Diagnosis of eccentric rotor in synchronous machines by analysis of split-phase currents - part I: theoretical analysis

This work shows a method to quantify rotor eccen- tricities in synchronous machines by exploiting the unbalance caused in the split-phase currents. The paper first develops a ma- chine model comprehensive of eccentricities and parallel circuits in the stator, by using symmetrical components. Then, the model is used for formal calculation of the unbalanced currents. Finally, the equations are reversed to obtain eccentricity degrees from current measurements. Practical formulas are given for fault assessment, only requiring machine line voltage and synchronous reactance. The method can be applied on load. This paper provides full de- tails of the theory underlying the method. The theory also clarifies some aspects about split-phase currents, not deepened before. It is proven that the air gap flux modulation due to eccentricities, acting through additional 2(p ± 1)-pole flux waves in 2p-pole machines, stimulates additional currents, which circulate in the stator and turn into 2(p ± 1)-pole rotating space vectors in the complex domain. Vector trajectories have shape and amplitude dictated by eccentricity type and degree, respectively. This study is limited to 2p-pole machines with p ≥ 2. The theory is cor- roborated by simulations of a practical 1950-kVA generator in this paper. Experimental proofs and simulations of a laboratory 17-kVA machine are provided in a sequel of this paper.