smoothTable

Quadratic in the condenser temperature through the rows at 35, 45 and 55 degC, linear between the source columns with the kinks smoothed over dTSou: a differentiable version of the table

FastSmoothBuildings.Hydronics.HeatPumps.Vitocal251A08.smoothTable, function (source)

Purpose

Heating capacity (heating = true) or electrical power of the Vitocal 251-A08 at a condenser outlet temperature and a source temperature: a version of the table with continuous derivatives, for the equations of HeatPump.

Equations

In the condenser outlet temperature T_c, a quadratic through the first three rows of the table, at T_C,1, T_C,2, T_C,3 = 35, 45 and 55 °C, with the Lagrange basis

L_k(T_c) = ∏_{m ≠ k} (T_c − T_C,m) / (T_C,k − T_C,m),   v_j = ∑_k=1..3 L_k Y_k,j

at each source temperature T_S,j of the table, Y being QHea or PEle. In the source temperature T_s, the piecewise linear interpolation of the v_j, written as the first segment plus the change of slope at each inner breakpoint, each kink smoothed by positivePart over δ = dTSou:

y = v₁ + s₁ (T_s − T_S,1) + ∑_j=2..8 (s_j − s_j−1) positivePart(T_s − T_S,j, δ),   s_j = (v_j+1 − v_j) / (T_S,j+1 − T_S,j).

Accuracy

• At 35, 45 and 55 °C the quadratic passes through the rows of the table; the rows at 65 and 70 °C are not used, and above 55 °C the quadratic extrapolates.
• At a distance x from a breakpoint of the source temperature, the value differs from the linear interpolation by (√(x² + δ²) − |x|)/2 times the change of slope there: δ/2 at the breakpoint, about δ²/(4 |x|) away from it.
• Below the first and above the last source temperature of the table, the value follows the first and the last segment: it extrapolates linearly, where interpolate holds the edge value.

Revisions

• October 2026: moved from trano's FastModel.Hydronics.HeatPumps.Vitocal251A08.