Dashboard › Deep Learning › Power Systems Analysis › Power electronics & renewables › Photovoltaic I-V curves and MPPT

Photovoltaic I-V curves and MPPT

PV cell I-V shape, MPP location, irradiance + temperature effects, and Perturb-and-Observe / Incremental-Conductance MPPT algorithms.

Sophomore ~11 min

Step 1 — PV cell: light-driven current source in parallel with a diode

0.55×
P_mpp — W V_mpp — V FF —

Reference notes

Use Next → on the narrator above to walk through PV cell I-V behaviour and maximum power point tracking — the front-end algorithm of every PV inverter.

The single-diode model

Electrically a PV cell is a light-driven current source I_ph in parallel with a forward-biased diode. The classical single-diode equation:

I = I_ph − I_0 · ( exp(V / (n · V_T)) − 1 )

where I_ph is the photo-current (proportional to irradiance G), I_0 is the diode saturation current, n is the ideality factor (1–2), V_T = k T / q ≈ 25.7 mV at 25 °C is the thermal voltage. Real cells include series resistance R_s and shunt resistance R_sh; for hand calculations the two-resistor "five-parameter" model is standard.

Three key points on the I-V curve

Fill factor

FF = P_mpp / (V_oc · I_sc)

FF measures the "squareness" of the I-V curve — how close the actual MPP is to the V_oc·I_sc rectangle. Typical values:

Environmental effects

Irradiance G (W/m²)

I_sc ∝ G (linear). V_oc has weak logarithmic dependence (V_oc varies by ~0.05 V per decade of G change). Net result: P_mpp ≈ linear in G. STC (standard test conditions): G = 1000 W/m², AM 1.5 spectrum, cell T = 25 °C.

Cell temperature T

V_oc(T) ≈ V_oc(25°C) + kV · (T − 25)

For crystalline silicon: k_V ≈ −0.32 %/°C (≈ −2.3 mV/°C per cell). I_sc has a small positive coefficient k_I ≈ +0.05 %/°C. Net P_mpp coefficient: −0.4 to −0.5 %/°C.

Real cell temperature is usually 20–35 °C above ambient at full sun (NOCT or "nominal operating cell temperature" rating). A 300 Wp module at 65 °C cell temp and 850 W/m² delivers roughly 240 W — about 80 % of nameplate.

Maximum Power Point Tracking (MPPT)

An MPPT is a DC-DC converter (usually a boost or buck-boost topology) with a control loop that continuously adjusts the PV operating voltage to the MPP. Two classical algorithms:

Perturb & Observe (P&O)

  1. Perturb V_op by +ΔV.
  2. Measure ΔP = P_new − P_old.
  3. If ΔP > 0, continue same direction next cycle. If ΔP < 0, reverse direction.

Simple, robust, dominant in residential inverters. Always oscillates around MPP with amplitude ±ΔV. Drawback: can momentarily walk the wrong way under rapidly-changing irradiance (passing clouds).

Incremental Conductance (IncCond)

At the MPP, dP/dV = 0, which expanded gives:

dI/dV = −I/V (at MPP)

The controller measures incremental conductance dI/dV and instantaneous conductance I/V at each step. If dI/dV > −I/V → left of MPP, increase V. If < −I/V → right of MPP, decrease V. If equal → at MPP, hold. Stops cleanly at MPP without oscillation; better dynamic response. Standard on utility-scale inverters.

Partial shading and bypass diodes

If part of a module is shaded, the shaded cell becomes a high-impedance current sink (reverse-biased by neighbouring lit cells), dissipating heat and risking a "hot spot." Every module includes bypass diodes (typically 3 per 60-cell module, one per 20-cell substring) that conduct around a shaded substring. The trade-off: bypass diodes cause the P-V curve to develop multiple local maxima under partial shading, which can fool a P&O MPPT into a local optimum below P_mpp. Modern inverters add a periodic "global MPPT scan" that sweeps V_op across the full V_oc range to find the global maximum.

Quick design check — string sizing

To match an MPPT's input voltage window, designers compute:

The number of modules in series falls out of those two inequalities.

Take-away. PV cell ≈ current source ‖ diode. Three key points on the I-V curve: I_sc (∝ G), V_oc (drops with T at −0.32 %/°C), and MPP at V_mpp ≈ 0.78·V_oc, I_mpp ≈ 0.95·I_sc. Fill factor 0.75–0.82 for c-Si. MPPT algorithms: P&O (simple, oscillating) and IncCond (uses dI/dV = −I/V at MPP, cleaner). Partial shading creates multiple P-V peaks → global MPPT scan needed periodically.

Keyboard shortcuts