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BACKGROUND STUDY
PV System and Principle of operation
A photovoltaic cell converts energy from the sunlight into electricity. The radiation from the sun is made up of tiny particles of energy called photons. As these photons impact on the cell, some of them are absorbed into the cell. The energy from the photons on impact causes electrons to be free [2]. The movement of the free electrons is what generates electricity.
A PV system is made up of a combination of many cells. Since a PV module is made up of cells combined in series and parallel, the equivalent circuit can obtained by first doing an analysis on a single cell. The equivalent circuit for a PV cell is given below
The circuit comprises of a Current source which delivers short circuit current ISC , A shunt diode connected across the current source with current ID representing diffusion current across the P-n junction and internal series and parallel resistances RS and RSH respectively
Mathematical Representation
Using Shockley’s diode equation
Where Is is reverse saturation current, q is charge of one electron, Tc is the cell temperature in Kelvin, V is output voltage, A is junction power factor which determines diode deviation from ideal p-n junction
The photocurrent Isc is given by
Where Tr is the reference temperature, ISCR is the short circuit current at reference temperature, ki is temperature coefficient and G is irradiance in mW/cm2.
Reverse saturation current is given by
I_s= I_OR (T_c/T_R )^3 exp{(qE_g)/KA [1/T_R -1/T_c ] } …..(3)
From figure 1 the cell current can be expressed as
Boost converter
A boost converter is a DC/DC switching converter which is normally used where a higher output voltage then what is supplied by the source is needed by the load [3] . The efficiency of the boost converter is usually very high [3]. A typical boost converter circuit is shown in figure (2) below.
When switch is on voltage applied to inductor is L di/dt= Vin .........(5).
This can also be written as Vin = Ldi/(kT_p ) ........(6)
Where K and Tp are duty ratio and switching period respectively. [1]
When switch is OFF, Ldi/dt=Vi – Vout = (-L di)/((1-k)T_p )........(7)
For the inductor, the rise in current is equal to the fall in current therefore
Di=(KTpVin )/L=(-(1-K) T_p (V_in-V_out ))/L ∴V_in=(1-k) V_out…….(8) [1]
Brief discription of a thyristor
A thyristor is a switching semi conductor device that is unidirectional, that is to say it can only conduct in a single direction [7]. It is also referred to a silicon controlled rectifier whose principle of operation could be described using the circuit below
The physical and schematic diagrams of thyristor are shown Figure 1a and 1b respectively.. It can be seen that a thyristor is basically a combination of PNP and NPN bipolar transistors. To make the thyristor conduct a voltage is applied at the gate which turns on the NPN transistor which in turn makes the PNP to start conducting. Once both transistors are ON, they remain ON until turned OFF. The thyristor could also be turned ON by applying sufficient voltage between the anode and cathode to make one of the transistors break down and begin to conduct . Once one of the internal transistors starts conducting there would be sufficient amount of base current at the second transistor to make it conduct .[6]
The thyristor can turn off by reducing the current flowing in the internal transistors until one of them stops conducting. This can be achieved by applying a negative voltage to the gate [6].
3 phase thyristor rectifier
Due the mode of operation and behaviour as described earlier, thyristors are used in 3 phase rectified circuits. This type of rectifier using thyristors is referred to as line commutated controlled rectifier. An example of a 3 phase thyristor converter is shown below.
The 3 phase rectifier shown in figure (4) above has 6 thyristors connected in two groups of 3 each. The first group has a common cathode connection and the second group have a common anode connection. The thyristors are fired at an interval of 1200. The firing sequence for the thyristors is 16,62,24,43,35 and 51.Each thyristor is fired after 600 of the previous thyristor being fired. This means at point ωt=π⁄6 (because it is 3 phase starting point is not ωt=0 ) T1 is triggered while T5 is still conducting and between 600 and 1200 both T1 and T5 would conduct together and the line to line voltage Vab=Van – Vbn would appear across the load. At 1800 thyristor T6 is fired and thyristor T5 is reversed biased thereby switching off. At 2400 T2 is triggered and T1 is switched off. The process continues for the rest of the sequence with the triggering action of one thyristor switching off the previous thyristor.[4]
PI Controller
A PI controller is a combination of a proportional controller and integral controller. By combining both controllers, the setbacks in one is corrected by the other. For example a proportional controller has non zero steady state error while a proportional integrator forces the steady state error to zero by accumulating all the errors
PART A
AIMS AND OBJECTIVES
To be able to understand and implement the construction of a PV system with control scheme using simulink in mat lab. To know how the different blocks that make up the PV system can be constructed separately and connected together to make a complete PV system.
To understand how simulink tool boxes can be used in implementing a dc to dc converter that is used to control a PV system.
RESULTS AND DISCUSSION
Boost converter model
The figure (4) shows a boost converter model made up of an input Dc source, an inductor at the input to keep the current steady and reduce current ripples, a Mosfet switch, a capacitor at the output to keep the voltage steady and reduce voltage ripples and a resistive load .
A dynamic PWM generator
Figure (5) above shows the PWM generator that has been created by a combination of various function blocks. The PWM is made up a of a pulse generator for input pulses of amplitude 2. In other to get desired amplitude of 1 and -1 for the pulse with to be generated, a constant block is added and together with pulse generator fed into the input of a subtractor. The output from the subtractor is amplified by a gain of 50e-6 and this is fed into an integrator to obtain a triangular waveform. The triangular waveform at the output of the integrator is compared to a constant duty ratio of 0.5. The results of the comparison is square wave which is positive when the triangular wave is less than the duty ratio an negative when the triangular wave is greater than the constant duty ratio as illustrated in the figure (6) below.
Subsystem
A subsystem is used to make a model more compact. The PWM generator in figure (5) is converted into a subsystem as shown in figure (7)
As can be seen from figure (8) the entire PWM generator system has been converted to a single box. Figure (9) shows the pulse width waveform at the output of the signal generator
Connecting the PWM generator model to the previously designed Boost converter gives the model shown in figure (10).2 oscilloscopes have been added to measure the output voltage response across the load and the current response in the inductor.
These measurements are plotted using the “to file” block component which saves the responses as vector variables under a file name.
Figure (10) shows the load voltage of the boost converter. It can be observed that the voltage has ripples and the magnitude is increased. The increase in voltage magnitude is due to the converter being a step up (boost) converter.
S function for pv model
The S-function processes input signals as states and generate outputs from these signals. Both the input and output signals are in vector form. The S-function is made of several call functions which are used by simulink during simulation.
Figure (14) above shows how an S function is integrated into a model. The S- function block is obtained from user defined functions in the simulink library. The name of the block is then changed to the same name that the S-function code was saved in, for this case it is named sfun1.
Two inputs are fed into the S-function block. The first is from a constant block of magnitude 10 and the second from a step block which changes from 0.5 to -0.5 in 0.025 seconds. The S-function block then computes the product of these two inputs at every time interval. The response is shown in figure (14)
It can be observed that the response changes from 5 to -5 in 0.025 seconds. This is because
When the step input is 0.5, the S-function computes the output as 0.5 X 10 = 5. And the amplitude remains 5 until the step input changes to -0.5, then the output becomes -0.5 X 10 = -5.