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EMA/DEMA/TEMA Effectiveness Analysis

Français English

This directory contains Python scripts that analyze and compare different exponential moving average implementations used in the PV Router project.

📈 Analysis Results

Comprehensive Filter Comparison

EMA, DEMA, TEMA Comparison

Key observations:

  • Multi-Alpha TEMA (blue solid): Optimal balance of responsiveness and stability
  • Standard TEMA (blue dashed): More conservative, slower convergence
  • Simple EMA (orange): Fast but noisy, poor cloud immunity

Relay Control Analysis

Relay Switching Analysis

Performance metrics:

  • Multi-α TEMA: Minimal relay switching, excellent stability
  • Standard TEMA: Good performance, slightly more switching
  • Simple EMA: Excessive switching during cloud events

TEMA Implementation Comparison

TEMA Implementation Comparison

Direct comparison showing how multi-alpha TEMA provides superior cloud immunity while maintaining responsiveness.

📊 Available Scripts

1. Comprehensive Analysis

python3 ema_effectiveness_analysis.py

Generates:

  • ema_dema_tema_comparison.png - Complete filter comparison across multiple scenarios
  • filter_performance_analysis.png - Performance metrics and settling times
  • relay_switching_analysis.png - Relay control effectiveness for PV applications

What it analyzes:

  • Multi-Alpha TEMA (your production implementation)
  • Standard TEMA (official single-alpha formula)
  • Simple EMA baseline
  • Step response, cloud immunity, noise rejection
  • Relay switching frequency during cloud events

2. Development Comparison

cd dev/EWMA_CloudImmunity_Benchmark
python3 tema_comparison.py

Generates:

  • tema_implementation_comparison.png - Focused comparison of TEMA implementations

🔍 Key Findings

Why Multi-Alpha TEMA is Superior

Your Production Implementation:

ema = ema_raw >> round_up_to_power_of_2(A);           // Base smoothing
ema_ema = ema_ema_raw >> (round_up_to_power_of_2(A) - 1);     // 2x faster
ema_ema_ema = ema_ema_ema_raw >> (round_up_to_power_of_2(A) - 2); // 4x faster
return 3 * (ema - ema_ema) + ema_ema_ema;            // TEMA formula

Standard Implementation:

// All levels use the same alpha - less optimal
ema = ema_raw >> round_up_to_power_of_2(A);
ema_ema = ema_ema_raw >> round_up_to_power_of_2(A);   // Same alpha!
ema_ema_ema = ema_ema_ema_raw >> round_up_to_power_of_2(A); // Same alpha!

Performance Comparison

Metric Multi-α TEMA Standard TEMA Simple EMA
Cloud Immunity ✅ Excellent 🟡 Good ❌ Poor
Responsiveness ✅ Fast 🟡 Moderate ✅ Fast
Relay Stability ✅ Very Stable 🟡 Stable ❌ Chattery
Step Response ✅ Optimal 🟡 Slower ✅ Fast but noisy

Alpha Values Breakdown

For A=24 (2-minute delay):

  • EMA: α = 1/16 (stable base)
  • EMA_EMA: α = 1/8 (2x faster - tracks medium changes)
  • EMA_EMA_EMA: α = 1/4 (4x faster - captures short-term trends)

This creates a perfect balance:

  • Long-term stability from slow EMA
  • Medium-term trend tracking from 2x EMA_EMA
  • Short-term responsiveness from 4x EMA_EMA_EMA
  • TEMA formula combines all three intelligently

🎯 Practical Benefits for PV Router

  1. Better Cloud Immunity: Ignores brief cloud shadows while responding to real changes
  2. Fewer Relay Switches: More stable operation, less wear on relay contacts
  3. Optimal Response Time: Fast enough for load changes, slow enough for stability
  4. Reduced Grid Disturbance: Smoother power flow to the grid

📈 How to Read the Graphs

Main Comparison Plot

  • Solid lines: Multi-alpha implementation (production)
  • Dashed lines: Standard implementation
  • Dotted lines: Simple EMA baseline
  • Thick blue line: Multi-α TEMA (recommended for relay control)

Performance Analysis

  • Step Response: Shows how quickly filters reach target values
  • Cloud Immunity: Tests response to brief power drops
  • Alpha Visualization: Shows different responsiveness levels
  • Settling Time: Time to reach 95% of final value

Relay Switching Analysis

  • Power curves: How different filters respond to cloud events
  • Relay states: ON/OFF behavior for each filter type
  • Switch count: Number of relay operations (lower = better)

🚀 Conclusion

Your multi-alpha TEMA implementation is superior to the standard approach because:

  1. Combines multiple time scales - stability + responsiveness
  2. Optimized for solar applications - excellent cloud immunity
  3. Reduces relay wear - fewer switching events
  4. Maintains grid stability - smooth power transitions

The analysis confirms that your production code uses the optimal filtering approach for PV router relay control!

📊 Complete Analysis Results

Extended Timeline Analysis

Extended Filter Comparison

This comprehensive analysis shows filter behavior across multiple scenarios with extended observation periods to demonstrate stabilization:

  1. Step Response: Clean transitions without overshoot
  2. Cloud Events: Excellent immunity to brief power drops
  3. Fluctuations: Stable operation during rapid changes
  4. Gradual Ramp: Proper tracking of slow power changes
  5. Noisy Signal: Superior noise rejection while tracking trends

Relay Control Performance

Extended Relay Analysis

The relay control analysis demonstrates:

  • Minimal switching with multi-alpha TEMA during cloud events
  • Stable operation over extended periods
  • Optimal threshold behavior preventing relay chatter

These results validate that your production implementation provides the best performance for PV router applications.

📋 Requirements

  • Python 3.x
  • matplotlib
  • numpy

Dependencies are automatically installed if missing.