When testing AC sources, generators, off-grid PV inverters or uninterruptible power supplies (UPSes), the output voltage and current characteristics have to be measured when the output is loaded. The load may be a passive resistor, inductor, capacitor or combination of them. The resistance, inductance and capacitance can be different from application to application.
Consequently, it’s ideal to have a load device that is capable to adjust the values of various components. However, it is very difficult to implement. To achieve that, the device needs to have countless switches, resistors, inductors and capacitors to composite the desired load circuit. But, the limitation of the component, for example, high power resistor, has poor temperature coefficient, makes the fine loading adjustment almost impossible, or too costly. Therefore, conventional load device uses fewer components and switches thus provide very limited load simulation conditions. One example of an E-load solution, which is capable to adjust the components values freely to increase the test coverage and give more valuable measurements, is the Chroma 63804 AC/DC load—and off the shelf solution for real world load simulations and measurements.
Theory of operation
There are eight operation modes available for Chroma 63804: CC mode, CR mode, CP mode, RLC mode, RLC-CP mode, DC mode, DC-RECT mode and INRUSH mode. Each mode has different equivalent circuit. User may select different load mode base on the output characteristic of the unit under test (UUT).
CC Mode
As seen in Figure 1, this load mode provides constant current simulation. When the loading current and relevant parameters were set, the 63804 will draw current base on user setting, disregarding what the output voltage of the UUT is. In this mode, its equivalent AC impedance theoretically is expected to be infinite high. Thus, the UUT sees infinite high AC impedance within defined bandwidth from the E-load. If one just wants to draw current out from UUT without simulating the load impedance effect, CC mode is the ideal operation mode.
In Figure 1, Zo = R+jx is the output impedance of the UUT, the voltage and current waveforms resulting from the CC mode are shown in Figure2. The circle highlights the voltage distortion which is caused by the output impedance of the UUT. The current is predefined as sinusoidal wave.
CR mode
Figure 3 shows equivalent circuit of CR mode. It’s quite straight forward that user sets the load resistance and the E-load will follow. Under CR mode, the loading current will be proportional to the UUT output voltage and the ratio of the voltage and loading current will then be the programmed resistance.
Under CR mode, the UUT sees constant resistance within defined bandwidth from the E-load which is equal to the setting value. To make it simple, it’s like connecting a resistor on the UUT output with resistive loading effect.
CP mode
Same as Figure 1, but the CP mode allows user to set the loading power and relevant parameters rather than loading current, the E-load will then load the UUT at constant power level. However, differ from CC mode, the loading current is relevant to the UUT output voltage to keep constant power manner. The AC impedance sees for UUT from E-load is same as the CC mode.
DC mode
There are four sub-operation modes for DC load simulation. They are CC, CR, CV and CP mode. Their operations and loading effects are same as the first three mentioned above. CV mode is basically same as CC mode except the UUT voltage will be measured to determine the loading current.
A UPS is a device designed to deliver rectified current which is commonly seen for most of the appliances connect to UPS. Most of the UPS designers use resistive load to load the Power Factor Correction (PFC) circuit thus the loading current will be close to DC. This does not reflect to the real circuit and application scenario, wherein the loading current will, in fact, show rectified pattern. As seen in Figure 4, the simplified PFC circuit, when using DC load current, the output ripple current cannot be predicted thus the value of C1 and C2 can’t be defined too. Chroma 63804 provides rectified loading mode which is synchronous to the mains frequency that gives real load simulation and measurement.
Figure 4 also shows the connection of using two E-loads to load the PFC circuit to simulate both positive (IL1) and negative (IL2), half circle rectified current. Figure 5 shows the waveforms of mains voltage and IL1 and IL2. Note that the phase of the IL1 and IL2 can be manipulated under DC-RECT mode.
RLC mode
Figure 6 shows the equivalent circuit of UUT and rectified load circuit. The intention of RLC mode is to replace those passive components, r, L, C, RL and diode. Using sophisticate algorithm and high speed DSP, the 63804 is capable to calculate the real time loading current base on UUT output voltage and r, L, C, RL settings. Detail will be described later.
As seen in Figure 6, the series resistor – r, is normally added to eliminate the inrush current. Sometimes an inductor (L) will be added to increase the power factor. The UUT (AC source or UPS) has output impedance (Zo), so we may simplify the equivalent circuit as Figure 7 for DSP calculation.
In Figure 7, Rs = R + r; Ls = Lx + L. R is the real (resistive) part of Zo in Figure 6, and Lx is transformed from jX which is the imaginary (reactive) part of Zo in Fig.6. Before the actual load current applied, the E-load will detect the Zo of the UUT, and then combine with component values set by user. The DSP will be able to calculate the loading current. RLC-CP mode
Under the RLC mode, when the UUT output voltage (rms) is varying, the loading current (rms) will vary too, according to Ohm’s law. Consequently, the power will be varied too. However, most of the UUT test plans specify the power rating rather than give component values of the rectify load device. The RLC-CP mode is designed to simplify user setting while they have no idea about the detail of the load. In this mode, user only needs to set the power and power factor of the load, the DSP will calculate the best solution and give appropriate R, L, C values to maintain the power and power factor after load on.
INRUSH mode
RLC mode simulates only steady-state and won’t give transient current such as inrush current as seen in real application. To simulate the inrush current, 63804 provides INRUSH mode. In INRUSH mode, the E-load will simulate only one-cycle load simulation because in reality, the current of the rectify circuit will be stable after one cycle. The maximum peak current is 200A. Figure 8 shows the inrush waveform.
RLC-mode calculation and analysis
There are two ways to get the RLC mode loading current. First is to calculate the differential, integration using analog approach. The second is to convert the frequency-domain transfer function to digitized transfer function then calculate it under time-domain. The 63804 uses the second approach, therefore we focus on that and elaborate the process as below.
Base on operation region of the diode, two calculations are described respectively:
a. Diode forward biased: See equivalent circuit in Figure 9.
If
Vrect(i) = The initial voltage across capacitor C when the diode is about to be ON.
fr = Reference frequency
fs = Sampling frequency
We can get
By using bilinear transformation, we may convert analog transfer function G1(s) ~ G4(s) to digital transfer function H1(z) ~ H4(z). Thus we get,
From above, we may derive the current and voltage functions as follows:
Using the functions above, we may then calculate the simultaneous Irect and Vrect values.
b. Diode reverse biased: See equivalent circuit in Figure 9.
If
Vrect(f) = The voltage across capacitor C when the diode is OFF.
We can get
Using the same digital conversion, we get:
We may use above function to calculate the Vrect while the diode is in off-state. During the calculation process, the Irect and Vrect will be used to determine when the diode should be ON and when it should be OFF.
The voltage waveform showed in Figure 10 is the waveform of the diode input; current waveform is the loading current waveform.
Below shows few examples under different input voltage and RLC settings.
Figure 11 is plotted based on the following conditions and settings:
Vs = 120V/60Hz
Rs = 50mÙ
Ls = 9ìH
C = 10mF
RL = 5Ù
Since the Ls is pretty small, we see the current phase leads the voltage slightly.
Figure12 shows another set of waveforms under different settings.
Vs = 120V/60Hz
Rs = 50mÙ
Ls = 200ìH
C = 10mF
RL = 5Ù
Right here, the current phase lacks of voltage because higher Ls is set.
From Figures 11 and 12, we know Rs, Ls have dramatic impact to the current phase and wave-shape. Figure 11 has higher Crest Factor. In contrast, Figure 12 has higher Power Factor. Another noticeable difference between CC mode and RLC mode is: the current wave-shape in CC mode is sinusoidal but RLC mode is not. Although the difference is not very big; but it represents different loading stress to the UUT. Under CC mode, what UUT sees from E-load is infinite high impedance but under RLC mode, it is combination of r, L, C, RL that reflects the real application scenario.
The UUT normally has its own control loop; the output impedance will influence the close loop gain and phase and eventually the system stability. Chroma 63804 and its RLC mode may simulate the passive components thus avoid oscillation that commonly seen on traditional AC load design.
Conclusion
RLC mode is working by using real time calculation of DSP. When the Sampling frequency of the DSP and current amplifier bandwidth are infinite high, and the calculation time is squeezed down to zero, its operation is literally same as analog circuit. The measurement results will then be identical.
However, the hardware sampling rate has its limit; the calculation time can’t be zero; plus the UUT output impedance (inductance) will limit the current amplifier bandwidth and also the control delay issue; these make the Power Factor, Crest Factor, power and current may be slightly different from the actual passive component circuit. But, the waveform and response will still be the same.
But, to make practical use, the UUT output frequency is limited to 70Hz. For frequency higher than 70Hz, the error becomes too high to ignore thus RLC mode is no longer recommended. In this case, user may select other load modes for load simulation.
Below are two examples that show the loading waveforms by using actual passive component circuits and loading waveforms simulated by using RLC mode of Chroma 63804.
Example 1
Test conditions:
AC source Output Impedance:
Ro = 50mÙ; Lo = 9ìH
L = 0
r = 0
RL = 12.5Ù
C = 4.8mF
AC = 120V/60Hz
Figure 13 is the waveform of actual passive component circuit and Figure 14 shows the simulated waveform by using 63804.
Example 2
Test Conditions:
AC source Output Impedance:
Ro = 50mÙ; Lo = 9ìH
L = 200ìH
r = 0
RL = 12.5Ù
C = 4.8mF
AC = 120V/60Hz
Figure 15 is the waveform of actual passive component circuit and Figure 16 shows the simulated waveform by using 63804.
As seen from the waveforms, Chroma 63804 simulated loading waveforms are almost identical to the actual passive component circuits, just very small unavoidable delay spotted whose reason was elaborated in earlier discussion.
If the UUT equivalent output inductance Lo = 200ìH but the series inductance of the load L = 0; the voltage waveform will be highly distorted as shown in Figure 17. This is caused by the drop over Lo of the UUT under loading. As we can see from Figure 13, when the Lo of UUT is low, even the loading current is still high, but very small voltage distortion can be observed.
Click here for Illustrations:
Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11
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