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Determination of electromechanical eigenvalues based on analysis of different disturbance waveforms of a power system

100%

Pruski P. , Paszek S.

tom Vol. 12

130--143

The paper presents the calculation results of the power system state matrix eigenvalues associated with electromechanical phenomena (i.e. electromechanical eigenvalues). There is compared the accuracy of eigenvalue calculations performed on the basis of the analysis of disturbance waveforms of instantaneous power, angular speed and power angle of generators of particular generating units of the power system. The method used for eigenvalue calculations consists in approximation of the disturbance waveforms of generating units with waveforms being a superposition of modal components whose parameters depend on the searched eigenvalues and their participation factors. A hybrid optimisation algorithm, being a serial combination of genetic and gradient algorithms, is used for minimisation of the objective function defined as a mean square error between the approximated and approximating waveforms. In order to increase the calculation accuracy, computations were repeated many times. The computation results were averaged.

Assessment of Polish Power System angular stability based on analysis of different disturbance waveforms

75%

Pruski P. , Paszek S.

tom Vol. 63, nr 2

435--441

The paper presents investigation results concerning assessment of the Polish Power System (PPS) angular stability based on power system state matrix eigenvalues associated with electromechanical phenomena, when using the angular stability factors calculated on the basis of these eigenvalues. The eigenvalues were calculated by analysis of the disturbance waveforms of the instantaneous power, angular speed and power angle of synchronous generators in PPS generating units when taking into account introduction of a disturbance to different units. There was assumed a disturbance in the form of a rectangular pulse introduced to the voltage regulation system of a generating unit. There was also analysed the effect of the duration of the introduced test disturbance on the calculation results of the eigenvalue influencing the measurement waveforms of the instantaneous power of generating unit no 5 in Rybnik Power Plant. The method for eigenvalue calculations used in the investigations consists in approximation of the disturbance waveforms in particular generating units with the use of the waveforms being a superposition of the modal components associated with the searched eigenvalues. The hybrid optimisation algorithm being a serial combination of the genetic and gradient algorithms was used for computations.

Obliczenia elektromechanicznych wartości własnych na podstawie przebiegów mocy chwilowej i prędkości kątowej zespołów wytwórczych przy zakłóceniu skokowym

75%

Pruski P. , Paszek S.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

2015

tom Nr 42

43--46

W artykule przedstawiono wyniki obliczeń wartości własnych (związanych ze zjawiskami elektromechanicznymi) macierzy stanu modelu systemu elektroenergetycznego (SEE) na podstawie analizy przebiegów zakłóceniowych mocy chwilowej i prędkości kątowej zespołów wytwórczych SEE. Wzięto pod uwagę przebiegi występujące po wprowadzeniu zakłócenia w postaci skokowej zmiany napięcia zadanego regulatora napięcia w jednym z zespołów wytwórczych SEE. W modelu SEE uwzględniono oddziaływanie centralnego regulatora częstotliwości. Wykorzystana w artykule metoda obliczeń wartości własnych polega na aproksymacji analizowanych przebiegów zakłóceniowych za pomocą przebiegów stanowiących superpozycję składowych modalnych związanych z poszukiwanymi wartościami własnymi. Uzyskano zadowalającą dokładność obliczeń wszystkich elektromechanicznych wartości własnych.

The paper presents the results of calculations of the eigenvalues (associated with electromechanical phenomena) of the state matrix of the power system (PS) model based on analysis of the instantaneous power and angular speed disturbance waveforms of the PS generating units. In calculations there were taken into account the waveforms occurring after introducing a disturbance in the form of a step change in the waveform of the voltage regulator reference voltage in one of generating units. In the PS model used there was taken into account influence of a central frequency regulator. The method for eigenvalue calculations used in the paper consists in approximation of the analysed disturbance waveforms with the waveforms being a superposition of modal components associated with the searched eigenvalues and their participation factors. The approximation consists in minimisation of the objective function defined as the mean square error that occurs between the approximated and approximating waveforms. For the minimisation of the so-defined objective function a hybrid optimisation algorithm consisting of serially connected genetic and gradient algorithms was used. This connection allows eliminating the basic weaknesses of those both algorithms. To avoid calculation errors caused by the optimisation algorithm freezing in the objective function local minimum, calculations of eigenvalues for each disturbance waveform were performed repeatedly. The calculation results with the objective function values larger than a certain assumed limit were rejected. The arithmetic means of the not rejected results were assumed to be the final calculation results of the real and imaginary parts of particular eigenvalues.