# What is the phenomena behind this DC generator plot?

There is a DC generator to be calibrated with its plot below. On the X-axis there is the ratio between the power of the generator/ nominal power of the generator. On the Y-axis there is the efficiency of the generator.

Can someone please explain what phenomena is behind the behaviour of the plot?

Efficiency sharply increases as the ratio increases, then peaks, then plateaus and declines at higher ratios of power of the generator/ nominal power of the generator.

Why is that happening?

Electric machines and other power conversion equipment have both fixed losses and variable losses. Variable losses are proportional to current and fixed losses are not. For that reason, the efficiency of such equipment is zero with zero output and rises as the output increases. Usually, the efficiency initially rises steeply then less steeply reaching a maximum before leveling off or declining somewhat.

The fixed losses for a DC generator running at a constant speed include:

1. Friction, including bearing and brush friction
2. Aerodynamic drag, also called windage, including drag effecting the motion of the rotor and also drag due to an internal or external fan or fins on the rotor that circulate air to cool the machine.
3. Field excitation loss. (field current squared x resistance)

The variable losses include:

1. Armature copper loss (armature current squared x resistance)
2. Field excitation loss for any portion of the field connected in series with the armature.

There can also be stray losses that may be revealed by a dynamometer test but not explained analytically.

If the output voltage of the generator is regulated, the regulator may increase the generator speed or excitation current as the load increases. That could introduce some variability to losses that would generally be considered to be fixed. Increasing the armature speed even a little will increase the aerodynamic drag torque is approximately proportional to speed squared and drag power is approximately proportional to speed cubed.

In Fitzgerald, Kingsley, Umans, Electric Machinery, 4th ed.1983, there is a very helpful graphical representation of 1-100 kW DC motor and generator losses shown below. Hysteresis and eddy-current losses are included. I took that as an indication that those losses are not significant in DC machines. However a comment by @Paul Ghobril prompted me to consult Khulmann, Design of Electrical Apparatus, 1940. There I found core losses exceeding armature copper losses in a 300 kW machine.

Efficiency is generally determined only for steady-state operation. Any power used to accelerate inertia or other wise transition from one steady-state operating condition to another is not considered.

Nonlinearity of the machine ie. increase in armature resistance as temperature increases may be responsible for efficiency declining rather than leveling off near maximum load.

I suspect that some of the efficiency curve shape is due to insufficient data to draw a smooth curve. Efficiency vs. load curves do not usually have sharp deflection points as shown in the following example from Kuhlmann.

At low load (low used power) the efficiency is low because the power is at the same order of mechanical losses like the friction losses and losses of coupling the motor to the alternator and losses at the alternator like field, hysteresis and eddy current losses.

However when the load increases these losses will become low compared to the load power.

When reaching full load the generator becomes overheated which decreases the efficiency and also the counter torque coming from the load (magnetic) will increase to limit the capacity of the motor to deliver the needed energy.

• I agree with the concept of this answer, but it is incomplete and in error in the details. It is unfortunate that it has been accepted by the asker. Oct 19 '20 at 12:52
• @CharlesCowie Hi Charles, thanks for commenting, well I did not receive another answer...it was the only one, would you have something to add to the answer? Cheers Oct 19 '20 at 13:01
• It is best to wait at least 24 hours for answers so that those living in all parts of the globe can answer. You should also include complete details in the question. It would be good to know if the generator is shunt, series, compound or separately excited. However, for the essentials, there may not be much difference. I will take a closer look when I have more time. Oct 19 '20 at 13:47
• @Paul Ghobril "power needed to gain the inertia" ... what is that? Also "torque coming from the load (magnetic) will increase to limit the capacity of the motor to deliver the needed energy" ... if you are talking about effects on the prime mover, those have no bearing on the question of DC generator efficiency. Oct 19 '20 at 17:58
• @CharlesCowie Thank you for your comments. Reviewing is the most important added value of this community. Reviews are always welcomed. No need to be upset if an answer is not up to your expectations, the choice can be modified, and the site is designed in a flexible way to overcome these issues. I understand your reaction to the inertia since it is a plot of steady state behavior (corrected). However, concerning the torque, it concerns the counter torque (added). I was trying to directly answer the question. By the way Eddy current and hysteresis are considered in both AC and DC generators. Oct 20 '20 at 5:13