I was recently asked about DC Offset during a paper I presented at the 2015 Hands-On Relay School and struggled with an answer because I know what it looks like and I know it exists, but I’ve never heard an explanation that made sense to me. The answer you usually get sounds something similar to, “The amount of offset depends on the X/R (power factor) of the power system and the first peak can be as high as 2.55 times the steady state level”, which is parroted from a textbook.
We can start to understand DC offset by imagining an electrical system that is running along with a relatively symmetrical sine wave where the positive and negative peaks are equidistant from zero.
A fault is suddenly applied to the system and the sine wave suddenly becomes asymmetrical (the positive and negative peaks are NOT equidistant from zero), and then returns to normal (symmetrical) after a few cycles.
The asymmetrical response to the fault is called DC Offset and it is a naturally occurring phenomenon of the electrical system. Design engineers need to compensate for DC Offset when creating engineering studies, high-voltage equipment must be able to interrupt the larger current created by DC offset, and electrical personnel who look at oscilligraph reports can use DC Offset to recognize real faults (as we discuss in our online training Course 1-1: The Three-Phase Power System). If this is such a normal part of the electrical system, why is it so hard to find a good description of DC offset?
Here are some other descriptions from various textbooks:
“The actual magnitude of the DC current is dependent on the point of the voltage wave where the fault occurs and the circuit angle (X/R).”
“A symmetrical fault is a balanced fault with the sinusoidal waves being equal about their axes, and represents a steady-state condition.
An asymmetrical fault displays a DC offset, transient in nature and decaying to the steady state of a symmetrical fault after a period of time…”
“Direct current offset…occurs as a result of two natural laws:
- Current cannot change instantaneously in an inductance and
- Current must lag the applied voltage by the natural power-factor…”
You can get a more detailed description in Protective Relaying: Principles and Applications, second edition, by J. Lewis Blackburn, but you have to have a very good understanding of power systems to understand all of the nuances in the description.
“When a current change occurs in the primary ac system, one or more of the three-phase currents will have some dc offset…from the necessity to satisfy two conflicting requirements….
- In a highly inductive network…, the current wave must be near maximum when the voltage wave is near zero; and
- The actual current at the time of change is determined by prior network conditions…”
An excellent description is also provided in Protective Relaying for Power Generation Systems by Donald Reimart:
“At first glance, the occurrence of a DC current in an AC power system seems illogical. To understand its existence, let us look at a few electrical rules learned in EE 101. First, in an inductive circuit, the current lags the voltage by 90°. If a fault occurs when the voltage is zero, the current must be at the positive or negative maximum value. Secondly, the generator is a large inductor. The current in an inductor cannot change instantaneously.”
Let’s break this explanation down into its components and look at a few different scenarios.
If you set your test-set to start with zero volts and zero amps and then apply a resistive condition (voltage and current in-phase), the test-set would produce symmetrical waveforms that start at zero and are in-phase as shown in the following image:
If we apply a purely inductive condition (current lags voltage by 90°), the output looks something like this:
Did you notice that the test-set cheated? It needed to maintain the pure inductive relationship of zero volts equals maximum current, so it started the voltage at the first peak while the current started at the zero-crossing. It could also cheat the other way by starting the voltage at the zero-crossing while the current starts at the peak:
The current can’t make an instantaneous jump in the real power system like a test-set can, but it still needs to maintain those two conflicting rules of electricity at the same time. Whenever the electrical system experiences a large jump in current, a DC signal appears to create asymmetrical waveforms so that both of our electrical rules can be true at the same time as shown in this image:
Do you remember the first rule? “…the current lags the voltage by 90°…” If we draw a vertical line through the positive peaks of the voltage and current in a cycle from the example, we can see that the current is lagging the voltage by 90°. Therefore, our example with DC Offset satisfies the first rule.
Let’s look at the second rule. “If a fault occurs when the voltage is zero, the current must be at the positive or negative maximum value”. The current waveform has a zero-crossing AND is at its negative peak, so we can see that the second rule is satisfied as well.
DC Offset is necessary to maintain the basic laws of electricity at the initial moment when the current in the system makes a sudden change, like what happens during a fault. However, the generators will be able to react to the new system conditions, and the DC Offset will decrease over a few cycles until the waveform is back to its normal symmetrical condition.
The size and duration of DC Offset depends on:
- The ratio of reactance and resistance (X/R) of the circuit during a fault. This includes the generator coils, and the equipment connecting the generator to the fault. The X/R ratio at the generator is typically very high because the generator is almost a pure inductor, which means that the DC Offset will be greater when the fault is closer to the generator. The system does not consist of pure inductors, so the resistance in the X/R ratio grows as the distance between the fault and the generator grows, which means the time constant will be larger. Also, the offset will be less extreme as a result of an increase in source impedance.
- The voltage magnitude at the exact moment of the fault. A fault at zero degrees on the A-Phase voltage means that there is zero voltage when the fault is applied to the system. When the voltage is zero in an inductive circuit, the current must be maximum. Therefore the maximum DC offset occurs when the voltage is zero. Remember that when the A-Phase voltage is zero, the other two phases will not be at zero, so different phases will react to the same fault differently.
- The ability of the generator(s) to react to the fault and time necessary to stabilize the system.
Faults rarely occur at exactly zero degrees as shown in our previous examples. Faults can occur at any point on a voltage waveform and different people may use different terms when describing this moment. For example:
- Manta Test Systems refer to it as the Fault Incidence Angle (FIA)
- Omicron uses the term Fault Inception Mode/Angle
The amount of time that it takes to go from fault inception with DC offset to to steady-state symmetrical waveforms can also have different descriptions:
- Doble uses the “Time Constant L/R” setting
- Manta Test Systems uses the setting “System Time Constant”
The next images show the same fault with different fault incidence, or fault inception, angles.
Fault Incidence at 0° with a 50ms Time Constant
Fault Incidence at 30° with a 50ms Time Constant
Fault Inception at 60° with a 50ms Time Constant
Fault Inception at 90° with a 50ms Time Constant
Did you notice that the three voltages experience the initial fault at different points on their waveforms? And that the DC Offset introduced to each current waveform is different even though the fault happens in the same moment for all phases? Do you see that the individual phases do not respond to the different angles in the same way?
DC Offset is something that all relay testers should understand because it is a normal part of the electrical system. You can use this information to properly interpret oscilligraph reports, or tweak your test plans so that they will be more realistic and therefore, more reliable.
I hope that I was able to properly answer this question and help you understand this ever-present, but seldom understood, aspect of the electrical system. If you want to get a different perspective that is much more comprehensive, you can click here to download an excellent white paper titled “Fault Calculations for Circuit Breakers that is courtesy of Erik C. Baker, P.E., Affiliated Engineers, Inc..
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