Section IV: Multimachine Stability
Consider Fig. 9.10, which depicts a number of weights that are suspended by elastic strings. The weights represent generators and the electric transmission lines being represented by the strings. Note that in a transmission system, each transmission line is loaded below its static stability limit. Similarly, when the mechanical system is in static steady state, each string is loaded below its break point. At this point one of the strings is suddenly cut. This will result in transient oscillations in the coupled strings and all the weights will wobble. In the best possible case, this may result in the coupled system settling down to a new steady state. On the other hand, in the worst possible scenario this may result in the breaking of one more additional string, resulting in a chain reaction in which more strings may break forcing a system collapse. In a similar way, in an interconnected electric power network, the tripping of a transmission line may cause a catastrophic failure in which a large number of generators are lost forcing a blackout in a large area.
Modern power systems are interconnected and operate close to their transient and steady state stability limits. In large interconnected systems, it is common to find a natural response of a group of closely coupled machines oscillating against other groups of machines. These oscillations have a frequency range of 0.1 Hz to 0.8 Hz. The lowest frequency mode involves all generators of the system. This oscillation groups the system into two parts - with generators in one part oscillating against those of the the other part. The higher frequency modes are usually localized with small groups oscillating against each other. Unfortunately, the inter-area oscillation can be initiated by a small disturbance in any part of the system. These small frequency oscillations fall under the category of dynamic stability and are analysed in linear domain through the liberalisation of the entire interconnected systems model.
Inter-area oscillations manifest wherever the power system is heavily interconnected. The oscillations, unless damped, can lead to grid failure and total system collapse. Low frequency oscillations in the range of 0.04 Hz to 0.06 Hz were observed in the Pacific North West region as early as 1950. Improper speed governor control of hydro units created these oscillations. The Northern and Southern regions of WSCC were interconnected by a 230 kV line in 1964. Immediately the system experienced a 0.1 Hz oscillation resulting in over 100 instances of opening of the tie line in the first nine months of operation. Some system damping was provided through the modification in the hydro turbine governors.
A 500 kV pacific intertie and another ± 400 kV HVDC system was commissioned in 1968. This raised the frequency of oscillation from 0.1 Hz to 0.33 Hz and these oscillations could no longer be controlled through governor action alone. In late 1980's a new intertie joined the WSCC system to Alberta and British Columbia in Canada . As a result of this interconnection, the two different oscillation frequencies manifested - one at 0.29 Hz and the other at 0.45 Hz.
Ontario Hydro is one of the largest utilities in North America . Due to the vast and sparsely populated topology of Canada , the operating span of Ontario hydro is over 1000 km from East to West and from North to South. The Ontario Hydro system is connected to the neighbouring Canadian provinces and the North Western region of the United States . In 1959 Ontario Hydro was connected to Michigan in the South and Quebec Hydro in the East. As a result of this connection, a 0.25 Hz oscillation was observed and a result of this it was decided to remove the tie with Quebec and retain the tie to Michigan . The Western portion of Ontario was connected to neighbouring Manitoba in 1956 and then Manitoba was connected to its neighbour Saskatchewan in 1960. This resulted in oscillation in the frequency range 0.35 Hz to 0.45 Hz often tripping the tie. As a result of this, Ontario Hydro decided to commission power system stabilizers for all their generating units since early 1960's. It has also sponsored extensive research in this area.
Through research it was established that the action of automatic voltage regulators caused these oscillations. An automatic voltage regulator (AVR) regulates the generator terminal voltage and also helps in the enhancement of transient stability by reducing the peak of the first swing following any disturbance. However, its high gain contributed to negative damping to the system. The knowledge of this relation resulted in the commissioning of power system stabilizers. It was observed that these oscillations were results of the periodic interchange of kinetic energy between the generator rotors. A power system stabilizer (PSS) provides a negative feedback of the changes in rotor kinetic energy when it is connected to the excitation system thereby providing damping to these small oscillations. The PSS has been a subject of extensive research. The team of Dr. P. Kundur, then with Ontario Hydro, and his co-workers has done extensive research in the area of PSS tuning and its characteristics. Through their vast experience and extensive research, they reported the enhancement of inter-area and local modes through PSS reported in. Since a power system is piece-wise linear, its system characteristics changes with operating point. Therefore an adaptive controller that can tune with the changes in the system has been developed and reported in. It was shown that the adaptive PSS is effective in damping large as well as small disturbances.
The power flow between generators, as evident from (9.4), is dependent on the angle between those generators. The stable operating point of the power system is where the generated power at each station is matched by the electrical power sent out from that station. When there is a mismatch between electrical power out and the generated mechanical shaft power, the generator will accelerate at a rate determined by the power mismatch and the machine inertia as given in (9.14).
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