A New Trend for Indoor Lighting Design Based on A Hybrid Methodology

2.1 Traditional Lighting Design Methods

Lumen Method: Focuses on achieving a target illuminance level (measured in lux) for a given space. It calculates the total required luminous flux and distributes it via an appropriate number of light fixtures. While accurate for uniform lighting, it can be computationally intensive and may not optimize for energy efficiency.

Specific Connected Load (or Wattage) Method: Simpler and faster, this method uses predefined power density values (Watts per square meter) for different room types/activities. It's efficient for initial estimates but lacks precision and can lead to over- or under-lighting.

2.2 Proposed Hybrid Methodology

The hybrid method strategically combines these approaches:

1. Initial Sizing with Specific Load Method: Use power density benchmarks for a rapid, first-pass estimation of the total connected load and approximate number of fixtures.
2. Precision Calibration with Lumen Method: Refine the initial layout using the lumen method to ensure the target illuminance is met precisely at all critical points, adjusting fixture placement and type.
3. Iterative Optimization Loop: An algorithm iterates between the two methods, minimizing the total connected load (energy) while strictly maintaining illuminance constraints, thereby finding the most economical design.

2.3 Mathematical Model Development

The methodology is formalized into a mathematical optimization model. The primary objective is to minimize total power consumption $P_{total}$:

$\min P_{total} = \sum_{i=1}^{N} n_i \cdot P_i$

Subject to the illuminance constraint at each calculation point $j$:

$E_j = \sum_{i=1}^{N} \frac{n_i \cdot \Phi_i \cdot CU \cdot MF}{A} \geq E_{target}$

Where:

• $n_i$: Number of fixtures of type $i$
• $P_i$: Power per fixture of type $i$
• $\Phi_i$: Luminous flux per fixture (lumens)
• $CU$: Coefficient of Utilization
• $MF$: Maintenance Factor
• $A$: Area of the space
• $E_{target}$: Required illuminance level (lux)

3.1 MATLAB® Implementation

The mathematical model was implemented in MATLAB® to automate the hybrid design process. The script performs the following core functions:

1. Input Module: Accepts room dimensions, reflectance values, target illuminance, and available fixture specifications (lumens, wattage, photometric data).
2. Hybrid Algorithm Core: Executes the iterative loop between the specific load estimation and the lumen-based verification/refinement.
3. Optimization Solver: Employs linear or integer programming techniques to find the optimal fixture count and layout.
4. Output & Reporting: Generates detailed reports including final layout, total energy consumption, cost analysis, and illuminance distribution maps.

3.2 Case Study Design

The methodology was tested on two primary case studies representing the Egyptian market:

• Case Study 1 (Residential): A standard apartment with living room, bedrooms, and kitchen.
• Case Study 2 (Commercial): An open-plan office space.

For each, designs were created using: a) Traditional Lumen Method, b) Traditional Specific Load Method, and c) The Proposed Hybrid Method. All designs used the same LED fixture specifications for fair comparison.

4.1 Energy Savings Results

The hybrid method consistently outperformed the traditional methods:

• Compared to Lumen Method: Achieved 8-15% reduction in connected load by optimizing fixture placement and count, not just meeting but not excessively exceeding illuminance targets.
• Compared to Specific Load Method: Achieved similar or slightly lower energy use while guaranteeing accurate and uniform illuminance, which the specific load method often failed to do.

Scaled National Impact (Egypt): The paper extrapolates the case study savings to the national level for residential and commercial sectors, projecting potential annual savings of approximately 4489.43 million E£ (≈ 280.59 million USD).

4.2 Cost-Benefit Analysis

Savings stem from two factors: 1) Reduced energy consumption, and 2) Potential reduction in the number of fixtures and associated installation costs (wiring, supports). The hybrid method's optimal design often led to a lower total number of higher-efficacy fixtures compared to a standard lumen method layout.

4.3 Validation with DIALux

To ensure practical validity, the lighting layouts generated by the hybrid method's MATLAB script were modeled in DIALux, a industry-standard lighting design software. The simulated illuminance values from DIALux closely matched the targets set in the hybrid model, validating the accuracy of the proposed methodology's photometric calculations.