[Pi Modul Of transmission line][Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.]

2015Swedish College of Engineering & Technology Rahim Yar

Prepaid By:Engr Muhammad ImranGroup Members:Muhammad Awais SharifM.umer FarooqSammiullah

Pi Model of Transmission LineTheoretical Background:In 1706 a little-known mathematics teacher William Jones first used a symbol to represent the platonic concept of pi, an ideal that in numerical terms can be approached, but never reached. Patricia Rothman discusses Jones’s significance among his contemporaries and the unique archive that forms his legacy. - See more at: http://www.historytoday.com/patricia-rothman/william-jones-and-his-circle-man-who-invented-pi#sthash.Nz0W2roi.dpuf

Mathematical analysis of the behavior of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable. The model correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher's equations.

Description

For a transmission line, the resistance, inductance, and capacitance are uniformly distributed along the line. An approximate model of the distributed parameter line is obtained by cascading several identical PI sections, as shown in the following figure.

Circuit Diagram:

Unlike the Distributed Parameter Line block, which has an infinite number of states, the PI section linear model has a finite number of states that permit you to compute a linear state-space model. The number of sections to be used depends on the frequency range to be represented.

An approximation of the maximum frequency range represented by the PI line model is given by the following equation:

fmax=N⋅v8⋅ltotwhere

For example, for a 100 km aerial line having a propagation speed of 300,000 km/s, the maximum frequency range represented with a single PI section is approximately 375 Hz. For studying interactions between a power system and a control system, this simple model could be sufficient. However for switching surge studies involving high-frequency transients in the kHz range, much shorter PI sections should be used. In fact, you can obtain the most accurate results by using a distributed parameters line model.

Frequency used for rlc specificationsFrequency f, in 50 hertz (Hz), at which per unit length r, l, c parameters are specified. Hyperbolic correction is applied on RLC elements of each line section using this frequency.

Resistance per unit lengthThe resistance per unit length of the line, in ohms/km (Ω/km).

Inductance per unit lengthThe inductance 1e-3 per unit length of the line, in henries/km (H/km). This parameter can not be zero, because it would result in an invalid propagation speed computation.

Capacitance per unit lengthThe capacitance 1e-6 per unit length of the line, in farads/km (F/km). This parameter can not e zero, because it would result in an invalid propagation speed computation.

Number of pi sectionsThe number of PI sections. The minimum value is 1.

MeasurementsSelect Input and output voltages to measure the sending end (input port) and receiving end (output port) voltages of the line model.

Application Of PI Model: The user can connect multiple pi section in series to form an equivalent for a long

transmission line. EMTP will need to compute all of the intermediate node voltage. Line constants program can be used to create coupled pi data.

Matlab Tools: Resistor Capacitor Voltage Measurement Current Measurement Scope RL Load Ac voltage source

PowerguiGraphical user interface for the analysis of circuits and systemsLibrary:Powerlib ( in Simulink)

Demonstration

1. Simulation using a continuous solver

Start the simulation and observe line voltage and load current transients during load switching and note that the simulation starts in steady-state.Use the zoom buttons of the oscilloscope to observe the transient voltage.

2. Using the Powergui to obtain steady-state phasors and set initial states

Open the Powergui block and select "Steady State Voltage and Currents" to measure the steady-state voltage and current phasors..

Using the Powergui select now “Initial States Setting” to obtain the initial state values (voltage across capacitors and current in inductances).Now, reset all the initial states to zero by clicking the “to zero" button and then "Apply" to confirm changes. Restart the simulation and observe transients at simulation starting.Fig. 6 Powergui Block

3. Discretizing your circuit and simulating at fixed steps

The Powergui block can also be used to discretize your circuit and simulate it at fixed steps.

Open the Powergui. Select “Discretize electrical model" and specify a sample time of 50e-6 s. The state-space model will now be discretized using trapezoidal fixed step integration. The precision of results is now imposed by the sample time. Restart the simulation and compare simultion resultswith the continuous integration method. Vary the sample time of the discrete system and note the impact on precision of fast transients.

4. Using the phasor simulation method

You will now use a third simulation technique. The "phasor simulation" method consists to replace the circuit state-space model by a set of algebraic equations evaluated at a fixed frequency and to replace sinusoidal voltage and current sources by phasors (complex numbers). This method allows a fast computation of voltage and current phasors at a selected frequency, disregarding fast transients. It is particularly efficient to study electromechanical transients of generators and motors involving low frequency oscillation modes.

Procedure: Open the mat lab software. Then open the simmulink in mat lab. Now we have to chose required parameters from simmulink i.e. voltage

measurement, current measurement,ac voltage source,RLC load, resistor, capacitor& inductor.

Now double click on each parameter to arrange the following value. Capacitance= 10e6 Frequency=50 Nominal voltage= 100kv Active Power=10e3 Inductive reactive power=100 Peak amplitude=150 Inductance= 100 Resistance= Now run the model.

Matlab Digram:

Graph: