The effects of harmonic resonance between the supply impedance and power factor correction capacitors on systems with large harmonic sources such as mine winders, are well known. The similar effects of resonance with cable capacitance are not commonly encountered and, hence, are not always considered in the design of medium voltage networks. This article considers some of the aspects of resonance between the supply impedance and cable capacitance and one particular approach to solving the problem that proved successful.
In recent years the increasing capacity of power semi-conductor devices has led to the proliferation of solid state power equipment in industry. These devices are used in many applications, one of which is large variable speed drives. Large modern mine winders are commonly powered by dc rectifiers or cycloconverters. Drives ranging from 4 MW to 8 MW are not uncommon. These power electronic devices distort the supply waveform, giving rise to harmonics on the supply network.
At the same time, the structure of electrical utility billing has led to the increased installation of large power factor capacitor banks to reduce maximum demand charges or penalties for poor power factor. The harmonics generated by large semi-conductor drives may excite the resonance between the power factor correction capacitors and inductance of the supply. This will have the effect of amplifying the generated harmonics, resulting in lower efficiencies of operating equipment and the possible damage to equipment, especially to the capacitors themselves.
These problems are well documented and designers of electrical power systems are cognisant of these difficulties and will usually install power factor correction in the form of harmonic filters in presence of large converter drives.
The effects of resonance with cable capacitance is not as well documented since it is encountered less frequently and because the effects are either not always noted or not traced to the converter drive as the source of the problem.
The resonant frequency of an electrical network is given by the equation:
Hr= The square root of MVAsc/MVARc = the square root of Xc/Xsc
where:
hr is the resonant frequency as a multiple of the fundamental frequency
MVAsc is the short-circuit duty at the point of connection
MVArc is the capacitor rating at the system voltage
Xc is the capacitive reactance of the capacitors at the fundamental frequency
Xsc is the short-circuit reactance at the point of connection.
The degree of interference with communications networks is defined by the telephone interference factor, TIF. In practice, a more commonly used measure of this interference is expressed as the IÑT product, which is the product of the harmonic current and the single frequency TIF for each individual harmonic.
The following example is based on a mine supplied at 50Hz by twin overhead lines approximately 100km in length. The mine distribution is shown in Figure 1. Each 20MVA 132-11kV transformer supplies a section of the mine. The right hand transformer feeds the concentrator, while the left hand transformer feeds a 4 MW dc-converter mine winder as well as the underground workings of the mine. At the time the measurements were taken, one of the four feeders from the main substation to the mine winder substationwas out of service. The distance between the two substations is approximately 2000 metres. Including the cable feeding the underground workings, the total length of cable connected to the rock shaft system was approximately 8000 metres. The cable consists mainly of 185 mm2 XLPE cable, with some smaller sizes feeding the underground sections. The cable capacitance is approximately 300nF per kilometre.
The winder is used for the hoisting of ore from the underground workings to the surface. Each hoisting cycle is approximately three minutes. The current drawn by the winder during each winding cycle is shown in figure 2. The peak current drawn by the winder is 440 amps (8.4 MVA) with an average current during the winding cycle of 210 amps (4.0 MVA).
The dc-converter comprises two six-pulse bridges which operate in sequence control mode. The winder harmonics up to the 50th harmonic were recorded with a digital harmonic analyzer. The harmonic spectrum of the peak and rms winder currents at 11kV is shown in figure 3. The 5th and 7th harmonic currents are dominant. The winder harmonic currents have been used to calculate the IT product at 132kV. The higher order harmonic currents which have the greater impact on the IT product, although small, are very evidently present.
Using these currents, the IT product at 132kV can be calculated by multiplying the measured current by the weighted TIF factor for each harmonic. The appropriate TIF factors for the dominant harmonics produced by a six pulse converter at 50 Hz are shown in Table 1. These values have been extrapolated from Table 6.2 of IEEE Std 519-1992. The calculated IT product is 14883. This places it in the Category II level that IEEE 519 states might cause interference with communications systems. As discussed earlier, the predicted interference was detected.
The voltage waveform was also measured at the incoming substation and is shown in Figure 4. The presence of high order harmonics can be seen in the waveshape.
The harmonic spectrum of the voltage waveform is shown in Figure 5. The characteristic harmonics associated with twelve pulse winders are present. The presence of unusually large higher order voltage harmonics indicates resonant conditions at these higher frequencies.
A recording of the total harmonic distortion (THD) of the supply voltage over an extended period shows that whenever the winder is operating, the THD is in excess of the 3% limit imposed by the utility. The recording of the THD is shown in Figure 6.
The interval to the right of the graph with the THD at about the 1% level is when the winder was out of service. This also serves as a good indication of the level of background harmonics on the supply system.
There are no power factor correction capacitors on this section of the mine electrical network. The only form of capacitance which could possibly lead to resonance is the cable capacitance. About 8km of cable is connected to the system. The cable capacitance of the cables is approximately 300 nF per km. The fault level at each of the main 11kV busbars is 185 MVA. Thus, calculating the resonant frequency, we find that
This confirms that resonance at the higher frequencies, as indicated by the harmonic recordings, is likely if a source of harmonic generation is present on the network.
Solution
The harmonics that were measured did not present any direct problems to the mine itself, as far as
was known, but created problems within the communication networks supplied via bare overhead
communication lines which ran parallel to the power lines. The mine was instructed by the utility
to install harmonic filters to reduce the total harmonic distortion and the telephone interference
factor at the point of common coupling.
Since the harmonics generated by the mine winder were clearly the source of the harmonics, the mine accepted the responsibility to solve the problem. In order to minimise the cost to the mine of filtering out the harmonics, it was decided to install harmonic filters with sufficient power factor correction capability to provide a return on the capital investment. The mine is charged for electricity by means of a two part tariff. The first part constitutes the energy charge per kW-hr of consumption. The second part of the tariff is made up by a maximum demand charge for the peak half hourly integrated kVA in each month. The power factor of the overall load is 85%. With a maximum demand of 16.5 MVA the amount of power factor correction required to raise the power factor to 0.99 is 7.2 MVAr. At the same time, the installation of the harmonic filters would address the engineering aspects of the problem.
A conventional harmonic filter, tuned to the 5thharmonic and a wide-band filter tuned to the 7thharmonic were designed and installed. The whole installation was circuit breaker switched with the 5th filter permanently connected and the 7th filter was contactor switched according to the power factor requirements. A further function of the wide-band 7th harmonic filter is to provide filtering for the higher orders of harmonics. A third order filter was chosen in preference to a second order filter as the losses are reduced by the introduction of a series capacitor in the resistive arm of the filter. The total filter capacity selected was 7.2 MVAr. The filters would thus provide a measure of harmonic filtration at the higher harmonic frequencies, while simultaneously improving the power factor of the load, thus reducing the kVA maximum demand and, consequently, the demand charges. The return on the investment of the capital was calculated on a simple payback basis to be of the order of six months. This was extremely satisfactory from an economic point of view.
The improvement in the harmonics is shown in the voltage harmonic spectra in Figure 7. The voltage harmonics have been reduced throughout the spectrum. As expected, the 5th and 7th harmonic voltages have been significantly lowered. In addition, there is a particularly marked reduction in the levels of the higher order voltage harmonics. The current harmonics are also significantly reduced.
The introduction of the harmonic filters reduces the calculated IT product to less than half of the original value. The new IT product is at 6493 which places it in the category I level. This category is one which is most unlikely to cause interference and, in fact, no interference with the communication system under discussion was reported after the filters were commissioned. The installation of the filters has addressed the problem of interference in the communication network while, simultaneously improving the power factor of the mine load.
Recommendations
The increasing use of non-linear loads in industry means that the effects of the harmonics
generated, particularly in the presence of system capacitance, need to be considered. This aspect
should be investigated by means of harmonic simulation at the design stage of new projects.
Where the non-linear loads on an existing facility are increased, the measurement of the harmonic
conditions, followed by harmonic simulation is recommended. Clearly, the possibility of
resonance affecting a system that includes non-linear loads increases with the presence of any
significant capacitance, whether as part of power factor correction equipment or an extensive
cable network.
Athol F Symonds is with Fluor Daniel Wright Ltd. in Vancouver, B.C.