Implementing Mamdani Fuzzy Logic for Real-Time IoT-Based Electrical Energy and Room Temperature Monitoring

Introduction: The Critical Need for Energy Monitoring in Modern Indonesia

Electricity has evolved from early experiments in the 17th century to become the backbone of modern civilization. From William Gilbert's pioneering work to Michael Faraday's electromagnetic discoveries and Nikola Tesla's alternating current systems, electricity has powered industrial revolutions and transformed human existence. Now, electricity supports everything from household appliances to industrial operations and emerging technologies like renewable energy and smart grids (Baldwin 2020; Heilbron 2020).

Indonesia faces a particularly pressing energy challenge. As the largest electricity consumer in ASEAN, the country accounts for 36% of regional energy demand and consumes 66% more energy than Thailand (Energy Agency 2016). This high consumption is driven by rapid economic growth, urbanization, and industrialization. With projections indicating Indonesia's population could reach 381 million by 2045, the strain on energy resources is becoming increasingly severe, exacerbated by significant energy waste in public sectors such as healthcare facilities, educational institutions, and office buildings (McNeil et al. 2019).

While Indonesia has made strides in renewable energy—exemplified by the 145 MW Cirata Floating Solar Power Plant, a collaboration between PT. PLN and Masdar that can power 50,000 homes and reduce carbon emissions by 214,000 tons annually—household electricity consumption remains high due to extensive use of electronic devices (Asmarini 2023). The industrial sector actively adopts energy conservation through audits to identify waste and cost efficiency, with IoT-based automated systems proving more effective than manual methods by enabling real-time monitoring and consumption pattern analysis (Chen et al. 2018; Henao-Hernández et al. 2019).

However, the lack of real-time monitoring systems in office environments leads to systematic energy waste. IoT-based solutions become crucial for providing data and designing optimization strategies. Implementing this technology not only supports efficiency but also drives energy sustainability for the future (Alavi et al. 2018).

Mathematical Foundation of Sensor Calibration and Accuracy Assessment

Sensor Error Calculation Methodology

The accuracy of sensor measurements was rigorously evaluated using mathematical error analysis. The percentage error for each sensor reading was calculated by comparing sensor values against reference measurements from calibrated instruments.

According to research by Sinaga and Irawati (2018), the accuracy of a measurement technique is inversely proportional to the Mean Absolute Percentage Error (MAPE) and directly proportional to Mean Absolute Error (MAE). Lower MAPE values and smaller MAE indicate higher accuracy levels.

DHT-11 Sensor Performance Analysis

The DHT-11 temperature sensor demonstrated exceptional performance with an average error of only 0.11% for temperature measurements and 0.15% for relative humidity when validated against the HTC-1 reference device. This exceptional performance translates to accuracy levels of 99.88% for temperature and 99.84% for humidity, validating the sensor's reliability for precise environmental monitoring applications. According to Components101 (2021), the DHT-11 consumes 0.3 mA during measurement operations and drops to 60 μA in standby conditions.

Electrical Parameter Analysis and Power Factor Calculations

The comprehensive electrical monitoring using the PZEM-004T sensor revealed critical insights into system efficiency. The power factor, a crucial indicator of electrical system efficiency, was calculated using the relationship between active power (P), apparent power (S), and reactive power (Q):

$$ \text{Power Factor} = \cos \phi = \frac{P}{S} $$

Where measurement data showed:

• Active Power (P) = 30.83 W
• Apparent Power (S) = 56.87 VA
• Reactive Power (Q) = 47.13 VAR

The power factor calculation:

$$ \text{Power Factor} = \frac{30.83}{56.87} = 0.542 $$

This low power factor indicates significant inefficiency, with only 54.2% of the apparent power being converted to useful work. The relationship between these power components follows the power triangle:

$$ S = \sqrt{P^2 + Q^2} = \sqrt{30.83^2 + 47.13^2} = 56.87 \text{ VA} $$

The sensor performance was validated against manufacturer specifications from the PZEM-004T datasheet (Peacefair 2019), confirming measurement consistency for voltage, current, power, and energy parameters.

Mamdani Fuzzy Logic System: Mathematical Implementation

Membership Function Formulation

The electrical monitoring system implements a sophisticated four-input, one-output Mamdani fuzzy logic system. Each input variable uses trapezoidal membership functions defined mathematically as:

For a trapezoidal membership function with parameters [a, b, c, d]:

$$ \mu(x) = \max\left(\min\left(\frac{x-a}{b-a}, 1, \frac{d-x}{d-c}\right), 0\right) $$

AC Current Membership Functions:

• Low: [0, 0, 2, 5]
• Medium: [4, 8, 12, 15]
• High: [14.5, 20.5, 101, 101]

AC Power Membership Functions:

• Low: [0, 60, 300, 600]
• Medium: [805.4, 925.4, 1825, 2425]
• High: [1920, 2880, 3120, 4080]

Reactive Power Membership Functions:

• Low: [0, 0, 240, 600]
• Medium: [480, 960, 1800, 2400]
• High: [1800, 2500, 3000, 3000]

Power Factor Membership Functions:

• Poor: [0, 0, 0.5, 0.7]
• Adequate: [0.65, 0.75, 0.8, 0.85]
• Good: [0.83, 0.9, 1, 1]

Output Variable and Defuzzification

The output variable Load_Status uses three trapezoidal membership functions:

• Normal: [-0.1, 0, 0, 0.1]
• Warning: [0.9, 1, 1, 1.1]
• Overload: [1.9, 2, 2, 2.1]

The defuzzification process uses the centroid method to convert fuzzy sets to crisp outputs:

$$ \text{Crisp Output} = \frac{\int \mu(x) \cdot x , dx}{\int \mu(x) , dx} $$

Temperature Classification System

The temperature monitoring system uses a single-input Mamdani fuzzy system with three membership functions:

Temperature Input Membership Functions:

• Cold: [0, 0, 20, 20] (0-20°C)
• Normal: [20, 20, 30, 30] (20-30°C)
• Hot: [30, 30, 40, 40] (30-40°C)

Output Categories:

• Cold: 0
• Normal: 1
• Hot: 2

Fuzzy Inference Process

The Mamdani inference method involves four key steps:

1. Fuzzification: Convert crisp inputs to fuzzy sets using membership functions

   $$ \mu_{\text{Low}}^{\text{Current}}(x) = \max\left(\min\left(\frac{x-0}{2-0}, 1, \frac{5-x}{5-2}\right), 0\right) $$

2. Rule Evaluation: Apply fuzzy operators (AND typically uses minimum)

   $$ \alpha_i = \min(\mu_{A_i}(x_1), \mu_{B_i}(x_2), \mu_{C_i}(x_3), \mu_{D_i}(x_4)) $$

3. Aggregation: Combine output fuzzy sets using maximum operator

   $$ \mu_{\text{aggregated}}(y) = \max_i (\min(\alpha_i, \mu_{E_i}(y))) $$

4. Defuzzification: Convert fuzzy output to crisp value using centroid method

System Performance and Latency Analysis

Real-Time Processing Efficiency

The system demonstrated exceptional real-time performance with end-to-end latency measurements consistently below 2 seconds. This comprehensive testing included:

• Sensor data acquisition and preprocessing
• Fuzzy logic inference computation
• Data transmission via HTTP protocol to Blynk servers
• Mobile application display updates

The latency can be mathematically expressed as:

$$ T_{\text{total}} = T_{\text{sensor}} + T_{\text{processing}} + T_{\text{transmission}} + T_{\text{display}} < 2\text{ seconds} $$

End-to-end validation verified data display on mobile applications, including timestamp accuracy, parameter values, and update intervals across various network conditions.

Energy Efficiency Calculations

The system identified significant energy inefficiency through power factor analysis. The poor power factor of 0.53 indicates substantial reactive power consumption. The required capacitor bank for power factor correction can be calculated using:

$$ Q_c = P \times (\tan \phi_1 - \tan \phi_2) $$

Where:

• $Q_c$: Required capacitor reactive power (VAR)
• $P$: Active power (30.83 W)
• $\phi_1$: Current phase angle ($\cos^{-1}(0.53) = 58^\circ$)
• $\phi_2$: Desired phase angle (targeting $\cos^{-1}(0.95) = 18^\circ$)

Calculation:

$$ Q_c = 30.83 \times (\tan 58^\circ - \tan 18^\circ) = 30.83 \times (1.600 - 0.325) = 39.3 \text{ VAR} $$

Conclusions and Mathematical Insights

The research successfully demonstrates an IoT-based prototype for real-time monitoring of electrical energy and room temperature using Mamdani fuzzy logic. Conducted at PT. Global Kreatif Inovasi from September 2024 to July 2025, this study achieved several key mathematical accomplishments:

• Sensor Accuracy: DHT-11 sensor with 99.88% temperature accuracy and 99.84% humidity accuracy, mathematically verified through comprehensive error analysis against HTC-1 reference measurements
• Electrical Efficiency: Identified 46.8% power factor inefficiency through rigorous power triangle analysis, with PZEM-004T providing consistent electrical parameter readings
• Fuzzy Logic Performance: Implemented 11-rule fuzzy inference system with precise mathematical membership functions for both energy load classification and temperature categorization
• Real-Time Processing: Achieved sub-2-second latency across the complete data pipeline with intuitive Blynk-based interface

The mathematical framework provides a solid foundation for future enhancements, including:

• Adaptive fuzzy systems with self-tuning membership functions
• Machine learning integration for predictive maintenance
• Multi-objective optimization for energy efficiency
• Larger-scale testing to evaluate system reliability across diverse operational scenarios

This research establishes that mathematical rigor combined with fuzzy logic principles can create intelligent energy management systems capable of adapting to dynamic environmental conditions while maintaining computational efficiency suitable for embedded IoT applications, ultimately supporting Indonesia's energy sustainability goals through technological innovation.

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