Active substring
Bypassed (shaded)
Obstruction & shadow
This 2D companion to the tilted-panel irradiance simulator turns to a question the original doesn't cover: what a single nearby obstruction does to a real, series-wired string. A top-down plan view tracks a pole or chimney's shadow as it sweeps across a six-substring array through the day, and a live bar chart shows the bypass-diode cliff — one shaded cell can collapse an entire substring's output, so actual losses run far ahead of the shaded ground area alone.
Move a pole, chimney or tree around a six-substring photovoltaic row and watch how its shadow interacts with the array's internal wiring. Each substring is protected by its own bypass diode, exactly like a real module's junction box: the moment a shadow's edge touches a substring, the cells inside it can no longer pass the same current as their unshaded neighbours, the diode conducts, and that substring's output collapses toward zero instead of shrinking gently with the shaded area.
The plan view shows the obstruction's ground-plane shadow sweeping across the row as the sun's altitude and azimuth change with latitude, day of year and hour, computed from the standard declination and hour-angle equations. The bar chart tracks each substring's instantaneous power, and the readouts compare a naive area-based loss estimate against the array's real output loss — the gap between the two is the extra "mismatch" cost that partial shading imposes on a series-wired string.
Why does a small shadow cause a large power loss?
Cells within a substring are wired in series, so the whole substring's current is limited by its darkest cell. Once the shading exceeds a small threshold, the substring's bypass diode starts conducting to protect it from reverse-bias heating, and the substring effectively drops out of the circuit — a sliver of shadow can cost an entire substring's worth of power.
What is a bypass diode?
It is a diode wired in parallel with a substring of cells, oriented so it stays off under normal sunlight. When that substring's current is choked by shading, the diode turns on and routes the rest of the string's current around it, protecting the shaded cells and letting the unshaded substrings keep producing power.
How is the obstruction's shadow computed?
The shadow length is the obstruction's height divided by the tangent of the sun's altitude, and it points directly away from the sun's azimuth. The simulator finds where that shadow line crosses the array's ground line and marks any substring the shadow overlaps as shaded.
What is the difference between naive loss and actual mismatch loss?
Naive loss assumes power drops in direct proportion to the shaded ground area. Actual mismatch loss is the real drop in array output once bypass-diode behaviour is included. Because a shaded substring contributes almost nothing rather than a proportionally reduced amount, actual loss is almost always larger than the naive estimate.
Near solar noon at low-to-mid latitudes in summer the sun is high overhead, so shadows are short and may not reach a row several metres away. Near sunrise, sunset or in winter the sun sits low on the horizon, shadows stretch out, and the same obstruction can shade the array for a large part of the day.
Splitting the row into more, narrower substrings (more bypass diodes) shrinks how much of the array each diode protects, so a given shadow disables a smaller slice of total power — at the cost of more wiring. This simulator fixes the row at six substrings to keep the trade-off visible without adding another control.
Here tilt only scales the irradiance each unshaded substring receives through the angle-of-incidence term, not the ground footprint of the shadow — the shadow calculation treats the array as flat ground plan for simplicity. A full 3D shadow-on-a-tilted-plane projection is a natural next step but was kept out to isolate the mismatch effect being demonstrated.
It captures the qualitative and roughly quantitative behaviour of near-shading and bypass-diode mismatch under clear-sky, direct-beam conditions, but it ignores diffuse sky light, row-to-row self-shading, soiling and real module datasheet curves. Treat it as an intuition-builder, not a substitute for a professional shading and yield study.