# Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes

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## Abstract

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## 1. Introduction

_{0}to the ranges of changeable (1 − LL) q

_{0}, and unchangeable LL q

_{0}loads, and is calculated as the ratio of unchangeable load LL q

_{0}to the total load q

_{0}.

_{0}while correspondingly growing the range of unchangeable load LL q

_{0}.

- -
- Determine the ranges of changeable thermal loads for optimal and rational refrigeration capacities of ACS, calculated according two methods of providing the maximum rate of the summarized annual refrigeration energy generation increment, or providing close to maximum refrigeration energy generation;
- -
- Develop a method to determine the range of artificially stabilized loads due to recuperation of excessive refrigeration energy, reserved at lowered current loads, to cover peak loads and the rest of the range of unstable loads regulated by SRC, thereby defining the level of regulated loads (LRL) of SRC and the load range of compressor operation.

## 2. Methods

_{0}according to air mass flow rate G

_{a}), they are presented in relative values as specific refrigeration capacity q

_{0}, id est, referred to in the unit of air mass flow rate (G

_{a}= 1 kg/s):

_{0}= Q

_{0}/G

_{a},

_{0}= ξ∙c

_{a}∙(t

_{a}− t

_{a}

_{2}), kW/(kg/s),

_{a}—initial or ambient t

_{amb}air temperature, K or °C;

- t
_{a2}—a set air temperature; - ξ—relative heat ratio as the total heat, removed from the air, related to its sensible heat;
- c
_{a}—air specific heat, kJ/(kg·K).

_{0}∙τ) = Σξc

_{a}∙(t

_{a}− t

_{a}

_{2})∙τ∙10

^{−3}, MWh/(kg/s).

_{0}used as a cumulative annual refrigeration energy characteristic:

_{0}∙τ) = f(q

_{0}).

_{0}as the indicative criterion Σ(q

_{0}∙τ)/q

_{0}to choose the optimal value of refrigeration capacity q

_{0.opt}corresponding to its maximum.

_{0.rat}within the range of cumulative annual refrigeration energy characteristics above the optimal value q

_{0.opt}to avoid the overestimation of refrigeration capacity accompanied by a negligible increment of annual output.

_{0.rat}’s specific refrigeration capacities while conditioning outdoor air were calculated for temperate climatic conditions in southern Ukraine (Mykolayiv region), 2017 (Figure 1).

_{0.rat}of the design refrigeration capacity enables us to offset the annual refrigeration consumption ∑(q

_{0}∙τ)

_{rat}= 48 MWh/(kg/s) that is close to its maximum value 50 MWh/(kg/s) but is also achieved at reduced design refrigeration capacity q

_{0.10rat}= 35 kW/(kg/s), which is less than q

_{0.10max}= 42 kW/(kg/s) (Figure 1).

_{cur}used in conventional practice: LL

_{10rat}= (q

_{0.10rat}− q

_{0.15rat})/q

_{0.10rat}≈ 0.3, where q

_{0.10rat}− q

_{0.15rat}is the range of stable thermal load and q

_{0.15rat}is the range of changeable thermal loads.

_{0}∙τ)/q

_{0}reflects the maximum rate of the summarized annual refrigeration energy increment, and naturally, the minimum deviation of the optimal value of refrigeration capacity q

_{0.opt}from the current loads q

_{0}, followed by minimum exceedances of q

_{0.opt}over q

_{0}. Therefore, the rational value of refrigeration capacity q

_{0.rat}, being higher than q

_{0.opt}, is characterized by larger deviation from the current loads q

_{0}and exceedances (excesses) of q

_{0.rat}over q

_{0}. The latter are considered the reserves for refrigeration exceedances (excesses)’ recuperation to cover peak loads and reduce a design refrigeration capacity less than q

_{0.rat}. The refrigeration exceedances (excesses) are associated with changeable load range of the total one. Therefore, the range of changeable loads is considered the object for partly stabilizing due to refrigeration exceedances (excesses) recuperation that leads to a reduction in its value and the total design refrigeration capacity q

_{0.rat}as result.

## 3. Results and Discussion

_{0.rat}as result. Such an approach, substantiated by the results of calculation of the summarized annual refrigeration energy generation Σ(q

_{0}∙τ) and optimal q

_{0.opt}and rational q

_{0.rat}refrigeration capacities (Figure 1), should be proven by the exceedances (excesses) of design refrigeration capacities q

_{0.opt}and q

_{0.opt}over current loads q

_{0}, and corresponding monthly summarized values of the refrigeration energy exceedances Σ(q

_{0}∙τ) within initial changeable load range q

_{0.15}reduced by its partially stabilization due to refrigeration energy exceedance’s recuperation in the range to q

_{0.20}.

_{0.10}needed for conditioning outdoor air to 10 °C can be sheared into the range of changeable values q

_{0.15}, which are needed for preconditioning outdoor air to 15 °C. Practically unchangeable refrigeration capacities q

_{0.10-15}are needed for subsequent conditioning of air from 15 °C to 10 °C. The calculation results for July 2017 in climatic conditions in southern Ukraine, Mykolayiv region, as example of temperate climate, are presented in Figure 2.

_{0.10}for conditioning outdoor air to 10 °C can be shared in the range of changeable load for preconditioning outdoor air to 15 °C, and in the range of practically unchangeable heat load q

_{0.10-15}for subsequent conditioning air from 15 °C to 10 °C. Accordingly, the latter is accepted as the basic practically unchangeable part, q

_{0.10-15}≈ q

_{0.10rat}− q

_{0.15rat}, of the total rational design value q

_{0.10rat}, whereas the rest, as a remainder of the rational design value q

_{0.10rat}, might be used as the residual booster one q

_{0.b10-15}= q

_{0.10rat}− q

_{0.10-15}, available for preconditioning outdoor air to 15 °C. It is chosen as the object for reduction through refrigeration exceedances (excesses)’ recuperation.

_{thr}, stabilizing the heat loads for further conditioning outdoor air below t

_{thr}= 15 °C, and as an indicator to share the overall range of design heat load q

_{0.10rat}(Figure 1) in two ranges according to different character of the loading.

_{0.10rat}over actual loads q

_{0.10}, reflected in the booster refrigeration capacity q

_{0.b10-15}= q

_{0.10rat}− q

_{0.10-15}and available for preconditioning outdoor air to 15 °C, the latter is accepted as the object for analyses in order to use the excess refrigeration capacity for covering the peak loads. Therefore, the next step of the analyses aims to partly stabilize the initially changeable heat loads q

_{0.15}, which would lead to reduce the booster load range from q

_{0.b10-15}to q

_{0.b10-20}, as the regulated load range and the LRL of SRC compressor recuperate the refrigeration energy exceedance.

_{0.15}by using the value q

_{0.20rat}to condition air to 20 °C, the latter might be accepted as the artificial threshold temperature t

_{thr}= 20 °C, and the range of heat loads q

_{0.10-20}as the artificially stable range in the initial approximation (Figure 3).

_{0.15}using the reduced rational refrigeration capacity q

_{0.20rat}are presented in Figure 3.

_{0.b10-20rat}= q

_{0.10rat}− q

_{0.10-20}, q

_{0.b10-20rat.ex}= q

_{0.b10-20rat}− q

_{0.15}, q

_{0.b10-20rat.def}= q

_{0.15}− q

_{0.b10-20rat}, ∑q

_{0.b10-20rat.ex}= ∑(q

_{0.b10-20rat}− q

_{0.15})τ.

_{0.b10-20rat}are mostly higher than the current requirement of q

_{0.15}for preconditioning outdoor air to 15 °C (Figure 3a). Accordingly, the current exceedances of the booster refrigeration capacities, q

_{0.b10-20rat.ex}, in the majority offset the current deficit, q

_{0.b10-20rat.def}, which is proven by the dominant rise in the summarized exceedance of booster refrigeration energy values ∑q

_{0.b10-20rat.ex}τ, except on a couple of days at the end of July (Figure 3b).

_{0.b10-20rat.ex}τ between the 10–13th and 20–26th July justifies that the daily values of deficit ∑q

_{0.b10-20rat.def}τ are compensated by their values of reserved refrigeration energy ∑q

_{0.b10-20rat.ex}τ. However, the briefly lowering values ∑q

_{0.b10-20rat.ex}τ within the 27–28th July indicate the presence of small daily refrigeration capacity deficit of q

_{0.20rat}.

_{0.b10-20rat.ex}confirms that the booster refrigeration energy enables it to cover the current need q

_{0.15}for preconditioning outdoor air to 15 °C instead of 20 °C, and to offset the actual deficit q

_{0.b10-20rat.def}by recuperating the daily excess of refrigeration energy ∑q

_{0.b10-20rat.ex}reserved at lowered current heat loads q

_{0.15}, with a significant monthly exceedance of 6600 kWh/(kg/s) (Figure 3). The latter indicates the refrigeration energy reserve for reducing the installed booster refrigeration capacity from q

_{0.15rat}to q

_{0.20rat}, and the total q

_{0.10rat}by the value of their difference q

_{0.15rat}− q

_{0.20rat}= 10 kW/(kg/s) according to Figure 1.

_{0.b10-20opt}, based on the optimal design value q

_{0.10opt}, are not able to offset the current need q

_{0.15}for preconditioning outdoor air to 15 °C (Figure 4).

_{0.b10-20opt}= q

_{0.10opt}− q

_{0.10-20}, q

_{0.b10-20opt.ex}= q

_{0.b10-20opt}− q

_{0.15}, q

_{0.b10-20opt.def}= q

_{0.15}− q

_{0.b10-20opt}, ∑q

_{0.b10-20opt.ex}= ∑(q

_{0.b10-20opt}− q

_{0.15})τ.

_{0.b10-20opt}are lower than the current need q

_{0.15}within 10–13th and later 20th of July, which leads to considerable values of the current deficit q

_{0.b10-20opt.def}(Figure 4a). Accordingly, the current deficits q

_{0.b10-20opt.def}are comparable with the current exceedance of booster refrigeration capacities q

_{0.b10-20opt.ex}that is proven by alternating the rising and falling of the summarized exceedance of booster refrigeration energy values ∑q

_{0.b10-20opt.ex}τ during July (Figure 4b).

_{0.20rat}, the optimal value q

_{0.20opt}is lower than the current need q

_{0.15}to be covered by daily reserved refrigeration energy ∑q

_{0.b10-20opt.ex}τ.

_{0.b10-20opt}and corresponding summarized monthly refrigeration energy values Σq

_{0.b10-20opt}τ = Σ(q

_{0.10opt}− q

_{0.10-20})τ, compared with the current exceedances of booster rational refrigeration capacities q

_{0.b10-20rat.ex}= q

_{0.b10-20rat}− q

_{0.15}, and corresponding summarized data on refrigeration energy Σq

_{0.b10-20rat.ex}τ = Σ(q

_{0.b10-20rat}− q

_{0.15})τ, are performed (Figure 5).

_{0.b10-20opt}= q

_{0.10opt}− q

_{0.10-20}, q

_{0.b10-20rat}= q

_{0.10rat}− q

_{0.10-20}, q

_{0.b10-20opt.ex}= q

_{0.b10-20opt}− q

_{0.15}, q

_{0.b10-20opt.def}= q

_{0.15}− q

_{0.b10-20opt}, q

_{0.b10-20rat.ex}= q

_{0.b10-20rat}− q

_{0.15}, Σq

_{0.b10-20opt}τ= Σ(q

_{0.10opt}− q

_{0.10-20})τ, ∑q

_{0.b10-20opt.ex}τ = ∑(q

_{0.b10-20opt}− q

_{0.15})τ, ∑q

_{0.b10-20rat.ex}= ∑(q

_{0.b10-20rat}− q

_{0.15})τ.

_{0.b10-20opt}τ = Σ(q

_{0.10opt}− q

_{0.10-20})τ are quite close to the summarized exceedances of the booster rational refrigeration energy Σq

_{0.b10-20rat.ex}τ = Σ(q

_{0.b10-20rat}− q

_{0.15})τ which remain from the excessive refrigeration recuperation and are unavailable for further reducing the booster rational refrigeration energy. Proceeding from this data, we can conclude that in the general sense, the booster optimal refrigeration energy exceedance ∑q

_{0.b10-20opt.ex}= ∑(q

_{0.b10-20opt}− q

_{0.15})τ is not enough to precondition outdoor air lower than 20 °C down to 15 °C; this is in contrast with the excessive booster rational refrigeration energy ∑q

_{0.b10-20rat}, which is able to cover q

_{0.15}, even with the rest ∑q

_{0.b10-20rat.ex}= ∑(q

_{0.b10-20rat}− q

_{0.15})τ.

_{0.b10-20opt/rat}= q

_{0.10opt/rat}− q

_{0.10-20}and the values of their refrigeration capacity exceedance q

_{0.b10-20opt/rat.ex}= q

_{0.b10-20opt/rat}− q

_{0.15}over q

_{0.15}were calculated to approve this assumption (Figure 6 and Figure 7).

_{0.b10-20opt}are lower than the current need q

_{0.15}from 10–13th and later 20th of July, which leads to considerable current deficit values of q

_{0.b10-20opt.def}(Figure 7a). Accordingly, the current deficits q

_{0.b10-20opt.def}are comparable with the current exceedances of the booster refrigeration capacities q

_{0.b10-20opt.ex}that are proven by alternating the rising and falling of the summarized exceedance of booster refrigeration energy values ∑q

_{0.b10-20opt.ex}τ during July (Figure 7b).

_{0.20rat}, the optimal value q

_{0.20opt}is lower than the current need q

_{0.15}to be covered by the daily reserved refrigeration energy ∑q

_{0.b10-20opt.ex}τ.

_{0.b10-20opt}/q

_{0.10-20rat}fluctuate within the range of the required design nominal value LRL

_{nom}= q

_{0.15rat}/q

_{0.10rat}, of about 0.7 to 0.3–0.2. The range of load, regulated by an SCR compressor, is characterized by the level of regulated load LRL as a ratio of the regulated load to the overall load q

_{0.10}, including the unregulated load.

_{0.10opt}and its rational value q

_{0.10rat}as the second stage in the generalized designing methodology [84,85] make it possible to define not only the value of LRL

_{nom}, but the range of the current values of LRL

_{cur}fluctuation too.

_{0.b10-20opt}of q

_{0.10opt}are enough to cover current need q

_{0.20}for cooling air to 20 °C with considerable exceedance q

_{0.b10-20opt.ex20}, but sometimes less than the current need q

_{0.15}for cooling air to 15 °C (Figure 8), when corresponding exceedance q

_{0.b10-20opt.ex15}drops to zero (Figure 9). The latter is also proven by the alternating the rising and falling of the summarized available exceedance of the booster optimal refrigeration energy values ∑q

_{0.b10-20opt.ex}τ = Σ(q

_{0.b10-20opt}− q

_{0.15})τ during July (Figure 9). There are opposite results for the summarized available exceedance of the booster rational refrigeration energy values ∑q

_{0.b10-20rat.ex}τ = Σ(q

_{0.b10-20rat}− q

_{0.15})τ, characterized by a continuous rise that demonstrates that the booster rational refrigeration energy is able to cover the current need q

_{0.15}for preconditioning outdoor air to 15 °C instead of 20 °C; this is achieved by recuperating the daily excess of refrigeration energy ∑q

_{0.b10-20rat.ex}reserved at lower current heat loads q

_{0.15}.

_{0.b10-20rat.ex}τ = Σ(q

_{0.b10-20rat}− q

_{0.15})τ between 10–13th and 20–26th July justifies that daily values of the deficit are compensated by the values of reserved refrigeration energy ∑q

_{0.b10-20rat.ex}τ.

_{0.b10-20opt.ex20}τ = Σ(q

_{0.b10-20opt}− q

_{0.20})τ indicates that operation of the compressor at optimal loads also requires refrigeration energy exceedance recuperation for booster air to be preconditioned to 20 °C.

_{0.10opt}and rational q

_{0.10orat}values calculated for temperate climatic conditions in southern Ukraine, 2017, are presented in Figure 10.

_{0.10opt}and by refrigeration energy exceedance recuperation in booster air preconditioning to 15 °C Δq

_{0.15-20rat}, resulting in reducing the rational value of design refrigeration capacity from q

_{0.15rat}to q

_{0.20rat}, are nearly the same. However, the annual refrigeration energy generation according to current consumption ∑(q

_{0}∙τ)

_{10opt}at the optimal refrigeration capacity q

_{0.10opt}is considerably lower than ∑(q

_{0}∙τ)

_{10rat}at the rational refrigeration capacity q

_{0.10rat}. In order to increase the annual refrigeration energy generation, as the primary criterion for the effect gained at optimal refrigeration capacity q

_{0.10opt}, the refrigeration energy exceedance Σq

_{0.b10-20opt}τ = Σ(q

_{0.10opt}-q

_{0.10-20})τ (Figure 8) has to be recuperated.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature and Units

ACS | Air conditioning system | |

LL | Level of load | |

LRL | Level of regulated load | |

SRC | Speed regulated compressor | |

VRF | Variable refrigerant flow | |

Symbols and units | ||

b | Booster | |

c_{a} | Specific heat of humid air | kJ/(kg·K) |

G_{a} | Air mass flow rate | kg/s |

Q_{0} | Total refrigeration capacity | kW |

q_{0} | Specific refrigeration capacity (per unit air mass flow rate) | kW/(kg/s) |

q_{0} τ | Specific refrigeration energy (per unit air mass flow rate) | kW/(kg/s) |

t | Air temperature | K, °C |

ξ | Specific heat ratio of the total heat (latent and sensible) removed from air to sensible heat | |

τ | Time interval | h |

Δt | Temperature decrease | K, °C |

∑(q_{0} τ) | Annual (monthly) specific refrigeration energy consumption (per unit air mass rate) | kWh/(kg/s) |

Subscripts | ||

10, 15, 20 | Air temperature | K, °C |

a | Air | |

amb | Ambient | |

b | Booster | |

max | Maximum | |

opt | Optimal | |

rat | Rational |

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**Figure 1.**Specific annual refrigeration energy consumption ∑(q

_{0}∙τ), rational q

_{0.rat}and optimal q

_{0.opt}refrigeration capacities while conditioning air to t

_{a}

_{2}= 10, 15 °C and 20 °C: LL

_{10rat}= (q

_{0.10rat}− q

_{0.15rat})/q

_{0.10rat}.

**Figure 2.**The current values of specific refrigeration capacities q

_{0.10}required for outdoor air conditioning to 10 °C; refrigeration capacities q

_{0.10-15}for subsequent air conditioning from 15 °C to 10 °C; available booster values q

_{0.b10-15}remained for outdoor air conditioning to 15 °C: q

_{0.10-15}= q

_{0.10}− q

_{0.15}; q

_{0.b10-15}= q

_{0.10}− q

_{0.10-15}.

**Figure 3.**Rational values of refrigeration capacities q

_{0.10rat}, q

_{0.15rat}and q

_{0.20rat}for conditioning outdoor air to 10 °C, 15 °C and 20 °C accordingly; actual refrigeration capacities q

_{0.15}needed for preconditioning air to 15 °C, and available booster refrigeration capacity q

_{0.b10-20rat}for preconditioning air and booster refrigeration capacity exceedance q

_{0.b10-20rat.ex}over q

_{0.15}(

**a**), and its deficit q

_{0.b10-20rat.def}, summarized monthly refrigeration energy exceedance ∑q

_{0.b10-20rat.ex}over q

_{0.15}(

**b**): q

_{0.b10-20rat}= q

_{0.10rat}− q

_{0.10-20}, q

_{0.b10-20rat.ex}= q

_{0.b10-20rat}− q

_{0.15}, q

_{0.b10-20rat.def}= q

_{0.15}− q

_{0.b10-20rat}, ∑q

_{0.b10-20rat.ex}= ∑(q

_{0.b10-20rat}− q

_{0.15})τ.

**Figure 4.**Optimal values of refrigeration capacities q

_{0.10opt}, q

_{0.15opt}and q

_{0.20opt}for conditioning outdoor air to 10 °C, 15 °C and 20 °C accordingly; actual refrigeration capacities q

_{0.15}needed for preconditioning outdoor air to 15 °C; booster refrigeration capacity q

_{0.b10-20opt}and its deficit q

_{0.b10-20opt.def}compared to needed q

_{0.15}(

**a**), booster refrigeration capacity exceedance q

_{0.b10-20opt.ex}over q

_{0.15}and summarized monthly refrigeration energy exceedance ∑q

_{0.b10-20opt.ex}(

**b**).

**Figure 5.**Current values of refrigeration capacities q

_{0.15}needed for preconditioning outdoor air to 15 °C; booster optimal refrigeration capacity q

_{0.b10-20opt}and corresponding summarized monthly refrigeration energy values Σq

_{0.b10-20opt}τ, current exceedances of booster rational refrigeration capacities q

_{0.b10-20rat.ex}and corresponding summarized data Σq

_{0.b10-20rat.ex}τ (

**a**), current booster optimal refrigeration capacity exceedance q

_{0.b10-20opt.ex}and its deficit q

_{0.b10-20opt.def}, summarized booster refrigeration energy exceedance for optimal ∑q

_{0.b10-20opt.ex}and rational data ∑q

_{0.b10-20rat.ex}(

**b**).

**Figure 6.**Actual values of refrigeration capacities q

_{0.15}needed for conditioning outdoor air to 15 °C, and booster refrigeration capacities q

_{0.b10-20opt}and q

_{0.b10-20rat}based on the optimal and rational design values q

_{0.10opt}and q

_{0.10rat}for conditioning outdoor air to 10 °C: q

_{0.b10-20opt}= q

_{0.10opt}− q

_{0.10-20}; q

_{0.b10-20rat}= q

_{0.10rat}− q

_{0.10-20}.

**Figure 7.**Actual values of booster refrigeration capacity exceedance q

_{0.b10-20opt.ex}and q

_{0.b10-20rat.ex}over q

_{0.15}(

**a**) and its deficit q

_{0.b10-20opt.def}and q

_{0.b10-20rat.def}based on the optimal and rational design values q

_{0.10opt}and q

_{0.10rat}for conditioning outdoor air to 10 °C; summarized monthly refrigeration energy exceedance ∑q

_{0.b10-20opt.ex}over q

_{0.15}; (

**b**): q

_{0.b10-20rat}= q

_{0.10rat}− q

_{0.10-20}, q

_{0.b10-20rat.ex}= q

_{0.b10-20rat}− q

_{0.15}, q

_{0.b10-20opt.def}= q

_{0.15}− q

_{0.b10-20opt}, q

_{0.b10-20rat.def}= q

_{0.15}− q

_{0.b10-20rat}, ∑q

_{0.b10-20rat.ex}= ∑(q

_{0.b10-20rat}− q

_{0.15})τ, ∑q

_{0.b10-20opt.ex}= ∑(q

_{0.b10-20opt}− q

_{0.15})τ.

**Figure 8.**Actual refrigeration capacities q

_{0.15}needed for preconditioning outdoor air to 15 °C, booster refrigeration capacity q

_{0.b10-20opt}and q

_{0.b10-20rat}based on q

_{0.10opt}and q

_{0.10rat}, the difference q

_{0.b10-20rat}− q

_{0.b10-20opt}= q

_{0.10rat}− q

_{0.10opt}, current LRL

_{cur}and nominal LRL

_{nom}: q

_{0.b10-20rat}= q

_{0.10rat}− q

_{0.10-20}, q

_{0.b10-20opt}= q

_{0.10opt}− q

_{0.10-20}q

_{0.b10-20rat.ex}= q

_{0.b10-20rat}− q

_{0.15}, q

_{0.b10-20rat.def}= q

_{0.15}− q

_{0.b10-20rat}, ∑q

_{0.b10-20rat.ex}= ∑(q

_{0.b10-20rat}− q

_{0.15})τ; LRL

_{nom}= q

_{0.15rat}/q

_{0.10rat}; LRL

_{cur}= q

_{0.b10-20opt}/q

_{0.10-20rat}; q

_{0}

_{.b10-20rat}− q

_{0.b10-20opt}= q

_{0.10rat}− q

_{0.10opt}.

**Figure 9.**Actual values of booster optimal refrigeration capacity exceedance q

_{0.b10-20opt.ex}over q

_{0.15}and q

_{0.b10-20opt.ex20}over q

_{0.20}; summarized monthly booster optimal refrigeration energy exceedances Σq

_{0.b10-20opt.ex}τ over q

_{0.15}and Σq

_{0.b10-20opt.ex}τ over q

_{0.20}; summarized data on booster rational refrigeration energy Σq

_{0.b10-20rat.ex}τ over q

_{0.15}and Σq

_{0.b10-20rat.ex20}τ over q

_{0.20}: q

_{0.b10-20opt.ex}= q

_{0.b10-20opt}− q

_{0.15}; q

_{0.b10-20opt.ex20}= q

_{0.b10-20opt}− q

_{0.20}; Σq

_{0.b10-20opt.ex}τ = Σ(q

_{0.b10-20opt}− q

_{0.15})τ; Σq

_{0.b10-20opt.ex}τ= Σ(q

_{0.b10-20opt}− q

_{0.20})τ; Σq

_{0.b10-20rat.ex}τ= Σ(q

_{0.b10-20rat}− q

_{0.15})τ; Σq

_{0.b10-20rat.ex20}τ = Σ(q

_{0.b10-20rat}− q

_{0.20})τ.

**Figure 10.**Specific annual refrigeration energy consumption ∑(q

_{0}∙τ); the rational q

_{0.10,15,20rat}and optimal q

_{0.10,15,20opt}values of design specific refrigeration capacity and their reductions Δq

_{0.10,15,20rat/opt}due to rational and optimal designing and refrigeration energy exceedance recuperation while conditioning air to t

_{a}

_{2}= 10, 15 and 20 °C: Δq

_{0.10,15,20rat}= q

_{0.10,15,20max}− q

_{0.10,15,20rat}; Δq

_{0.10opt}= q

_{0.10rat}− q

_{0.10opt}; Δq

_{0.15-20rat}= q

_{0.15rat}− q

_{0.20rat}.

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## Share and Cite

**MDPI and ACS Style**

Radchenko, M.; Radchenko, A.; Trushliakov, E.; Pavlenko, A.; Radchenko, R.
Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes. *Energies* **2023**, *16*, 2417.
https://doi.org/10.3390/en16052417

**AMA Style**

Radchenko M, Radchenko A, Trushliakov E, Pavlenko A, Radchenko R.
Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes. *Energies*. 2023; 16(5):2417.
https://doi.org/10.3390/en16052417

**Chicago/Turabian Style**

Radchenko, Mykola, Andrii Radchenko, Eugeniy Trushliakov, Anatoliy Pavlenko, and Roman Radchenko.
2023. "Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes" *Energies* 16, no. 5: 2417.
https://doi.org/10.3390/en16052417