Lecture 20 computational technique (1).pptx

computational technique in power system

1. Single phase representation of three phase (1) Figure in the left shows the balanced three phase system: in balanced three phase system the neutral impedance Zn does not affect the behavior of the network. Figure in the right gives the single phase equivalent of a balanced three phase network shown in figure left.

2. Single phase representation of three phase (2) The equivalent single phase representation is a complete diagram of a power system. Representing all the three phase quantities by single phase network composed of one of the three phase and neutral under balanced condition. Representation of three phase system by single phase system is done because while representation all the three phase system becomes too complicated.

3. Single line diagram The single line diagram shows the main connection and arrangement of system components along with their data. The system components are done in the formed of symbols. Single Line diagram is used when information about the circuit is required but detail of actual wire connection and operation of circuit is not required. It provides a fast and easy understanding of the connection and use of component.

4. Symbol used in SLD

5. SLD of general power system

6. Impedance diagram The single line diagram can be further simplified by representing impedances only. Each component is represented by its equivalent circuit. Neutral earth impedance does not appear in diagram since balanced condition are assumed.

7. Reactance diagram The impedance diagram can be further simplified by representing the line with reactance's only. The line resistances are quite small in comparison to leakage reactance and shunt path which include line charging and transformer magnetizing circuit provide very high impedance, so are neglected.

8. Single Subscript Notation (1) Let, the emf is E g and the voltage between the node ‘a’ and ‘o’ is defined as V t . The current is I L and the voltage across the load is V L . In an AC circuit the terminal mark is positive is positive with respect to terminal mark negative for half cycle and is negative for next half cycle. Voltage between the terminal is positive when mark positive is at higher potential. The direction of current in an AC circuit reverses in each half cycle.

9. Single Subscript Notation (2) When the current flows in same direction to that of arrow ( ) IL is positive and when the direction is opposite it is negative. The voltage may be represented by single letter subscript identifying the node whose voltages are represented with respect to reference node. (i.e. and )  

10. Double subscript notation The use of polarity marks for voltage and direction arrows for current can be avoided by double subscript notation. In figure the current is positive when current flow from ‘a’ to ‘b’ and it is represented by I ab The voltage of node ‘a’ with respect to ‘b’ i.e. Vab is positive when V a > V b . During positive half cycle which is given by, Reversing the order of subscript of current or voltage gives a current or voltage 180 degree out of phase with original  

11. Complex Power (1) If the phasor expression for voltage and current are known the calculation of real and reactive power can be done in complex form. The complex power is the product of voltage and conjugate of current. If the voltage is, then,  

12. Complex Power (2) Now, Comparing real and imaginary part, The reactive power is positive when the current is lagging and negative when current is leading the voltage. For inductive circuit Q is positive and for capacitive circuit Q is negative.  

13. Direction of Power flow (1) For DC Source:

14. Direction of Power flow (2) For AC System: Generator action assumed: If P is positive emf supplies power If P is negative emf consumes power If Q is positive emf supplies reactive power (I lags V) If Q is negative emf consumes reactive power ( I leads V) Motor action assumed: If P is positive emf consumes power If P is negative emf supplies power If Q is positive emf consumes reactive power (I lags V) If Q is negative emf supplies reactive power ( I leads V)

15. Any Question ?