Monitoring motor supply pays off

Supply voltage phase imbalance and harmonics can have a significant effect on the life of a three-phase motor, making the case for supply monitoring and filtering to improve efficiency and reduce downtime.

The life of three-phase motors is often cut short because of voltage imbalance and voltage harmonics. It is sometimes argued that the use of a variable speed drive removes the effect of problems with the supply lines, but this is usually a false argument because of problems that occur on the input converter and DC link when there is voltage imbalance and voltage harmonics. There is a case for monitoring of supply conditions in particular when critical motor applications are involved, but monitoring by itself is not enough. However, monitoring with programmable critical limits of imbalance and harmonics, etc, combined with logic functions as inputs to PLCs, relays and active filters, has significant advantages. No doubt a lot depends on the application as to the cost-effectiveness but monitoring and control can provide a smooth running mechanical plant. Think of high inertia loads that must be brought up to speed reliably — and within specified time limits — when supply conditions are less than ideal.

Why voltage imbalance is bad for motors

In short, unless derated, motor life is badly affected by line voltage imbalance. The NEMA derating curve shows that under a 4% imbalance, 20% derating is required. Somehow 4% imbalance sounds small but the effects are magnified. Apart from a reduction in torque as a result of negative sequence components, there is the imperilling of insulation because of excessive current. In addition there can be problems associated with harmonics, particularly the 5th, causing large counter torque. The solution is not found by increasing the rating of motors because apart from the capital cost, the result is excessive use of electrical energy as a result of lower efficiency.

Imbalance: the new norm

Network providers might take issue with the bald statement that voltage imbalance is the new norm. However, the growth of distributed generation — think of rooftop solar as one example — is one very good reason. Quite apart from non-uniform loading of phases, the power flow on much of our distribution networks is no longer a one-way thing — from substation to load — and solar rooftop PV is not necessarily balanced. In short, much depends on at what point you are connected to the network as to what level of imbalance might be encountered. For a new installation of a motor control centre a thorough power quality analysis is more than a good idea because power quality is increasingly under pressure.

Figure 1: Motor derating versus % voltage imbalance.

Symmetrical components

Unbalanced voltages and currents can be analysed into a set of three components comprising two balanced pairs, one rotating in the normal phase rotation of the supply, the other rotating in the opposite direction, and in the case of four wire circuits, an in-phase (zero) component effectively flowing in-phase through the three-phase conductors and returning via the neutral. For the majority of motors, and with the exception of star-delta starters, there is no zero phase component.

The theory of symmetrical components is due to Charles Fortesque (1918)² and, if one has time, there are many textbook references to enjoy. Practical aspects of symmetrical components are the province of transmission engineering in which generators, lines, transformers, etc are described in terms of positive, negative and zero sequence impedances. In Figure 2, there is a graphical representation of the three components making up a set of unbalanced three-phase phasors. It might look a little confusing but on a step-by-step basis, V_a, V_b and V_c are the phase to neutral voltages of a 4-wire system. Obviously the diagram represents a severely unbalanced scenario but it makes for easier visualisation. The positive sequence voltages are V_a1, V_b1, and V_c1. These have the same phase rotation as V_a, V_b and V_c. The phasors, V_a2, V_b2 and V_c2, have opposite phase rotation (look carefully and you’ll note that V_c2 follows V_a2 and V_b2 follows V_c2. The zero sequence, V_a0, V_b0 and V_c0 are in phase with one another. The latter sequence is responsible for neutral current but obviously this cannot occur in a three-wire system.

Figure 2: A set of unbalanced 3-phase phasors (for a larger image click here).

We will take a somewhat less dramatic example, with two sets of unbalanced phase voltages, as set out below.

• The red phase voltage is 237.37 volts, phase angle 0°
• The blue phase voltage is 235.84 volts, phase angle -119.02°
• The yellow phase voltage 237.46 volts, phase angle 120.31°

In symmetrical components, this yields:

• Positive sequence of 236.88 V
• Negative sequence of 1.47 V
• Zero sequence of 1.12 V

This is a happy situation but what would be the case if with the same angles the blue phase was only 210 volts? The results would be:

• Positive sequence of 228.27 V, with corresponding line voltages of 395.38 V (V_l = √3.V_p)
• Negative sequence of 9.57 V, with corresponding line voltage reduction of 16.57 V
• Zero sequence of 8.83 V

The zero phase is not present and the imbalance ratio is 4.19%. While this also doesn’t look too frightening, it actually is.

The negative sequence and its negative influence

When an induction motor is on full load, slip is very small and the motor draws rated line current. When it starts from the locked rotor position, the current is something of the order of 6 to 8 times larger than the rated line current. Now assume there is a negative sequence component. The rotor is spinning in the positive sequence phase rotation order, but relative to the negative sequence, the slip is very large — in fact equal to 2-s, where s is the fractional slip on full load.

Let us take a specific example of a motor with a full load slip of 5%. In that case, relative to the negative sequence voltage the slip would be 195%. Just consider that for a moment; under locked rotor conditions slip is 100%. Consequently for the motor the negative sequence voltage is definitely akin to a starting status, drawing a high negative sequence current which adds to additional losses in the stator as well as the rotor.

In the above example with a negative sequence ratio of 4.19%, the negative sequence current would be equal to the ratio of start to full load current — let’s assume 7 — multiplied by 0.042, adding close to 30% to line current. How do we arrive at that? The impedance of an induction motor is low at high slip, and high at low slip. Now, instead of locked rotor impedance we use Z₂ to designate the negative sequence impedance of the motor and Z₁ for the higher impedance at full load. The negative sequence voltage is V₂ and the positive sequence voltage is V₁. Negative sequence (‘starting’) current as a ratio of running (full load) current is equal to Z₁/Z₂. The negative sequence current I₂ is equal to V₂/Z₂ and likewise the positive sequence current is equal to V₁/Z₁. Therefore:

As can be seen from the above equation, and the foregoing numerical example, negative sequence voltage, the automatic result of phase imbalance, is harmful to safe motor operation due to an excessive increase in line current.

Monitoring voltage imbalance and harmonics

You may have seen in technical literature that voltage imbalance should be measured on line voltage and not phase voltage. The reason is that unless angle information is provided as well as magnitude, the imbalance cannot be computed correctly. Line voltage incorporates both phase angle and magnitude information, being the vector difference between a pair of phase-to-neutral voltages. There is a somewhat fierce IEE formula (but accurate), which is reproduced below for getting the negative to positive sequence ratio (V_-/V₊) based only on line voltages, V_ab, V_bc and V_ca.

where:

However, rather than doing the maths, appropriate smart panel instrumentation is a much better solution, the more so if harmonic monitoring is incorporated. As has already been mentioned, the presence of negative sequence harmonics (5th, 11th, etc) can be equally harmful to motors.

Figure 3: Converter line current waveform under balanced conditions.

Variable speed drives

Variable speed drives are so common that there is an argument that DOL stands for Delete On Line. However, the use of variable speed drives doesn’t remove the problem of voltage imbalance. The common six-pulse, three-phase converter supplying the DC link of a drive in theory has the characteristic ‘golden arches’ line current (see Figure 3) with harmonics starting at the 5th. Note: the harmonic numbers (in theory) are given by 6n±1 where n is an integer. The practice is often very different. As unbalanced voltages creep in, one of the twin peaks collapses, and third and ninth harmonics present themselves — worse, the DC link voltage decreases so that motor torque also decreases (Figure 4).

Figure 4: Converter line current waveform under an imbalance of 3.75%.

Motor protection should also be considered. Although, as has been explained, current levels can increase under imbalance conditions, it may be wise not to rely on thermal trips but to employ negative sequence relays in combination with other motor protection gear. An alternative solution is the use of smart panel meters with the ability to monitor a host of power quality parameters including imbalance by means of symmetrical components, and a suite of logic functions for control purposes. An obvious one for protection purposes is an external trip signal to protection breakers — but equally to PLCs controlling task allocations.

References

1. Christie C V 1952, Electrical Engineering: The Theory and Characteristics of Electrical Circuits and Machinery, 6th edition, McGraw-Hill.
2. Fortescue C L 1918, Method of Symmetrical Co-ordinates Applied to the Solution of Polyphase Networks, AIEE Transactions, vol. 37, part II, pp 1027–1140.
3. Von Jouanne A 2001, Assessment of Voltage Imbalance, IEEE Transactions on Power Delivery, vol. 16, no.4, October 2001, IEEE.

Image: ©stock.adobe.com/taitai6769