HARMONICS
EFFECTS ON EQUIPMENT NOVEMBER 1, 2016
Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Brett Board, P.E.
Main Topics • Review of Selected Circuit Theory Fundamentals • Variable Frequency Drive (VFD) Components & Operating Principles • Load Side Issues • Line Side Issues (where IEEE 519 is relevant)
Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Fundamental Laws of Engineering
• Conservation of Energy • Conservation of Mass • Conservation of Sorrows
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Fundamental Laws of Power Systems
• Everything is a second order circuit • Ohm’s Law always applies • Kirchoff’s Current Law always applies
Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Ohm’s Law
𝑉𝑉 = 𝐼𝐼𝐼𝐼 where 𝑍𝑍 = 𝑅𝑅 + 𝑗𝑗𝑗𝑗 𝑋𝑋𝐿𝐿 =2𝜋𝜋𝜋𝜋𝜋𝜋 −1 𝑋𝑋𝐶𝐶 = 2𝜋𝜋𝑓𝑓𝑓𝑓
I will use the impedance formula to emphasize the frequency dependence.
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Kirchoff’s Current Law
• An application of the conservation of energy • The sum of all currents flowing into a node must be zero • Related to the mathematical concept of superposition Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Superposition and Harmonic Analysis
• Any waveform can be written as the sum (superposition) of an infinite number of sinusoids • Each sinusoid can be analyzed separately 𝑓𝑓 𝑡𝑡 = 𝐴𝐴0 + 𝐴𝐴1 sin 𝜔𝜔𝜔𝜔 + 𝜃𝜃1 + 𝐴𝐴2 sin 2𝜔𝜔𝜔𝜔 + 𝜃𝜃2 + 𝐴𝐴3 sin 3𝜔𝜔𝜔𝜔 + 𝜃𝜃3 + ⋯
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Superposition and Harmonic Analysis Harmonics are typically presented as a percentage of the fundamental (the An of the Fourier Series)
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Superposition and Harmonic Analysis Fundamental and 5th
Through 7th
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Through 23rd
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Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
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Superposition and Harmonic Analysis Harmonic currents pretty much always generate counter EMF (imbalance) and, therefore, produce heat.
K-rated transformers are simply de-rated transformers to account for the excess heat caused by harmonics. I1
I5
I7
I11
I13
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Inductors
Looks a bit like a single phase representation of a motor, doesn’t it?
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Inductors
Looks a little bit like a single phase representation of a VFD inverter, doesn’t it?
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Fundamental Aspects of VFD Operation
• Contain 3 distinct sub-systems • Line side and load side effects differ • Rely on fast switching of transistors
The term switch-mode power supply for computers and PLCs comes from a similar reliance on fast switching transistors. Pretty much any DC power supply today generates harmonics.
Copyright © 2016 Magna IV Engineering. All Rights Reserved.
VFD Components
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
VFD Operation (Load Side)
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
VFD Carrier Frequency
The carrier (switching) frequency is the frequency at which output transistors are switched on and off. Generally this ranges from 3 to 15 kHz.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Frequency and Rise Time 1 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑓𝑓 = 𝑇𝑇 Higher frequencies are associated with faster rise times, and vice versa.
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Frequency and Rise Time The carrier frequency may be 3-15 kHZ, but the rise time on the square wave yields much higher frequency effects. This has been measured in the lab in MHz. Probably don’t want any signal wires near a VFD load cable. High frequency cross talk can interfere with signal integrity.
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Harmonic Content of a Square Wave
The ideal square wave contains only odd harmonics
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Harmonic Content of a Square Wave
The 25th harmonic still contributes 4% voltage distortion.
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Voltage/Current Relationship
Remember Ohms Law always applies and every power system is a second order system. 4 𝑉𝑉 𝜋𝜋 𝐼𝐼𝐿𝐿 = = 𝑍𝑍𝐿𝐿
∞ sin(2𝜋𝜋 2𝑘𝑘 − 1 𝑘𝑘=1 2𝑘𝑘 − 1
𝑉𝑉 4 = 2𝜋𝜋𝜋𝜋𝜋𝜋 ∙ 𝐼𝐼𝐶𝐶 = 𝑍𝑍𝐶𝐶 𝜋𝜋
2𝜋𝜋𝜋𝜋𝜋𝜋
∞
𝑘𝑘=1
𝑓𝑓𝑓𝑓)
sin(2𝜋𝜋 2𝑘𝑘 − 1 𝑓𝑓𝑓𝑓) 2𝑘𝑘 − 1
As frequency increases capacitive reactance drops such that harmonic current flows through system capacitance. Where is the capacitance in a motor circuit?
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Skin Effect
Skin effect is the tendency of an alternating electric current to have the largest current density near the surface of the conductor. ACSR takes advantage of skin effect by putting the high tensile strength, non-current carrying steel in the center of the cable. High end speaker wire is often wrapped around a non-conductive core.
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Skin Effect
At frequencies below 300 MHz, skin depth can be estimated with the following formula: At 60 Hz in copper the skin depth is about 8.5 mm.
𝛿𝛿 =
2𝜌𝜌 𝜔𝜔𝜔𝜔
At 3 kHz in copper the skin depth is about 1.2 mm. At 15 kHz in copper the skin depth is about 0.5 mm. At 1 MHz in copper the skin depth is about 0.07 mm.
Circuit Theory Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Inverter Duty Motors
• Designed to handle lower speeds without overheating. • Capable of withstanding higher voltage spikes without insulation failure.
Copyright © 2016 Magna IV Engineering. All Rights Reserved.
High Frequency Harmonic Current
The capacitance in a motor circuit is primarily turn to turn in the motor windings, stator to shaft, and phase to ground. Harmonic current, therefore, induces voltage on the shaft and case (skin) of the motor.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
High Frequency Harmonic Current
Voltage induced on the shaft will discharge to ground through any path it can find. Typically this is through the lowest impedance path…the bearings. Good thing the windings are designed with higher insulation levels.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
High Frequency Harmonic Current
Typical bearing damage caused by periodic voltage discharge from the shaft.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
High Frequency Harmonic Current
One solution is to provide a low impedance path from the shaft to ground. Many inverter rated motors include a shaft grounding ring, but not all. Check the spec sheet carefully.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
High Frequency Harmonic Current
Another solution is to provide a low impedance path from the feeder cable to ground. Remember the high frequencies will seek the outside of the conductor due to skin effect. Proper bonding of the shield or armor to the motor case is essential. This shunts high frequencies to ground.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Reflected Wave When a transmitted wave strikes an interface barrier some of that wave reflects back. The magnitude of the reflection is a function of the impedance on either side of that barrier. The reflected wave then combines with any subsequent incident wave by the principle of superposition.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Reflected Wave The inline inductance of a cable is much less than the motor windings. In fact the inductance of cable is typically ignored. Therefore, the motor windings act as a barrier to traveling waves, especially higher frequency waves in the kHz range. 𝑋𝑋𝐿𝐿 =2𝜋𝜋𝜋𝜋𝜋𝜋
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Reflected Wave Remember that 480 V is actually an RMS measurement. Nominal DC bus voltage for a 480 V drive is around 680 VDC (around the actual peak voltage of a 480 VAC wave form). Reflected wave superposition at the motor terminals is commonly 1200 V or more. Some reports claim voltage spikes can be 2000 V or more.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Reflected Wave
The motor may be inverter duty rated, but is the cable? A fault in either disables the system.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Reflected Wave
Another option is to move the reflection point away from the motor terminals.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Natural Frequency 1 𝜔𝜔0 = 𝐿𝐿𝐿𝐿
Cable Resonant Frequency 20000 18000
The blue line is bare cable. The green line is with a load reactor.
16000
Frequency (Hz)
14000
C = 50 pf/ft L = 1.33x107 H/ft
12000 10000
8000 6000 4000 2000
Ever wonder why manufacturers specify a maximum cable length?
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VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
300
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700 Length (ft)
900
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Load Side Summary
• Fast switching transistors make VFDs possible but also generate 3 distinct wave types. • The desired, controlled frequency • The 3-15 kHz carrier frequency • The MHz fast rise time traveling waves • System capacitance offers a low impedance path for high frequencies. This induces voltage on the shaft and case. Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Load Side Summary
• Remove voltage from the shaft with a shaft grounding ring to protect bearings. Not all inverter rated motors include shaft grounding. • Remove voltage from the case with a shielded cable. Ensure the shield is bonded to the case and to ground properly. • Reduce traveling waves with a load reactor. Some situations require a load (dV/dt) filter. Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Load Side Summary
• Economics usually drive the best “system” solution. Just because we can doesn’t necessarily mean we should.
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Line Side Issues Harmonics are typically presented as a percentage of the fundamental (the An of the Fourier Series)
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Line Side Issues Ih
NOT the PCC
Ih
Total Harmonic Distortion (THD) at the VFD terminals can be as high as 35% for a 6 pulse drive. IEEE 519 states that THD at the Point of Common Coupling (PCC) must be less that 5%. 375 hp on the bus, 150 hp at 35% distortion (ignore the line reactors for this example) yields about 14% distortion on MCC bus.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Line Side Issues
Still NOT the PCC Additional 200 hp of linear load on the upstream bus yields about 10% distortion on MCC bus. The generator will see 14% distortion.
Ih Ih
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Line Side Issues
The PCC
The supply transformer does offer some additional harmonic impedance before the distortion enters the local distribution system. In this case there is also a substation transformer before the actual PCC. However, by Kirchoff’s Law, all sources of harmonic distortion on the customer side of the PCC must be considered.
Ih
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Line Side Issues Ih
NOT the PCC What if the other loads were larger? If there were 10,000 hp on the bus with150 hp at 35% distortion the THD on the bus would only be about 0.5%.
Ih
IEEE 519 compliance (5% THD) at the drive terminals is usually not necessary and is always expensive.
VFD Operating Principles Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Line Side Issues
• Harmonic currents create heat and voltage spikes. • Is every motor and every cable in your system inverter duty rated? • Capacitor banks are especially vulnerable to resonant frequencies. • A facility can be IEEE 519 compliant, but still burn up their own machines. Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Line Side Options
• • • •
Stiff source Line reactors Higher pulse count VFD Individual passive filters • Some manufacturers actually imbed a passive filter inside the VFD
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Line Side Options
• Bus level active filters • De-tuned power factor correction capacitor banks
Copyright © 2016 Magna IV Engineering. All Rights Reserved.
Questions?
Brett Board, P.E. Copyright © 2016 Magna IV Engineering. All Rights Reserved.
