Slot Harmonics Define
Troubleshooting harmonic problems can be like trying to find a needle in a haystack. Every individual load on every branch circuit is a potential harmonic source. However, you can significantly reduce troubleshooting time by determining the harmonic power flow direction on a circuit. Let's say there's a harmonic issue on a branch circuit with ten loads. You would need to connect a monitoring instrument to each load individually, recording the information as you move from load to load. But instruments with a harmonic power flow feature would allow you to conduct the “half way” method of troubleshooting. This means you can connect the instrument after the first five loads to determine if the harmonic is coming from the load or the source. From there, you can connect half way on the initial first five loads and repeat the process.
Most monitoring instruments determine harmonic power flow direction the same way — by comparing the voltage and current waveforms of a harmonic frequency for a particular phase. If the waveforms are inphase ±90 deg, the harmonics come from the source. If they are out-of-phase ±90 deg, they come from the load.
- Feb 07, 2010 In some technical papers and advanced text books, slot harmonics are probably described elegantly and completely with diagrams and equations. Unfortunately, no one has answered this question with a reference to such an explanation, so I will attempt an explanation without any supporting references.
- 1 to 9 meaning that one side of the coil is inserted in slot #1, and the other side in slot #9. Coil Span: The number of core slots spanned by the sides of the coil. In the above example, the span would be 8 slots (9 – 1). Slots Per Pole: The number of slots in the armature core divided by the number of poles constituting the field.
The Music Theory behind Acoustics and Harmonics If you were to break music down into pure mathematics, you would end up dealing with acoustics and harmonics. An instrument’s acoustics and harmonics define that instrument’s unique sound; they’re also the reason you rarely hear songs that use a tuba or a bassoon for the lead instrument. Harmonics Defined Harmonics are multiples of the sine waveform produced by the generator. For example, 60 Hz is the fundamental waveform, then 180 Hz (60 Hz x 3) is third harmonics, 300 Hz is fifth harmonics, 420 Hz is seventh harmonics, etc. Only odd-numbered harmonics are important in this discussion.
Despite this similarity, monitoring instruments use different methods for compensating for induced phase shifts — if they do at all. In addition, instruments vary widely in how they capture and display data. You'll need to consider these factors to ensure accuracy in determining power flow direction.
Potential Errors
There are a number of items that can cause inaccurate harmonic direction, including current-transformer (CT) and potential-transformer (PT) phase shifts, calibration, sampling, and frequency response. Because direction is based on the phase relationship between voltage and current, any phase shift causes a degree of uncertainty that correlates with a potential error.
Table 1 shows the specifications for a typical clamp-on transformer. Note that the phase shift changes as the load changes. Table 2, on page 36, shows how the accuracy changes as the frequency changes. This could adversely affect the harmonic direction indication by reducing the level of amplitude on the current.
In Fig. 1, on page 36, you'll see typical response curves from current transducers. As the frequency increases, the phase shift also increases. Therefore, if a current transformer has a ±3 deg phase shift, the degree of uncertainty (or the chance of coming up with incorrect power flow direction) would be 12 ÷ 360 × 100 or 3.33%. The reasoning is as follows: Because direction changes from the source to the load (or vice versa) at 90 deg and 270 deg and the transformer error is ± 3 deg, there is a degree of uncertainty between 87 deg and 93 deg and 267 deg and 273 deg.
This error also can occur if you use an instrument that employs internal PTs, if you connect an instrument to external PTs, or if you clip a CT around the secondary of another CT. (Caution: These errors are additive. If you connect the instrument to all of these transformers, the error can be substantial.)
Sources of other potential errors include the following:
- The harmonic magnitude of the voltage and/or current waveform is low. In this case, the circuitry may not be able to accurately distinguish the phase angle, thus hampering the accuracy of the harmonic direction.
- A CT pointing the wrong way or voltage leads connected incorrectly cause inaccurate directional indications. Many manufacturers allow users to view phasor diagrams, which show the phase rotation between phases. This helps ensure that the voltage and current leads are connected properly. Negative power or power factor can be indicative of a CT pointing the wrong way or improperly connected voltage leads.
To help minimize any errors that may arise, it's best to select a quality current transducer with a low phase shift and a good frequency response.
Fortunately, some manufacturers have gotten into the act by enhancing their products with features also designed to minimize errors. At some facilities, instruments are calibrated for phase shift by matching current transducers to the CTs being used. This eliminates CT errors — as long as the CTs are not interchanged.
Yet another instrument provides a calibration probe that calibrates current transducers in the field. This permits users to switch CTs and still get accurate readings. It also compensates for any frequency response errors. The challenge here is similar to the one for CTs. That is, the accuracy of the probes must be recognized or additional error will be introduced.
Power Flow Presentation
Most instruments that determine harmonic power flow direction display the resulting information in waveform captures or snapshots. For example, some instruments display the harmonic magnitude and cosine of the phase angle (or power factor). Because the power factor's sign is indicative of direction, the user can determine if harmonic power flow comes from the source or from the load.
Other instruments display the angle of the harmonic and voltage waveform. This allows the user to interpret the direction visually from the angle. If the angle is to the right of the y-axis, the harmonic stems from the source; if it's on the left, it comes from the load.
Still other instruments display a directional bar graph that shows a harmonic spectrum. If the harmonic appears above the x-axis, it comes from the source. If it appears below the x-axis, it originates from the load.
The problem with relying on waveform captures or snapshots is the possibility of inaccurate assumptions. Because the information is recorded at intervals, any change in the harmonic information between the snapshots is not recorded and missed forever.
Fortunately, there are instruments available that can display graphs of harmonic magnitudes and phases over time. This type of display captures harmonic data between snapshots, providing a cycle-by-cycle resolution of the harmonic (see Fig. 2, on page 36). The phase graph indicates whether harmonic direction comes from the load or from the source.
Some instruments have no display area and require a computer to view information. Others have graphical or alphanumeric displays for viewing real-time bar graphs and values.
In many cases, instruments with built-in displays cost significantly more than those with no displays, and they can sometimes compromise the weatherproof rating of the case. Memory slots and push buttons can leak and cause damage to the monitoring equipment.
Some engineers use optional hand-held devices to download real-time data. This eliminates the need for a graphical display and typically lowers the cost of the base unit. The user can then download and view the information in a controlled environment.
Instruments that indicate harmonic power flow direction are beneficial for troubleshooting harmonic problems. However, engineers should watch for errors that could adversely affect direction accuracy. These errors include incorrect hookups, low voltage or current, the frequency response of current transducers, and the phase shift of potential and current transformers.
To minimize these errors, some manufacturers have added enhanced features such as phasor diagrams, probe calibration coils, and factory calibration of current transducers. Whatever instrument you decide to use, you'll have the added advantage of understanding how it gathers and displays information.
Lou Barker is a sales manager for Power Monitors Inc. in Harrisonburg, Va. You can reach him atlbarker@powermonitors.com.
harmonic content
[här′män·ik ′kän·tent] (physics)
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Slot Harmonics Definition
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