In a salient pole alternator, the d-axis reactance is larger than the q-axis reactance due to the geometry and magnetic characteristics of the rotor. The d-axis corresponds to the direction of the rotor's field winding, where the magnetic flux is concentrated, resulting in stronger inductive effects and higher reactance. Conversely, the q-axis, which is perpendicular to the d-axis, experiences less magnetic coupling and thus exhibits lower reactance. This difference is crucial for the machine's performance, affecting its stability and reactive power capability.
In salient pole alternator Xar is unequal in D-axis and Q-axis, due to non uniform air gap where as in non-salient pole Xar is equal in every axis due to uniform airgap between stator and rotor. Xar is armature reaction reactance.
Direct axis transient reactance, often denoted as X'd, refers to the reactance of a synchronous machine during transient conditions when the rotor angle changes, such as during sudden disturbances or faults. It represents the machine's ability to produce or absorb reactive power in response to these transients. This reactance is typically lower than the synchronous reactance (Xd), allowing for a quicker response to changes in load or system conditions. Understanding direct axis transient reactance is crucial for analyzing the stability and dynamic performance of power systems.
Kamal Koshal has written: 'Direct and quadrature-axis synchronous reactance measurement'
If the stator winding of a synchronized machine, which consists of many coils that are basically connected as a series circuit, is not connected to a load then the resulting emf from all the coils is the open circuit emf of the phase winding. Closing the circuit on to a load causes a steady state current to flow in the stator coils. Each coil creates a flux and their total flux opposes the field flux from the rotor. The resulting flux in the air gap is reduced. The emf corresponding to the air-gap flux drives the stator current through the leakage reactance and conductor resistance of the stator coils. The voltage dropped across this winding impedance is small in relation to the air-gap voltage. Deducting this voltage drop from the air-gap voltage gives the terminal voltage of the loaded generator. In the circumstance described thus far the reduction in air-gap flux is called armature reaction and the resulting flux is much smaller than its value when the stator is open circuit. Restoring air gap and terminal voltage requires the field current to be increased, which is the necessary function of the automatic voltage regulator and the exciter. When the rotor pole axis coincides with the axis of the stator coils the magnetic circuit seen by the stator has minimum reluctance. The reactance corresponding to the armature reaction in this rotor position is called the 'direct axis synchronous reactance Xsd '. If the stator winding leakage reactance, Xa, is deducted from Xsd the resulting reactance is called the 'direct axis reactance Xd '. A similar situation occurs when the rotor pole axis is at right angles to the axis of the stator coils. Here the magnetic reluctance is at its maximum value due to the widest part of the air gap facing the stator coils. The complete reactance in this position is called the 'quadrature axis synchronous reactance Xsq '. Deducting Xa results in the 'quadrature axis reactance Xq '.
An impedance triangle has resistance (always positive) in the x axis and reactance (at a right angle to resistance) in the y axis. The line that completes this triangle (the hypotenuse) is the absolute value of the impedance.
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for salient type motor Lq>Ld, and non-salient type motor Lq=Ld; Lq and Ld are q-d axis inductanceAnswer'Salient' means to 'stick out', so a 'salient pole' machine is one whose rotor windings are fitted to pole pieces that stick out from the rotor shaft. A 'non-salient pole' machine is one in which the windings are placed in slots machined along the length of the rotor.Salient pole machines run slower and have more poles than slotted-rotor machines, and are typically used in alternators run by water turbines; slotted-rotor machines are typically used in alternators run by high-speed steam/gas turbines.
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There would be no four seasons if the earths axis was not titled.
Xd (synchronous reactance in the direct axis) and Xq (synchronous reactance in the quadrature axis) are determined for synchronous machines to analyze their performance under different operating conditions. Xd is crucial for understanding the machine's behavior during steady-state operation and when supplying or absorbing reactive power, while Xq is important for evaluating the machine's response to load changes and transient stability. These parameters help in the design of control systems and in the stability analysis of power systems. Knowing Xd and Xq allows engineers to effectively model and predict the machine's performance in various scenarios.
The operator, 'j', is used to indicate a phasor quantity that has been rotated, counterclockwise, through an angle of 90 degrees.So, if (for example) the operator is applied to a voltage U, then it is written as jU, which indicates means that the voltage lies along the vertical positive axis. A further operation by j, results in jjU, or j2 U, which means that the voltage lies along the horizontal negative axis -so, j2 is equivalent to -1U (or j is equivalent to the square-root of -1) or, simply, -U.A further operation by j, results in the voltage lying along the negative vertical axis: that is: jjjU = jj2U=-jU.But to answer your question, for inductive reactance (XL), we express impedance (Z) a follows: Z = R+jXL and, for capacitive reactance (XC), we express impedance as Z = R - jXC (the L and C should be subscripts).Strictly-speaking the operator j doesn't actually apply to impedance, because impedance, resistance, and reactance or not phasor (vector) quantities. So if we wanted to be strictly accurate, the above equations should be written as:(E/I) = (UR/I) + j (UL/I) and (E/I) = (UR/I)- j (UC/I)...but this is being rather pedantic.