Comparative Analysis of Horticultural Lighting Systems: A Computational and Experimental Approach

Abstract

This paper presents a comprehensive comparative analysis of two horticultural lighting systems: a novel system that employs COB LEDs arranged in a centered square sequence and a conventional system that utilizes a uniform matrix of Samsung Gen 2 Horticulture Modules. Luminous flux simulations are conducted using a custom radiosity model that is integrated with a global optimization algorithm based on Differential Evolution (DE) — which generates initial luminous flux assignments that are subsequently validated using DIALux, an industry standard lighting simulation tool. The lux values output by DIALux were converted to PPFD using a methodology based on the LED’s normalized spectral power distribution, yielding conversion factors of 0.0179 and 0.0138 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}\,\mathrm{lux}^{-1}$ for the Samsung Gen~2 module ($\lambda\in[380,780]$ nm) and the Samsung COB, respectively (See section: Lux to PPFD Conversion for details). The DE-based global optimization algorithm is applied to refine LED intensity assignments in a stratified arrangement (described by the centered square number sequence, $C(n) = (2n-1)^2$). The results indicate that the novel design achieves superior PPFD uniformity (Degree of Uniformity (DOU) of approximately 98%) and lower LED component costs (up to 3.7× lower) compared to conventional systems. These findings underscore the technical and economic advantages of the novel design for advanced horticultural applications.

1. Introduction

Efficient and uniform illumination is critical for optimal plant growth and yield in controlled environment agriculture (CEA). This study investigates the performance of a novel horticultural lighting system, comparing it to a conventional approach. The primary focus is on analyzing the distribution of Photosynthetic Photon Flux Density (PPFD), a key metric for assessing lighting effectiveness. Luminous flux simulations were performed using a custom radiosity model integrated with a DE-based global optimization algorithm, in conjunction with DIALux, where the radiosity model is used only to provide initial luminous flux assignments and DIALux (a trusted standard) validates the results. The simulated lux values are then converted to PPFD using a conversion factor specific to the spectral characteristics of the LEDs (expressed in $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$).

2. System Descriptions

2.1 Novel Lighting System

The novel lighting system utilizes a plurality of chip-on-board (COB) LEDs (Samsung BXRE-30E6500-C-83). These COBs exhibit a near-Lambertian radiation pattern without secondary optics. The corresponding .ies ray file for the COBs was sourced from Samsung and used in the DIALux simulations.

Their arrangement follows a centered square number sequence pattern (OEIS: A001844)(Sloane, N. J. A. (n.d.). The On-Line Encyclopedia of Integer Sequences.), rotated by 45 degrees to form a square or rectangular lighting array. Mathematically, the pattern is described by:

$C(n) = (2n-1)^2$

$n$: layer (with 1 LED in the center, 4 in the first square ring, 8 in the second, etc.)

For example, in some embodiments, a square grow space may use 61 COBs, whereas a rectangular space may incorporate 127 COBs by combining two 61-COB squares with a 5-COB connector module. This design is intended to optimize the uniformity of the PPFD in the illuminated area by enabling layer-wise luminous flux assignments informed by the proprietary DE-based global optimization algorithm.

2.2 Conventional Lighting System

The conventional system employs a plurality of Samsung Gen 2 Horticulture Modules (MFG. PN: SI-B8T502560WW), arranged in a uniform rectangular matrix—a common configuration in horticultural lighting. The corresponding .ies ray file was sourced from Samsung and used in the DIALux simulations.

3. Simulation Methodology

The simulations were performed using our custom radiosity model in conjunction with DIALux evo lighting design software. The radiosity model accurately predicts interreflections within the enclosed environment and utilizes a DE-based global optimization algorithm to discover optimal layer-wise luminous flux assignments for the COBs. It is used solely to generate initial intensity assignments that are then manually entered into DIALux. All LED modules in the conventional arrangement were assigned the same luminous flux, following the standard approach.

The photometric data (from the .ies files) along with the geometric arrangement and surface reflectances are used by DIALux to produce validated lux distributions. These lux values are converted to PPFD (expressed in $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$) using a conversion factor (See section: Lux to PPFD Conversion for details on this conversion), with justification based on the Samsung COB and Gen 2 module datasheets.

3.1 Lux to PPFD Conversion

The conversion from illuminance (lux) to photosynthetic photon flux density (PPFD, in $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$) is determined by digitizing the LED’s normalized spectral power distribution (SPD), $I(\lambda)$, over a wavelength range $[\lambda_1,\lambda_2]$. In our approach, the PPFD is calculated as

\[ \text{PPFD} = \frac{10^6}{N_A\,h\,c} \int_{\lambda_1}^{\lambda_2} I(\lambda) \; \Bigl( \lambda\times10^{-9}\Bigr) \, d\lambda \]

$h$: Planck's constant
$c$: the speed of light
$N_A$: Avogadro's number
$10^6$: converts moles to micromoles

The illuminance is determined by

\[ E = 683 \int_{\lambda_1}^{\lambda_2} I(\lambda)\, V(\lambda) \, d\lambda \]

$V(\lambda)$: the CIE photopic luminous efficiency function
$683\,\mathrm{lux\,W}^{-1}$: the maximum luminous efficacy of radiation

Consequently, the lux-to-PPFD conversion factor, $C$ (in $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}\,\mathrm{lux}^{-1}$), is given by

\[ C = \frac{\text{PPFD}}{E} = \frac{\frac{10^6}{N_A\,h\,c} \displaystyle \int_{\lambda_1}^{\lambda_2} I(\lambda) \; \Bigl( \lambda\times10^{-9}\Bigr) \, d\lambda}{683 \displaystyle \int_{\lambda_1}^{\lambda_2} I(\lambda)\, V(\lambda) \, d\lambda} \]

For the Samsung Gen 2 Horticulture Module ($\lambda \in [380,780]$ nm) and the Samsung COBs (with their corresponding measured SPD), our analysis yields conversion factors of 0.0179 and 0.0138 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}\,\mathrm{lux}^{-1}$, respectively. A more accurate determination would require absolute SPD measurements; however, these values provide a useful basis for comparison in our study.

4. Results and Discussion

4.1 PPFD Uniformity Analysis

Figures 3 and 4 show the PAR maps for the novel and conventional systems, respectively. Figures 5 and 6 display the corresponding heatmaps.

Tables 1 and 2 summarize the key performance metrics: average PPFD, RMSE, Degree of Uniformity (DOU), MAD, Coefficient of Variation (CV), and the minimum and maximum PPFD values. The novel system achieves a DOU of 98.14% versus 84.98% for the conventional system.

**Table 1:** Simulation Results - Novel System
Metric	Value
RMSE	10.28
DOU (%)	98.77
MAD	7.99
CV (%)	1.23
Average PPFD	838.98 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$
Min. PPFD	815.14 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$
Max PPFD	865.25 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$
Min/Max PPFD	0.94
Min/Avg. PPFD	0.97

**Table 2:** Simulation Results - Conventional System
Metric	Value
RMSE	138.10
DOU (%)	83.37
MAD	119.40
CV (%)	16.63
Average PPFD	830.55 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$
Min. PPFD	481.42 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$
Max PPFD	1010.28 $\mu\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$
Min/Max PPFD	0.48
Min/Avg. PPFD	0.58

Mathematical Representation of Metrics

Here, we define the mathematical formulations used to calculate the metrics presented in Tables 1 and 2. Let $P_i$ represent the PPFD value at the $i$-th measurement point, and let $n$ be the total number of measurement points (in this case, $n=98$).

Average PPFD ($\text{PPFD}_{\text{avg}}$): The average PPFD is simply the arithmetic mean of all PPFD measurements:

\[\text{PPFD}_{\text{avg}} = \frac{1}{n} \sum_{i=1}^{n} P_i\]
Root Mean Squared Error (RMSE): RMSE quantifies the difference between the measured PPFD values and the average PPFD:

\[\text{RMSE} = \sqrt{\frac{\sum_{i=1}^{n} (P_i - \text{PPFD}_{\text{avg}})^2}{n}}\]
Degree of Uniformity (DOU): DOU is calculated based on the RMSE and the average PPFD:

\[\text{DOU} = 100 \times \left(1 - \frac{\text{RMSE}}{\text{PPFD}_{\text{avg}}}\right)\]
Mean Absolute Deviation (MAD): MAD measures the average absolute difference between each PPFD value and the average PPFD:

\[\text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |P_i - \text{PPFD}_{\text{avg}}|\]
Coefficient of Variation (CV): CV is the ratio of the standard deviation ($\sigma$) to the average PPFD, expressed as a percentage:

\[\text{CV} = 100 \times \frac{\sigma}{\text{PPFD}_{\text{avg}}}\]

where the standard deviation, $\sigma$, is calculated as:

\[\sigma = \sqrt{\frac{\sum_{i=1}^{n} (P_i - \text{PPFD}_{\text{avg}})^2}{n}}\]

Note: In this specific case, since we are calculating sample statistics and using all data points, the sample standard deviation and population standard deviation are equivalent.

4.3 Cost Analysis

A preliminary cost analysis reveals that using 127 Samsung COBs at $11.81352 per COB results in a total LED cost of $1,500.32. In contrast, employing 210 Samsung Gen 2 modules at $26.56317 per module results in a cost of $5,578.27. This indicates that the conventional system’s LED cost is approximately 3.7 times higher than that of the novel design.