Derive a d-q seventh order state-space currents model of the synchronous generator whose equivalent circuit shown in figure 1
EEE7006- Assignment Part A (Presentation)Β 
Students need to research, analyse, and present one of the following tasks:
1. A: Synchronous Generator Modelling and Simulation Using MATLAB/SIMULINK
Introduction: The synchronous generator is the main source of the electricity supply of the power system where it injects continuously active and reactive power to the power network. To understand the operation and analyse its steady-state and transient responses we use MATLAB/SIMULINK investigations including small signal and big disturbance effects on the operation of synchronous generator. The MATLAB help us greatly to design efficient controllers for the excitation and the speed governing systems so that generators and the power system remain stable ensuring good power supply security and system reliability.
Objectives:
- Derive a d-q seventh order state-space currents model of the synchronous generator whose equivalent circuit shown in figure 1. (10%)
- Use the MATLAB to find
- Eigen values (5%)
- Transfer function (5%)
- Use MATLAB scripts to simulate the step time response of the system for the two inputs individually: Field Excitation voltage and Prime Mover mechanical power. (10%)
- For the SIMULINK model shown in figure 2 use the basic SIMULINK library blocks to build this model and simulate the performance of a synchronous generator with its excitation and mechanical torque control loops following a 3-phase short-circuit at the machine terminals. show:
The load angle and voltage responses without excitation and torque control when the machine is subjected to 20% step in the inputs. (10%)
The load angle and voltage responses with excitation and torque control when the machine is subjected to 20% step in the inputs. (10%)
To achieve overshoot less than 5%, settling time less than 2 seconds steady state error equals to zero using these two methods:
- PID controller (15%)
- State feedback controller (15%)
- Compare and discuss the results. (10%)
- Answer the discussion questions. (10%)
- Text book βPower Systems Control and Stabilityβ on Moodle.
- In MATLAB command Window type the matrices A, B, C, D as follows: A= [a11β¦a1n;a21 β¦..a2n;β¦β¦.; an1β¦β¦β¦ann];
Resources:
B= [b11β¦.b1n; b21β¦..b2n;β¦..;bn1......... bnn];
C= [c11β¦..c1n; β¦β¦..;cn1.......... cnn];
Where a.s, b.s, and c.s are the parameter coefficients of the system that can be obtained from any reliable source.
D=0; U= [β¦.,Vf,β¦,Tm];
Where Vf and Tm are the field winding voltage and mechanical torque respectively.
- Use the following instructions on MATLAB Sys=ss (A, B, C, D); % this is the state-space model
Step(Sys)Β Β Β Β Β Β % this will show the step response of the system
Eig(A)Β Β Β Β Β Β Β % this will produce the eigen values of the system state matrix A
[b,a]=ss2tf(A,B,C,D) % this will give transfer function of the system where βbβ are the coefficients of the numerator and βaβ are the coefficients of the denominator.
Figure 1 synchronous generator d-q equivalent circuit
Figure 2 SIMULINK model of a simplified synchronous generator model (Use lecture slides of the complete model on Moodle)
Discussion:
- Prove that the transfer function of the power system described by its state space model
π₯Λ = π΄. π₯ + π΅. π’
π¦ = πΆ. π₯ + π·. π’ where D=0
IsΒ Β Β Β Β πΊ(π ) = πΆ. (π πΌ β π΄)-1. π΅
- What are the methods used to improve system stability and the effect of using FACTs devices in power systems dynamic operation?
- Suggest a coordinated control method between excitation control and a series capacitor FACTs device.
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SIMULINK Model of Inductive Link Wireless Power Transfer (WPT) Device
Introduction:
The purpose of this part of assignment is to practice MATLAB/SIMULINK basic library blocks to create a full dynamical model of the WPT device. The inductive link has two parts namely transmitter and receiver. The transmitter has class E inverter while the receiver has also class E rectifier. Students need to build a complete state-space mathematical model of the device and use the basic library blocks of SIMULINK to simulate the performance of this device.
A dynamic response analysis model of a Class E2 converter for wireless power transfer applications is the main task of this assignment. The converter operates at 200 kHz and consists of an induction link with its primary coil driven by a class E inverter and the secondary coil with a voltage-driven class E synchronous rectifier. A state-space model is required to obtain the eigenvalues of the system for the four modes resulting from the operation of the converter switches and to simulate the efficiency of this device using SIMULINK environment. A dynamic analysis needs to be carried out to investigate the effect of changing the separation distance between the two coils, based on converter performance and the changes required of some circuit parameters to achieve optimum efficiency and stability. Figure 3a shows a photograph of the Wireless Power Transfer (WPT) device and the experimental setup that had been used in research
Figure 3a. Photograph of the experimental setup.
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Aim
To analyse the operation and performance of inductive link wireless power transfer device.
Objectives:
- Explain the operation of WPT device using inductive link and class E2 converters showing the parameters that have control to optimize the device efficiency and stability. (10%)
- Using circuit laws deriving the 7thorder mathematical model. (10%)
- Use MATLAB scripts to find the state matrix of this device for the ON and OFF periods of the MOSFETs. (5%)
- Use MATLAB scripts to find the eigen values of the state matrix of this device for the ON and OFF periods of the MOSFETs and comment on the results (5%)
- Build a SIMULINK model of the mathematical model given in Figure 3b and test the responses when separation distance changes. (25%)
- If we are going to use this device for charging batteries of a flying drone, Using SIMULINK suggest a method to control the device to keep its efficiency greater or equal to 78% with constant output voltage of 11 V. Take into consideration that you have control to make changes in the transmitter side only as the receiver sits in the drone itself. (45%)
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The circuit diagram (figure 3b) shows:
Q1 and Q2 are the switches (MOSFET)
C1, C2, C3, C4 are capacitors (tuning and smoothing functions)
Lp, Ls, and M are the primary leakage inductance, the secondary leakage inductance, and the mutual inductances respectively.
R is the load resistor. You can use the attached parameters.
V is the DC input voltage (10 V) and Lf is the inductance of an inductor.
Figure 3b. The circuit diagram of the Inductive Link Wireless Power Transfer Device
π₯ = [π₯1 β¦. . π₯7]= [π£1 π£2 π£3 π£4 πf πp πs ], simply the voltage across C1 , the voltage across C2 , the voltage across C3 , the voltage across C4 (the output voltage), the inductor Lf current, the primary current, and the secondary current respectively.
Device parameters:
πON1 = πON2 = 0.15 πβπ
ππ = ππ = 0.18 πβπ
π = 10 πβππ
πΆ1 = 55 ππΉ
πΆ2 = 45 ππΉ
πΆ3 = 26 ππΉ
πΆ4 = 6.6 ππΉ
πΏπ = πΏπ = 24 ππ»
ππ = 1 ππβπ
πΏπ = 1 ππ»
Both coils have maximum Q factor of 230 at 200 kHz Operating frequency= 200 kHz
Duty cycle of Q1=0.5 Duty cycle of Q2=0.511 Delay angle of Q1=0
Delay angle of Q2=229.864O
For a separation distance of 3mm, the measured mutual inductance is approximately 12
ΞΌH, which corresponds to a coupling coefficient (k) value of 0.50. Reference:
Dynamic analysis model of a class E2 converter for low power wireless charging links - Bati
- 2019 - IET Circuits, Devices & Systems - Wiley Online Library
https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cds.2018.5091
