Synchronous Motors

A \(1{,}000\) kVA, \(11\) kV, \(3\)-phase Y-connected synchronous motor has a resistance of \(3\) ohms and a reactance of \(25\) ohms per phase. Determine the induced emf per phase when fully loaded at \(0.8\) power factor lagging.

A \(500\)-hp, \(2200\) V, \(3\)-phase star-connected synchronous motor has a synchronous impedance of \(0.3 + j3.0\ \Omega\) per phase. Determine the induced emf per phase if the motor works on full load with an efficiency of \(94\%\) and a power factor of \(0.8\) leading.

A three-phase, star connected synchronous motor takes \(50\) kW at \(660\) V, the power factor being \(0.8\) lagging. This machine has a synchronous reactance of \(1\) ohm per phase with a negligible resistance. If the emf is increased by \(30\%\), the power taken remaining the same, find the new leading pf current.

A single-phase synchronous motor gives an output of \(9.46\) kW at \(0.9\) pf lagging with \(600\) V. If stray power loss is \(600\) W and field losses is \(900\) W, while effective armature resistance is \(0.6\) ohm, find the efficiency of the synchronous motor.

A \(230\)-V, \(60\)-Hz, single-phase synchronous motor is taking a current of \(20\) A at \(0.866\) lagging pf. Effective armature resistance is \(0.3\) ohm. Iron and friction losses amount to \(450\) W. Determine the efficiency of the motor at this load. Neglect losses in the excitation.

A three-phase star-connected synchronous motor draws \(70\) A at \(0.8\) pf leading when connected from a \(6.6\) kV, \(60\)-Hz, \(3\)-phase source. At this load the machine operates with an efficiency of \(90\%\). If the synchronous impedance of the machine is \(2 + j15\) ohms, determine stray power losses.

A \(20\) hp, \(440\) V, \(60\)-Hz, \(3\)-phase star-connected synchronous motor has an armature resistance per phase of \(0.4\) ohm. It is giving its full load output at a power factor of \(0.9\) leading. If the stray power losses amount to \(500\) watts, find the armature current.

A \(500\)-V, \(60\)-Hz, single-phase synchronous motor develops \(20\) hp and is operating at a pf of \(0.8\) lagging. Effective resistance of armature is \(1\) ohm. Iron and friction losses amount to \(500\) W. Determine power drawn by the motor from the source.

A group of induction motors rated \(2200\)-V, \(3\)-phase, \(60\) Hz delivers a total of \(600\) hp and is operating at an average power factor of \(0.8\) lagging. If half of this total load is replaced by a group of synchronous motors operating at an average pf of \(0.8\) leading, determine the percentage reduction in the line current? Assume all motors operate at an average efficiency of \(92\%\).

A three-phase transmission line having a capacity of \(10{,}000\) kVA serves a balanced load that draws \(5{,}000\) kW at a lagging power factor such that the transmission line is loaded to its capacity. An additional load of induction motors operating at an average pf of \(0.80\) is connected to the line. In order to make use of the line to its full capacity in active power, a synchronous condenser having losses of \(300\) kW will be connected to the line. What is the kVA rating of the synchronous motor required?

A three-phase Y-connected synchronous motor with a line-to-line voltage of \(440\) V and a synchronous speed of \(900\) rpm operates with a power of \(9\) kW and a lagging power factor of \(0.8\). The synchronous reactance per phase is \(10\) ohms. The machine is operating with a rotor current of \(5\) A. It is desired to continue carrying the same load but to provide \(5\) kVAR of power factor correction to the line. Determine the required rotor current to do this.

A \(3{,}600\) volts three-phase star connected turbo synchronous generator of synchronous reactance of \(0.5\) ohm per phase and negligible resistance is supplying \(30{,}000\) kVA at \(0.8\) pf lagging to a large power system. If the steam supply is cut-off, calculate the amount of current that the generator will then carry assuming negligible losses.

A wye-connected turbo alternator having a synchronous reactance of \(0.5\) ohm and negligible resistance is connected to a large power system having a busbar voltage of \(13.8\) kV supplying a load of \(15{,}000\) kVA at \(0.80\) lagging power factor. If the steam supply is cut-off, what armature current will the machine carry assuming negligible losses?

A \(1{,}000\) kVA, \(6{,}600\) V wye-connected three-phase alternator having a reactance of \(8.8\ \Omega\) and a negligible resistance is supplying power to a constant frequency busbar. The open circuit emf at this instance is \(4{,}311\) V per phase. If the steam supply is suddenly cut-off, the armature current in amperes is nearest to

A 200-hp, 2,200 V, 3-phase star connected synchronous motor has a synchronous impedance of 0.3 + j3 Ω per phase. Determine the induced emf per phase if the motor works on full load with an efficiency of 94% and a power factor of 0.8 leading.