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Abstract
The market for variable-speed ductless heat pump (DHP) systems has grown in North America in recent years. However, the tools available for modeling their performance within building simulation programs have not kept pace. In general, simple empirical models are typically used for characterizing equipment performance for use in system simulation. However, unlike more conventional single-speed systems, DHPs have complicated control algorithms for managing electronic expansion valve opening, compressor speed, fan speed, and defrost operation. Very little work has been done in the development of empirical models that explain the impact of these characteristics on the performance of DHP systems. In this article, an empirical approach is introduced to model the heating and defrost performance of DHP systems under a wide range of conditions. The model incorporates separate relationships for performance associated with maximum, minimum, and intermediate (part-load) heating capacities. The defrost operation of the systems is also modeled empirically. The approach was tested on data from two DHP systems and the agreement is very good. The performance of the systems under different building loads was simulated and it is shown that the performance is highly dependent on the system control characteristics.
Nomenclature
| C | = | empirical coefficients, varies |
| COP | = | coefficient of performance |
| DHP | = | ductless heat pump |
| f | = | adjustment factor |
| J | = | objective function, W2 |
| n | = | number of measurements to calculate the average value of x |
| Nx | = | number of x variables that y depends on |
| q | = | dimensionless heat transfer rate |
| = | heating capacity, W | |
| T | = | Temperature, K |
| t | = | time, s or t-statistics |
| = | volumetric air flow, m3/s | |
| v | = | dimensionless airflow |
| = | power consumption, W | |
| w | = | dimensionless power consumption |
| x | = | experimental observation |
| y | = | calculated value determined from the experimental observations of x |
Greek
| α(x) | = | uncertainty of x |
| ρ | = | density, kg/m3 |
| σ(x) | = | sample standard deviation of observation x within the period of data acquisition |
Subscripts
| a | = | air |
| amb | = | ambient |
| cond | = | condenser |
| de | = | defrost cycle |
| end | = | end of defrost cycle |
| high | = | high changeover temperature |
| in | = | indoor unit |
| ind | = | individual observation |
| inlet | = | inlet |
| low | = | low changeover temperature |
| max | = | maximum |
| min | = | minimum |
| nozzle | = | nozzle |
| out | = | outlet |
| outdoor | = | outdoor unit |
| p | = | part-load model |
| Q | = | heating capacity |
| rated | = | rated condition in |
| start | = | beginning of defrost cycle |
| t | = | time ratio |
| W | = | power consumption |
Acknowledgment
The authors would like to acknowledge Ecotope Inc., in particular Ben Larson, in supporting the testing of the ductless heat pump systems. The authors would also like to acknowledge Simbarashe Nyika for his help in the preparation and testing of the experimental setups.