Download presentation

Published bySidney Burham Modified over 3 years ago

1
Example: Jacobian Matrix and Power flow Solution by Newton-Raphson Determine the dimension of the jacobian matrix for the power system in ex:6.9. Also calculate ΔP2(0) in step(1) and Ji24(0) In step(2) of the first Newton Raphson iteration, Assume zero initial phase angle and 1.0 p.u. initial voltage magnitudes (except V3=1.05)

2
**Solution: Since N=5 buses. NO**

Solution: Since N=5 buses NO. of eqns=2(N-1)=8 Jacobian matrix will have dimension 8х8 There is one voltage controlled bus, bus 3 Therefore V3 and Q3 could be eliminated .: J(i) is reduced to 7x7 matrix ΔP2 = P2 – P2(x) = P2 – V2(0) {Y21V1 cos[δ2(0)-δ1(0)-θ21] Y22V2 cos [-θ22] Y23V3 cos [δ2(0)-δ3(0)-θ23] Y24V4 cos [δ2(0)- δ4(0)-θ24] Y25V5 cos [δ2(0)-δ5(0)-θ25]

3
ΔP = [ *1.0*cos(84.624) *1.0*cos( ) *1.0*cos( )] = p.u. For step(2) and Ji Ji 24(0) = V2(0)Y24V4(0)sin[δ2(0)-δ4-θ24] = 1.0* *1.0*sin[ ] = PU See EX 6-11 Power World Simulator

4
**Example: Using the power flow system in Ex 6**

Example: Using the power flow system in Ex 6.9, Determine the acceptable generation range at bus3, keeping each line and transformer loaded at a below 100% of its MVA. Computer Simulate

5
6.8 SPARSITY TECHNIQUES - Sparse matrix has only a few non zero elements. - Newton Raphson power flow program employ sparse matrix techniques to reduce computer and time requirement . These techniques include compact storge of Ybus and J(i).

6
Consider the following matrix: One method for compact storage of S consists of four vectors DIAG=[ ] OFFDIAG=[ ] Col=[ ] Row=[ ]

7
Fast Decoupled Power Flow - Contingencies are a major concern in Power system operations. For example, operating personnel need to know what power flow changes will occur due to a particular generator outage a transmission line outage. - Contingency information when obtained in real time ,can be used to Anticipate problems caused by such outages and can be used to develop operating stategies to overcome problems. - Fast power flow algorithms have been developed to give power flow solutions in second or less.

8
These algorithms ak based on the following simplification of the jacobian matrix. * Neglect J2(i) and J3(i) This will reduce the problem ( power flow ) to : J1(i)Δδ(i)=ΔP(i) J4(i)ΔV(i)=ΔQ(i) * Further reduction in computer time can be obtained, for ex Assume Vk≅Vn≅1 p.u. and δk=δn Then J1 and J4 constant matrices this means that J1 and J4 do not have to be Recalculated during successive iterations.

9
**Chapter 7 SYMMETRICAL FAULTS**

10
**7.1 Series R-L Circuit Transients Consider the series R-L circuit shown:**

The switch is closed at t=0. This represent a shot circuit across the circuit. For simplicity assume here fault impedance. This is usually called solid or bolted fault.

11
**To get the current after closing the switch**

13
- The total fault current I(t) is called the asymmetrical fault current. - The ac component is called the steady state fault current. - The dc component is called the offset current or the complementary current. This component decays with time constant The rms value of the ac component is (A) .

14
- The rms value of i(t) is give by: (A) In terms of the time constant and frequency w, This can be written in the following from

15
Example: A bolted short circuit occurs in the series R-L circuit shown before with V=20KV, X=8Ω, R=0.8Ω and with the maximum dc offset current. The circuit breaker opens 3 cycles after fault inception. Determine: a) The rms ac fault current. b) The rms momentary current at τ=0.5 cycle which pass through the breaker before it opens. c) The asymmetrical fault current the breaker interrupts.

Similar presentations

OK

TCIPG Reading Group Today’s Plan: Discuss Read and Work Ahead

TCIPG Reading Group Today’s Plan: Discuss Read and Work Ahead

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt online compressor software Animated ppt on solar system Free ppt on water cycle Ppt on elements compounds and mixtures Ppt on indian political environment Ppt on tata steel company Ppt on remote server monitoring system Ppt on endangered species of plants in india Ppt on financial ratio analysis Ppt on water cycle for class 9