The Golden Rules

The basic laws of physics have been unchanged for the most part since Newton postulated gravity. These include the two principal laws that we use in solving many power quality problems, namely Kirchoff’s Law and Ohm’s Law. Though one of the unspoken rules about writing interesting articles is to limit use of equations, these two are too valuable not to have in one’s tool kit. If the data you collect shows that you are about to disprove the validity of these rules, you might want to recheck it before trying for the Nobel Peace Prize. Ohm’s Law equates the voltage to the product of current times impedance (V= I * Z). Likewise, the current drawn is equal to the voltage divided by the impedance (I = V / Z). Impedance is the combination of the resistance, inductance, and capacitance. Kirchoff’s Law states that the sum of the voltages at each load and source (generator) around a closed loop must equal zero. Wiring is considered a load, since it has resistance (as well as some inductance and capacitance). If you think of generators as adding in voltages, and loads as subtracting away the voltage, the net result around a closed circuit would end with all of the voltages equally zero when summed together. In the simple, single-phase circuit example in Figure 1, there are two loads and one source, hence VS - VZ - VL = 0. The impedances of the wiring, transformers, capacitors, and breakers between the generator and the load are all lumped together into one equivalent value called the source impedance. All of the loads on that branch circuit are lumped together and called the load impedance. Therefore, the generator is considered an ideal generator with no impedance, only an output voltage. When loads normally are energized, there is an increase in current (I load) based on the load’s impedance (Z load) and line voltage (V source). An increase in current caused by a load change will result in an increased voltage drop across the source impedance (Vz = I load * Zsource). If the source voltage remains constant (which is a reasonable assumption if the source is considered as the electric utility generator), then the voltage across the load will decrease (a sag) by the amount of the voltage drop across the source impedance. Inversely, if a load is suddenly turned off, there will be a decrease in current and subsequent decrease in the voltage drop across the source impedance, resulting in a swell or increase in voltage at the load. This same basic methodology is used when analyzing sags and swells or harmonics, voltage fluctuation, and transients. Kirchoff’s and Ohm’s Laws still apply to these other phenomena, though the mathematics of determining the impedances and effects are more complex. Figure 2 shows an example of a voltage sag beginning in the second cycle of the displayed waveforms caused by the periodic cycling of the heating element in a laser printer. The top waveform is the Line-to-Neutral voltage, the middle is the Line current, and lower is the Neutral-to-Ground (N-G) voltage. Observe how the N-G voltage and current waveforms are very similar. If the source impedance is split between both legs feeding the load, then it can be easily seen how an increase in line current would develop a voltage drop in the neutral leg, which would result in the neutral-to-ground swell seen here. With electric motors, the load impedance changes over time when energized and as the load changes, and results in the current swell and voltage sag in Figure 3. When the load current returns to a smaller, steady state value, the voltage at the load recovers somewhat, since there is less of a voltage drop across the source impedance. Occasionally, I receive a file with data collected from a power quality monitor where the story of the person monitoring the data would result in one or both of these laws being invalid if the situation was really as the person described it. Figure 4 shows an example of such. The monitoring took place on a three-pole, 150-Amp breaker 480V delta feeding pumps and heating, ventilating, and airconditioning (HVAC) units at a chemical plant in western Pennsylvania. The voltage waveform is shown here, while the current waveform recorded during the same time showed undistorted sine waves. The recorded transients are large, negative ones that even cross the zero axis at times. In addition, the rise and fall times of the transients are very fast, suggesting that the monitoring was in close proximity to the cause, such as very near the point where a lightning strike is coupled into the wiring. To have such a voltage waveform with current waveform showing no effects raised a flag. To have that much energy taken out of the voltage without any change in the current was saying that the golden rules were getting tarnished. When encountering such conflicting data, look to see that the monitoring points are truly where you intended them to be. A quick look at the phasor diagram, which most power quality monitors can display, may yield the source of the problem. The voltage and current connections should be on the same pair of wires to get correlating data. Monitoring the line-to-line voltage and line current on a delta circuit with even slightly unbalanced phase loads can produce interesting results, since you can’t actually monitor the current going through the load. The sum of the currents that will split and go through two of the phase loads, for which you are monitoring the voltage across each, is being recorded. Hence, there may not be a one-to-one correspondence between voltage and current. Having the CTs connected off by one phase compared to the voltage on a wye circuit can be a problem (Va and Ib, Vb and Ic, etc.). While single-phase circuits seem pretty simple, some power quality monitors require that you connect the line, neutral, and ground voltage connections in order to measure just the L-N voltage correctly. The bottom line is that, if you think you are ready to book a flight to Sweden and share your results for the Nobel Peace Prize on a revolutionary new concept in physics, check and check again. In the aforementioned example, the problems turned out to be that the voltage monitoring lead was not properly connected, and would open-circuit the monitoring input when the motors below caused a vibration during start-up. Hence, those voltage transients weren’t real, the undistorted current was correct, and there was no need to put all of the transient voltage surge supressor (TVSS) devices in the facility. BINGHAM, manager of products and technology for Dranetz-BMI in Edison, N.J., can be reached at (732) 287-3680.

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