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# Power Flow in a Transmission line

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### Power Flow in a Transmission line

1. 1. Power Flow in Transmission Line Presented by T.S.L.V.Ayyarao Assistant Professor GMRIT
2. 2. Power Flow in Transmission Line Fig 1: A Simple two-machine System E1 and E2 are the magnitude of the bus voltages,δ the angle between two and X the line reactance The driving voltage drop EL is phasor difference E1-E2 The line current I = EL/X and lags EL by 900 The current flow in the line can be controlled by controlling EL or X or δ
3. 3. Power Flow in Transmission Line The rating of series controller would be a fraction of the rating of the line If the angle δ is small, the current flow largely represents the active power Increase or decrease of line reactance X will greatly affect Fig 2. Phasor diagram the active power flow It is the cost effective means of controlling the power The active power at E1 end is P1 = E1E2 sin δ/X Reactive power at E1 end is Q1 = E1(E1-E2 cos δ)/X
4. 4. Power Flow in Transmission Line The active power at E2 end is P2 = E1E2 sin δ/X Reactive power at E1 end is Q1 = E2(E2-E1 cos δ)/X Active power flow increases up to δ = 900 and then falls to 0 Control is possible well below δ = 900 Sufficient margin is required for transient and dynamic stability Increase or decrease of X will raise or lower the curves Fig 3. power angle curves for different X
5. 5. Power Flow in Transmission Line Power flow can be controlled by regulating the magnitude of E1 or E2 The driving voltage EL doesn’t vary by much but its phase angle does The change of magnitude Fig 4. regulating the magnitudes has much effect on of voltages the reactive power than the active power flow
6. 6. Power Flow in Transmission LineFig. 5 (a) quadrature (b) with phase angle Current and hence power flow can be controlled by injecting a voltage in series of the line By varying the magnitude and phase angle of the injected voltage, active and reactive power flow can be controlled.