(Refer to **ELECTRICAL CONTRACTOR** magazine for tables and graphs.)

Two invaluable tools for solving power quality problems have been Ohm’s Law and and Kirchoff’s Laws. They provide the basis to make a fundamental calculation that helps to analyze many types of PQ phenomena, from transients to sags to harmonics to voltage fluctuations.

This column discusses a certain power quality phenomenon. It is impedance, also known as the symbol of that masked man, “Z.” “Z” comes into play in many components of an electrical distribution system, including the source impedance, load impedance, wiring impedance, transformer impedance, and so on.

In its simplest form, Z = Voltage ÷ Current. Impedance can be a complex calculation, because it involves not only resistance, but also frequency-dependent parameters, such as inductance and capacitance. Sometimes we are only concerned with the impedance at the power line frequency, 50 or 60 (or 400) Hz. Other times, it is the harmonic impedances, or the impedance of the system to frequencies between fundamental frequency and 3,000 Hz.

In most cases, we strive for the lowest possible source impedance for these two types. This results in less voltage drop from the source to the load; hence, more magnitude and less distorted voltage available for the loads. Generally, the goal is less than 1 ohm because 15A of current flowing through 1 ohm would produce a 15V drop, which on a 120V, 15A circuit would mean 105V left for the load, or a sag to 88 percent of nominal.

The opposite is often true for the high-frequency impedance. In most cases, having high impedance to the high frequencies is desirable, so things like transients from adjacent lightning strikes are attenuated. Fortunately, the wiring often provides such by itself, though attenuating filters may be needed in some applications. Figure 1 shows such from the *IEEE Std 1100*,* Recommended Practice for Powering and Grounding Sensitive Electronic Equipment*, also known as the “Emerald Book.”

The “Emerald Book” also provides a quick calculation to approximate source impedance. The source impedance is the Thevin equivalent of all of the different types of impedance looking back towards the source. This includes generators, wires, transformers, more wires, breakers, etc. If you monitor the voltage and current at a distribution panel, point-of-common-coupling, or even a load, you can readily derive this value by looking at the voltage and current values at various points in time.

Referring to Figure 2, it is assumed that V source is an ideal source with no impedance, and that all of the impedance between this source and the load is lumped into Z source. Therefore, V source = V z + V load, and Z load = V load ÷ I load. The difference between the voltage and current values at different times can be used to approximate the source impedance. This is not a fully accurate value, as it doesn’t take into account the changing impedance over frequency. However, it is a good rule-of-thumb value.

Figure 2 illustrates an example of a single-phase load. The same concept can be applied to three-phase loads. The voltage and current probes were placed at service panel feeding a residential single-phase loads.

Since simultaneous samples of the voltage and current are taken, an equivalent impedance can be derived for the load and the source by exporting the data points into Excel and using a simple spreadsheet calculation, as shown in Table 1. It shows the values calculated from the voltage and current. The voltage and current values were obtained from a PC software program and exported into Excel, could easily be obtained from a product such as that shown by viewing the “ALL CHAN-ALL PARAM” report zoomed into a waveform in a time plot.

This could also be done by plotting the voltage and current data pairs on a graph, with the voltage value being the “y” axis and the current value as the “x” axis. The slope of the line that approximates the best fit of the most data points would be the source impedance. This method also works well at the harmonic frequencies. For harmonic frequencies, the “Y” intercept (where the line crosses the “y” axis) gives you the background harmonic level that would be present if the load were not present.

Once you have the impedance, you can look for issues, such as a too-high impedance source (> 1ohm), a significantly varying source impedance (0.5-1.5 ohm), load impedance of too low a value as compared to source impedance (<20:1), and other factors that signify potential problems. Doing the same calculations for each of the harmonic values points out resonant points (where a small harmonic current can result in a big harmonic voltage). And perhaps most important, you can predetermine the loads’ effect on the voltage stability of a feeder, such as the inrush current causing excessive voltage sags that trip other equipment offline. **EC**

** BINGHAM**, manager of products and technology for Dranetz-BMI in Edison, N.J., can be reached at (732) 287-3680.