Long motor cables
Today we gonna talk about long motor cables and their impact on drive systems. In some projects the physical distance between VFD and motor as well as cable routing cause motor cables to be fairly long. This fact has impact on system design. The motor control might not work as intended. When long motor cables are not properly considered, a motor insulation failure could appear. This post provides a look into the topic. It explains the physical limitations and lists possible risks when the maximum motor cable length is exceeded. Are you wondering about questions such as:
– How long are long motor cables?
– Where does the limitation in length come from?
– How does a motor cable impact the motor terminal voltage?
– How to model long cables?
– How does a high frequency motor model look like?
If you answered at least one time ‘yes’ then keep reading this post.
Remark: We will publish another article specifically discussing the requirements on power cables of inverter duty motors. This article focuses on effects of motor cables as explained above.
Maximum motor cable length depends on the VFD topology and selected options. The manufacturers typically mention the standard cable length in their catalogues and brochures. Check out the supported cable lengths. Longer cables are sometimes available as (engineered) option or on request.
Where does the limit of cable length come from? And what are the consequences when maximum recommended cable length is exceeded?
Before answering all above questions let’s start with a brief theory. Most modern VFDs are based on voltage source inverter technology [1] and therefore our main focus is on those drives. However, we mention the current source inverters as well. As both technologies, voltage source inverter (VSI) and current source inverter (CSI), are almost dual [2], it does not surprise that also the interaction inside the inverter-cable-motor system is quite different for each of them.
1. Voltage source inverter
General principle of any voltage source inverter is to chop a quasi-constant DC voltage into AC voltage of variable frequency and RMS value. A suitable modulation therefore makes a sequence of voltage pulses that are sent to the motor. The voltage step and number of voltage levels is directly dependent on specific VFD realization. The simplest VSI topology is a 2-level inverter.
The output voltage consists of series of pulses with magnitude of +Vdc and -Vdc. The waveform is commonly used in low voltage drives, but practically unused in medium voltage. The voltage has high distortion. In order to get somewhat smooth inverter current a fairly high switching frequency would be required. That would mean power derating and increased losses. Main challenge would however be the dielectric system of the motor to handle such large and steep voltage steps (for 6 kV machine the VFD would switch pulses of +10 kV and -10 kV!).
Therefore, the state of the art solution is a multi-level inverter. The higher the number of levels, the smaller the voltage steps. But it also means higher parts count and potential need for n+1 redundancy. Although the voltage steps in some multi-level inverters are relatively small (especially the cascaded H-bridge topology), the LV IGBT semiconductors are extremely fast in terms of voltage rate of change (dv/dt). The authors in [3] investigated motor power cables when used with PWM modulated voltage source inverters. They present typical switching times of most commonly used power semiconductors:
Now let’s come to the inverter-cable-motor interaction. Every cable has, apart from its resistance, certain inductance and capacitance. These values are normally provided as specific values, i.e. inductance in nH/m (nano Henry per meter) and capacitance in pF/m (pico Farad per meter). The inductance and capacitance is roughly equally distributed along the cable length. As you know, inductance L and capacitance C in a circuit create a resonance.
From the equation above it is obvious that the longer the motor cable, the lower the resonance frequency. For short cables the resonance frequency is very high and not much excited from the inverter. There are two reasons: 1. inverter produces no harmonics at such frequencies or harmonics with very small magnitude (remember the amplitude law) and 2. high frequencies are generally much better damped (due to skin effect etc). However, as the motor cable length increases, the resonance frequency drops into a range where interaction of inverter and cable is likely to happen.
When the cable resonance frequency lies within the bandwidth of the inverter, the resonance can basically be excited continuously right after every switching instant.
We can observe characteristic “ringing”. Such condition creates additional stress for the cable, additional inverter current to charge and discharge those capacitance and most importantly increased peak voltage at motor terminals. The inverter voltage is basically amplified in the resonance condition so that motor insulation system witnesses increased voltage peaks. Those peaks, when present over longer period of time, may lead to increased partial discharge activity and accelerated aging of insulation system.
How to mitigate adverse interaction of inverter-cable-motor system? The basic remedy is to install a dv/dt filter at the inverter output. As we described earlier, every sound VFD manufacturer includes such filter inside their VSI type of inverter. The filter reduces the dv/dt at the converter output making it more motor friendly. Moreover, the dv/dt filter is a low-pass filter and as such provides damping of higher frequencies. Depending on the design of dv/dt filter, certain standard motor cable length is allowed.
As long as the motor cables are within the specified range, the resonance will be sufficiently damped and not of a concern. That brings us to the question: At what length is the motor cable considered as long cable? As explained above, it depends on the design of the output filter (usually a dv/dt filter, but some VFD also feature a sine filter at the output). Typical allowable cable lengths of VSI medium voltage drives range from 300 m up to 1’000 m. Products incorporating a sine filter allow several kilometers of motor cables. There are also special systems using a step-up output transformer, cable transmission of 10-50 km and step-down transformer to adapt the voltage for the motor.
Some people would tend to think that the longer the motor cables the more amplified voltage and the worst the condition for the motor. Well, this is only half true. In fact, short motor cables are unproblematic as the cable resonance is very high and practically cannot be excited. Medium range of cable length might be the most challenging. Special applications with very long cables are again easier to handle as those cables have higher resistance (also increasing with length) and are therefore very well damped.
Studying the inverter-cable-motor interaction is not so simple. Especially simulation results are sensitive to the way how the cable model is incorporated in overall simulation. Tools such as Matlab/Simulink are popular to model and simulate power electronic systems, but less suitable to model the cables in a realistic way. Note also that the closed loop control of the VFD impacts the results. People often perform the studies as open loop, i.e. impose certain voltage waveform at the feeding terminal of cable-motor system.
Such model obviously does not respect the VFD control. In reality, the VFD measures the inverter output current and uses it as input in its real-time motor model.
Again, sound VFD manufacturers have several software functions to support smooth VFD operation in a system with longer motor cables. These algorithms are confidential and therefore not discussed further. We just close the point with our testimony that suitable software functions can provide substantial control damping.
An inverter-cable-motor study shall, among others, deliver
– peak voltages phase to ground
– peak voltages phase to phase
– frequency of occurence of peaks (seldom, often, periodically)
– dv/dt values of voltage rise and fall rate of change
As the subject is sensitive to proper modeling and parameterization, the results shall be verified by real field measurements. The measurement setup requires high sampling rate and rather high accuracy. Without such benchmark the risk is high to consider incorrect or misleading values.
Various comparisons of simulations and field measurements clearly show that the damping in simulation is by several factors lower than real damping and the simulated oscillation (both peak value and decay time constant) is far too high.
2. Current source inverters
Current source inverters are almost opposite to voltage source inverters. Their output voltage is almost sinusoidal making the inverter-cable-motor interaction somewhat easier. However, CSI drives still have certain harmonics in the output current. Those harmonics can excite the parallel resonance introduced by motor cable. Resonance condition means elevated motor voltage peaks and potential dielectric issues same as in voltage source inverters.
The increased voltage may also be problematic for the bipolar capacitors on the AC side of the inverter. It may also disturb the VFD control that is more complex than control of voltage source inverters and eventually also more sensitive to such disturbances.
Cable construction
Medium voltage cables for inverter duty typically have following design:
– aluminum or copper conductor
– inner thin semiconducting layer
– insulation layer* (typically XLPE or PVC)
– outer semiconducting layer
– copper wire screen and tape
– non-conducting tape
– outer sheath
Depending on manufacturer and technology additional layers may be used.
* typically meshed polyethylene (XLPE) or polyvinyl chloride (PVC)
Cable parameters
Basic cable parameters can be freely found in the Internet. Very rudimentary datasheets do not state the capacitance and inductance, but if you search a bit more, you will find plenty of examples. By comparing them you notice that the parameters have minimum variation depending on manufacturer. When you focus on specific insulation class and cable cross section you obtain practically the same values regardless of cable manufacturer.
The cable is typically modeled as a series of pi-elements, e.g. one pi-element for each 50…100 meters of cable length. It is not granted that the more element are used the more accurate results are obtained. Detailed cable models are supported by programs such as PSCAD where the frequency dependence of the R, L and C elements can be properly considered.
From above values it is easy to calculate the oscillation frequency depending on actual cable length. As a general rule, the inverter output filter shall have its cut-off frequency below the cable oscillation frequency. This rule ensures that the excitation is negligible and resonance frequency is well damped. As the motor cable length increases, the resonance frequency is reduced. Therefore, there is a higher risk of interaction, voltage reflections and voltage amplification.
Cable model
Equivalent model of a cable consists of longitudinal resistance and inductance and parallel capacitance. Cable model is often represented using π-sections. A good practice is to use one π-section per every x meters (e.g. one section per 100 meters of cable). Note that increasing number of π-elements does not guarantee more accurate results. In fact, there are several other parameters that have very essential impact on the outcome of the study.
The equivalent resistance represents the Ohmic losses in the cable (losses in the conductor). Manufacturers usually state DC resistance and AC resistance at specified reference temperature (e.g. 20°C, 25°C, 40°C). They often provide formulas how to calculate the resistance at higher operating temperature using resistance temperature coefficient α (aluminum has α = 0.00403 [1/°C] and copper has α = 0.00393 [1/°C]). AC resistance is always higher than DC resistance due to skin effect. Note that the AC resistance is valid, if not stated differently, for power frequency of 50 Hz or 60 Hz. However, inverter duty motors may generally be supplied with higher fundamental frequency than 50/60 Hz. And of course, the resistance will be quite different for very high frequencies when investigating switching transients caused by inverter switching of power semiconductors.
The inductance value contains both self and mutual inductance and therefore depends on cable laying (e.g. trefoil arrangement or parallel laying on the same level).
The capacitance value is mainly determined by the insulation thickness and conductor cross section (geometry of cable). The specific capacitance values are therefore almost identical for given insulation class and cross section regardless of the cable manufacturer.
High-frequency motor model
The motor model for high frequencies is also much different than the standard equivalent circuit diagram that is usually provided in datasheets. Motor surge impedance is extremely important for the investigation of motor terminal voltage overshoots. Without reliable information on surge impedance you cannot expect reliable results on voltage overshoot (trash in – trash out).
Using incorrect motor surge impedance typically results in too negative results like illustrated in figure below.
Cable length
Motor cables in many medium voltage industrial applications lie within 200 meters. The range 200 – 500 meters is supported by many VFD products as ‘standard’. However, don’t forget that besides cable length also the number of parallel cables have an impact.
Generally the lower the cut-off frequency of the inverter output filter (dv/dt filter, reinforced dv/dt filter, additional output reactor, sine filter etc) the longer motor cables are supported by the product.
Below table provides rough estimation of max. motor cable length. Note that actual permissible lengths vary depending on VFD manufacturer and his design of output filter. The maximum cable length also depends on cable cross section and number of parallel cables.
Summary
Motor cables may affect the voltage waveform at motor terminals. Increased voltage peaks due to overshoots can impact the lifetime of motor insulation system. Of course, the voltage peaks stress the insulation of the power cable as well. Each VFD has an allowable motor cable length. Increased length is sometimes feasible as engineered option. In case of longer motor cables (over 200-300 meters) please consult the VFD manufacturer to ensure seamless system integration.
References
[1] Medium voltage drives portfolio, https://new.abb.com/drives/medium-voltage-ac-drives
[2] Current source and voltage source inverter, https://mb-drive-services.com/current-source-and-voltage-source-inverter/
[3] John M. Bentley, Patrick J. Link, Evaluation of Motor Power Cables for PWM AC Drives, IEEE Trans. on Industry Applications, vol. 33, No. 2, March/April 1997
[4] F. Endrejat, P. Burmeister, P. Pillay, Large adjustable speed and soft-started drives with long cable lengths
[5] NKT runs all its power cable factories with renewable energy, https://www.nkt.com/news-press-releases/nkt-runs-all-its-power-cable-factories-with-renewable-energy-saving-over-48-000-tons-of-co2-annually
