ELEC5206 Chap.9 Maximum Power Point Tracking
Maximum Power Point Tracking
Maximum power point tracking keeps a PV system at the peak of its power curve as the weather changes. The lecture frames it as load matching: only one load resistance extracts maximum power, and a converter presents a variable virtual resistance set by its conversion ratio.
Hill climbing, also called perturb and observe, searches blindly by stepping the reference and keeping or reversing direction depending on whether power rose; it is simple but oscillates around the MPP. Incremental conductance uses the slope condition dP/dV = 0 with two successive samples, yet its truncation error still causes oscillation.
The design numbers are the perturbation rate, set by the settling time of the PV link, and the perturbation size, set by ripple, noise and the weather. Lab 4 implements a current-sensor-free version on a microcontroller.
A worked trace follows hill climbing on a 72-cell module from 43 V down to its three-level oscillation about 37 V, and a ripple table shows why switching ripple at the PV terminals costs power roughly with the square of its size.
What this chapter covers
- 01
Short-term steady state and the maximum power point
- 02
Load matching and the MPP resistance
- 03
The converter as a virtual resistance
- 04
Hill climbing on the power-voltage and power-duty curves
- 05
Incremental conductance and the slope condition
- 06
Truncation error and residual oscillation
- 07
Perturbation rate from the settling time
- 08
Perturbation size, ripple, noise and weather
Worked example · free
Choosing a boost duty ratio to match a resistive load
- 1RMPP = 37.0/7.79 = 4.75 Ω.
- 1For a boost, R = (1 − D)²RL, so (1 − D)² = 4.75/20 = 0.2375, 1 − D = 0.487 and D = 0.513.
- 1Check: vo = 37.0/0.487 = 75.9 V and P = 75.9²/20 = 288 W, the module’s MPP power.
Key terms
- Virtual resistance
- The resistance a converter presents at the PV terminals, R = (vpv/vo)²RL for a loss-free converter.
- Perturb and observe
- Another name for hill climbing: step the reference, observe the power change, and keep or reverse the step.
- Incremental conductance
- An MPPT method that compares ΔI/ΔV with −I/V to locate the zero of dP/dV.
- Perturbation size
- The step applied to the reference in each MPPT cycle, trading steady-state accuracy against tracking speed.
- Short-term steady state
- A period of steady irradiance and temperature in which the PV curve and its MPP are fixed.
Maximum Power Point Tracking FAQ
Why does hill climbing oscillate even in steady sunshine?
It only learns that it has passed the peak by observing a drop in power, so it must keep stepping. At steady state it cycles among the voltage levels around the MPP, three levels in the lecture's illustration, and the size of that oscillation is set by the perturbation step.
Does incremental conductance remove the steady-state oscillation?
In principle it stops when the incremental and instantaneous conductances balance, but the backward-Euler estimate of the derivative carries a truncation error of order ΔV². The exact condition is rarely met, so in practice it oscillates much like hill climbing.
How fast should the tracker perturb?
No faster than the PV link settles after each step. The lecture's buck plant needs 9.6 ms without a voltage loop and 1.7 ms with one, so the chosen 200 Hz rate, 5 ms per step, is valid only with the dedicated voltage loop in place.
Why can the lab tracker work without a current sensor?
With a resistive load, output power equals the output voltage squared over the load resistance, so maximising output voltage maximises power. The lab's version therefore compares only successive output-voltage readings. The shortcut holds only for a resistive load and a single-peak PV curve.
Exam move
Practise one hill-climbing trace on a P-V table you compute yourself, writing keep or reverse at every step, and one incremental-conductance decision from two samples. Memorise the virtual-resistance relation and its buck and boost forms. Then rehearse the two tuning arguments, rate from settling time and size from ripple and weather, because exam questions often ask you to justify a chosen value.
Link the chapter to Lab 4’s output-voltage-only tracker. Practise explaining which reference, voltage or duty, the tracker should perturb, and why.
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