An introduction to electrodynamics from the standpoint of by Leigh Page

By Leigh Page

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Extra resources for An introduction to electrodynamics from the standpoint of the electron theory

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VsЈ Є␦sЈ). Controlling one parameter (voltage magnitude or its phase angle) using a power flow controller (PFC) affects both the active and reactive power flows (Pr and Qr) in the line simultaneously. The key to regulate the active and reactive power flows (Pr and Qr) so they become a particular pair of values is to control the sending-end voltage to a specific magnitude (VsЈ) and phase angle (␦sЈ). , Vs Є␦s) as shown in Figure 2-2a. For point-to-point transfer of power between two isolated networks or interconnection of two transmission lines with different voltages or 18 POWER FLOW CONTROL CONCEPTS Ps , Q s Vs's Ps' , Q s' Pr , Q r VX I X Vs Vs' Vr (a) Ps' , Q s' Pr , Q r VX X X TIE E I Vs' Vr (b) Figure 2-2.

13 14 POWER FLOW CONTROL CONCEPTS Psn, Qsn Prn, Qrn VXn I I X VXn Vs V1 Vs I qs 90 I Vr Vm V2 Vs I ο Vr δ Ids I I qr Vr Idr Figure 2-1. Simple power transmission system and the related phasor diagrams. 1 15 THEORY where VV An = s r X (2-5) The natural reactive power flow at the sending end is ( ( ) ) Qsn = Vs I sin δ s − θ I = Vs I sin −θI = −Vs I sin θI (2-6) Then equations 2-2b and 2-6 can be combined as ⎛V ⎞ Q = A ⎜ s − cos δ ⎟ sn n ⎜V ⎟⎠ ⎝ r (2-7) where An is given in equation 2-5. , ␦r = 0°), the current through the transmission line is I= VXn V ∠δ − Vr ∠ 0° Vs cos δ + jVs sin δ − Vr = s = jX jX jX V sin δ V − Vs cos δ = s + j r = I ∠θ I X X or I = I cos θ I + jI sin θ I (2-1) V sin δ I cos θ I = s X (2-9a) V − Vs cos δ I sin θ I = r X (2-9b) where and 16 POWER FLOW CONTROL CONCEPTS The natural active power flow at the receiving end is ( ( )= Vr Icos θI ) Prn = Vr I cos δ r − θ I = Vr I cos −θ I (2-10) Then equations 2-9a and 2-10 can be combined as Prn = An sin δ (2-11) where An is given in equation 2-5.

The compensating voltage in the PAR is in quadrature (+90° or –90°) with the line voltage and, therefore, regulates the phase angle of the transmission line voltage. The ST creates a series compensating voltage that is variable in magnitude and phase angle and can control the transmission line voltage in both magnitude and phase angle in order to achieve independent control of active and reactive power flows in the line. This compensating voltage may be thought of as two orthogonal compensating voltages of separate autotransformer and PAR.

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