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Fibonacci search method pSP + − PI Kv 0 200 0 200 0 200 400 600 400 600 400 600 800 1000 1200 800 1000 1200 800 1000 1200 Time t (s) 1400 1600 1400 1600 1400 1600 1800 2000 1800 2000 1800 2000 COP Vehicle model (including heat pump) θ 4 3.5 3 2.5 2 1.5 140 120 100 80 60 50 40 30 θSP + 4 p p cd PIθ Fig. 6. R744 heat pump control loop. − 3.5 3 2.5 2 1.5 140 120 100 80 60 50 40 30 20 0 200 400 600 0 200 400 600 0 200 400 600 800 1000 1200 800 1000 1200 800 1000 1200 Time t (s) 1400 1600 1800 2000 1400 1600 1800 2000 1400 1600 1800 2000 Fig. 9. Cooling vehicle cabin (with fresh air from outside) and ambient temperature change. but at the time of 1000s a change of ambient temperature occurred. The temperature fell from 40 ◦C to 30 ◦C during a 30s ramp. After that change the optimal high-side pressure was considerably different, so a new run of Fibonacci search method was started at the time of 1200 s. After approximately 200 s a new high-side pressure setpoint (96.2 bar) was found, what is quite far from the previous optimal pressure setpoint (109.5 bar), with a COP improvement of 0.22. V. CONCLUSION In this paper we proposed a novel method of R744 heat pump high-side pressure determination using Fibonacci opti- mum seeking method. This method operates in real-time, what brings significant advantages over the offline methods (which use tables or some static equations). Firstly, the method is resistant against parameter changes and disturbances, which can often occur. Secondly, no pre-measured data or expres- sions, both describing relationship between heat pump cycle variables and optimal high side pressure, are necessary for the method operation (compared to offline methods, which usually need some). The main drawback of the method is the fact that it can not be used during fast transients. The FOS method of optimal high-side pressure searching was verified using simulations in Matlab Simulink and em- ploying heat pump model, which was constructed with the use of Modelica language. We presented three examples of optimal high-side pressure searching. All of them demonstrated the method suitability for this purpose, the COP maximum was found during quite short time and with minimum changes of control input (EXV opening degree). This makes our method preferable against ex- tremum seeking methods with continuous perturbation, where the lifetime of the EXV can be shortened due to frequent changes (valve hunting). Future work will focus on method verification during heat pump real operation. It might require combining FOS method Fig. 7. Vehicle cabin cool down and COP maximum searching (recirculated air). 4 3.5 3 2.5 2 1.5 140 120 100 80 60 50 40 30 0 200 0 200 0 200 400 600 400 600 400 600 800 1000 1200 800 1000 1200 800 1000 1200 Time t (s) 1400 1600 1400 1600 1400 1600 1800 2000 1800 2000 1800 2000 Fig. 8. Cooling vehicle cabin (with fresh air from outside). was sucked into the cabin). The result is shown in Fig. 8. The last simulation was almost the same as the second, Temperature High-side Temperature High-side (àC) pressure p (bar) COP (-) (àC) pressure p (bar) COP (-) High-side (àC) pressure p (bar) COP (-) TemperaturePDF Image | high-side pressure of R744 automotive heat pump using Fibonacci search
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