Solar PV Dynamic Characterization, Global MPPT & Boost Stage Solver

Multi-physics Python package (pv-mppt-solver), command-line suite (pv-mppt). And Live Interactive GitHub Pages Workbench coupling CEC/pvlib-verified Single-Diode PV Physics, Schottky Bypass-Diode Partial Shading. Global MPPT (PSO & Hybrid Global-Scan + Adaptive INC), CENELEC EN 50530 Dynamic Irradiance Ramps with Coupled Electro-Thermal Cell ODE & Sera dP-P&O. And a State-Space Averaged DC-DC Boost Power Stage with 2-Loop Cascaded Current-Mode PI Control.

Subsystem Verification Summary

Subsystem	Module	Key Verified Metric
Single-Diode CEC Extraction	src/pv_model.py	300.1152 W STC (< 1e-8 A vs. pvlib Lambert-W across -10..75 °C)
Schottky Bypass Partial Shading	src/partial_shading.py	Exact KVL multi-peak staircases (148.16 W @ 22.28 V, 3 peaks under 1000/700/350 W/m²)
Global MPPT (PSO & Hybrid INC)	src/global_mppt.py	92.47% Hybrid dynamic / 99.57% PSO settled vs. 80.60% conventional LMPP trap
CENELEC EN 50530 & Thermal ODE	src/en50530_benchmark.py	99.94% Sera dP-P&O (0.25 V RMS error) vs. 87.18% Standard P&O ramp drift
State-Space Boost & Cascaded PI	src/dynamic_boost.py	η_Euro = 97.67% (60 V LVDC), 69.5 mV RMS voltage-servo tracking error
CLI & Interactive Web Explorer	src/cli.py, src/web_dashboard.py	pv-mppt (info, iv, shading, en50530, boost, benchmark, web) + real-time browser lab

Mathematical System Formulation

1. Single-Diode Cell Equation

I = I_ph - I_0 [ exp( (V + I R_s)/(n N_s k T / q) ) - 1 ] - (V + I R_s)/(R_sh(G))

solved for I at every grid voltage with a vectorized, monotone-convergent Newton iteration (bisection fallback).

2. Self-Consistent Reference-Parameter Extraction

The diode parameters (I_(ph,ref), I_(0,ref), n) are not hand-picked. At construction time the solver exactly satisfies the three STC datasheet constraints

I(V=0) = I_sc, I(V=V_oc) = 0, I(V=V_mp) = I_mp

For fixed n, the first two constraints are linear in (I_(ph,ref), I_(0,ref)); the third is a scalar root-find in n (bracketed bisection). If the datasheet values are inconsistent with the single-diode model for any physical ideality factor (0.5 ≤n ≤2.5), the constructor raises ValueError rather than silently under-predicting STC power.

3. Temperature / Irradiance Scaling (De Soto / CEC convention)

I_ph(G,T) = (I_(ph,ref) + K_i (T - T_ref))G/G_ref, 
I_0(T) = I_(0,ref)(T/T_ref)^3 exp((E_(g,ref))/(k_eV T_ref) - (E_g(T))/(k_eV T))

E_g(T) = 1.121eV·(1 - 2.677×10^(-4)(T - T_ref)), 
R_sh(G) = R_(sh,ref)G_ref/G

4. Boost Converter Duty Cycle Translation

To match the dynamic PV array MPPT voltage V(mpp) to a fixed DC link voltage V(out):

D = 1 - V_mpp/V_out

5. Series-String Bypass-Diode Partial Shading

For a series string of M = N(mod) ×N(bp) cell substrings under non-uniform irradiance G(m) and cell temperature T(m). Kirchhoff's Voltage Law gives V(string)(I) = Σ_(m=1)^M V(m)(I), where each substring is protected by an anti-parallel Schottky bypass diode conducting in reverse bias (V(m) < 0):

I_(sub,m)(V_m) = I_(cell,m)(V_m) + I_(0,bp)[exp(-V_m / V_(t,bp)) - 1], for V_m < 0;
0, for V_m ≥0

6. Global MPPT Under Multi-Peak Partial Shading

Conventional hill-climbing trackers (PerturbAndObserve, IncrementalConductance) follow local dP/dV sign and become trapped in high-voltage local maxima (LMPPs). src/global_mppt.py provides two Global MPPT (GMPPT) engines with zero steady-state oscillation lock and bypassed-plateau cloud-clearance watchdog probing:

• ParticleSwarmMPPT: Stratified N(p)-particle voltage swarm with annealed inertia w(k): w(max) →w(min), velocity clamping, convergence lock, and event-triggered re-dispersion.
• HybridGlobalScanINC: Fast coarse global voltage sweep across [V(min), V(max)] followed by Variable-Step Adaptive Incremental Conductance (ΔV(k) = clip(α |dP/dV|, ΔV(min), ΔV(max))).

7. CENELEC EN 50530 Dynamic Ramp Standard & Coupled Electro-Thermal Cell Transient

src/en50530_benchmark.py evaluates dynamic MPPT efficiency η_(MPPT,dyn) = ∫_0^T P(DC)(t)dt / ∫_0^T P(MPP)(G(t). T(c)(t))dt across standardized trapezoidal irradiance ramps (100--500W/m^2 and 300--1000W/m^2) coupled with a first-order lumped module energy-balance ODE:

C_th dT_c/dt = α_abs G(t) - P_elec(t)/A_mod - U_th(T_c(t) - T_amb)

Includes Sera's irradiance-compensated DeltaPPO (dP-P&O) controller, eliminating ramp-induced voltage drift (99.94% EN 50530 efficiency vs. 87.18% for standard P&O).

8. State-Space Averaged Boost Power Stage, Cascaded Current-Mode PI Control & Loss Map

src/dynamic_boost.py upgrades the steady-state duty translator to a coupled 2nd-order [v_pv, i_L] non-ideal boost stage integrated via 4th-order Runge-Kutta with discontinuous-conduction diode blocking (i_L >= 0):

C_in dv_pv/dt = i_pv(v_pv, G, T_c) - i_L, L di_L/dt = v_pv - R_eq(D) i_L - (1 - D)(V_bus + V_fd)

• CascadedBoostPIController: Decouples the lightly damped input L--C(in) tank into an outer PV-voltage PI loop commanding i_(L,ref) (with i(pv) feedforward) and an inner average-current-mode PI loop commanding PWM duty D (69.5 mV RMS voltage-servo error across 1000 -> 550 -> 900 W/m² irradiance steps).
• BoostLossBreakdown & Weighted Efficiencies: Resolves inductor winding copper (I(rms)^2 R(L)), MOSFET conduction (D I(rms)^2 R_(ds(on))), switching + C(oss) + reverse-recovery Q(rr).
• Freewheeling diode conduction, and magnetic core ripple losses, alongside European (η(Euro) = 97.67%) and California CEC (η(CEC) = 97.66%) weighted ratings at V(bus) = 60V.

Reference Module & Data Provenance

Default constructor parameters are the STC datasheet values of the AU Optronics PM060MBR_300W monocrystalline 60-cell module, taken verbatim from the NREL SAM / CEC module database. Record version "SAM 2018.11.11 r2" (dated 2019-01-03), as bundled with pvlib 0.16.1 (sam-library-cec-modules-2019-03-05.csv, SHA-256 a7c3b1ad3dabb5425368615c16322f2e35185fc416380b471c4e48dd545b1920).

Quantity	Value	Source
I_sc_ref	9.91 A	record datasheet value (model input)
V_oc_ref	40.45 V	record datasheet value (model input)
I_mp_ref	9.24 A	record datasheet value (model input)
V_mp_ref	32.48 V	record datasheet value (model input)
R_s	0.358977 Ω	record CEC fit (model input)
R_sh_ref	171.705124 Ω	record CEC fit (model input)
alpha_sc	0.004162 A/K	record (model input, K_i)
STC	300.1152 W	record rating, verification target only
a_ref	1.550532 V	record CEC fit, verification target only
I_L_ref / I_o_ref	9.930718 A / 4.536912e-11 A	record CEC fit, verification targets only

Independent verification (see tests/test_reference_cec.py and tests/test_pvlib_crosscheck.py):

• Extraction from the datasheet values alone reproduces the record's own CEC-fitted diode parameters: a = 1.55053183 V vs a_ref = 1.550532, I_ph_ref = 9.93071844 A vs I_L_ref = 9.930718, I_o_ref = 4.5369e-11 A vs 4.536912e-11.
• Model STC maximum power = 300.1152 W, matching the record's STC field and pvlib's own singlediode result (300.1151 W) to solver precision.
• Full I-V curves agree with pvlib's Lambert-W evaluation (i_from_v) to < 1e-8 A across 9 (G, T) conditions from −10 °C to 75 °C and 50–1100 W/m².
• Implied temperature coefficients are physical and close to the record's: β_voc ≈ −0.125 V/K (record −0.114069), γ_p ≈ −0.391 %/K (record −0.386).

Provenance disclaimer. The identity of the module that the original hard-coded defaults (I(sc)=9.35, V(oc)=38.2, I(mp)=8.80, V(mp)=34.1, R(s)=0.221, R(sh)=415.6, n=1.3) were meant to represent could not be established: no CEC/SAM record matches them, and they are mutually inconsistent with the single-diode model, reproducing their nameplate 300.08 W would require a non-physical ideality factor (n ≈ 0.47). The old implementation silently ignored I(mp)/V(mp) and produced 266.898 W at STC. The constructor now rejects such inconsistent sets with a ValueError (regression-tested). The AU Optronics record above is a pinned, traceable replacement reference, not a claim that it was the original panel.

Validity Envelope

• Irradiance: finite, real, G >= 0 W/m² (G < 0 raises ValueError; G = 0 returns zero generation on a well-formed grid).
• Cell temperature: finite, real, −40 °C ≤ T ≤ +85 °C (standard c-Si module operating envelope).
• All outputs are real, finite float64; current is reported in the generating quadrant (clamped at 0 beyond V(oc)).
• Known simplifications vs.
• SAM/pvlib: CEC Adjust factor taken as 0; R_s temperature independent; ideality factor constant with temperature.
• The model is an engineering-grade single-diode solver, not a manufacturer-level performance prediction tool.

Installation & Engineering CLI (pv-mppt)

python3 -m venv .venv
source .venv/bin/activate # Windows: .venv\Scripts\activate
python -m pip install --upgrade pip setuptools wheel
pip install -r requirements.txt -r requirements-dev.txt
pip install --no-build-isolation -e .

# optional: independent pvlib 0.16.1 CEC cross-validation (Python >= 3.11)
pip install -r requirements-validation.txt

# Inspect CEC reference module & single-diode extraction
pv-mppt info

# Solve operating point, partial shading, EN 50530 ramps & boost stage (ASCII or --json)
pv-mppt iv --irradiance 850 --temp 40 pv-mppt shading --irradiances 1000 700 350 --run-gmppt pv-mppt en50530 --json pv-mppt boost --v-bus 60 --stages 1000:45 550:45 900:45

# Run full test suite & regenerate all 7 publication figures
python -m pytest pv-mppt benchmark --output-dir results pv-mppt web --output-dir site # build interactive HTML5/Canvas workbench

Simulation Artifacts & Dynamic Results

STC PV Characteristic Curves

Dynamic MPPT Step Response

Thermal Power Derating

Bypass-Diode Partial-Shading & Multi-Peak P-V Curves

Global MPPT (PSO & Hybrid Scan + Adaptive INC) vs. Local-Trap Conventional MPPT

CENELEC EN 50530 Dynamic Irradiance Ramps & Coupled Electro-Thermal Cell Transient

State-Space Averaged Boost Stage, Cascaded PI Servo & Loss Breakdown

Testing & CI

• pytest suite (230 tests) covers the STC reference point.
• The historical 300.08 W / 266.898 W defect, invalid-input rejection (negative/NaN/complex irradiance, out-of-envelope temperature), zero & low irradiance.
• Thermal derating, MPPT convergence/steady-state stability/dynamic step response/voltage bounds, boost-converter math & clamping, and the pinned CEC reference data.
• pvlib cross-checks (tests/test_pvlib_crosscheck.py) run automatically when pvlib is installed and skip otherwise.
• The core suite is hermetic and needs no network access.
• GitHub Actions (.github/workflows/ci.yml) installs pv-mppt-solver in editable mode and runs ruff, pytest, pv-mppt CLI smoke tests.
• And main.py across Python 3.10–3.13 (pvlib cross-checks on 3.11/3.12).

Citation

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