⚡ electrical engineering

Monte Carlo Pareto Tuning of the Siemens 7UT5121 Differential Relay on a 60 MVA150/20 kV Distribution Transformer

This paper proposes a Monte Carlo-based Pareto optimization framework to replace deterministic manufacturer settings with a statistically robust, three-dimensional commissioning window for the Siemens 7UT5121 differential relay, significantly enhancing sensitivity to incipient faults and inrush blocking while maintaining 100% security against through-faults for a 60 MVA distribution transformer.

Original authors: Dimas Nur Prakoso, Basuki Winarno, Budi Triyono, Yuli Prasetyo, Suyitno Muslim

Published 2026-07-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Dimas Nur Prakoso, Basuki Winarno, Budi Triyono, Yuli Prasetyo, Suyitno Muslim

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a massive electrical transformer as the heart of a city's power grid, pumping electricity from high-voltage lines down to the streets where your lights and phones live. This specific heart is a 60 MVA beast, stepping down voltage from 150 kV to 20 kV. To protect this heart from a sudden, catastrophic failure (like a short circuit inside), engineers use a "differential relay"—think of it as a super-smart bouncer standing at the door, checking the current flowing in against the current flowing out. If they don't match, the bouncer slams the door shut to save the heart.

For decades, setting this bouncer's rules has been like guessing the weather: engineers picked a single, fixed setting based on the manufacturer's manual and hoped for the best. They assumed the world was perfectly predictable. But in reality, the power grid is chaotic. The current transformers (the sensors) make tiny errors, the load changes every day, and sometimes the sensors get "saturated" (overwhelmed) during big faults, sending false signals that look like a heart attack when it's just a heavy load.

The Old Way vs. The New Way
This paper argues that the old "single-setting" approach is too rigid. It's like trying to fit a square peg in a round hole by only measuring the peg once. Instead, the authors treated the problem like a video game with thousands of possible scenarios. They used a computer simulation called pandapower to run a massive "Monte Carlo" experiment. Imagine rolling dice 500 times for every possible setting combination, simulating everything from minor daily load swings to massive external faults and even the sensors getting temporarily confused (saturated).

They didn't just look for a setting; they looked for the Pareto-optimal settings. In plain English, this means finding the "sweet spots" where you get the maximum safety without sacrificing the ability to catch real faults. It's the difference between locking your front door so tight you can't get out in an emergency versus leaving it wide open for burglars. The goal was to find the perfect balance where the door stays shut during a storm (security) but opens instantly for a real fire (sensitivity).

The Big Discovery
After running roughly 126,000 simulated scenarios, the authors found that the "standard" settings recommended by the manufacturer (Siemens 7UT5121) were actually too conservative. The old rules were too cautious, potentially missing small, early-stage faults (incipient faults) that could grow into disasters.

The paper suggests a new, wider "commissioning window" (a safe zone of settings) rather than a single point:

Slope 1 ( $m_1$ ): Should be between 0.30 and 0.40 (instead of the old 0.25). Think of this as making the bouncer slightly more tolerant of sensor errors so they don't panic and shut down the power for no reason.
Pickup Floor ( $I_{pickup}$ ): Should be between 0.10 and 0.15 (lower than the standard 0.20). This makes the bouncer more sensitive, able to hear the "whispers" of a small internal fault that the old settings would ignore.
Second-Harmonic Blocking ( $h^*_2$ ): This is a special filter to stop the relay from tripping when the transformer is first turned on (inrush current), which looks messy. The authors found that the standard setting of 15% was too high. They proved via simulation that lowering it to 0.10 (10%) is actually better. It blocks the "fake" inrush signals 9.2 percentage points more effectively without accidentally blocking real faults.

How Sure Are They?
The authors are very confident in these numbers, but with a specific caveat: these results come from simulations and a small-scale laboratory test, not a full-scale 60 MVA power plant explosion.

They ran their simulations with 500 random fault scenarios per setting, repeated three times with different random seeds, to ensure the results weren't just luck.
They confirmed their logic with a laboratory trainer (a small-scale model), which showed the relay behaved exactly as the math predicted, though the trainer couldn't replicate the massive power of a real 60 MVA fault.
They explicitly ruled out the idea that the old, conservative settings are the best choice for this specific type of transformer. Their data shows the old settings leave too much "headroom" for error, making the system less sensitive to real problems.

The Takeaway
The paper doesn't claim to have "solved" all protection problems forever. Instead, it offers a new, statistically backed recipe for tuning these relays. It suggests that by moving from a single, rigid setting to a flexible "window" of settings (specifically $m_1 \in [0.30, 0.40]$ , $I_{pickup} \in [0.10, 0.15]$ , and $h^*_2 \in [0.10, 0.125]$ ), engineers can build a power grid that is both safer against real faults and less likely to shut down unnecessarily during normal chaos. It's a shift from guessing to calculating, ensuring the bouncer knows exactly when to slam the door and when to let the power flow.

Technical Summary: Monte Carlo Pareto Tuning of the Siemens 7UT5121 Differential Relay

Problem Statement
Conventional commissioning of transformer differential relays, such as the Siemens 7UT5121, typically relies on deterministic, single-point settings derived from manufacturer guidance. This approach assumes a representative operating point and ignores the stochastic variability inherent in real-world service conditions. Specifically, standard procedures fail to account for the statistical spread of current transformer (CT) class errors, tap-changer drift, variations in source short-circuit capacity, daily load fluctuations, and CT saturation during through-faults. In the context of Indonesian distribution networks, where increasing rooftop photovoltaic (PV) and inverter-based resource (IBR) penetration alters short-circuit infeed characteristics, these deterministic settings may lack the necessary robustness. The core problem addressed is the lack of a quantitative, probabilistic framework to determine relay settings that balance sensitivity (detecting internal faults) and security (avoiding false trips during external faults or inrush) across a wide range of operating uncertainties.

Methodology
The authors recast the relay setting problem as a two-dimensional robustness optimization over the slope ( $m_1$ ) and pickup ( $I_{pickup}$ ) plane, extending to a third dimension involving the second-harmonic blocking threshold ( $h^*_2$ ).

Simulation Environment: The protected zone (a 60 MVA, 150/20 kV transformer) was modeled using pandapower 3.4, an open-source, IEC 60909-compliant Python library. This replaced closed-source tools to ensure reproducibility.
Monte Carlo Experiment: A stochastic framework was employed where each candidate setting pair $(m_1, I_{pickup})$ $(m_{1}, I_{p i c k u p})$ was evaluated against $N=500$ $N = 500$ shared fault realizations. These realizations sampled seven stochastic parameters:
- Fault severity.
- CT class errors (within IEC 61869 Class 1.0).
- Tap-changer drift.
- Daily load fraction.
- Source short-circuit capacity.
- Fault arc impedance.
- Per-event CT saturation factor.
Operating Scenarios: The model was exercised under four scenarios: near-rated load, internal (in-zone) faults, external (through) faults, and incipient internal faults.
Optimization Criteria: Sensitivity (probability of tripping on internal faults) and Security (probability of stability on external faults) were calculated with Wilson 95% confidence intervals. The Pareto front was identified to find non-dominated settings where neither sensitivity nor security could be improved without degrading the other.
Third-Dimensional Extension: A time-domain B–H simulation was used to analyze the second-harmonic blocking threshold ( $h^*_2$ ) under inrush conditions, treating it as a third optimization variable.
Hardware Verification: Independent three-phase laboratory measurements using a trainer unit and a Siemens 7UT5121 relay were conducted to verify relay logic and three-phase symmetry, though not to replicate full 60 MVA fault levels.

Key Results

Pareto-Optimal Settings: The analysis identified a set of Pareto-optimal cells in the high-slope, low-pickup region. The optimal settings were found at $(m_1, I_{pickup}) \in \{(0.35, 0.10), (0.40, 0.10)\}$ , achieving a sensitivity of 93.8% and 100% security.
Commissioning Window: Rather than a single point, the authors propose a statistically justified 3-D commissioning window:
- Slope 1 ( $m_1$ ): $[0.30, 0.40]$
- Pickup ( $I_{pickup}$ ): $[0.10, 0.15]$
- Second-harmonic threshold ( $h^*_2$ ): $[0.10, 0.125]$
Harmonic Threshold Optimization: The study demonstrated that lowering the second-harmonic blocking threshold from the manufacturer's conventional 15% to 10% strictly dominates the conventional setting. This lower threshold improves inrush blocking security by 9.2 percentage points without compromising the ability to allow internal faults (which exhibit negligible second-harmonic content).
Budget Allocation: A decomposition of the 25% Slope-1 budget revealed that CT ratio mismatch (11.8%), class error (1%), and tap-changer drift (2%) consume a significant portion, leaving only ~10% as headroom. This suggests that the conventional 25% slope is often too narrow to absorb worst-case stochastic residuals, justifying the shift toward higher slopes (30–40%).
Validation: Laboratory measurements confirmed that the relay logic correctly interprets balanced three-phase currents and suppresses tripping under load, while the simulation confirmed the settings' robustness against the modeled stochastic variations.

Significance and Claims
The paper claims to close the gap between deterministic commissioning practices and the stochastic reality of modern distribution networks, particularly those with high IBR penetration. Its primary contributions are:

Open-Source Reproducibility: Providing a fully reproducible, open-source (pandapower) implementation of the differential protection study, contrasting with proprietary tools.
Probabilistic Commissioning: Moving from a "does this setting work?" question to "how robust is this setting?" by quantifying performance across a population of operating conditions using Monte Carlo methods.
Quantitative Justification for Ranges: Replacing single-point manufacturer recommendations with a statistically grounded 3-D commissioning window that offers operational flexibility while maintaining robustness.
Hardware-Logic Cross-Check: Validating the simulation logic against independent laboratory-scale hardware measurements to ensure the relay's decision-making behavior is consistent across scales.

The authors position this work as a quantitative recipe for re-tuning differential elements under IBR-perturbed envelopes, offering a framework that can be adapted by commissioning engineers for their specific transformer and CT specifications.

Technical Summary: Monte Carlo Pareto Tuning of the Siemens 7UT5121 Differential Relay

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