## TYPES OF SUBSYNCHRONOUS RESONANCE INTERACTIONS

There are several ways in which the system and the generator may interact with subsynchronous effects. A few of these interactions are basic in concept and have been given special names. We mention three of these that are of particular interest:

- Induction generator effect
- Torsional interaction
- Transient torque

Each of the above effects will be discussed briefly.

### 1) INDUCTION GENERATOR EFFECT:

The induction generator effect (IGE) is caused by the self-excitation of the electrical network. The resistance of the generator to subsynchronous current viewed looking into the generator at the armature terminals, is a negative resistance over much of the subsynchronous frequency range. This is typical of any voltage source in any electric network.

The network also presents-a resistance to these same currents that is a positive resistance. However, if the negative resistance of the generator is greater in magnitude than the positive resistance of the network at one of the network’s natural frequencies, growing subsynchronous currents can be expected. This is the condition known as the induction generator effect. Should this condition occur, the generator may experience subsynchronous torques at or near a natural shaft frequency, which may cause large and sustained oscillations that could beÂ damaging to the shaft.

### 2) TORSIONAL INTERACTION:

Torsional interaction occurs when a generator is connected to a series compensated network, which has one or more natural frequencies that are synchronous frequency complements of one or more of the torsional natural modes of the turbine-generator shaft.

When this happens, generator rotor oscillations will build up and this motion will induce armature voltage components at both subsynchronous and super synchronous frequencies. Moreover, the induced subsynchronous frequency voltage is phased to sustain the subsynchronous torque. If this torque equals or exceeds the inherent mechanical damping of the rotating system, the system will become self-excited. This phenomenon is called torsional interaction (TI).

The network may be capable of many different subsynchronous natural frequencies, depending on the number of lines with series compensation and the degree of compensation installed on each line. Moreover, switching the network lines can cause these natural frequencies, as viewed from the generator, to change. The engineer must evaluate the network frequencies under all possible switching conditions to determine all possible conditions that may be threatening to the generators. Another condition that can greatly increase the number of discrete network subsynchronous frequencies is the outage of series capacitor segments.

The series compensation in high-voltage systems usually consists of several capacitor segments that are connected in series, with each series segment consisting of parallel capacitors as required to carry the line current. This permits individual segments to be removed from service for maintenance and still permits nearly normal loading of the lines. However, individual segments can fail, thereby changing the network’s natural frequencies and greatly increasing the number of possible frequencies that can be observed from an individual generator. This increases the work required to document and analyze the network frequencies as seen by each generating station.

Another possible source of subsynchronous currents is the presence in the network of HVDC converter stations. The controls of these converters are very fast in their control of depower, but the controls can have other modes of oscillation that may be close to a natural mode of oscillation of a nearby generator. Systems that include HVDC converters also must be carefully checked to see if these controls might induce subsynchronous currents in the generator stators, leading to torsionalÂ interaction.

### 3) TRANSIENT TORQUES:

Transient torques are torques that result from large system disturbances, such as faults. System disturbances cause sudden changes in the network, resulting in sudden changes in currents with components that oscillate at the natural frequencies of the network. In a transmission system without series capacitors, these transients are always de-transients, which decay to zero with a time constant that depends on the ratio of inductance to resistance. For networks that contain series capacitors, and will contain one or more oscillatory frequencies that depend on the network capacitance as well as the inductance and resistance. In a simple radial R-L-C system, there will be only one such natural frequency.

If any of these frequencies coincide with the complement of one of the natural modes of shaft oscillation, there can be peak torques that are quite large and these torques are directly proportional to the magnitude of the oscillating current. Currents due to short circuits, therefore, can produce very large shaft torques both when the fault is applied and also when it is cleared. In a real power system there may be many different subsynchronous frequencies involved and the analysis is quite complex.

Of the three different types of interactions described above, the first two, IGE and TI, may be considered as small disturbance conditions, at least initially. The third type, transient torque, is definitely not a small disturbance and nonlinearities of the system also enter into the analysis. From the viewpoint of analysis, it is important to note that the induction generator and torsional interaction effects may be analyzed using linear methods.

Eigenvalue analysis is appropriate for the study of these problems and the results of eigenvalue studies give both the frequencies of oscillation and also the damping of each oscillatory mode. The other method used for linear analysis is called the frequency scan method, where the network seen by the generator is also modeled as a function of frequency and the frequency is varied over a wide range of subsynchronous values. This requires that the generator be represented as a tabulation of generator impedance as a function of subsynchronous frequency, which must be provided by the generator manufacturer. This is considered the best model of the generator performance at subsynchronous frequencies, and is often the preferred method of analysis, with eigenvalue analysis used as a complementary check on the frequency scan results.

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