uy represent a corresponding group of grid phase voltages. After analysis, equations 1 and 2 are satisfied in each interval.

(1)

(2)

Among them, ud represents the conduction voltage drop of a diode, which is 2.0V, ulb represents the voltage before the bridge, that is, the terminal voltage of the filter capacitor, and uxy represents the voltage of the power grid line. After solving equations (1) to (2), we get the expression (3) of the voltage before the bridge ulb and the expression (4) of the power grid current phase a. The coefficients in

(3) are:

(4)

The coefficients are a1=29.41, b1=314.4, c1=-12.54.

Then, the same process is used to solve the expressions of the phase voltage before the bridge, the DC output voltage, the filter capacitor current, the current before the bridge, the current after the bridge, the electrolytic capacitor current, and the load resistor current. The waveforms of each are plotted and compared with the corresponding waveforms obtained by simulation analysis using the same parameters. The similarity is basically 1 when compared with Figure 2(b), indicating that this method of finding the optimal parameters of l and c is effective. The derived expressions are relatively accurate and can be used as the basis for actual parameter selection.

2.3 The optimal line voltage waveform before the bridge

If you want to obtain the best power factor correction effect, it is believed that the optimal line voltage waveform must be obtained. The optimal line voltage waveform before the bridge is not necessarily the same for different input filter types. For the input filter type of simple series connection, the optimal line voltage waveform must be the same. For the single-stage and two-stage LC filter types, the optimal line voltage waveform must be different. For the single-stage LC filter type, the characteristics of the optimal line voltage waveform are:

(1) The voltage at the inductor terminal is not a sinusoidal waveform, but 6 segments of 60° sine wave segments connected in sequence, reflecting the process of commutation of the rectifier bridge diode every 60°. In each process, the entire circuit is a linear circuit, and the commutation process is a nonlinear circuit. The voltage at the inductor terminal includes the fundamental voltage drop and the 5th, 7th, 11th, and 13th harmonic voltage drops. The fundamental voltage drop lags the fundamental current by 90°.

(2) The inductor current has a high sinusoidal degree, but it is not a true sinusoidal waveform, which reflects the commutation process of the rectifier bridge diode.

(3) The phase voltage waveform before the bridge lags the grid phase voltage waveform by about 30°. The reason is that the voltage at the filter inductor terminal lags the grid phase voltage by about 90°.

(4) The line voltage waveform before the bridge is almost synchronized with the grid phase voltage, presenting an alternating trapezoidal wave. The flat top of the waveform occupies about 120°, and the bottom of the waveform occupies about 180°. The amplitude is greatly improved. The reason is that the filter capacitor passes the parallel resonant capacitive current and part of the harmonic current. The former has a smaller proportion, and the latter has a larger proportion. In this case, it is almost all the harmonic current. In half a cycle, the current in the middle 60° time is approximately zero, and the harmonic current at both ends 60° time increases exponentially. This distribution of harmonic current, through integration, makes the bridge front line voltage present this special waveform, and its effective value and average value are greatly increased, exceeding the effective value and average value of the grid line voltage. This bridge front line voltage is synchronized with the grid phase voltage, which is conducive to the diode conduction angle of 120°. The

above analysis explains several key issues of the single-stage LC filter-three-phase rectifier bridge-electrolytic capacitor-load system: the optimal bridge front line voltage problem, the DC voltage increase problem, and the ripple voltage peak-to-peak value reduction problem.

3 Simulation and experimental verification

3.1 Simulation verification

The simulation software MATLAB/Simulink was used to conduct a comprehensive and detailed simulation analysis of the single-stage LC filter-three-phase uncontrolled rectifier bridge-electrolytic capacitor-resistance load system. Given a rated load of 7.5kw constant power load, converted to a three-phase resistance load of 45ω, a three-phase LC filter circuit, a filter inductor of 25mh, and a filter capacitor of 35mf (Y connection), the system principle is shown in Figure 4.

Figure 4 Simulation principle of single-stage LC filter-three-phase uncontrolled rectifier bridge-electrolytic capacitor-resistance load system The

terminal voltage expression of the filter capacitor is:


(5)

In the formula: uc is the capacitor voltage, us is the power supply voltage, rs is the power supply resistance and the distributed resistance of the reactor, rl is the load resistance, and 1/rl reflects the load power. When the load power is not very large, since rs is at the mw level, rs/rl can be ignored, then the voltage gain is:

(6)

The above formula shows that, under the condition of ignoring the line voltage drop, the increase in load power is the only reason for the voltage drop when the rectifier-electrolytic capacitor-load system is connected. The relationship between the voltage gain and the filter inductance is more complicated. When the capacitor value remains unchanged, the voltage gain is 1.527 times the maximum when the inductance is 54mh. When the inductance is less than 54mh, it is a monotonically increasing function, and when the inductance is greater than 54mh, it is a monotonically decreasing function. The voltage gain shows an increasing function with the increase of the filter capacitance. When the load

is large enough, the voltage gain approaches zero. When it is unloaded, the voltage gain is as shown in formula (7).


(7)

In the formula, IC is the capacitor current, Xs is the inductive reactance, Xc is the capacitive reactance, and RS plays the role of reducing the capacitor voltage amplitude. When the load power is not very large, since RS is at the mw level, ωICRS can be ignored. Then:

(8)

The above formula shows that the use of LC filter will produce parallel resonance, which can increase the output voltage. This is also an important reason for the voltage boost when the rectifier-electrolytic capacitor-load system is connected later.

Simulation results: The line voltage of the filter capacitor (D connection method) is synchronized with the grid line voltage, a sine waveform, an industrial frequency of 50 Hz, a leading phase voltage of 30°, an amplitude of 1.35 times the grid line voltage amplitude, an amplitude of 727.0V, a grid line voltage amplitude of 538.6V, and a grid phase voltage amplitude of 311V. The phase voltage of the filter capacitor (D connection method) is synchronized with the grid phase voltage, a sine waveform, an industrial frequency of 50 Hz, an amplitude of 1.35 times the grid phase voltage amplitude, and an amplitude of 419.5V. The filter inductor voltage is a sine waveform, with a power frequency of 50 Hz and an amplitude of 0.35 times the grid phase voltage amplitude, which is 108.9 V. The grid current is a sine waveform, leading the phase voltage by 90°, with a power frequency of 50 Hz and an amplitude of 13.85 A. The capacitor (D connection) current is a sine waveform, leading the phase voltage by 120°, with a power frequency of 50 Hz and an amplitude of 8.0 A. The above simulation data is consistent with the theoretical analysis results.

Figure 5 Experimental principle diagram of single-stage LC filter-three-phase uncontrolled rectifier bridge-electrolytic capacitor-resistance load system

3.2 Experimental verification

In order to verify the effectiveness of harmonic suppression of single-stage LC filter in three-phase uncontrolled rectifier system, experimental verification is carried out. The system principle is shown in Figure 5. In Figure 5, the three-phase uncontrolled rectifier bridge is 35A/1200V, the silicon steel inductor is 10MH~35MH, the CBB65 capacitor is 5μF~35μF/1200V, and the maximum output power is close to 7.5kW. The experimental results are consistent with the theoretical analysis and simulation analysis results. When the inductor is 25MH/Y and the capacitor is 35μF, the input and output parameters and harmonic current content are shown in Tables 1~2 respectively. When the inductor is 25MH/Y and the capacitor is 35μF, the waveforms of the grid current and DC voltage are shown in Figure 6.

(a) Light load (4.464a)

(b) Overload (10.03a)

Figure 6 Grid current and DC voltage waveforms

Notes:

(1) When using a single-stage LC filter, the inductance should not be too small, and the common core should not be used, otherwise the filtering effect will be affected. The filter capacitor should be placed between the inductor and the rectifier bridge;

(2) When the LC is unloaded, it will resonate in parallel and generate high voltage. In addition to considering the voltage resistance of the selected components, it is also necessary to deal with the starting problem of the subsequent converter such as the inverter-motor transmission system. The design of the starting procedure should consider soft starting;

(3) When the grid voltage changes, the output DC voltage changes accordingly, and when the load changes, the output DC voltage also changes accordingly. This following characteristic is conducive to the selection of LC parameters.

Table 1 Input and output parameters (inductance 25mh/Y connection capacitance 35μf)

Table 2 Harmonic current content (inductance 25mh/Y connection capacitance 35μf)

4 Conclusion

Through theoretical analysis, simulation analysis and experimental verification, the use of single-stage LC filter will shift the harmonic source characteristics of the uncontrolled rectifier bridge-electrolytic capacitor-load system from voltage source characteristics to current source characteristics. The larger the inductance value, the stronger the current source characteristics, and the harmonic source characteristics can be changed; the principle of output DC voltage boost is the result of the combined effect of LC generating parallel oscillation and harmonic current generating capacitive voltage through filter capacitor. For rated output power, the optimal LC parameter configuration can be found through theoretical analysis and simulation analysis, and the optimal bridge front line voltage waveform approximating alternating trapezoid can be obtained, and a high input power factor can be achieved; the experimental results of the three-phase LC filter-rectifier bridge-electrolytic capacitor-resistance load system with a maximum output power of 7.5kw also verified that the three-phase uncontrolled rectifier adopts LC filter, which can obtain a higher power factor in a wider load range, and can also improve the average value of output DC voltage; under no-load and light load, the capacitive current generated by the power grid is also conducive to compensating the lagging reactive power of the power grid. The single-stage LC filter has a simple structure and low cost, and is particularly suitable for applications such as high-power variable frequency air conditioners in three-phase power supply.