Application of AI in Electrical/Electronics Engg. (EX-802 (D)) - Unit 5 Short Notes

UNIT 5: APPLICATION OF AI IN ELECTRICAL/ELECTRONICS ENGINEERING

I. NEURAL NETWORKS & LEARNING ARCHITECTURES

A. Radial Basis Function (RBF) Networks

• Architecture: Three-layer feedforward network.

  1. Input Layer: $n$ nodes, passes input vector $$\displaystyle \mathbf{x} \in \mathbb{R}^n $$.

  2. Hidden Layer (Radial Basis Layer): $m$ nodes. Each node computes a radial basis function (typically Gaussian) centered at a vector $$\displaystyle \mathbf{c}_i $$ (prototype/center).

$$ \phi_i(\mathbf{x}) = \exp\left(-\frac{||\mathbf{x} - \mathbf{c}_i||^2}{2\sigma_i^2}\right) $$

    $$\displaystyle \sigma_i $$ is the spread (width) of the $i$-th basis function.

3.  **Output Layer:** Linear combination of hidden layer outputs.

$$ y_k = \sum_{i=1}^{m} w_{ki} \phi_i(\mathbf{x}) + b_k $$

    where $$\displaystyle w_{ki} $$ are weights, $$\displaystyle b_k $$ biases.

• Learning Mechanism:

  • Centers ($$\displaystyle \mathbf{c}_i $$) & Spreads ($$\displaystyle \sigma_i $$): Often determined unsupervised using K-means clustering on input data.

  • Output Weights ($$\displaystyle w_{ki} $$): Determined supervised via linear regression (e.g., Moore-Penrose pseudoinverse) after fixing centers. This makes training fast compared to MLP.

• Key Property: RBF networks are universal approximators with a single hidden layer, and their response is localized.

• Application: Function approximation, pattern classification, time-series prediction.

[!TIP] Exam Focus: Distinguish RBF from MLP. RBF hidden layer uses distance-based (non-linear) activation; output layer is linear. Learning is often two-stage (unsupervised then supervised).

B. Functional Link Networks (FLN)

• Architecture & Concept: A single-layer neural network where the input vector $$\displaystyle \mathbf{x} = [x_1, x_2, ..., x_n]^T $$ is non-linearly expanded to a higher-dimensional functional expansion vector $$\displaystyle \mathbf{F}(\mathbf{x}) = [F_1(\mathbf{x}), F_2(\mathbf{x}), ..., F_M(\mathbf{x})]^T $$ ($M \gg n$).

  • The expansion includes polynomial terms (e.g., $$\displaystyle x_i x_j $$, $$\displaystyle x_i^2 $$), trigonometric functions, etc., making the problem linearly separable in the expanded space.

  • Output: $$\displaystyle y = \mathbf{W}^T \mathbf{F}(\mathbf{x}) $$, where $\mathbf{W}$ are weights.

• Advantage: Avoids the need for multiple hidden layers and associated training complexities (like vanishing gradient). Learning reduces to solving a linear problem.

• Application: Pattern classification where input features have complex, non-linear relationships.

C. Self-Organizing Maps (SOM) / Kohonen Maps

• Topology & Principle: Unsupervised, competitive learning. A grid (usually 2D) of neurons, each with a weight vector $$\displaystyle \mathbf{w}_i $$ of same dimension as input $\mathbf{x}$.

  1. Competition: For input $\mathbf{x}$, find Best Matching Unit (BMU) $c$ with weight vector closest to $\mathbf{x}$ (using Euclidean distance).

  2. Cooperation: BMU's neighborhood on the grid is defined (e.g., Gaussian neighborhood function). Neurons within this neighborhood cooperate.

  3. Adaptation: Update weights of BMU and its neighbors towards $\mathbf{x}$:

$$ \mathbf{w}_i(t+1) = \mathbf{w}_i(t) + \alpha(t) \cdot h_{ci}(t) \cdot (\mathbf{x} - \mathbf{w}_i(t)) $$

    $\alpha(t)$: learning rate, $$\displaystyle h_{ci}(t) $$: neighborhood kernel (decreases with time and distance from BMU).

• Training Algorithm: Initialize weights (often random). Present inputs repeatedly, decreasing $\alpha$ and neighborhood radius over epochs.

• Applications: Data clustering, visualization of high-dimensional data, vector quantization, feature extraction, pattern recognition (e.g., speech, image).

• DiagramSEARCH: Kohonen self-organizing map topology grid neurons

[!TIP] Common Pitfall: SOM is unsupervised; it does not use target labels. It learns topology-preserving mappings, grouping similar inputs together on the grid.

D. Learning Paradigms & General Tasks

General Learning Tasks in Neural Networks:

1. Approximation: Fit a continuous function to data (Curve fitting, regression).

2. Classification: Assign input to discrete categories.

3. Clustering: Group similar inputs without prior labels.

4. Prediction: Forecast future values from past sequences (time-series).

5. Optimization: Find optimal solution (weights) for a given objective.

II. FUZZY LOGIC SYSTEMS

A. Fuzzy Set Theory Fundamentals

• Fuzzy Set: Extension of crisp set. Element $x$ has degree of membership $$\displaystyle \mu_A(x) \in [0,1] $$.

$$ A = \{ (x, \mu_A(x)) \mid x \in U \} $$

• Operations on Fuzzy Relations (for sets A, B):

  • Union: $$\displaystyle \mu_{A \cup B}(x) = \max[\mu_A(x), \mu_B(x)] $$

  • Intersection: $$\displaystyle \mu_{A \cap B}(x) = \min[\mu_A(x), \mu_B(x)] $$

  • Complement: $$\displaystyle \mu_{\bar{A}}(x) = 1 - \mu_A(x) $$

  • Algebraic Sum: $$\displaystyle \mu_{A+B}(x) = \mu_A(x) + \mu_B(x) - \mu_A(x)\mu_B(x) $$

  • Algebraic Product: $$\displaystyle \mu_{A \cdot B}(x) = \mu_A(x) \cdot \mu_B(x) $$

  • Bounded Difference: $$\displaystyle \mu_{A-B}(x) = \max[0, \mu_A(x) - \mu_B(x)] $$

B. Fuzzy Rule-Based Systems

• Structure:

  1. Rule Base: Collection of IF-THEN rules.

     IF (antecedent) THEN (consequent)

     e.g., IF Temperature is Hot AND Pressure is High THEN Valve is Slightly_Open.

  2. Database: Defines membership functions for linguistic terms (Hot, High, Slightly_Open).

  3. Decision-Making Unit (Inference Engine): Performs:

     • Fuzzification: Convert crisp inputs to fuzzy values.

     • Inference: Apply rules (Mamdani or Sugeno).

     • Aggregation: Combine outputs of all rules.

     • Defuzzification: Convert fuzzy output to crisp value (e.g., Centroid method).

• Inference Mechanisms:

  • Mamdani: Both antecedent and consequent are fuzzy sets. Uses max-min or max-product composition. Output is fuzzy set, requires defuzzification.

  • Sugeno (TSK): Consequent is a crisp function of inputs (e.g., linear: $$\displaystyle z = p x + q y + r $$). Output is weighted average of consequent functions. Efficient for optimization and adaptive control.

• DiagramSEARCH: fuzzy logic controller block diagram

C. Example Application: Fuzzy Logic Controller for DC Motor Speed

• Objective: Maintain constant speed despite load torque variations.

• Variables:

  • Inputs: Speed Error $$\displaystyle e = \omega_{ref} - \omega_{actual} $$, Change in Error $\Delta e$.

  • Output: Control voltage $$\displaystyle V_{control} $$ to motor armature.

• Linguistic Variables: Error (NB, NM, NS, Z, PS, PM, PB), ΔError (NB, NM, NS, Z, PS, PM, PB), Output (NB, NM, NS, Z, PS, PM, PB).

• Rule Base (Sample):

  1. IF $e$ is PB AND $\Delta e$ is NB THEN $$\displaystyle V_{control} $$ is PB (Brake hard, reverse).

  2. IF $e$ is Z AND $\Delta e$ is Z THEN $$\displaystyle V_{control} $$ is Z (No change).

  3. IF $e$ is NS AND $\Delta e$ is PS THEN $$\displaystyle V_{control} $$ is NM (Slight reduce).

• Process: Fuzzify $e$, $\Delta e$ → Apply all rules (min for AND, max for OR) → Aggregate all rule outputs → Defuzzify (Centroid) → Get crisp $$\displaystyle V_{control} $$.

• Advantage: Handles non-linearities and uncertainty without precise mathematical model.

[!TIP] Key Distinction: Mamdani is intuitive (human-like rules), Sugeno is computationally efficient for optimization/adaptive systems.

III. EVOLUTIONARY COMPUTATION: GENETIC ALGORITHMS (GA)

A. Genetic Operators

B. Mutation Operator in Detail

• Role in Maintaining Diversity:

  • Introduces new genetic material not present in current population.

  • Helps escape local optima by randomly perturbing solutions.

  • Ensures ergodicity (theoretical ability to reach any point in search space given enough time).

• Application in Optimization Problems:

  • Parameter Tuning: In real-coded GA for ELD, Gaussian mutation perturbs generator power values slightly.

  • Constraint Handling: Can be used to repair infeasible solutions (e.g., if mutation causes $$\displaystyle P_i < P_i^{min} $$, set to $$\displaystyle P_i^{min} $$).

  • Adaptive Mutation: Mutation rate often decreases over generations (exploration → exploitation).

• Trade-off: High mutation → random walk; Low mutation → premature convergence. Typically $$\displaystyle P_{mutation} \in [0.001, 0.1] $$.

[!TIP] Exam Insight: Mutation is a background operator (low probability) while crossover is primary. Emphasize its role in diversity, not primary search.

IV. AI APPLICATIONS IN POWER SYSTEM OPERATION & CONTROL

A. Economic Load Dispatch (ELD)

• Problem Formulation:

  • Objective: Minimize total fuel cost $$\displaystyle F_{total} = \sum_{i=1}^{N} F_i(P_i) $$.

$$ F_i(P_i) = a_i P_i^2 + b_i P_i + c_i \ \text{\$ / hr} $$

    $$\displaystyle a_i, b_i, c_i $$: cost coefficients, $$\displaystyle P_i $$: power from unit $i$.

*   **Constraints:**

    1.  **Power Balance:** $$\displaystyle \sum_{i=1}^{N} P_i = P_D + P_{loss} $$ ($$\displaystyle P_D $$: demand, $$\displaystyle P_{loss} $$: transmission loss).

    2.  **Generator Limits:** $$\displaystyle P_i^{min} \leq P_i \leq P_i^{max} $$.

    3.  **Ramp Rate Limits:** $$\displaystyle |P_i(t) - P_i(t-1)| \leq UR_i $$ (Up/Down Ramp).

• Solution using AI (GA/PSO):

  • Chromosome/Position Vector: $$\displaystyle \mathbf{X} = [P_1, P_2, ..., P_N] $$.

  • Fitness Function: Minimize $$\displaystyle F_{total} $$ (or maximize $$\displaystyle -F_{total} $$). Penalty functions for constraint violation.

  • Process: Initialize population → Evaluate fitness → Apply GA operators → Iterate → Best solution.

• Example Problem: 2 generators, $$\displaystyle P_D=150 $$ MW.

  • $$\displaystyle F_1 = 0.0015 P_1^2 + 2.5 P_1 + 150 $$, $$\displaystyle P_1^{min}=30 $$, $$\displaystyle P_1^{max}=150 $$.

  • $$\displaystyle F_2 = 0.0010 P_2^2 + 1.8 P_2 + 100 $$, $$\displaystyle P_2^{min}=20 $$, $$\displaystyle P_2^{max}=120 $$.

  • Ignoring losses, $\lambda$-iteration gives $$\displaystyle P_1=80.77 $$ MW, $$\displaystyle P_2=69.23 $$ MW, Cost ≈ 697.5 $/hr.

B. Load Frequency Control (LFC)

• Purpose: Maintain system frequency $\Delta f$ and tie-line power exchange $$\displaystyle \Delta P_{tie} $$ at scheduled values after load change.

• 1. Single Area System:

  • Block Diagram:

    DiagramSEARCH: single area load frequency control block diagram

    Components: Load ($$\displaystyle \Delta P_L $$), Governor (with speed regulation $R$), Turbine (time constant $$\displaystyle T_t $$), Generator (inertia $H$, damping $D$), Frequency sensor.

  • Control Strategy: Area Control Error (ACE) is the key feedback signal.

$$ ACE = \Delta P_{tie} + B \Delta f $$

    $B$: Frequency bias factor ($$\displaystyle B = \frac{1}{R} + D $$). ACE is integrated (Integral Controller) to generate $$\displaystyle \Delta P_{ref} $$.

• 2. Two Area System:

  • Interconnected Model: Two control areas linked by tie-line. Each area has its own ACE.

  • Tie-line Power Flow Change:

$$ \Delta P_{tie1} = \frac{P_{scheduled}}{\delta} (\Delta f_1 - \Delta f_2) $$

    $\delta$: Synchronizing coefficient, $$\displaystyle P_{scheduled} $$: scheduled tie-line power.

*   **ACE for Area 1:** $$\displaystyle ACE_1 = \Delta P_{tie1} + B_1 \Delta f_1 $$

• 3. Control Parameters Dependence:

  • Governor Speed Regulation ($R$): Lower $R$ → smaller frequency change for given load change, but increases steady-state $$\displaystyle \Delta P_{tie} $$.

  • Load Damping ($D$): Higher $D$ → inherent frequency stability, reduces need for control action.

  • Inertia ($H$): Higher $H$ → slower initial frequency drop (more time for control), but larger frequency deviation if control is slow.

  • AI Role: Tune PID/Integral controller gains ($$\displaystyle K_p, K_i $$) using GA/PSO for optimal transient response (minimal overshoot, settling time).

C. Small Signal Stability Analysis

• Concept: Stability of power system to small, continuous disturbances (e.g., minor load fluctuations). Analyzed by linearizing system equations around an equilibrium point.

  • System represented by state-space: $$\displaystyle \dot{\mathbf{x}} = \mathbf{A} \mathbf{x} $$.

  • Stability criterion: All eigenvalues of system matrix $\mathbf{A}$ must have negative real parts.

• AI-Based Techniques:

  • ANN for Stability Assessment: Train ANN (input: system operating point features like loading, generation mix; output: stability margin or eigenvalue real part). Enables online stability prediction.

  • GA/PSO for Power System Stabilizer (PSS) Tuning: Optimize PSS parameters to shift eigenvalues left (more negative) for better damping of oscillations.

  • Fuzzy Logic: For adaptive control based on stability indicators.

D. Load Forecasting

• Types:

  • Short-Term (STLF): 1 hour to 1 week. For unit commitment, economic dispatch.

  • Medium-Term (MTLF): 1 week to 1 year. For maintenance scheduling, fuel planning.

  • Long-Term (LTLF): >1 year. For expansion planning.

• AI Models:

  • Artificial Neural Networks (ANN): MLP, RBF, LSTM (for time-series). Inputs: historical load, weather (temp, humidity), day type, time.

  • Fuzzy Logic: Handle uncertainty in weather and human behavior. Often hybridized with ANN (Neuro-Fuzzy).

  • Hybrid Models: ANN + GA (GA optimizes ANN weights/architecture), ANN + Fuzzy, Wavelet + ANN.

  • DiagramSEARCH: load forecasting using neural network architecture

V. INTEGRATED SYSTEMS & CASE STUDIES

A. Case Study: Electric Vehicles (EVs)

• Role of AI:

  1. Battery Management System (BMS):

     • State of Charge (SOC) Estimation: ANN/Fuzzy logic for accurate SOC prediction considering temperature, aging, current.

     • State of Health (SOH) Estimation: ML models to predict capacity fade.

     • Thermal Management: Fuzzy logic for cooling/heating control.

  2. Motor Control: BLDC/PMSM control using Fuzzy Logic or ANN for robust speed/torque control under varying load and battery voltage.

  3. Energy Optimization: GA/PSO for optimal route planning considering battery level, charging stations, traffic, and energy consumption.

B. Case Study: PV Fed Water Pumping Systems

• AI for Maximum Power Point Tracking (MPPT):

  • Problem: PV output varies with irradiance/temperature. MPPT extracts max power.

  • AI Techniques:

    • Fuzzy Logic MPPT: Handles non-linear PV characteristics, fast under changing conditions. Inputs: error (dP/dV) and change in error. Output: duty cycle.

    • ANN MPPT: Trained to map PV voltage/current/irradiance to optimal voltage. Fast, no oscillations.

    • Hybrid (P&O + Fuzzy): Combine simplicity with adaptability.

• System Optimization: GA for sizing PV array, pump, and storage tank based on water demand and solar profile.

C. Comparative Analysis of AI Techniques

[!TIP] Exam Strategy: For "which technique is best?" questions, link technique strength to problem nature: Optimization → GA; Control with uncertainty → Fuzzy; Data-rich prediction → ANN.