Power, speed and torque
The purpose of variable speed drive systems is basically the ability to provide required torque at corresponding speed. In simple words: to turn the shaft. Of course, the quantities of power, speed and torque are coupled together. This article is a bit more theoretical review. However, we emphasize the key take aways relevant for drive dimensioning and optimization. And as usual, we illustrate the relationships on practical examples to make the things more obvious and make this article more fun to read.
Relationship between torque, speed and power
The mentioned three quantities are directly linked together. Mechanical power is a product of shaft torque and angular frequency of the shaft. The mechanical speed in rpm, as we are used to think, is the angular frequency multiplied by a constant 30/π.
The formula (4) is correct for synchronous machine. Asynchronous machine, as the name reveals, operates with certain slip. Therefore, the mechanical angular frequency in motor (driving) mode will be slightly lower than acc. (4). Nominal slip of medium and large electric motors is in the range 0.2 – 0.6%.
Observations from power, speed and torque relationship
What can we derive from basic formulas (1) to (4)?
1. Describing a motor purely with shaft power is not very meaningful. Two machines, low speed and high speed, can have same power rating, but their electrical and mechanical design is completely different. Therefore, motor shall always be defined, among others, by a combination of shaft power and corresponding speed or rated torque and speed. The third quantity can always be calculated from equations (1) and (2).
2. In order to reach same power at lower speed the torque must increase. Vice versa, high-speed machine has comparably lower torque and is more compact. Note that rotor mass is proportional to torque. High torque machines have larger diameter (shaft height), higher weight and larger inertia.
3. In VFD drive systems, unlike direct on-line motors, the nominal motor shaft speed can be achieved by combination of motor pole pairs and supply electric frequency. For example, to reach 1’000 rpm nominal speed you can use 6-pole machine supplied with approx. 50.2 Hz electric frequency from the inverter. Or you use 4-pole machine with nominal electric frequency of approx. 33.5 Hz.
Note that most people talk about power. When talking about VFD drive systems we shall understand one crucial thing:
– For VFD the dimensioning quantity is apparent power that translates into certain voltage and current
– Some VFDs, like LCI or MMC topologies, scale the power with voltage (to reach higher power means putting more thyristors or more cells in series)
– Other VFDs, like the NPC/ANPC based converters, scale the power with current (to reach higher power more modules are connected in parallel)
— For motor dimensioning it is mainly the TORQUE (and sometimes also speed) that is relevant:
– 5 MW high-speed motor is quite compact and light
– 5 MW special very low speed machine has large diameter, is heavy and very costly
Both machines have same power stated on the rating plate, but that is also basically the only common thing. Their designs are completely different.
Let’s leave the dry theory for the moment and look at a practical example. We compare three different machines. All of them have rated output of 5.0 MW. However, they have different rated speed and torque.
Table 1: Torque versus inertia and weight of different machines with 5 MW rated output
We can observe that a low speed machine (Motor 3) has much higher inertia. This is because low speed machines have larger diameter. Machines with higher speed have lower diameter as centrifugal forces and surface speed are limiting factors.
Generally the lower the speed the higher the weight of the machine, especially the rotor weight (rotor mass increases with torque). The trend is clearly visible when comparing machines 1 and 3 or machines 2 and 3. When comparing machines 1 and 2 you may wonder how it fits with what was just said. 2’500 rpm machine is lighter than 3’400 rpm machine. First of all, the machines in Table 1 are from different manufacturers. The main reason, however, is that Motor 1 with 3’400 rpm is a 2-pole machine while Motor 2 is of 4-pole design. 2-pole machines have lower utilization of their electromagnetic design.
High torque versus high power
There is one more example to demonstrate how torque requirement affects the size and weight of electric motor. It is really mind blowing. Note that this is an extreme comparison, but is based on real machines built recently (both machines manufactured after 2010) and being both successfully in operation.
Machine A:
First machine is a special ultra low speed design for a wind turbine test stand. Although the rated shaft power is “only” 5 MW, it corresponds at rated speed of 11 rpm to impressive 4’341 kNm and the rotor itself weights over 130’000 kg! Rotor of this ultra-high torque machine has 30 poles, large diameter and short axial length.
Machine B:
The second machine is a large turbogenerator in a thermal power plant. As usual for such machines, the stator is water cooled and rotor is cooled by hydrogen. Generators are described with apparent power rated than shaft power. In this case the nominal apparent power is almost 1’200 MVA. With design power factor 0.8 it translates to approx. 950 MW. The turbogenerator has 2-pole rotor and rated speed of 3’000 rpm.
Table 2: High-torque versus high-power electric machines
Although the turbogenerator has almost 200-times higher rated power, the low-speed high-torque motor actually has a heavier rotor. If you calculate the rotor weight/torque ratio, you will see that it is almost the same for both machines!
The 5 MW high-torque machine has 30 kg/kNm while the huge turbogenerator has 31.9 kg/kNm.
This example very clearly shows that motor power itself does not tell very much. The motor design is heavily influenced by the required torque in low speed range and by the maximum speed and resulting forces at higher speeds.
Use of a gearbox
So far we have not discussed use of a gearbox. Of course, gear is part of many drive applications. It is both speed-increasing gear as well as speed- reducing gear. The role of a gear in mechanical world is similar to the role of a transformer in electric world.
Speed-increasing gear is used in applications that require very high speeds. An example is centrifugal compressor. Although there are high-speed direct drive solutions enabling gearless drive systems, the conventional solution is typically a 4-pole motor with rated speed in the range 1’500 – 2’000 rpm in combination with a speed increasing gear.
For very low speed applications a speed-reducing gear is an alternative to extremely low speed motor that becomes large in diameter, very heavy and correspondingly costly.
Take aways
Here is a summary of the most important things from this article:
– Torque is essential quantity for the electromechanical design of rotating electric machines. The higher the torque the more weight and inertia of the rotor. High torque machines are generally heavier and more expensive than machines with same shaft power, but higher nominal speed.
– Motor design is governed by torque and speed requirements.
– VFD design is governed by current and voltage. Depending on VFD topology the power is either scaled with current (paralleling of semiconductors or modules) or with voltage (series connection of semiconductors or cells).
– In VFD driven applications the nominal electric frequency can be selected arbitrarily and does not have to be either 50 Hz or 60 Hz. Compared to direct on-line (DOL) machines there is an additional degree of freedom to find the optimum machine design.
In upcoming articles we will discuss multiple related topics. For example, a basic explanation of how asynchronous machine works. Also, we will explain how the selection of nominal motor electric frequency allows to optimize the performance and mitigate vibrations.
References
[1] Motor start with VFD, https://mb-drive-services.com/vfd-motor-start/
[2] Load types and characteristics, https://mb-drive-services.com/load-types-and-characteristics/
[3] ABB motors and generators, https://new.abb.com/motors-generators
[4] Medium voltage AC drives, https://new.abb.com/drives/medium-voltage-ac-drives
[5] Synchronous machines brochure, Download brochure
