---
title: Pump Curve Non-Convexity
created: 2026-04-07
updated: 2026-04-07
status: proven
tags: [curves, interpolation, C5, non-convex]
sources: [nodes/generalFunctions/datasets/assetData/curves/hidrostal-C5-D03R-SHN1.json]
---

# Pump Curve Non-Convexity from Sparse Data

## Finding
The C5-D03R-SHN1 pump's power curve is non-convex after spline interpolation. The marginal cost (dP/dQ) shows a spike-then-valley pattern:

```
C5 dP/dQ across flow range @ ΔP=2000 mbar:
  6.4 m3/h → 1,316,610  (high)
 10.2 m3/h → 2,199,349  (spikes UP)
 17.7 m3/h → 1,114,700  (dropping)
 21.5 m3/h →   453,316  (valley — cheapest)
 29.0 m3/h → 1,048,375  (rising again)
 44.1 m3/h → 1,107,708  (high)
```

## Root Cause
The C5 curve has only **5 raw data points** per pressure level. The monotonic cubic spline (Fritsch-Carlson) creates a smooth curve through all 5 points, but with such sparse data it introduces non-convex regions that don't match the physical convexity of a real pump.

## Impact
- The equal-marginal-cost theorem (KKT conditions) does not apply — it requires convexity
- The BEP-Gravitation slope estimate at a single point can be misleading in non-convex regions
- The marginal-cost refinement loop fixes this by using actual power evaluations instead of slope assumptions

## Recommendation
Add more data points (15-20 per pressure level) to the C5 curve. This would make the spline track the real convex physics more closely, eliminating the non-convex artifacts.