1. Peak-Power Operation In Solar PV
Presented by,
Sudarshan B S
Assistant Professor
Dept. of EEE
RVCE, Bangalore

2. Need For Maximum Power Point Tracking
As described before, PV panels have a single operating point where the values of current and voltage of the cell result in a maximum power production.
The V-I relationship of a PV panel is exponential, and there is only one point on the V-I curve that gives the maximum power, called the maximum power point (MPP).
The MPP depends on two important parameters, viz., the intensity of irradiation (in W/m2) falling on the PV panel and the temperature of the cell (in degree Celsius or Kelvin).
It is obvious that the irradiation intensity and temperature of cell will not be a constant throughout the day and hence the MPP varies with time.
Therefore, it is necessary to track the MPP constantly to optimize the power production.

3. Introduction
When sun tackers are used, they move the panels to collect maximum solar radiation. This is called mechanical tracking.
However, this alone cannot guarantee production of maximum power from the module.
The module must operate electrically at a particular voltage and current, Vm and Im respectively, which correspond to peak power point under a given irradiance and temperature conditions. Only then maximum power can be extracted from the PV cell.
When the module is operating at an point on the I-V curve, the voltage and current corresponding to the point is V and I respectively. The corresponding power will be
P = V*I

4. P+ ΔP = (V*I) + (ΔV*ΔI) + (ΔV*I) + (V*ΔI)
Introduction
If the operating point now moves to a new point due to different irradiance and temperature conditions, then the current changes by a small amount ΔI and voltage changes by ΔV. Thus, the new operating point will be V+ΔV and I+ΔI.
The corresponding power will be
P+ Δ P = (V+ΔV)*(I+ΔI)
P+ ΔP = (V*I) + (ΔV*ΔI) + (ΔV*I) + (V*ΔI)
Since ΔV and ΔI are small, (ΔV*ΔI) term can be neglected. Then, taking P = VI we get,
ΔP = (ΔV*I) + (V*ΔI)

5. Dynamic Impedance Zd = -Static Impedance Zs
Introduction
At maximum power point (MPP), there should not be any further change in power. That is,
ΔP = 0
Therefore,
ΔP = (ΔV* 𝐼 𝑚 ) + ( 𝑉 𝑚 *ΔI) = 0
(ΔV* 𝐼 𝑚 ) = _ ( 𝑉 𝑚 *ΔI)
Δ𝑉 Δ𝐼 =− 𝑉 𝑚 𝐼 𝑚
Generally, we can write
𝑑𝑉 𝑑𝐼 =− 𝑉 𝐼
The term dV/dI is called the dynamic impedance of the source and V/I is the static impedance. Thus, at MPP,
Dynamic Impedance Zd = -Static Impedance Zs

6. Electrical Methods For Maximum Power Point (MPP) Tracking
As per maximum power transfer theorem, to obtain maximum power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as seen from its output terminals.
Consider the case when a load is directly connected to the solar panel. Then the operating point of the panel will rarely be at the maximum power point.
The operating point of the panel is derived by the resistance seen by the panel. Thus if we vary the impedance seen by the panel, the operating point can be moved towards peak power point.
Since panels are DC devices, DC-to-DC converters must be utilized to equate the source impedance to the load impedance.
The impedance as seen by the panel can be varied by changing the duty ratio of the DC-to-DC converter. At a particular impedance (i.e., at a particular duty ratio of the DC-to-DC converter) the operating point will be at the maximum power transfer point.

7. Electrical Methods For Maximum Power Point (MPP) Tracking
Concept of Duty Ratio (δ)
A DC-to-DC converter has a controllable switch. The control signal to this switch (at ‘gate’ terminal) determines when the switch is conducting (or ON) and when it is blocking (or OFF) the current flowing through it. If the control signal is positive, the switch conducts and when the control signal is zero the switch does not conduct.
The duration for which the control signal is ON (switch conducting) is called the ON-time (ton) and the duration for which the control signal is OFF (switch blocking current) is called the OFF-time (toff).
The total switching time (T) is the sum of the ON- and OFF-times. The total time is the inverse of the frequency of the control signal.

8. Electrical Methods For Maximum Power Point (MPP) Tracking
(Control signal to the switch)
The ratio of the total ON-time to the total switching time is called the duty cycle or duty ratio of that switch used in the DC-to-DC converter.
𝜹= 𝒕 𝑶𝑵 𝑻

9. Electrical Methods For Maximum Power Point (MPP) Tracking
How does variation of duty ratio change the impedance? During one switching cycle (switch ON fro ton and OFF for toff once), the output of the converter depends on the duty ratio. For different DC-to-DC converter circuit topologies, the dependence is different. For example in a step-down (buck) converter the output voltage (V0) and input voltage (Vin) are related to duty cycle as V0 = δ*Vin. Thus, as the duty cycle increases (ton increases) the output voltage also increases. On the other hand for a step-up (boost) converter the output and input voltages are related as V0 = Vin/δ. Thus as the duty cycle increases the output voltage decreases. Such relations can be derived for other converter circuit topologies also. As the output voltage changes, the output current also correspondingly changes. Since voltage and current are changing, the resistance of the converter-load combination also virtually changes (R = V/I). Thus, by controlling the duty ratio, we can control the resistance seen by the panel and ensure MPP operation.

10. Maximum Power Point Tracking
A control circuit or logic should be designed in order to track the MPP. Such a system is called the maximum power point tracker (MPPT) and it allows the converter circuit to extract the maximum possible power from the cell.
The MPPT is designed to optimize the operating voltage of the PV system to maximize the current.
A maximum power point tracker is “a high-efficiency DC-to-DC converter that functions as an optimal electrical load for a solar panel or array and converts the power to a voltage or current level that is more suitable to load”.

11. Electrical MPP Tracking Methods
One should also note that the duty ratio of the converter cannot be fixed at a particular value. This is because the panel irradiation and temperature conditions are not constant and hence the output parameters of the panel vary continuously. Therefore, a system that adjusts the duty cycle of the DC-to-DC converter must be designed for tracking the peak power point.
There are four conventional methods of electrical MPP tracking. They are:
1. Fractional open-circuit voltage method
2. Fractional short-circuit current method
3. Perturb and Observe Method
4. Incremental Conductance Method

12. Fractional Open-Circuit Voltage (OCV) Method
In this method, a linear relationship between the open-circuit voltage (VOC) and voltage at maximum power point (Vm) is assumed under different environmental conditions.
The method can mathematically be described by the simple linear equation,
𝑉 𝑚 ≈𝑘 ∗ 𝑉 𝑂𝐶
where k is a constant
The value of k depends on the characteristics of the solar cell and is to be derived empirically. Generally, a value within the range of 0.73 and 0.8 can be considered for polycrystalline PV cells.
At each instant of time, the open-circuit voltage is determined and the MPP voltage is calculated based on the above mathematical model.
The value of MPP so determined is assumed to remain relatively constant for variable irradiation and temperature conditions.

13. Fractional Open-Circuit Voltage (OCV) Method
Advantages:
Implementation is very simple
Cost of implementation is less
Less computational load on the processor (digital implementation)
Limitations:
MPP may not be tracked accurately since the linear relationship assumption is not very correct.
Measurement of Voc requires keeping the panel in open circuit condition. i.e., shedding of the connected load. This leads to loss of power to the consumer.

14. Fractional Short-Circuit Current (SCC) Method
This method is relatively similar to the OCV method.
An approximate relationship is assumed between the short-circuit current of the PV panel (Isc) and the current at maximum power point (Im) and is modelled mathematically as,
𝐼 𝑚 ≈𝑘 ∗ 𝐼 𝑆𝐶
where k is a constant
The value of k depends on the characteristics of the solar cell and is to be derived empirically. Generally, a value within the range of 0.8 and 0.9 can be considered

15. Fractional Short-Circuit Current (SCC) Method
Advantages:
This method is more accurate and efficient than the OCV method
Less computational load on the processor (digital implementation)
Limitations:
To measure Isc, a separate boost converter must be used, where the switch in the converter itself can be used to apply short circuit to the PV array. However, this is not simple and involves increased cost.

16. Perturb & Observe (P&O) Method
P&O is one of the most commonly used algorithms for MPP tracking. In this algorithm, the reference voltage or current of the PV system is perturbed.
The goal of the method is to force the PV system to operate at Vmpp, which causes the PV voltage to track Vmpp at every instant. This is achieved by applying small and constant perturbations to the PV voltage.
After applying each perturbation, the variation in output power (dP) is measured. A positive dP indicates that output power will approach MPP. Therefore, a positive perturbation is applied to the voltage in the next step. On the other hand, if dP is negative, a negative perturbation is applied.
These steps are repeated until the MPP of the system is reached where dP is equal to zero.

17. Perturb & Observe (P&O) Method

18. Perturb & Observe (P&O) Method
Voltage perturbation
Power perturbation
Next voltage perturbation
dV>0
dP>0
Vnew = Vold + ΔV
dP<0
Vnew = Vold - ΔV
dV<0
Vnew = Vold – ΔV

19. Perturb & Observe (P&O) Method
Advantages:
Implementation of the algorithm is easy with processors (digital implementation using microcontrollers or DSP)
The MPP as determined by the algorithm is almost equal to the true MPP (theoretically calculated)
The speed of the MPP determination can easily be controlled by controlling the perturbation value.
Limitations:
Determination of the ideal perturbation value is difficult. One should carefully perform the trade-off between speed of algorithm and accuracy to determine the perturbation value. A very small perturbation value slows down the algorithm, while a large perturbation value leads to oscillations around the MPP.
When the irradiation and/or cell temperature vary, the error in P&O algorithm is more.

20. Incremental Conductance (Incond) Algorithm
This MPPT method is based on the principle that the slope of the P-V curve is positive when the actual power is less than MPP, is negative when the actual power is more than the MPP, and zero when the actual power is equal to the MPP.
In other words, this method uses the slope of the V-I curve of the system to track the MPP.
We have previously shown the following relationship,
Δ𝐼 Δ𝑉 = −𝐼 𝑉 at maximum power point
By evaluating the expression, the MPP can be tracked.
The term I/V is called the ‘conductance’ and hence the name of the method.

21. Incremental Conductance (Incond) Algorithm
The conditions to track MPP are as follows:
𝑑𝑃 𝑑𝑉 =0 → Δ𝐼 Δ𝑉 =− 𝐼 𝑉 𝑎𝑡 𝑀𝑃𝑃
𝑑𝑃 𝑑𝑉 >0 → Δ𝐼 Δ𝑉 >− 𝐼 𝑉 𝑙𝑒𝑓𝑡 𝑜𝑓 𝑀𝑃𝑃
𝑑𝑃 𝑑𝑉 <0 → Δ𝐼 Δ𝑉 <− 𝐼 𝑉 𝑎𝑡 𝑀𝑃𝑃
Advantages:
Better suited than P&O for changing environmental conditions
Limitations:
The ΔV can be used to speed up the MPP tracking, but a large value of ΔV will cause the system to oscillate around the MPP, which is not acceptable.
Implementation is complex

22. Incremental Conductance (Incond) Algorithm