Compute the transfer function

Assignment Help Electrical Engineering
Reference no: EM13747

In this project we will consider the control of a synchronous generator supplying electricity to the grid. We will focus on the problem of frequency stability. The frequency at which the generator rotates is directly proportional to the frequency of the currents and voltages in the power grid. Hence, keeping the rotational frequency constant is of fundamental importance to the correct operation of the grid. A simpli ed model to study the stability of a single generator connected to the grid is the so called swing equation given by:

1973_Compute the transfer function.png

In this model ωs is the synchronous rotational velocity 2Π50 rad/s. The constant D = 5 represents the damping induced by mechanical and electrical losses and the constant H has the value 4. The term Pm = 1/2 represents the mechanical power that is transformed by the generator into electrical power and the term Usinδ represents the electrical power and describes the e ect the grid has on the generator. We will take U as the input since we can change its value by the voltage across the excitation coil in the generator's rotor.

A synchronous generator, when operating in steady state, maintains a constant angular velocity achieved by matching the supplied mechanical power Pm with the power lost through dissipation -D/H(ω - ωs) and the electrical power Usinδ . When a fault occurs and a transmission line is tripped (opened) there is a sudden change in the electrical power and some generators will accelerate while other generators will decelerate. Once the fault is cleared and the transmission line is re-closed, di erent generators will be rotating at di erent angular velocities and voltages and currents in the power grid will no longer be sinusoids with a frequency of 50 Hz.

The objective of this project is to design a controller that will resume the steady state operation of the generator at 50 Hz. Please justify all your answers including relevant plots if necessary.

Attach the Simulink diagram to your report.

1. For which values of U and  is the pair ((δ; ωs); U) an equilibrium point?
2. Linearize the swing equations around an equilibrium point.
3. Compute the transfer function from the input U to the output ω.
4. For which equilibria is the linearizes system stable?
5. Using the equilibrium point ((Π/6; ωs); 1), simulate the linearized system and the non-linear swing equations for di erent initial conditions. Comment on what you observe.

6. When a fault occurs in a transmission line the generator will either accelerate or decelerate. We will simulate this by using the initial value for ω to be 1% higher than ωs.

7. Design a controller to reduce by 50% the time to reach the equilibrium (under the initial conditions of the previous question). Show a plot of the evolution of the system when using the designed controller.

8. Keep increasing the value of ω until the system (swing equation+controller) becomes unstable. Compare with what happens when you do not use a controller.

9. Redesign your controller so that it stabilizes the angular velocity under faults that change the initial value of ω no more than 10% of its equilibrium value. Illustrate the operation of your controller with the relevant plots.

Reference no: EM13747

Questions Cloud

Create a vector in matlab : Create a three dimensional diagram of function.
Define a suitable functional unit : Define a suitable functional unit for a comparative study between two different types of paint.
Technical community blog : Write a blog article for a coding/technical community blog
Distributed random variables : Daily Airlines fies from Amsterdam to London every day. The price of a ticket for this extremely popular flight route is $75. The aircraft has a passenger capacity of 150.
Compute the transfer function : In this project we will consider the control of a synchronous generator supplying electricity to the grid.
Implement avl tree : Implement AVL trees that allows both iterative traversal and recursive traversal.
Memory allocation in operating system : Analysis and implementation of algorithms for memory allocation in operating system, Explain First- t and best- t methods are used in memory allocation in operating systems.
Development of the current strategic potential of airline : Evaluate the organisation's current external and internal strategic position
Ethics and social responsibility : Ethics and social responsibility at McDonalds

Reviews

Write a Review

Electrical Engineering Questions & Answers

  Lithium ion battery technology

The paper includes Lithium ion battery technology with its advantages and disadvantages. The paper discusses about the Lithium air battery in which detailed reactions of Lithium with air including nonaqueous as well as aqueous are given.

  Power transformers and tariffs

Construction of different types of power transformer, significant energy savings

  Paper on orthogonal frequency-division multiplexing

This document is shown a paper on Orthogonal frequency-division multiplexing with advantages, disadvantages and uses.

  Function of the hmi in a scada system

This assignment contains electronics engineering questions like State the commonly found components of a SCADA (Supervisory control and data acquisition) system. and decribe the function of the HMI in a SCADA system.

  Resultant waveform of the odd harmonic series

Prepare an Excel graph showing the individual components and summated resultant waveform of the odd harmonic series resulting in an approximate square wave.

  Explain scada system

Explain the function of the HMI in a SCADA system.

  Design a 2-digit 24 second shot-clock

Design a 2-digit 24 second "shot-clock" countdown timer with pushbutton controller.

  Model a discrete-time system

To understand di erent signal models To be able to model a discrete-time system and design simple signal processing algorithms.

  Draw a relay construction diagram

Draw a relay construction diagram and briefly explain the operation of a relay.

  Frequency division multiplexing

Write a short technical report on Frequency Division Multiplexing

  Impact of electron energy

Briefly discuss the impact of electron energy, electron current and target on the Bremsstrahlung generated.

  Traffic light controller

The schematic of the traffic light controller

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd