This blog provides an introduction of the Spline-Based Table Look-up (SBTL) method as well as a sample use case from Ford Motor Company who utilized the SBTL refrigerant package to speed up their air conditioning system model simulations.

SBTL is a modeling method used for processing large simulations in less time without compromising accuracy.  As part of Modelon’s 2018.2 release of the Air Conditioning Library (ACL) and upcoming 2019.1 release of the Vapor Cycle Library (VCL), the SBTL method is integrated in each library to create new computationally efficient implementations of existing working fluids. This approach improves the tradeoff for air conditioning system model simplifications using ACL or VCL.

How SBTL works

The SBTL modeling method uses piece-wise quadratic splines on an equidistant grid to approximate refrigerant properties (denoted by ). The table lookup part of SBTL stems from the fact that using an equidistant grid enables a simple algorithm to retrieve spline coefficients from pre-generated tables, as shown in below equations where is the first knot. In Figure 1, nodes represent raw data points and knots are points where two adjacent splines meet with a continuous first-order derivative constraint.

Figure 1 – Illustration of the SBTL method. A black dot represents a knot, while nodes are represented by white dots.

SBTL Implementation in ACL and VCL 

Modelon has implemented R1234yf and R134a refrigerants using SBTL. The mediums are accessed from ACL and VCL in the exact same way as other two-phase medium implementations (e.g. drop-down list in Dymola). In order to reduce calculation time, C is used to implement evaluation, inversion, and differentiation of the quadratic splines. The used spline coefficients are derived a priori and afterward accessed from external data tables. However, the external C function calls do not impact the user-friendliness as the top level two-phase medium functions are all implemented in the Modelica languagethus wrapping the C functions and enabling easy access in simulation modelsFigure 2 shows the implementation of the SBTL method in ACL and VCL.  

Upon customer request, we can now add new SBTL media for any pure fluid that is available in REFPROP in a short amount of time. It is faster to add new medium using the SBTL implementation than the equivalent Helmholtz model. 

Figure 2 – SBTL implementation used in Modelon’s air conditioning and vapor cycle libraries. Coefficient data for the piece-wise splines is only generated once.

In Figure 3, the high accuracy of SBTL is exemplified for the R134a refrigerant with respect to density calculations. The comparison is done with the solution to the original Helmholtz equation. The only case when the error is larger than 2 % is inside the two-phase region, close to the critical point. Outside of this region, the error is well below 0.5 %.  

Figure 3 –Density deviation in % between reference R134a Helmholtz implementation and the SBTL version.

Meanwhile, a substantial improvement in computation time is obtained with SBTL while maintaining high accuracy, as indicated by the results in Table 1. 

Table 1 – Comparison of individual function calls between Helmhotz and SBTL implementations.

Table 1 – Comparison of individual function calls between Helmhotz and SBTL implementations.


Ford Motor Company worked with Modelon to try the new SBTL refrigerant package in efforts to speed up the AC system model simulations (read the full paper here). It is common to use the SC03 Supplemental Federal Test Procedure to represent emissions and engine load associated with air-conditioning systems in FTP-75 cycle certified vehicles. The system simulation model is described in Figure 4. The 1st evaporator, 2nd evaporator, and chiller are modeled using both SBTL and Helmholtz based implementations of R1234yf for simulation performance comparison.

Figure 4 – Model of an AC system with two evaporators and one chiller connected in parallel in the loop. The used R1234yf refrigerant was modeled with both Helmholtz equations and SBTL to compare the performance.

The calculation performance for the different subsystems is compared with respect to R1234yf implementation in Figs 5-6. It can be concluded that using the SBTL refrigerant model it is possible to simulate the complete SC03 cycle faster than the real total cycle time (598 s) while keeping the same numerical performance as the Helmholtz based model.

Figure 5 – Cooling power of the evaporators and the chiller (see Figure 3) using Helmholtz property model and SBTL model.
Figure 6 – CPU time comparison of the AC system model with shown in Figure 4. The AC system using the Helmholtz property model is 2.7 times slower than the AC system using the corresponding SBTL model.

More in-depth information on what SBTL refrigerants in ACL and VCL has to offer can be found in [1]. If you are curious what Modelon can contribute to your business when it comes to accurate and fast system model simulations, contact us below.

[1]: Fast Calculation of Refrigerant Properties in Vapor Compression Cycles Using Spline-Based Table Look-Up Method (SBTL)”, Lixiang Li et al., Proceedings of the 1st American Modelica Conference, 2018,