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- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/12%3A_Permanent_magnet_Brushless_DC_motors/12.02%3A_Zeroth_Order_RatingIn determining the rating of a machine, we may consider two separate sets of parameters. The first set, the elementary rating parameters, consist of the machine inductances, internal flux linkage and ...In determining the rating of a machine, we may consider two separate sets of parameters. The first set, the elementary rating parameters, consist of the machine inductances, internal flux linkage and stator resistance. From these and a few assumptions about base and maximum speed it is possible to get a first estimate of the rating and performance of the motor. More detailed performance estimates, including efficiency in sustained operation, require estimation of other parameters.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/02%3A_AC_power_flow_in_linear_networks/2.08%3A_A_Conservation_Law\[\ \sum_{\text {terminals }} \underline{V I}=\sum_{\text {resistances }} \underline{V I}+\sum_{\text {inductances }} \underline{V I}+\sum_{\text {capacitances }} \underline{V I}\label{69} \] \[\ \sum...\[\ \sum_{\text {terminals }} \underline{V I}=\sum_{\text {resistances }} \underline{V I}+\sum_{\text {inductances }} \underline{V I}+\sum_{\text {capacitances }} \underline{V I}\label{69} \] \[\ \sum_{\text {terminals }} \underline{V I}=\sum_{\text {resistances }} R|\underline{I}|^{2}+j \sum_{\text {inductances }} \omega L|\underline{I}|^{2}-j \sum_{\text {capacitances }} \omega C|\underline{V}|^{2}\label{70} \]
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/01%3A_Review_of_network_theory/1.09%3A_Inductive_and_Capacitive_Circuit_ElementsAgain, remember that the whole solution is the sum of the particular and a homogeneous solution, and that the homogeneous solution is the un-driven case. Finally, if the capacitor is initially uncharg...Again, remember that the whole solution is the sum of the particular and a homogeneous solution, and that the homogeneous solution is the un-driven case. Finally, if the capacitor is initially uncharged \(\ \left(v_{c}(t=0+)=0\right)\), we can add in the homogeneous solution (we already know the form of this), and find the total solution to be:
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/09%3A_Synchronous_machine_and_winding_models/9.04%3A_Continuous_Approximation_to_Winding_PatternsNow let’s try to produce those surface current distributions with physical windings.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/01%3A_Review_of_network_theory/1.03%3A_Node_Voltages_and_ReferenceThus, if we take one of the nodes in the network to be a reference, or datum, each of the other nodes will have a unique potential. The voltage across any network branch is then the difference between...Thus, if we take one of the nodes in the network to be a reference, or datum, each of the other nodes will have a unique potential. The voltage across any network branch is then the difference between the potentials at the nodes to which the element is connected. The potential of a node is the sum of voltages encountered when traversing some path between that node and the datum node.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/06%3A_Magnetic_circuit_analog_to_electric_circuits/6.01%3A_Electric_Circuits_and_Kirchoffs_LawsThis is not a wonderful assumption for any systems with capacitor plates, but if one considers capacitors to be circuit elements so that both plates of a capacitor are part of any given element the ri...This is not a wonderful assumption for any systems with capacitor plates, but if one considers capacitors to be circuit elements so that both plates of a capacitor are part of any given element the right hand side of this expression really is zero. Thsn, if we note current to be the integral of current density: Over some area, a fraction of the whole area around a node: where I is to total current and h and w are height and width of the conductor, respectively.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/01%3A_Review_of_network_theory/1.02%3A_Examples-_Voltage_and_Current_Dividersv_{1}=R_{1} i_{1} \\ v_{2}=R_{2} i_{2} \(\ V_{s}=\left(R_{1}+R_{2}\right) i_{1}\) We may solve for the voltage across, say, R 2 , to obtain the so-called voltage divider relationship: \(\ v_{2}=V_{s} ...v_{1}=R_{1} i_{1} \\ v_{2}=R_{2} i_{2} \(\ V_{s}=\left(R_{1}+R_{2}\right) i_{1}\) We may solve for the voltage across, say, R 2 , to obtain the so-called voltage divider relationship: \(\ v_{2}=V_{s} \frac{R_{2}}{R_{1}+R_{2}}\label{4}\) \(\ R_{1} i_{1}-R_{2} i_{2}=0\) \[\ i_{2}=I_{s} \frac{R_{1}}{R_{1}+R_{2}}\label{5} \] Once we have derived the voltage and current divider relationships, we can use them as part of our “intellectual toolkit”, because they will always be true.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/12%3A_Permanent_magnet_Brushless_DC_motors/12.04%3A_Current_Rating_and_ResistanceThe last part of machine rating is its current capability. This is heavily influenced by cooling methods, for the principal limit on current is the heating produced by resistive dissipation. Generally...The last part of machine rating is its current capability. This is heavily influenced by cooling methods, for the principal limit on current is the heating produced by resistive dissipation. Generally, it is possible to do first-order design estimates by assuming a current density that can be handled by a particular cooling scheme.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/10%3A_Analytic_design_evaluation_of_induction_machines/10.03%3A_Squirrel_Cage_Machine_ModelNow we derive a circuit model for the squirrel-cage motor using field analytical techniques.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/02%3A_AC_power_flow_in_linear_networks/2.01%3A_Transmission_LinesIn the case of a short circuit, of course, the magnitude of the voltage is zero, the current in the short is double the current of the pulse itself, and the pulse is reflected, but going in the revers...In the case of a short circuit, of course, the magnitude of the voltage is zero, the current in the short is double the current of the pulse itself, and the pulse is reflected, but going in the reverse direction with a polarity the opposite of the forward-going pulse.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Introduction_to_Electric_Power_Systems_(Kirtley)/12%3A_Permanent_magnet_Brushless_DC_motors/12.03%3A_Parameter_EstimationWe are now at the point of estimating the major parameters of the motors.
