The machine models represent the machine as a Norton current source into the EMTDC network. This approach uses the terminal voltages to calculate the currents to be injected.
Figure 7-5 shows a synchronous machine model interfaced to the EMTDC program. The synchronous machine model makes use of the phase voltages calculated by EMTDC to update the injected currents into EMTDC. It is also shown in this figure that multiplying the phase currents by an integer N simulates, from the system point of view, N identical machines operating coherently into the AC system.
Figure 7-5 - Synchronous Machine Model Interface to EMTDC
It is important to note that representing machines as a Norton current source can have drawbacks. For instance, each machine must be computationally 'far' from other machines for stable operation. In the past, this was usually achieved by separating subsystems containing machines by distributed transmission lines (which are essentially time delays). Since the machine was represented by a simple current source (which was dependent on voltages from the previous time step), any sudden change in voltage would cause a current response only in the next time step. Thus, for the previous time step, the machine looked like an open circuit and spurious spikes appeared on the machine terminal voltage. The cumulative effect of many machines causing this error simultaneously in the same subsystem was proven to be de-stabilizing.
It was found that when the machine neared open circuit conditions a smaller time step was required to maintain computational stability. Alternatively a small capacitance or large resistance could be placed from the machine terminals to ground to prevent the machine from being totally open-circuited. Although the physical meaning of parasitic capacitance or leakage resistance could be applied to these elements, it was not a satisfactory solution.
This idea led to the concept of terminating the machine to the network through a terminating 'characteristic impedance' as shown in Figure 7-6. The effect of this added impedance is then compensated (corrected) by an adjustment to the current injected.
Using this technique, the machine model behaviour has been uniformly good. It essentially combines the compensation-based model and the non-compensated model, while eliminating the restriction of adjacent machines and the necessity of calculating the network Thevenin equivalent circuit.
Figure 7-6 - Interface with Terminating Resistance
Where,
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Calculated machine current |
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The impedance r" is calculated where L" is the 'characteristic inductance' of the machine, N is the number of coherent machines in parallel and Dt is the EMTDC time step. This resistance is placed from each node of the machine terminal to ground within the EMTDC network. Instead of injecting the calculated machine current 
, a compensated current 
is injected, where V(t – Dt) is the terminal voltage in the previous time-step. Thus, the actual current injected into the network is,
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(7-16) |
r" is usually quite large, due to the Dt in its denominator. Also, for a small time step V(t – Dt) = V(t), and thus 
, and the error introduced vanishes in the limit with a small Dt. However, for a sudden voltage change, as 
is not calculated until the next time step, the network sees the impedance r" for this instant (instead of the open circuit discussed earlier). This is exactly the instantaneous impedance it would have seen had the machine been represented in the EMTDC program main matrix. Therefore, the network current calculated in this instant is more accurate, and the spurious spikes discussed earlier do not arise. Thus this concept of terminating the machine with its 'characteristic impedance' and then compensating for this in the current injection, is a convenient way for assuring accurate solutions.
Compensating current
Terminating 'characteristic impedance'