Current Sharing Analysis of Parallel Inverter Systems without Interconnection Lines

1 Introduction

At present, equipment powered by special power supplies requires the power supply system to have high reliability and high power, both of which are closely related to the parallel operation control of inverter power supplies.

There are many types of inverter parallel control technologies. Among them, the interconnection-free control strategy based on voltage amplitude and frequency droop characteristics [1][2][3] has become a research hotspot in recent years because there is no mutual interference between communication lines between modules and there is no strict restriction on the location of parallel inverters. When the parameters of the inverter modules are consistent, the droop characteristic control scheme can achieve a good current sharing effect; but in practice, the parameters of each inverter module cannot be completely consistent, which will lead to power inequality. This paper deeply analyzes the reasons why the power cannot be shared due to inconsistent inverter parameters, and gives corresponding improvement methods to improve the accuracy of power sharing.

2 Single inverter control principle

Figure 1 Block diagram of a single inverter

A typical inverter usually consists of a DC voltage source, a bridge (half-bridge in this article) PWM inverter and an output filter. Figure 1 is a block diagram of a single inverter. The control circuit of a single inverter adopts a voltage and current dual closed-loop feedback control method. The voltage outer loop adopts the traditional PI regulation (represented by G1(s) in Figure 1), and the current inner loop adopts the inductor current instantaneous value feedback control, using a two-state hysteresis current tracking method. When the modulation frequency is high enough (much higher than the output filter bandwidth), the current loop can be equivalent to a current follower, that is, equivalent to a proportional link k[4].

3 Analysis of inverter output power imbalance

3.1 Power theory

Figure 2 Equivalent circuit of inverter parallel system

The equivalent model of the parallel system composed of two inverters is shown in Figure 2, where E1∠φ1 and E2∠φ2 are the no-load output voltages of the two inverters respectively; UOL∠0 is the parallel bus voltage; Z1∠θ1 and Z2∠θ2 are the inverter equivalent output impedances, which are composed of the inverter output impedance and the line impedance of the inverter connected to the AC bus; ZL is the load impedance. Let Z1∠θ1=R1+jX1, Z2∠θ2= R2+jX2. From the physical meaning of power, the expressions of active power P and reactive power Q emitted by the inverter in parallel are:

From equations (2) and (3), the voltage-frequency control block diagram when the equivalent output impedance is inductive can be drawn as shown in Figure 3. The difference between the time integral of the inverter output frequency ωo and the time integral of the AC bus voltage frequency ωn is the phase difference between E∠φ and UOL∠0. From Figure 3, the system transfer function with no-load frequency and bus voltage frequency ωn as input and output active power P as output can be obtained:

Formula (5) shows that the active power output by the inverter in steady state is independent of the connection impedance X. Even if the connection impedance between each inverter and the load is different, the active power they output can still be equal by controlling the frequency droop.

Similarly, according to formula (1), the expression of reactive power at this time can be obtained:

From formula (9), it can be obtained that the output reactive power in steady state is related to the connection impedance. When the connection impedance is different, the output reactive power is also different. The inverter with large impedance outputs less reactive power, and the inverter with small impedance outputs more reactive power.

B) When the equivalent output impedance is resistive: Z∠θ=R

Similar to the analysis when the output impedance is inductive, it can be obtained that when the equivalent output impedance is resistive: regardless of whether the connection impedance between each module and the load is equal, the reactive power they output is the same; when the connection impedance is unequal, the active power output by each inverter is unequal. The one with larger impedance outputs less active power, and the one with smaller impedance outputs more reactive power.

[page]4 PQ droop coefficient adjustment method

Here, we only take the case of inductive equivalent output impedance as an example to give a method to improve the accuracy of power sharing. From equation (6), we can see that Q is affected by both the output impedance X and the output voltage amplitude E. Therefore, Q can be controlled by controlling their sizes, and the regulation of E can be achieved by adjusting the amplitude droop coefficient n.

From the previous analysis, the smaller the inverter output inductive reactance X is, the greater the reactive power it outputs; otherwise, the reactive power it outputs is smaller. Because the reactive power output of the inverter increases (decreases) with the increase (decrease) of the voltage amplitude, if the voltage amplitude droop coefficient of the inverter with larger reactive power is larger, and the voltage amplitude coefficient of the inverter with smaller reactive power is smaller, the output reactive power error during stability can be reduced. The corrected current sharing equation is:

(10)

Where nk=n(1+KQ), k is defined as the adaptive adjustment factor of the amplitude droop coefficient.

5 Simulation and experimental verification

The theoretical analysis of the power distribution when the output inductance of the parallel inverter is unequal is verified by Matlab software simulation. In order to observe the dynamic adjustment process of active power P and reactive power Q, the initial frequency of module 1 is 400.4Hz, the initial voltage value is 113.8V, and the output inductance X1=0.7536Ω; the initial frequency of module 2 is 399.6Hz, the initial voltage value is 115.3V, X2=0.88Ω, and the droop equation is as follows (i=1,2):

During the simulation, the inductive load (cosφ=0.75) suddenly increased from 1000VA to 2000VA at 30ms. Figure 5 shows that when the output inductive reactance is unequal, the active power P output by the two inverter modules can be evenly divided through the droop current sharing method, but the reactive power Q cannot be evenly divided, and the reactive power difference increases with the increase of load.

(b) Reactive power distribution

Figure 5 Power distribution when the output inductance of the two inverters is inconsistent

In order to reduce the reactive power deviation, the droop control equation (11) is modified as follows:

The parallel system is simulated using Matlab software, and the initial conditions and parameter settings are the same as the previous simulation. Figure 6 shows that the introduction of the control equation shown in equation (12) can reduce the reactive power deviation caused by the unbalanced line inductive reactance without affecting the equal distribution of active power.

Figure 6 Power distribution after introducing the modified equation

The experiment was conducted on a parallel system consisting of two half-bridge inverters, with the following parameters: input voltage 360VDC; output voltage 115V±3%AC; rated power 1KVA; voltage feedback coefficient Kvf=0.028; current magnification K=3.3; proportional coefficient KP=12.14; integral coefficient KI=35700; filter inductor Lf=1.2mH; filter capacitor Cf=10μF; output frequency 400±0.8Hz. Figure 7 shows the output current waveform of the parallel system when the traditional PQ droop method is used for current sharing control when the two inverters have different series inductances at the output end (X1=0.88Ω, X2=0.7536Ω); Figure 8 shows the output current waveform of the parallel system when the amplitude droop coefficient adjustment method is used for control. Due to the unequal output inductance, the reactive power cannot be well evenly distributed, and there is a phase difference in the output currents of the two inverters. The larger the phase difference, the larger the reactive power difference. By comparing the two figures, it is easy to find that the phase difference of the current is reduced after the droop coefficient adjustment method is adopted, indicating that the accuracy of reactive power sharing is improved.

Figure 8 Parallel output current after using the droop coefficient adjustment method

6 Conclusion

The power distribution of parallel-controlled inverters without interconnection lines when the equivalent output impedance is unequal is discussed and analyzed:

1) When the output impedance is inductive, unbalanced output impedance will cause reactive power sharing error.
2) When the output impedance is resistive, unbalanced output impedance will cause active power sharing error.
3) The power deviation caused by unequal output impedance can be reduced by using the PQ droop coefficient adjustment method.

References

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