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Abstract
Ageing inevitably leads to capacity degradation in a chiller plant. Hence in the life-cycle performance analysis of a chiller plant, ageing always represents a crucial consideration for designers. Ageing is normally quantified using maintenance factor. A conventional analysis recommends that the maintenance factor should be 0.01 for systems that undergo annual professional maintenance, and 0.02 for those that are seldom maintained. However, this recommendation is mainly based on a rule of thumb, and may not be accurate enough to describe the ageing for a given chiller plant. This research therefore proposes a method of identifying the chiller maintenance factor using a Bayesian Markov Chain Monte Carlo method, which can take account of the uncertainties that exist in the estimation of the ageing. Details of the identification will be provided by applying the proposed method to a real chiller plant, and results will be compared with that of the conventional analysis.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 124012).
Nomenclature
| Age | = | time that the chiller plant already served (year) |
| L | = | sample generated for ln R |
| = | sample generated at the (j − 1)th run | |
| Lj | = | sample generated at the jth run |
| = | candidate sample at the jth run | |
| L1 | = | initial sample generated for ln R |
| LD | = | actual peak cooling load (kW) |
| MF | = | maintenance factor |
| K | = | remaining service life (year) |
| Q | = | maximum cooling capacity supplied by the chiller plant (kW) |
| Qa,p | = | predicted maximum cooling capacity at the ath year (kW) |
| = | predicted maximum cooling capacity at the (a + 1)th year (kW) | |
| = | predicted maximum cooling capacity at the (a + K)th year (kW) | |
| Qdata | = | in-situ maximum cooling capacity data (kW) |
| Qi | = | individual in-situ maximum cooling capacity (kW) (i = 1,2, … N) |
| Qs | = | simulated maximum cooling capacity data (kW) (i = 1,2, … N) |
| Q0 | = | chiller plant maximum cooling capacity when it is newly installed (kW) |
| R | = | degradation remaining factor |
| R′ | = | calibrated degradation remaining factor |
| T | = | temperature (°C) |
| a | = | time of operation (year) |
| cp | = | specific heat capacity of the chilled water (kJ/(kg·°C)) |
| g | = | a constant |
| = | natural logarithm of degradation remaining factor | |
| = | calibrated natural logarithm of degradation remaining factor | |
| m | = | mean of R |
| = | mass flow rate (kg/s) | |
| n | = | standard deviation of R |
| nmcmc | = | number of required samples by the Markov Chain Monte Carlo method |
| ra | = | acceptance ratio |
| y | = | model output |
| Greek symbols | ||
| μ | = | mean of ln R |
| σ | = | standard deviation of ln R |
| θ | = | model inputs |
| κ | = | a constant which equals to 1/P (y) |
| ε | = | random variance term |
| δ | = | random number within the range [0, 1] |
| Φ | = | cumulative probability |
| γ | = | reliability indicator |
| = | reliability indicator at the (a + K)th year | |
| γlow | = | user-defined lower limit of reliability indicator |
| Subscripts | ||
| min | = | minimum value |
| max | = | maximum value |
| return | = | return side |
| set-point | = | set-point |
| supply | = | supply side |