For many years, the application of series capacitors in power transmission systems has been haunted by a spectre called sub-synchronous resonance (SSR). The origin was a report on turbine shaft damage resulting from mechanical torsional vibrations in a steam power plant in New Mexico in the 1970s, where the cause of the damage was traced to a series of events linked to a lightly loaded, series compensated line.

The phenomenon was studied in detail and its nature thoroughly explored. Sure enough, due to detailed understanding of the phenomenon and the proper countermeasures, it has not happened since, even though series compensation has been widely used all over the world. Nevertheless SSR has remained a matter for caution, and, whenever called for, it is common practice to establish safe margins against the problem as part of any series compensation installation.

This is done by means of system studies. These can include simple frequency scanning in order to investigate potential hazards, plus time domain simulations for more detailed analysis in cases where initial frequency scanning indicates a risk of SSR.

From theoretical investigations and long experience of the use of series capacitors in power systems, it has been established that SSR is not usually a problem when transmitting hydro power. In cases of thermal power carried by series compensated transmission lines, the first step is to look for degrees of compensation that are safe from an SSR point of view. The series resonance peaks of compensated grids depend on the degree of compensation, and it can be shown that the smaller the ratio between the capacitive reactance of the series capacitor and the inductive reactance of the transmission line, the lower is the risk of SSR occurring.

In most cases, this is sufficient precaution against SSR in the system. Of course, there will usually be a lowest limit for the degree of compensation to enable the series capacitor to perform its intended task in the grid. In cases where the risk of SSR cannot be completely ruled out, the classical counter measures have been either to bypass the series capacitor when SSR is detected or, in the worst case, to trip the generator. These measures, effective as they are for their purpose, are not attractive from a system point of view, as they mean loss of power transmission capability or loss of generation. Therefore, more sophisticated ways of dealing with SSR are needed. Thyristor controlled series compensation (TCSC) provides one such solution.

Causes of SSR

SSR is caused by electro-mechanical coupling between the turbogenerator shaft and the series compensated network, and appears as torsional vibrations of the shaft. The coupling is via the generator air gap. For growth of mechanical vibrations, negative overall system damping is a prerequisite.

If a torsional shaft vibration is started for some reason, it is superimposed on the rotation of the generator rotor and consequently transferred to the stator as a periodically varying component of the magnetic flux. The result is a voltage component generated in the stator superimposed on the mains frequency voltage and having the same frequency content as the torsional vibration. A corresponding current component will then flow.

If the power grid happens to have a characteristic showing series resonance at any of the frequencies corresponding to the difference between the power frequency and the torsional frequency spectrum, the corresponding current component will see a low impedance in its path. Unless proper countermeasures are taken, the torsional vibration can grow until it results in mechanical damage.

SSR reduction

Series capacitors in power transmission systems always have a degree of compensation k < 1. From this it follows that resonance due to series compensation occurs at frequencies below the power frequency. Consequently, the frequency range which has to be watched in conjunction with SSR, being equal to the power frequency minus the torsional vibration frequency, will always be in the range below the power frequency as well, hence the name sub-synchronous resonance.

Incidentally, this explains why thermal generation is more susceptible to SSR than hydro generation is. Turbo-generator sets have large rotating masses connected by a shaft that is up to 50m long on large units. This produces low frequency torsional vibration modes, several of which are usually below the mains frequency (50 Hz or 60 Hz). Hydro generators, on the other hand, are compact, with the majority of the mass concentrated at one end of the turbine-generator set. This means higher mechanical resonance frequencies, plus better mechanical damping.

From this, it follows that if there are no electrical resonances to be found within the sub-synchronous frequency range, which is typically in the range between 10 Hz and 40 Hz in a 50 Hz system and between 10 Hz and 50 Hz in a 60 Hz system, SSR simply cannot arise. Therefore, the task is to de-tune the grid within these ranges.

TCSC characteristics

In a series compensated grid, the way to make sure that there is no series resonance within a certain frequency band is simply to make the series capacitor inductive, not capacitive within that band. This may sound like a paradox but by means of a controlled inductor in parallel with the capacitor, plus a suitable control algorithm, it is possible to create precisely this characteristic of the series capacitor.

A control method called Synchronous Voltage Reversal (SVR) is used to achieve the desired inductive apparent reactance of the series capacitor at sub-synchronous frequencies.

The waveforms associated with a TCSC operating in steady-state. The thyristor conduction intervals are substantially shorter than the network frequency half-cycle time and they occur around the peak values of the line current. When the thyristor valve is fired, a current pulse repolarizes the capacitor voltage. In other words, a capacitor voltage reversal occurs during the thyristor conduction interval. The idea of SVR is to directly control the timing of the equivalent, instantaneous voltage reversals since this provides the required inductive apparent impedance at sub-synchronous frequencies.

On the other hand, the series capacitor must behave as a capacitor at power frequency (50 Hz or 60 Hz), so a transition of the virtual reactance of the TCSC from inductive to capacitive outside the sub-synchronous frequency band is achieved by means of a reactance controller, providing a controllable capacitive reactance around the power frequency.

The controllability of the capacitor reactance at power frequency is a very useful feature, as it enables the TCSC concept to be used for power oscillation damping (POD), as in the Brazilian case, discussed later.

In summary, the SVR approach to TCSC control offers several benefits to the user:

  • An elimination of SSR risk throughout the potential sub-synchronous frequency range.

  • Robustness with respect to changes in network configuration as well as to uncertainty in mechanical resonance modes.

  • SSR mitigation as well as POD, or, if called upon, a combination of both.

    The robustness to changes in network configurations and to uncertainties in mechanical resonance modes is a useful feature since it reduces the quantity of data collection and system studies needed prior to the installation of series compensation in the grid. In times of deregulation of the power industry, this becomes even more important, since generating and transmission functions may be completely separate from each other, making data collection and processing more complicated than before.

    The Swedish power grid

    The Swedish power system is part of the synchronous Nordic power system which connects Sweden, Finland, Norway and the eastern part of Denmark. The installed capacity in Sweden is around 35 GW and the country’s annual electric energy consumption is about 140 TWh.

    The main consumption areas are in the central and southern areas of the country. The major parts of the electric energy are based on hydro generation (45 per cent) and nuclear generation (50 per cent). Most of the hydro power plants are located in the north, while the nuclear plants are in the southern coastal areas.

    A total of eight 400 kV transmission lines connect the hydro plants in the north to the large load areas in the centre and south. Each line is up to 500 km long and series compensation is used on them all, with degrees of compensation ranging up to 70 per cent.

    This extensive use of series compensation enables up to 8000 MW of environmentally friendly hydro power to be carried over the lines under stable conditions. The alternative to series capacitors would have been the construction of several additional, very long 400 kV lines, something which would have been impossible in reality for political, economic and environmental reasons.

    The usefulness of series compensation under these circumstances has been proved again recently with the installation of three new series capacitors in a double circuit 400 kV cross-border interconnection in the north between Sweden and Finland. With these series capacitors in operation, the power transmission capacity of the existing interconnection was increased by nearly 40 per cent, from 800 MW to 1100 MW.

    SSR: a case study

    Forsmark, one of Sweden’s main nuclear plants, is interconnected via two of the 400 kV lines mentioned previously. One of the nuclear units, Forsmark III, is a large unit, with an output of 1150 MW. The 400 kV lines connecting it in the northern direction were equipped with series capacitors with a very high degree of compensation long before the construction of the nuclear plant, so as a precaution the nuclear unit was equipped with monitoring and protective devices to prevent any possible damage due to SSR. This included means for generator tripping.

    Further protective systems were installed on the series capacitors, where any possible sub-synchronous current component in the transmission line is measured locally, to enable the bypassing of the series capacitor if necessary.

    The Stöde series capacitor was originally erected in 1974 using PCB impregnated capacitors. In the early 1990s the installation was refurbished completely with state of the art components including non-PCB capacitors. At the same time, the degree of compensation of the series capacitor was adjusted slightly. Shortly after the series capacitor was re-commissioned in late 1994, the sub-synchronous current relay at Forsmark III started triggering repeatedly. The series capacitor also was bypassed several times.

    A study of the SSR conditions using frequency scanning showed that sub-synchronous oscillations with poor damping may occur under certain conditions in the power transmission system. In the study, the Swedish 400 kV and 220 kV network was represented including the series capacitors in the eight 400 kV lines. Forsmark III was represented as an induction generator model, a model relevant for SSR studies. The program utilized for the frequency scanning produced the system impedance, the electrical undamping, and the sub-synchronous currents at specified points in the network.

    The study confirmed that the resonant frequency of the network coincided with the electrical frequency corresponding to a shaft torsional vibration mode at Forsmark with a frequency slightly higher than 21 Hz. The total damping at this sub-synchronous frequency was close to zero even with an intact network, so any small disturbance could excite oscillations.

    The situation was found to be even worse in the case where a particular 400 kV line near Forsmark was disconnected. In this case, undamping would increase to a point where self-excited SSR could not be ruled out.

    TCSC for SSR reduction

    To improve the situation, it was decided to use TCSC at Stöde. The existing series capacitor, rated at 493 MVAr at 400 kV and with a degree of compensation k = 70 per cent, was to be divided in two segments. One segment, representing 70 per cent of the original series capacitor rating, was to remain a conventional fixed series capacitor, while the other segment was to be converted to a TCSC.

    The whole of the existing series capacitor could have been remade into a TCSC, but that was not necessary in order to achieve the goal of SSR mitigation. Calculations showed that it was sufficient to have 30 per cent of the capacitor rating controllable; the remaining 70 per cent of fixed compensation would not contribute to any SSR hazard. For economic reasons, this was the solution adopted.

    The rebuilding of Stöde started in early 1997 and the equipment was put into operation at the end of the year. It is notable that commissioning and testing of the new equipment was carried out with the remaining fixed series capacitor still in service.

    A compact design has been achieved for the controllable part of the series capacitor because spark gaps, which are usually part of traditional series capacitor installation, are not required. Furthermore, the energy rating of the protective metal-oxide varistor could be kept low because the thyristor valve enables fast bypassing of the series capacitor in the event of a fault in the surrounding grid.

    Communication between platform and ground is performed by means of fibre-optics. Currents, voltages and other data at platform level needed for monitoring and control purposes are measured by means of a high bandwidth optically powered data link system.

    The thyristor valve is equipped with LTT (light-triggered thyristors) in order to minimize the complexity of this outdoor equipment. The valve is water-cooled, with a mixture of glycol to allow for the sub-zero outdoor temperatures common in winter in this part of the world. A small building, housing control, protection and monitoring devices as well as thyristor cooling equipment, is also part of the installation.

    The Stöde TCSC is solely intended for mitigation of SSR, and is not used for power oscillation damping, so the ability to control virtual reactance at 50 Hz is not being utilized in this case. Consequently, the TCSC is operated at a constant, low boost level (1.20). A low level is advantageous from a cost point of view, because it enables a corresponding reduction in the rating of the capacitor bank. However, at the same time, the boost must be sufficiently high to ensure a safe apparent impedance characteristic of the TCSC during SSR conditions.

    The Stöde TCSC comprises several novel technical solutions that are expected to contribute to continuing development of solutions adapted to customers’ needs:

  • ABB VarMACH control equipment for TCSC with a control algorithm for SSR mitigation and boost level control.

  • A novel outdoor TCSC valve based on ABB Power Systems’ SVC technology and experience.

  • The use of direct light triggered thyristors (LTT).

  • A high bandwidth optically powered data link system for measurement of quantities on the platform.

  • A station control and monitoring (SCM) system providing operator interface to the TCSC with remote diagnostics.

    The SCM is housed in the control room. Its main components are an SCM computer and an operator work station. The task of the SCM computer is to collect and store information from the VarMACH system. Signals are updated and stored continuously in a database. The TCSC can be controlled by the operator from the operator work station. Protective settings can be adjusted, and various reports can be produced, such as an operator’s list, event recordings and alarm recordings.

    Evolution of thyristor controlled series compensation (TCSC)


    Stöde TCSC technical data

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