Power System Loss Analysis and Quality Loss Indicator Calculation using ETAP and MATLAB

This repository contains the engineering modeling, simulation, and analytical calculations for a 7-bus electrical power transmission network. The project integrates ETAP 19.0.1 for steady-state load flow simulation and MATLAB R2022a for calculating active and reactive quality loss indicators ($\lambda'$ and $\lambda''$) for both transmission lines and network nodes under electrically asymmetric conditions.

1. Project Overview & Abstract

The main objective of this study is to model a 110 kV steady-state power transmission grid to analyze its operational behavior and accurately allocate active and reactive power losses. By simulating a steady-state load flow in ETAP 19.0.1, line active/reactive power transfers, bus voltages, and branch losses are extracted. These simulated values are then imported into MATLAB R2022a, where customized path-tracing algorithms and mathematical formulations calculate localized quality loss indicators. This dual-software approach provides power system engineers with a precise, quantitative framework to evaluate grid transmission efficiency, identify loss-heavy branches, and prioritize system reinforcements.

2. Problem Statement

In modern power systems, active and reactive power losses directly impact grid efficiency, operating costs, and voltage stability. To mitigate these losses, utility engineers must identify which specific lines and nodes are most responsible for loss propagation. However, standard power loss calculations do not incorporate a localized "quality" dimension that shows how power injected or drawn at a particular node contributes to cumulative network losses.

Furthermore, real-world networks exhibit electrical asymmetry due to non-uniform line topologies (e.g., a mix of overhead lines and underground cables with highly differing $X/R$ ratios). This impedance mismatch renders standard symmetric assumptions invalid and complicates loss tracing, especially at branching/multi-path nodes. This project addresses these challenges by developing a mathematical model that correctly calculates line and node loss indicators under asymmetric ring and branch topologies.

3. Methodology & Software Used

The analysis utilizes a coordinated, sequential engineering workflow across two industry-standard software environments:

1. ETAP 19.0.1 (Electrical Transient Analyzer Program):
   • Network Modeling: Modeling a 7-bus, 110 kV transmission network containing a main utility grid connection (Slack Bus), 9 transmission lines, and 6 regional lumped loads.
   • Load Flow Analysis: Running steady-state load flow simulations using the Newton-Raphson method to solve the power flow equations and extract exact node voltages ($U_{end}$), active and reactive power flows ($P_{start}, Q_{start}$), and active/reactive branch losses ($P_{loss}, Q_{loss}$).
2. MATLAB R2022a:
   • Line Indicator Calculation: Implementing mathematical formulations to determine active quality loss indicators ($\lambda'$) and reactive quality loss indicators ($\lambda''$) for all 9 transmission lines.
   • Node Path-Tracing & Branch Handling: Constructing path matrices from the reference slack bus to all other nodes. For branching nodes (e.g., Bus-3) with multiple parallel supply paths, a path-averaging methodology is implemented to resolve electrical asymmetry and balance loss allocations.

4. System Architecture & Design Details

4.1. Grid Parameters & Line Impedances

The network is designed around a nominal operating voltage of 110 kV. It is characterized by severe electrical asymmetry, combining overhead lines (having a high inductive-to-resistive ratio, $X/R \approx 1.5$) and underground cables (having low ratios, $X/R \approx 0.19$ to $0.34$).

The detailed physical and electrical parameters of the 9 transmission lines are summarized below:

Line Segment	Transmission Type	Resistance $R_i$ ($\Omega$)	Reactance $X_i$ ($\Omega$)	Impedance Ratio ($X_i / R_i$)
Line 1–2	Overhead	10.5	16.0	1.52
Line 2–3	Overhead	12.6	19.1	1.52
Line 1–4	Underground Cable	17.8	6.0	0.34
Line 1–5	Overhead	12.6	19.1	1.52
Line 5–6	Overhead	8.4	12.6	1.50
Line 3–4	Underground Cable	16.9	3.3	0.19
Line 4–6	Underground Cable	12.7	2.5	0.19
Line 3–7	Underground Cable	16.9	3.3	0.19
Line 6–7	Underground Cable	21.1	4.1	0.19

4.2. Network Single-Line Diagram (SLD)

The single-line diagram modeled in ETAP consists of:

• Bus-1 (Reference Bus): Connected to an external Power Grid utility source (U1).
• 6 Loaded Buses: Supporting heavy industrial or regional lumped loads (Lump1 to Lump8) with ratings ranging from 29 MVA to 93 MVA.

5. Results & Analysis

5.1. ETAP Load Flow Simulation Results

Executing the Load Flow Analysis in ETAP yields the actual steady-state operating voltages and power flows across the grid. Due to heavy loading, substantial voltage drops are observed at the electrically distant nodes:

• Bus-1 (Slack/Ref): 121.00 kV (110.0% of nominal)
• Bus-2: 102.00 kV (92.7%)
• Bus-3: 85.23 kV (77.5%) — Severe Voltage Drop
• Bus-4: 90.65 kV (82.4%)
• Bus-5: 97.24 kV (88.4%)
• Bus-6: 85.53 kV (77.8%) — Severe Voltage Drop
• Bus-7: 81.74 kV (74.3%) — Critical Voltage Drop (Lowest operating voltage)

5.2. Mathematical Formulations & Line Indicators

Using MATLAB, the active quality loss indicator ($\lambda'$) and reactive quality loss indicator ($\lambda''$) for each line segment are calculated according to the following formulas:

$$\lambda' = \frac{2 \cdot P_{end} \cdot R}{U_{end}^2}$$

$$\lambda'' = \frac{2 \cdot Q_{end} \cdot R}{U_{end}^2}$$

Where:

• $P_{end} = P_{start} - P_{loss}$ represents the active power at the end of the line segment.
• $Q_{end} = Q_{start} - Q_{loss}$ represents the reactive power at the end of the line segment.
• $R$ is the line segment's resistance.
• $U_{end}$ is the operating voltage of the bus at the end of the line.

The computed line loss indicators are:

Line Segment	Active Loss Indicator ($\lambda'$)	Reactive Loss Indicator ($\lambda''$)
Line 1–2	0.13463	0.15582
Line 2–3	0.12048	0.17970
Line 1–4	0.60262	0.19755
Line 1–5	0.17403	0.20708
Line 5–6	0.08180	0.12727
Line 4–3	0.13005	-0.01671
Line 4–6	0.12166	-0.01575
Line 3–7	0.07475	0.05281
Line 6–7	0.08359	0.05205

Note: Negative reactive loss indicators (e.g., on Line 4–3 and Line 4–6) indicate local reactive power support or reverse reactive power flow direction under current loading.

5.3. Node Loss Indicators & Branching Resolution

To find the quality loss indicators for a specific node, the line indicators along the transmission path from the reference slack bus (Bus-1) are summed.

Branching Handling at Bus-3:

Bus-3 operates as a branching node reachable from the reference bus via two distinct topological paths:

1. Path 1 (1–2–3): Composed of Line 1–2 and Line 2–3.
2. Path 2 (1–4–3): Composed of Line 1–4 and Line 4–3.

Because of the network's electrical asymmetry, calculating the node loss indicator along these different paths yields different values. MATLAB resolves this by taking the arithmetic mean of the path sums:

$$\lambda'_{node}(Bus\text{-}3) = \text{mean}\left[ (\lambda'_{1\text{-}2} + \lambda'_{2\text{-}3}), (\lambda'_{1\text{-}4} + \lambda'_{4\text{-}3}) \right] = \text{mean}\left[ 0.25511, 0.73267 \right] = 0.49389$$

$$\lambda''_{node}(Bus\text{-}3) = \text{mean}\left[ (\lambda''_{1\text{-}2} + \lambda''_{2\text{-}3}), (\lambda''_{1\text{-}4} + \lambda''_{4\text{-}3}) \right] = \text{mean}\left[ 0.33552, 0.18084 \right] = 0.25818$$

The final calculated quality loss indicators for all network nodes are:

Node (Bus)	Active Node Indicator ($\lambda'_{node}$)	Reactive Node Indicator ($\lambda''_{node}$)
Bus-2	0.13463	0.15582
Bus-3	0.49389	0.25818
Bus-4	0.60262	0.19755
Bus-5	0.17403	0.20708
Bus-6	0.25583	0.33435
Bus-7	0.32986	0.38833

6. Key Engineering Findings & Design Decisions

1. Critical Active Loss Bus: Bus-4 exhibits the highest active node loss indicator ($\lambda'_{node} = 0.60262$). This indicates that any load increases at Bus-4 will trigger the highest rate of active power loss escalation across the transmission network.
2. Critical Reactive Loss Bus: Bus-7 possesses the highest reactive node loss indicator ($\lambda''_{node} = 0.38833$) combined with a highly critical voltage drop ($81.74$ kV or $74.3%$). This indicates a severe local deficit in reactive power support.
3. Network Operation Topology Decision: Operational simulations were executed to test the conversion of this ring grid into a radial grid by opening the loop at various candidate points. The results proved that the closed-loop (ring) configuration yields the minimum overall active power losses for this network, making it the mathematically optimal operational topology despite the asymmetry.

7. Future Work

To enhance grid efficiency and address the severe voltage drops, several engineering solutions are proposed:

• Optimal Capacitor Placement (OCP): Placing shunt capacitor banks at Bus-7 and Bus-6 to provide reactive compensation, raise operating voltages above the $90%$ threshold, and lower the reactive loss indicators.
• FACTS Devices Implementation: Integrating Flexible AC Transmission Systems (like TCSC or STATCOM) to regulate power flows through the high-impedance asymmetric branches, balancing the power distribution.
• Heuristic Optimization: Employing optimization algorithms (such as Genetic Algorithms or Particle Swarm Optimization) in MATLAB to dynamically determine optimal open-loop configurations under changing load profiles.

Project Structure

flowchart LR
    %% Root Node
    Root["📂 <b>Project Root</b>"]

    %% Main Directories & Files
    ETAP["📁 <b>ETAP/</b>"]
    MATLAB["📁 <b>MATLAB/</b>"]
    LATEX["📁 <b>Presentation_LaTeX/</b>"]
    README["📘 <b>README.md</b><br/><small>Main Project Documentation</small>"]

    %% ETAP Files
    OLV["📄 <b>OLV1.otg</b><br/><small>Single-Line Diagram & Grid Database</small>"]
    PDF_ETAP["📑 <b>LoadFlow_Results.pdf</b><br/><small>Detailed Load Flow Report</small>"]

    %% MATLAB Files
    M_SCRIPT["📜 <b>Pointers_of_the_Grid.m</b><br/><small>Line & Node Loss Indicators Script</small>"]
    TXT["📝 <b>Results_Output.txt</b><br/><small>Printed Command Window Results</small>"]

    %% LaTeX Presentation Files
    SLIDES_PDF["📑 <b>grid_power_loss_indicators.pdf</b><br/><small>Final Project Slides (Beamer/PDF)</small>"]
    TEX_SRC["🔤 <b>grid_power_loss_indicators.tex</b><br/><small>LaTeX Source Code</small>"]

    %% Connections
    Root --> ETAP
    Root --> MATLAB
    Root --> LATEX
    Root --> README

    ETAP --> OLV
    ETAP --> PDF_ETAP

    MATLAB --> M_SCRIPT
    MATLAB --> TXT

    LATEX --> SLIDES_PDF
    LATEX --> TEX_SRC

    %% Styling & Colors
    style Root fill:#0f172a,stroke:#38bdf8,stroke-width:2px,color:#fff
    style ETAP fill:#1e293b,stroke:#3b82f6,color:#fff
    style MATLAB fill:#1e293b,stroke:#f97316,color:#fff
    style LATEX fill:#1e293b,stroke:#099268,color:#fff
    style README fill:#1e1e38,stroke:#818cf8,color:#fff
    
    style OLV fill:#0f172a,stroke:#64748b,color:#e2e8f0
    style PDF_ETAP fill:#0f172a,stroke:#ef4444,color:#e2e8f0
    style M_SCRIPT fill:#0f172a,stroke:#f97316,color:#e2e8f0
    style TXT fill:#0f172a,stroke:#10b981,color:#e2e8f0
    style SLIDES_PDF fill:#0f172a,stroke:#ef4444,color:#e2e8f0
    style TEX_SRC fill:#0f172a,stroke:#099268,color:#e2e8f0

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Note: This project was prepared as part of the "Electrical Power System Analysis" course at the Faculty of Electrical and Electronic Engineering, Department of Electrical Power Systems, University of Aleppo.