Proxy-Calibration Approach for Transient Simulation of Variable Refrigerant Flow Systems in Energy Performance Assessment of an Existing Building

Abstract

This study investigates a Proxy-Calibration method for modeling Variable Refrigerant Flow (VRF) systems in TRNSYS, addressing the absence of a dedicated simulation component. The approach approximates part-load behavior through indoor-unit combination mapping, utilizing empirical data from a public office building in Seoul. Simulation results were compared with one year of monitored data. While indoor temperature trends showed moderate agreement (R² = 0.68), electricity consumption diverged significantly from actual measurements. The coefficient of variation in the root mean square error (CVRMSE) ranged from 95% to 118% for the boiler and 153% to 590% for the VRF system, indicating a substantial discrepancy well beyond standard calibration thresholds. These findings underscore the limitations of using static performance maps without explicit control logic. Consequently, this study defines the proposed method as an exploratory investigation; while it establishes a procedural framework for approximating VRF operation, rigorous energy prediction requires further refinement through empirical curve fitting and detailed control representation.

1. Introduction

In response to global efforts to achieve carbon neutrality, the building sector has increasingly adopted high-efficiency technologies such as Variable Refrigerant Flow (VRF) systems. VRF systems are particularly favored in high-density urban areas for their ability to simultaneously provide heating and cooling to multiple zones, offering significant advantages in part-load efficiency and space utilization compared to conventional HVAC systems [1,2,3,4,5,6,7,8,9,10]. However, accurately predicting the energy performance of VRF systems during the retrofit of existing public buildings remains a significant challenge due to the complexity of their dynamic operation.

Prior research on VRF modeling can be categorized into two main approaches: studies using dedicated simulation modules and those focusing on control optimization. Studies utilizing tools like EnergyPlus, which features a dedicated VRF module, have demonstrated relatively high accuracy in performance prediction [11,12,13,14,15,16,17]. Similarly, Wang et al. [12] and Qian et al. [13] developed control-oriented models or analyzed large-scale operational datasets to capture dynamic behaviors. Despite these advancements, TRNSYS—one of the most widely used transient simulation platforms—lacks a dedicated VRF component [11,12,14,15,16,17]. Consequently, practitioners often rely on generic air-source heat pump (ASHP) models, such as Type954c, which cannot explicitly represent the intricate control logic and part-load interactions of multi-unit VRF systems [12,18,19]. This technological limitation creates a significant methodological gap in assessing VRF performance within the TRNSYS environment.

To address this gap, this study establishes a research framework (as illustrated in Figure 1) grounded in three critical contexts: Place (Seoul’s distinct urban climate), Time (hourly transient analysis), and User (occupant behavior). Within this framework, we identify the lack of standardized modeling procedures for VRF in TRNSYS 17 as the primary barrier to reliable energy assessment for retrofitting projects.

Figure 1. Research framework and knowledge roadmap.

Therefore, the primary aim of this study is to propose a standardized “Proxy-Calibration” method that enables the simulation of multi-unit VRF systems in TRNSYS in the absence of a dedicated component. The central hypothesis is that classifying operational states based on indoor-unit combinations can effectively approximate the part-load behavior of the system. The main contribution of this work is twofold: (1) establishing a procedural framework for this proxy modeling approach, and (2) quantitatively identifying the performance gap and limitations of such an approximation compared to field measurements. This study serves as an exploratory investigation, providing a pragmatic interim solution while highlighting the necessity for future empirical curve fitting and advanced control integration.

Figure 1 illustrates the research roadmap designed to bridge the gap between standard simulation capabilities and the real-world operation of VRF systems. The framework consists of three key phases: (1) Data Acquisition, where site-specific weather conditions and operational data from the public office in Seoul are collected; (2) Proxy-Calibration, which involves developing the TRNSYS model using the proposed indoor-unit combination mapping technique; and (3) Performance Assessment, where the simulation results are validated against monitored data to evaluate the model’s accuracy and limitations.

2. Target Building Description

2.1. Building Description

The case study building is a reinforced concrete public office located in Seoul, South Korea, with a site area of 537.20 m², a building footprint of 176.72 m², and a total floor area of 353.44 m². The site features a temperate climate with four distinct seasons. According to ASHRAE Standard 169 [20], Seoul is categorized as Climate Zone 4A (Mixed-Humid). This region is characterized by hot and humid summers requiring significant cooling and dehumidification, and cold, dry winters necessitating substantial heating loads. These climatic conditions impose high part-load variability on HVAC systems throughout the year. Although the exact construction year is undocumented, it is presumed to date from the 1970s to–1980s. The first and second floors each provide 176.72 m² of office space, and a small third-floor extension (27.79 m²) containing a staircase and a water tank room was added in 2018. The floor-to-ceiling height is 2.4 m on both floors. An on-site investigation was conducted to identify construction details and equipment installations. Most exterior windows have been replaced with PVC-framed double glazing, while some aluminum single-glazed units remain in secondary spaces. The 300 mm-thick external walls consist of double masonry with 50 mm of polystyrene insulation, and roof insulation was found to be partially detached, resulting in poor thermal performance. Overall, the envelope provides limited insulation performance. No central mechanical ventilation system is installed, except for small exhaust fans in restrooms. Lighting fixtures have been mostly retrofitted with LEDs, and occupancy is concentrated in the second-floor offices and the director’s office. Typical equipment includes personal computers, a photocopier, and a projector. Figure 2, Figure 3 and Figure 4 show the architectural drawings, floor plans, and interior/exterior views of the building, serving as the geometric baseline for the thermal zoning and input parameters in the TRNSYS simulation model.

Figure 2. Floor plans of the case study building: (a) First floor, including a lobby with stairs, auditorium, men’s and women’s restrooms, pantry, preparation room, and storage room; (b) Second floor, including offices, meeting room, director’s office, women’s restroom, and pantry.

Figure 3. Staircase cross-section of the case study building.

Figure 4. Exterior and interior photographs of the case study building.

2.2. Equipment

2.2.1. Air-Source Heat Pump

The building is equipped with a reversible multi-unit heat pump system configured as a VRF system [21]. The system architecture connects multiple indoor units to a single outdoor unit, with independent circuits serving each floor. Figure 5 illustrates the schematic of the refrigerant piping network. On the first floor, outdoor unit OAC-2 serves the auditorium via two ceiling-mounted indoor units (IAC-3). On the second floor, outdoor unit OAC-1 connects to four indoor units: two ceiling-mounted units (IAC-3) in the main office, one wall-mounted unit (IAC-1) in the meeting room, and one wall-mounted unit (IAC-2) in the director’s office. An additional indoor unit of equivalent capacity was subsequently installed in January 2023.

Figure 5. Piping system of a VRF system.

The nominal cooling and heating capacities of the indoor units are summarized in Table 1, ranging from 3.2/3.6 kW (IAC-1) to 13.0/14.6 kW (IAC-3). All units operate at a 220 V, 60 Hz power supply, with rated fan power inputs ranging from 30 to 135 W and airflow rates spanning 10 to 33 CMM.

Table 1. Indoor unit equipment list of VRF system [21].

Category	IAC-1	IAC-2	IAC-3
System type	1-Way Cassette	1-Way Cassette	4-Way Cassette
Model	R-W0320C2S (LG Electronics Inc., Seoul, Republic of Korea)	R-W0400C2S (LG Electronics Inc., Seoul, Republic of Korea)	R-W1300A2U (LG Electronics Inc., Seoul, Republic of Korea)
Quantity	1	1	4
Rated cooling (kW)	3.2	4.0	13.0
Rated heating (kW)	3.6	4.5	14.6
Rated power input (Fan and Control) (W)	20	30	97
Fan flow rate (CMM)	10.0	10.9	26/29/33
Rated power for fan (W)	30	30	135

Two outdoor units (OAC-1 and OAC-2) are currently installed, providing cooling/heating capacities of 23.3/25.9 kW and 29.2/32.8 kW, respectively. The nominal cooling and heating capacities of these outdoor units are summarized in Table 2.

Table 2. Outdoor unit equipment list of VRF system [21].

Category	OAC-1		OAC-2
System type	Cooling/heating switch type		Cooling/heating switch type
Model	RPUW08GX9E (LG Electronics Inc., Seoul, Republic of Korea)		RPUW10GX9E (LG Electronics Inc., Seoul, Republic of Korea)
Quantity	1		1
Rated cooling (kW)	23.3		29.2
Rated heating (kW)	Rated	25.9	Rated	32.8
	$-15 °$C	22.6	$-15 °$C	28.3
Power for cooling (W)	Rated	4.8	Rated	6.6
Power for heating (W)	Rated	5.4	Rated	7.2
	$-15 °$C	10.5	$-15 °$C	13.5
EER	7.31		6.98
Power Supply	$3\varnothing$, 380 V, 60 Hz		$3\varnothing$, 380 V, 60 Hz
Rated Current (Cooling/Heating) (A)	12.5/12.3		16.5/15.5

2.2.2. Boiler

In April 2023, the existing gas boiler was replaced with an electric boiler configured in a cascade heat pump system arrangement [22]. The system operates via a two-stage cycle, where the refrigerant from the outdoor unit serves as the primary heat source, allowing the secondary boiler unit to generate high-temperature water (25–80 °C). The installed assembly, comprising one outdoor and one boiler unit, delivers a rated heating capacity of 25.0 kW with a nominal power consumption of 9.9 kW, as summarized in Table 3. These specifications were integrated into the TRNSYS model, where the cascade configuration was represented using an equivalent component. Figure 6 illustrates the boiler system incorporating the cascade heat pump technology.

Table 3. Boiler equipment list.

Category	SB-25
System type	Cascade heat pump boiler
Model	HNT2502B9A (Indoor unit)/HUT2502B9A (Outdoor unit) (LG Electronics Inc., Seoul, Republic of Korea)
Quantity	1
Rated heating (kW)	25.0
Rated power (W)	9.9

Figure 6. Boiler system of a cascade heat pump system.

2.2.3. Lights

The on-site survey cataloged the lighting inventory, as summarized in Table 4. Most fixtures have been retrofitted with LED lamps, while residual fluorescent units (i.e., 2 × 28 W, 22 in total) remain in the auditorium and stairwell. In the simulation, the total rated power was assigned to each thermal zone, and lighting operation schedules were derived from real-time electricity consumption data.

Table 4. Lighting installation information.

Target space			Lights
Floor	Zone	Area (m2)	Type	Power (W)	Quantity
1	Auditorium	126.67	FL 28W × 2	56	20
	Preparation Room	9.65	LED 150$\mathrm{\varnothing }$	15	2
	Toilet (Men)	3.68	LED 150$\mathrm{\varnothing }$	15	2
	Toilet (Women)	7.84	LED 150$\mathrm{\varnothing }$	15	2
	Staircase	23.71	FL 28W × 2	56	2
			LED 150$\mathrm{\varnothing }$	15	2
	Storage	10.08	LED 150$\mathrm{\varnothing }$	15	1
2	Office (Large)	82.60	LED 1200 × 300	50	15
			LED 150$\mathrm{\varnothing }$	15	2
	Office (Small)	44.51	LED 1200 × 300	50	2
			LED 500 × 500	50	2
			LED 150$\mathrm{\varnothing }$	15	14
	Director’s Office	14.73	LED 1200 × 300	50	2
			LED 150$\mathrm{\varnothing }$	15	4
	Preparation Room	5.08	LED 150$\mathrm{\varnothing }$	15	2
	Toilet	10.11	LED 150$\mathrm{\varnothing }$	15	2
	Staircase	17.13	LED 150$\mathrm{\varnothing }$	15	4

2.3. Monitoring System

A real-time monitoring system was deployed in April 2023 to quantify electricity consumption and indoor environmental conditions (see Figure 7). A full year of data (1 July 2023–30 June 2024) was acquired to validate the simulation model; notably, data from 29 February 2024 were excluded to maintain temporal consistency. Power consumption was monitored at 11 sub-circuits (six on the first floor and five on the second) at two-min intervals. This coverage included the main meter, VRF heat pumps, the system boiler, and lighting; however, energy use for individual outdoor units could not be disaggregated. Occupancy patterns were recorded via entrance sensors at ten-minute intervals, while indoor environmental parameters—including temperature, humidity, CO₂ concentration, and illuminance—were measured near the ceiling of the main office. Noise levels were also logged at two-minute intervals. These multi-domain datasets served as empirical boundary conditions and validation data for the simulation model.

Figure 7. Indoor environment measurement location.

3. Methodology

3.1. VRF System Modeling

Table 5 summarizes the key modeling parameters and boundary conditions applied in the simulation. It encompasses meteorological boundary conditions based on Seoul, the thermal properties of the building envelope, including infiltration rates, and internal heat gain assumptions regarding occupants and equipment. Furthermore, it details the HVAC operational settings derived from field measurements, along with the specific TRNSYS components utilized to model the VRF (Type 954c) and boiler (Type 927) systems.

Table 5. Key modeling parameters and assumptions.

Category	Parameter	Value/Description	Source/Note
Simulation	Location/Weather Data	Seoul, South Korea/ASOS Data	Korea Meteorological Administration [23]
	Simulation Period	1 July 2023–30 June 2024	1-year transient simulation
	Time Step	15 min
Building Envelope	Total Floor Area	353.44 m2	2 stories + rooftop extension
	Exterior Walls	300 mm double masonry + 50 mm polystyrene
	Windows	PVC-framed double glazing	Retrofitted
	Infiltration Rate	0.4−1 h (Constant)	Derived from tracer gas test
Internal Gains	Occupants	120 W/person	Sensible: 65 W, Latent: 55 W [24]
	Equipment (PC)	150 W per occupant	Linked to occupancy schedule
	Lighting	Rated power per zone (LED/Fluorescent)	Schedule based on measured power
HVAC Settings	Cooling Setpoint	27 °C	Derived from measured seasonal average
	Heating Setpoint	23 °C	Derived from measured seasonal average
	VRF Component	Type 954c (Air-Source Heat Pump)	Proxy-model with PLR mapping
	Boiler Component	Type 927 (Water-Source Heat Pump)	Simplified cascade model
	Boiler Capacity	Rated Heating: 25.0 kW	Input Power: 9.9 kW

3.1.1. Calibration Scenario

In the case study building, the multi-unit VRF heat pump system connects multiple indoor units to a single outdoor unit. As TRNSYS lacks a dedicated component for such multi-unit systems, the air-source heat pump module Type954c from the TESS Library was utilized [25]. While this module calculates part-load performance using performance maps under varying indoor–outdoor conditions, it cannot explicitly replicate the behavior of individual indoor units. To address this limitation, multiple Type954c instances were implemented, with each representing a specific indoor-unit combination. For the second floor, outdoor unit OAC-1 serves four indoor units: two ceiling-mounted and two wall-mounted. Three distinct operating scenarios were defined: Case 1 (wall-mounted only, PLR 31%), Case 2 (ceiling-mounted only, PLR 112%), and Case 3 (all units active, PLR 142%). Given that manufacturer data were limited to PLRs between 50% and 130%, performance values for out-of-range cases were fixed at the boundary limits. On the first floor, where two ceiling-mounted units connected to outdoor unit OAC-2 serve a single zone, the system was represented as Case 4 using a single Type954c module. In total, four Type954c modules were integrated into the TRNSYS environment, and their calculated supply air temperatures and flow rates were coupled with Type56 to simulate zone-level heating and cooling delivery (see Table 6).

Table 6. Load ratio according to indoor unit combination.

Outdoor Unit			Indoor Unit				Part Load Ratio
Equipment Number	Rated Performance		Case	Equipment Number	Rated Performance		Estimated	Determined
	Cooling	Heating			Cooling	Heating
OAC-1	23.3 kW	25.9 kW	Case 1	IAC-1 + IAC-2	7.2 kW	8.1 kW	31%	50%
			Case 2	IAC-3 + IAC-3	26.0 kW	28.6 kW	112%	110%
			Case 3	Case 1 + Case 2	33.2 kW	36.7 kW	142%	130%
OAC-2	29.2 kW	32.8 kW	Case 4	IAC-3 + IAC-3	26.0 kW	28.6 kW	89%	90%

3.1.2. Basic Assumption

Given that Type954c is limited to on/off control, an additional calibration process was conducted to represent part-load conditions for individual indoor units. Three basic assumptions were established.

(1)

The total and sensible cooling capacities and power consumption were assumed to increase proportionally with indoor wet-bulb temperature, independent of dry-bulb temperature under identical wet-bulb conditions.

(2)

The supply airflow rate was considered constant regardless of part-load conditions.

(3)

Performance outputs were calculated by applying weighting factors from external performance files to rated capacities and power input. These factors depend on outdoor and indoor dry-bulb temperatures, indoor wet-bulb temperature, and airflow ratio. Detailed input data are summarized in Appendix C.

3.1.3. Calculation Procedure

For each case, performance data corresponding to the applied part-load ratio (PLR) were derived by determining the supply airflow rate that satisfied Equations (1)–(3). This airflow rate was used to calculate the outlet dry-bulb temperature and enthalpy of the supply air, assuming saturation conditions (100% relative humidity). Here, $Q_t$ and $Q_s$ denote the total and sensible cooling capacities, respectively.

$$Q_t=m\times (h_{ei}-h_{eo})$$

(1)

$$Q_s=m\times c_p\times (D{T}_{ei}-D{T}_{eo})$$

(2)

$$h_{eo}=1.0048D{T}_{eo}+A{H}_{eo}(2501+1.85D{T}_{eo})$$

(3)

Based on these relationships, total and sensible capacities and power consumption were expressed as functions of indoor dry-bulb, indoor wet-bulb, and outdoor dry-bulb temperatures. Performance ratios were normalized to the baseline condition defined by an airflow ratio of 1. Detailed results for each case are provided in Appendix C.

3.1.4. Control Logic and Setting

Primary control signals were derived from real-time power consumption data of indoor-unit groups, determining their on/off operation. During operation, the units maintained set-point temperatures of 27 °C for cooling and 23 °C for heating, based on measured seasonal averages. For Case 1 and Case 3, where multiple zones were conditioned simultaneously, inlet air temperature and humidity were calculated as volume-weighted averages of the respective zones. The airflow from each Type954c module was distributed proportionally to zone volume, assuming uniform supply air temperature and humidity. Table 7 summarizes the modeling assumptions and the key input–output variables of Type954c.

Table 7. Input/output data conditions of Type954c.

Input		Output
Parameter	Set/From	Parameter	To
Return air temperature	Type56	Supply air temperature	Type56
Return air humidity	Type56	Supply air humidity	Type56
Return air flow rate	Type954c	Supply air flow rate	Type56
Outdoor air temperature	Type9a	Cooling capacity	Type25c
Outdoor air humidity	Type9a	Heating capacity	Type25c
Control signal for cooling	Type108	Power consumption	Type25c
Control signal for heating	Type108	COP	Type25c
Outdoor unit ambient temp.	Type9a

3.2. Boiler

The cascade heat pump boiler in the case study building functions as a unified system combining the outdoor unit and the boiler heat pump module, which limits the feasibility of detailed component-level reproduction in TRNSYS. To approximate its behavior, the water-source heat pump component Type927 from the TESS Library was utilized [25]. The nominal capacity of Type927 was calibrated using measured boiler power data, under the assumption of constant inlet temperatures on both the source and load sides. Floor heating was modeled by distributing the thermal output of Type927 to the second-floor office, meeting room, and director’s office proportionally to floor area, where it applied as a thermal gain in each zone. Domestic hot water was excluded, as the analysis focused solely on space heating. Detailed modeling parameters are summarized in Table 8.

Table 8. Input/output data conditions of Type927.

Input		Output
Parameter	Set/From	Parameter	To
Heat source inlet temp.	40	Heating capacity	Type56
Heat source flow rate	36 LPM	Power consumption	Type25c
Heat sink inlet temp.	20
Heat sink flow rate	36 LPM
Control signal	Type9a

3.3. Simulation Overview

3.3.1. Simulation Studio Model

The building energy simulation was conducted within the TRNSYS Simulation Studio. The model integrated five key components: weather data input, building load analysis, HVAC system modeling, control logic, and calculation modules. Weather data were imported via Type9a, while zone loads were calculated in Type56 based on TRNBuild definitions. The VRF and cascade boiler systems were modeled using Type954c and Type927, respectively. Specifically, the floor heating system, supplied by the Type927 boiler, serves the second-floor office, meeting room, and director’s office. The heating setpoint was maintained at 23 $°$C during occupied hours, consistent with the building’s operational schedule. Heating and cooling mode switching was managed through Type108, and the Equation module was used to determine indoor-unit load ratios, apply performance corrections, and allocate thermal output, as summarized in Table 9.

Table 9. Overview of components used in building energy performance simulation.

Parameter	Name	Function
Type9a	Data reader	External data input
Type16a	Radiation processor	Tilted surface solar radiation
Type33e	Psychrometric chart	Psychrometric chart
Type69b	Sky temperature calculator	Sky temperature
Type56	Multi-zone building	Building model
Type93	Input value recall	Calculated data call
Type927	Water-to-water heat pump	System boiler
Type954c	Air source heat pump	Electric heat pump
Type108	5 stage thermostat	Temperature control
Equation	Equa	Equation solver
Type65c	Online plotter	Simulation output
Type25c	Printer	Simulation output

Figure 8 illustrates the overall Simulation Studio model configuration, centered on the building module. Weather data were processed via the solar radiation processor and input into the building model. Control signals for the boiler and VRF systems were derived from measured power consumption data and used to govern their on/off operation. Model outputs recorded and utilized in feedback loops to replicate the building’s actual heating and cooling operation. Figure 9 depicts the Simulation Studio input interface used for analyzing heating and cooling energy demand.

Figure 8. Building energy performance simulation process.

Figure 9. Schematic of simulation studio model.

3.3.2. Weather Data

The simulation period spanned one year from 1 July 2023, to 30 June 2024, with 15 min calculation steps and hourly output intervals. Weather data were acquired from the Automated Synoptic Observing System (ASOS) of the Korea Meteorological Administration, specifically utilizing records from the Seoul station located near the case study site [23]. Key input parameters included outdoor dry-bulb temperature, relative humidity, and global horizontal irradiance.

3.3.3. Building Model

The building was divided into 14 thermal zones based on the actual floor plan. The first-floor pantry was integrated into the auditorium zone due to the lack of physical separation. Envelope properties, including wall and window configurations, were defined using field survey data, and the renovated PVC-framed double glazing was modeled using an equivalent TRNSYS component. Floor heating on the second floor was modeled by assigning the boiler output in proportion to the zone floor area. Material properties and thermal parameters followed the national Building Energy Saving Design Standards [26]. The dynamic heat transfer through the building envelope and the thermal storage effect of the floor heating system were calculated using the Transfer Function Method (TFM) within TRNSYS Type 56 (see Table A4).

3.3.4. Inner Heat Gain

Internal heat gains were divided into lighting, equipment, and occupants. To account for the stochastic nature of occupant behavior, measured lighting power consumption was utilized as a proxy for occupancy presence, thereby enhancing the fidelity of the simulation model. The rated lighting capacity of each space was assigned, and floor-level power measurements were used to define on/off schedules. Equipment loads were modeled assuming one 150 W personal computer per occupant, sharing the same operation schedule as lighting. Occupant heat gains were set to 120 W per person (65 W sensible and 55 W latent) [24], with occupancy schedules similarly derived from measured lighting power data.

3.3.5. Ventilation

Ventilation in the simulation was defined by infiltration and mechanical ventilation. Infiltration rates were determined based on a tracer gas test conducted prior to this study, and a uniform air exchange rate of 0.4 h⁻¹ was applied to all zones. This value was assumed constant throughout the year due to the unavailability of more detailed temporal data. As no mechanical ventilation system was installed in the building, and no significant natural ventilation through windows or openings was identified during the site survey. Accordingly, no forced ventilation was modeled.

3.3.6. Metrics and Criteria

Model calibration was evaluated using statistical indicators commonly adopted in building energy simulation studies, namely the coefficient of determination (i.e., $R^2$), the root mean square error (RMSE), and the coefficient of variation in the root mean square error (CVRMSE). These metrics quantify the degree of agreement between simulated and measured data by assessing both the magnitude and variability of prediction errors. According to guidelines such as ASHRAE Guideline 14, a model is generally considered calibrated when the CVRMSE is below 30% for hourly data and 15% for monthly data [24]. RMSE provides an absolute measure of the average deviation between predicted and measured values, while $R^2$ indicates the proportion of variance in the measured data explained by the model. Consequently, higher $R^2$ and lower RMSE and CVRMSE values therefore signify superior model performance and stronger calibration reliability. The mathematical formulations for each indicator are as follows:

$$R^2=1-{\displaystyle \frac{{\sum \left(y_i-{\widehat{y}}_i\right)}^2}{\sum {\left(y_i-\overline{y}\right)}^2}}$$

(4)

$$RMSE=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{n}}}$$

(5)

$$CVRMSE={\displaystyle \frac{\sqrt{\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2/(n-1)}}{\overline{y}}}$$

(6)

4. Results

Table 10 summarizes statistical performance metrics for the simulation model.

Table 10. Summary of statistical performance metrics for the simulation model.

Variable	Unit	R2	RMSE	CVRMSE	ASHRAE Guideline 14 (Hourly)	Status
Indoor Temperature	°C	0.68	7.7–10.6	24.3–42.4%	N/A	Moderate Agreement
VRF Electricity	kWh	0.32	2.0–2.7	153–590%	<30%	Not Calibrated
Boiler Energy	MJ	-	0.2–4.4	95–118%	<30%	Not Calibrated

4.1. Indoor Temperature

Figure 10 presents the scatterplot comparing measured and simulated indoor temperatures throughout the monitoring period. Each data point is shown as a blue cross, revealing a general alignment along the 1:1 reference line. Although deviations are observed, particularly in higher temperature ranges, most data points cluster around the 1:1 line, indicating that the simulation replicated the overall trend of the measured indoor conditions. The fitted regression line lies below the 1:1 line, suggesting a systematic bias in the model predictions. The regression slope, being less than unity, indicates that fluctuations in the measured temperature are dampened in the simulated results, while the non-zero intercept implies a consistent offset. The coefficient of determination, $R^2$ was 0.68 indicating a moderate level of agreement. This suggests that the simulation captures a substantial portion of the variance in measured indoor temperatures but exhibits discrepancies, notably under extreme conditions. These findings highlight the limitations of the current modeling and calibration approach.

Figure 10. Comparison of measured and simulated indoor temperatures.

Figure 11a depicts the time series of measured and simulated indoor temperatures for the second-floor office in January, alongside simulated profiles for the adjacent meeting room and director’s office. The measured temperature remained relatively stable between 22 and 24 °C during occupied hours, with noticeable drops during unoccupied periods, reflecting the actual heating schedule. In contrast, the simulated results exhibited greater fluctuations, with frequent peaks exceeding 30 °C, which were not observed in the measurements. The baseline of the simulated curves was consistently higher than the measured profiles, indicating systematic overestimation. The RMSE for January was 7.7 °C, corresponding to a CVRMSE of 34.5%. While the model partially captured the diurnal heating trend, it substantially overpredicted indoor temperatures, leading to a relatively high error. Figure 11b presents the corresponding results for July. The measured indoor temperatures remained within a narrow range of approximately 27–29 °C, consistent with cooling operation. The simulated profiles, however, exhibited considerable variability, with frequent short-term spikes exceeding 35–40 °C, and in some cases approaching 60 °C. Such unrealistic oscillations indicate that the model did not adequately replicate the actual cooling system control behavior. The monthly performance indicators further reflect this discrepancy, with an RMSE of 10.6 °C and a CVRMSE of 37.9%, both substantially above acceptable thresholds. These results confirm that the model demonstrated limited capability in replicating realistic indoor cooling performance, particularly under summer peak load conditions.

Figure 11. Measured vs. simulated indoor temperatures in the 2F office during (a) winter (January) and (b) summer (July).

Figure 12 compares the monthly mean indoor temperatures of the second-floor office between measured and simulated data. The measured values ranged from 20 to 28 °C, exhibiting seasonal variation consistent with heating in winter and cooling in summer. By contrast, the simulated values were consistently higher, frequently exceeding 29 °C in summer and surpassing 30 °C even in transitional months. The bar chart highlights this systematic bias, demonstrating that the model tended to overestimate indoor temperatures across all seasons.

Figure 12. Comparison of measured and simulated monthly mean indoor temperatures for the 2F office.

Quantitatively, the CVRMSE for monthly mean indoor temperatures ranged from 24.3% to 42.4%, with typical values around 30–35%. These relatively high errors indicate that, while the simulation mirrored the overall seasonal patterns of indoor temperature, it lacked the precision to capture absolute temperature levels with sufficient accuracy under both heating and cooling conditions.

4.2. VRF Heat Pump System

Figure 13 depicts the scatterplot comparing measured and simulated hourly electricity consumption of the VRF system. The data points are widely dispersed, forming clusters at discrete load levels that reflect the staged operation of indoor units. The red dashed line represents the 1:1 reference, while the black dashed line indicates the linear regression fit. Most points fall below the 1:1 line, demonstrating a consistent underestimation of electricity consumption by the simulation model, particularly under high-load conditions. The coefficient of determination ($R^2$) of 0.32 indicates only a weak correlation between measured and simulated values, implying that although some operational patterns are reflected, the model fails to capture the magnitude and variability of actual power demand. The discrepancy is especially pronounced at low and intermediate loads, where the simulated results exhibit limited variation relative to the measurements.

Figure 13. Scatterplot comparing measured and simulated electricity consumption of the VRF system.

These deviations can be attributed to the inherent constraints of the proxy-calibration approach in TRNSYS. The Type954c module does not explicitly account for inverter-driven compressor dynamics or electronic expansion valve control, which are critical to the non-linear load–power relationship of VRF systems. Moreover, the absence of disaggregated indoor unit power data restricted calibration to aggregated values, further reducing model fidelity. Collectively, Figure 13 demonstrates that the adopted proxy-calibration can provide only a first-order approximation of VRF power consumption. While it serves as a valid baseline, the low $R^2$ and systematic underestimation emphasize the need for more advanced methods, such as empirical curve-fitting and control logic representation, to improve predictive capability.

Figure 14a presents the time-series comparison of measured and simulated electricity consumption for January, representative of heating season operation. The measured profile (i.e., blue solid line) exhibits intermittent peaks aligned with actual heating demand, whereas the simulated profile (i.e., red dashed line) displays more frequent and pronounced spikes. This mismatch indicates systematic overprediction of peak loads and underprediction during low-demand periods, leading to excessive variance in the simulated data. The monthly error analysis yields an RMSE of 2.0 kWh and a CVRMSE of 245.6%, confirming a significant discrepancy relative to field measurements. Figure 14b illustrates the July results, representing cooling season performance. Consistent with the heating season results, the simulated profile overestimates both the frequency and magnitude of power consumption. While measured values remain within a relatively narrow band, the simulation exhibits excessive oscillations and higher peaks. The RMSE of 2.7 kWh and CVRMSE of 343.6% again highlight the large deviation from actual operation.

Figure 14. Time series comparison of measured and simulated electricity consumption of the VRF system during (a) Winter (January) and (b) Summer (July).

Figure 15 compares the monthly average electricity consumption of the VRF system. The measured values (i.e., solid blue bars) exhibit seasonal variation, with pronounced loads during summer and winter and reduced consumption in transitional months. By contrast, the simulated results (i.e., striped bars) deviate substantially, underpredicting winter consumption while significantly overestimating summer consumption, particularly from June through August, where the predicted demand nearly doubles the observed values. This discrepancy illustrates the model’s difficulty in capturing seasonal performance consistently. Quantitatively, the CVRMSE for monthly VRF electricity consumption ranged from 153% to 590%, far beyond acceptable calibration thresholds. While the simulation reflects broad seasonal demand trends, its predictive accuracy remains severely limited, especially under peak cooling conditions. The persistently high error levels confirm that the proxy-calibration method, though useful for approximating VRF operation in TRNSYS, is insufficient for representing the actual dynamics of electricity consumption.

Figure 15. Comparison of measured and simulated monthly electricity consumption of the VRF system.

4.3. Boiler

Figure 16 depicts the scatterplot of measured versus simulated boiler energy consumption. The measured data exhibit a wide range, reaching nearly 40,000 MJ, whereas the simulated outputs remain constrained below 6000 MJ. Most simulated points are located far below the 1:1 reference line, indicating substantial underestimation. The regression line further highlights a weak statistical relationship and a systematic bias. This discrepancy stems primarily from the simplified representation of the system using Type927, which cannot accurately replicate the cascade operation characteristics of the installed boiler. Consequently, the model provides only a coarse estimate of energy demand and lacks sufficient accuracy for rigorous performance analysis.

Figure 16. Scatterplot comparing measured and simulated boiler energy consumption.

Figure 17a depicts the time-series comparison for January. The measured profile, characterized by frequent peaks approaching 40,000 MJ, reflects the significant heating demand during the winter. In contrast, the simulated values remain consistently low and nearly flat, failing to replicate both the magnitude and temporal variability of actual operation. Figure 17b illustrates the results for July, when actual boiler operation was limited but still exhibited sporadic low-level activity. The simulation, however, yielded negligible consumption throughout, effectively omitting these minor events altogether.

Figure 17. Comparison of measured and simulated boiler energy consumption: (a) January time series, (b) July time series, and (c) monthly averages.

Figure 17c presents the monthly comparison. The measured data reveal a distinct seasonal pattern, with substantial consumption in the winter months and negligible use in summer, consistent with typical heating demand. By contrast, the simulated values underestimate consumption across nearly all months, exhibiting limited sensitivity to seasonal variation. The error analysis underscores this discrepancy, with monthly RMSE values ranging from 0.2 to 4.4 MJ and CVRMSE levels generally exceeding 90%. These results clearly demonstrate that the simplified boiler model fails to replicate the observed seasonal demand profiles and operational dynamics.

Overall, the findings confirm that while the simplified TRNSYS representation offers a broad approximation of boiler performance, it lacks the fidelity required for detailed energy performance assessment. Future work should incorporate more advanced modeling approaches or test-bed–based calibration to better represent cascade operation and partial-load dynamics.

Collectively, the substantial discrepancy between simulated and measured boiler energy consumption underscores the limitations of using a single-stage heat pump model (Type927) to represent a cascade system. This finding emphasizes the critical need for more advanced modeling approaches to accurately replicate the operational dynamics of complex heating systems.

5. Discussion

This study evaluated a method to approximate the performance of a multi-unit VRF system in TRNSYS using a load-ratio mapping derived from indoor-unit combinations. While this approach effectively captured part-load behavior, it does not constitute a comprehensive calibration, which necessitates systematic parameter tuning against measured data. Consequently, this method is termed “Proxy-Calibration”, serving as a foundational step toward empirical curve fitting in future research. A key contribution of this work lies in proposing a standardized procedural framework applicable when no dedicated VRF component exists in TRNSYS. Although power consumption for individual indoor units was not monitored, group-level data allowed for approximate correction through state classification and coefficient fitting. However, several technical limitations were identified, specifically the necessity to truncate out-of-range load ratios (below 50% or above 130%) and the absence of advanced extrapolation techniques such as spline interpolation or constrained regression.

5.1. Analysis of Physical and Modeling Discrepancies

The substantial deviations observed in electricity consumption—with CVRMSE values reaching 153–590% for the VRF system—can be attributed to the fundamental structural limitations of the proxy components used in TRNSYS. Unlike dedicated VRF modules in tools such as EnergyPlus, which explicitly model variable refrigerant flow dynamics and inverter compressor modulation, the Type954c component relies on a static performance map derived from specific testing conditions. This “black-box” approach fails to capture the non-linear part-load efficiency characteristics of modern inverter-driven outdoor units, particularly under low-load conditions where cycling losses and control logic significantly impact power consumption. Furthermore, the extreme underestimation of boiler energy (CVRMSE 95–118%) highlights the inability of the single-stage water-to-water heat pump model (Type927) to replicate the operational logic of the installed cascade system. The actual system operates multiple units in series to maintain high-temperature water output, a behavior that cannot be simulated by merely scaling the capacity of a generic heat pump model.

A quantitative comparison with previous studies underscores this “performance gap.” Research utilizing dedicated VRF modules (e.g., EnergyPlus) typically reports CVRMSE values in the range of 15–25% for electricity consumption [17,27]. The significantly higher errors in this study confirm that while the Proxy-Calibration method can approximate thermal capacity trends ($R^2$ = 0.68), it lacks the fidelity required for precise energy prediction due to the absence of explicit control logic. From the perspective of human indices, specifically thermal comfort, the overestimation of indoor temperatures implies that the simulation may predict a higher level of occupant satisfaction than actually experienced [28,29,30]. Given the nature of public office buildings, where sedentary activities (approx. 1.0–1.2 MET) dominate, even minor deviations in indoor temperature can significantly impact the perceived thermal environment [31,32]. Therefore, the discrepancies found in this study suggest that while the proxy model captures general thermal trends, it necessitates careful interpretation when used for comfort-based performance assessment.

5.2. Evaluation of Practical Applicability and Limitations

Based on the validation results, the practical utility of the proposed Proxy-Calibration method warrants clear delineation. The high prediction errors render this approach unsuitable for applications requiring rigorous energy accounting, such as Measurement and Verification (M&V) protocols or energy performance contracting, where compliance with ASHRAE Guideline 14 is mandatory. The model’s inability to replicate precise energy consumption levels confirms its limitation as a “black-box” approximation. However, the method retains significant practical value as a procedural framework for comparative analysis and early-stage design. In scenarios where dedicated VRF simulation modules are unavailable—a common constraint in TRNSYS—this proxy approach provides a critical means to represent multi-unit system interactions. While absolute energy values are underestimated, the model successfully reproduces indoor thermal trends and captures the relative impact of part-load conditions. Therefore, this approach is well-suited for trend analysis, such as evaluating the relative efficiency of different indoor-unit zoning strategies or sizing system capacities based on thermal load patterns, serving as a pragmatic interim solution until explicit VRF libraries are fully integrated into the platform.

5.3. Measurable Improvements and Future Research Directions

To overcome the identified limitations and bridge the performance gap, future iterations of this proxy method should incorporate specific, quantifiable enhancements. First, the reliance on static manufacturer catalog data must be replaced by empirical curve fitting derived from controlled test-bed measurements. The development of regression models that explicitly correlate part-load ratio and outdoor conditions with power consumption will significantly reduce the black-box uncertainty inherent in the current Type954c model.

Second, explicit control logic must be integrated into the simulation loop to replicate the non-linear behavior of inverter-driven compressors. This entails programming custom controllers (e.g., utilizing Type155 or equation-based logic) to simulate the modulation frequency and electronic expansion valve openings, as opposed to relying on simple on/off signals. Finally, validating these enhanced models within a controlled environmental chamber—where occupant behavior and weather variability are strictly regulated—will allow for the isolation of mechanical performance errors from stochastic behavioral factors, thereby providing a rigorous pathway toward compliance with ASHRAE calibration standards. Specifically, introducing calibration coefficients to address uncertainties related to building heat capacity and equipment part-load efficiency will serve as the primary mechanism to mitigate integral deviations observed in this study.

6. Conclusions

This study evaluated a standardized “Proxy-Calibration” framework to approximate the performance of multi-unit VRF systems in TRNSYS, specifically addressing the absence of dedicated simulation components. By defining indoor-unit combinations as state variables, the proposed method enables the representation of part-load behavior in software environments where explicit modeling is unavailable. However, given the identified limitations, this study characterizes the method as a preliminary investigation rather than a definitive solution.

The validation results using field data revealed a distinct decoupling between thermal and energy performance. While the proxy model effectively reproduced indoor thermal trends ($R^2$ = 0.68), it failed to predict electricity consumption accurately. The CVRMSE values ranged from 95% to 118% for the boiler and 153% to 590% for the VRF system. These substantial deviations confirm that the method, in its current form, does not yield a validated prediction tool that complies with standard calibration criteria (e.g., ASHRAE Guideline 14). The discrepancies are primarily attributed to the “black-box” nature of the generic components (Type954c/Type927), which cannot capture the complex control logic of inverter-driven compressors and cascade heating operations.

Consequently, future research should extend the current specifications to bridge this performance gap. Critical next steps include the following: (1) implementing empirical performance curve fitting based on controlled test-bed measurements to replace static manufacturer data; (2) integrating explicit control logic for inverter modulation and electronic expansion valves into the simulation loop; and (3) validating these advanced models in environmental chambers to isolate mechanical performance from behavioral uncertainties. Ultimately, this study serves as a methodological baseline, highlighting both the procedural feasibility and the quantitative limitations of proxy modeling for existing building retrofits.