Evaluation of the usability of the Canay’s equivalent circuit diagrams for the calculation of subsynchronous resonances

Marek Gołębiowski (The Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, Rzeszow, Poland)
Carsten Göbel (Siemens AG, Dynamowerk Berlin, Berlin, Germany)



In the shaft and end windings of large turbogenerators, unacceptably high mechanical stresses can occur as a result of subsynchronous resonances (SSRs) in the system network-generator-shaft. These stresses can cause severe damages. Subsynchronous resonances are characterized by the occurrence of currents and electromagnetic torques in the air gap of the generator with frequencies that are significantly below the synchronous frequency. When simulating the balancing processes in multi-machine networks, the generators are represented by Canay’s equivalent circuit diagrams. The parameters used here are determined from geometric dimensions of the generator, taking into account material properties, and verified by means of surge short-circuit tests in which the 50 and 100 Hz components are dominant. This paper aims to examine whether the parameters of the equivalent circuit diagram determined in this way reproduce correctly the dynamic behavior of a synchronous machine, even if the SSR occur.


The simulation program NETOMAC is used to simulate the SSRs for different parameters. The results of these simulations are then compared with those obtained by the finite difference (FD) method calculations.


The comparison of the waveforms calculated with NETOMAC and FELMEC for an SSR shows that the original equivalent circuit diagram parameters provide satisfactory results. An extension of Canay’s equivalent circuit diagram is not necessary. Optimization of the discussed parameters leads to a significant improvement in comparison to the calculation with the parameters from the generator data sheet.


The unresolved doubt has been proven, that the Parka generator model with the manufacturer’s parameters can also be used for subsynchronous studies of electromechanical resonances of systems. However, it was advisable to improve the simulation results by optimizing the generator parameters used in the calculations. By optimizing the parameters for the SSRs, the calculation of the occurring torques has been significantly improved.



Gołębiowski, M. and Göbel, C. (2019), "Evaluation of the usability of the Canay’s equivalent circuit diagrams for the calculation of subsynchronous resonances", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 4, pp. 1347-1356. https://doi.org/10.1108/COMPEL-10-2018-0419



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