Distribution state estimation under sparse metering
An electrical engineering study of voltage-state estimation, bad-data detection, and uncertainty when distribution-feeder measurements are sparse or noisy.

Project definition
Problem statement
Distribution feeders often have only a small number of direct voltage measurements, while many bus injections are represented by uncertain pseudo measurements.
The engineering problem is to estimate the complete feeder voltage state, measure the effect of meter density, identify corrupted observations, and report uncertainty without claiming field validation.
Project objectives
- Build four repeatable operating cases on the IEEE 33-bus radial feeder.
- Generate sparse voltage measurements and uncertain active-power and reactive-power pseudo measurements.
- Compare weighted least squares with Huber robust weighted estimation.
- Measure clean accuracy, corrupted-meter resilience, residual detection, interval width, and coverage.
- Explain how meter density and feeder condition affect the evidence and its limitations.
Project structure
Project components
Feeder model
Builds the benchmark feeder, applies each operating scenario, solves AC load flow, and records voltage truth.
Sensitivity model
Perturbs active and reactive injections to construct a transparent local voltage-sensitivity matrix.
Measurement simulator
Creates seeded pseudo measurements, sparse voltage meters, declared uncertainty, and an optional corrupted observation.
Estimators
Solves inverse-variance WLS and iterative Huber robust weighting under the same inputs.
Evaluation
Calculates RMSE, maximum error, uncertainty coverage, interval width, conditioning, and bad-data localisation.
Methodology
Project workflow
- 01Select a case
Choose light load, nominal, evening peak, or midday distributed-generation operation.
- 02Set meter coverage
Use 10, 20, 35, or 55 percent voltage-meter coverage with the declared pseudo-measurement errors.
- 03Generate evidence
The seeded simulator produces clean or single-corruption measurements for the selected repetition.
- 04Estimate the state
WLS and Huber methods reconstruct the non-slack bus voltages and calculate uncertainty intervals.
- 05Compare results
Retained CSV, JSON, figures, and the offline dashboard show accuracy, coverage, detection, and robustness.
Demonstration scenario
The evening-peak feeder is tested at 10, 20, 35, and 55 percent voltage-meter coverage. One direct voltage measurement is corrupted by 0.03 p.u. WLS and Huber estimates are compared using voltage error, uncertainty coverage, interval width, and largest-residual localisation.
Engineering
Tools and method
- Tools
- The project uses Python, pandapower, NumPy, SciPy, Pandas, Matplotlib, Jupyter for subject analysis, simulation, and results.
- Power flow
- pandapower Newton-Raphson AC load flow supplies controlled truth for the balanced benchmark feeder.
- Numerical model
- Python and NumPy construct local voltage sensitivities from declared active-power and reactive-power perturbations.
- Estimation
- SciPy and NumPy solve weighted normal equations and Huber iterative reweighting.
- Evidence
- Pandas retains all 1,280 runs and Matplotlib creates eight labelled result figures.
- Verification
- Automated tests check feeder construction, measurements, estimation, metrics, experiment output, and command behaviour.
Testing
Evaluation
Evaluation measures
- Mean and maximum voltage-state error under clean measurements
- Voltage-state error after one corrupted direct measurement
- Ninety-five percent uncertainty-interval coverage and mean interval width
- Largest-residual bad-data localisation rate
- Sensitivity to meter coverage and operating scenario
- Sensitivity-matrix conditioning and estimator repeatability
Project boundaries
- The project is a balanced static benchmark study and not an operational distribution management system.
- Measurements, errors, and corruption are controlled synthetic evidence rather than utility field data.
- Phase imbalance, switching and topology error, protection, communications, and control actions are outside this version.
- A real deployment requires feeder-specific data, calibrated sensors, field validation, and review by qualified electrical engineers.
Included
- 01IEEE 33-bus radial distribution-feeder model
- 02AC power-flow truth cases and numerical voltage sensitivities
- 03Sparse voltage meters and uncertain pseudo measurements
- 04Weighted least squares and Huber robust estimators
- 05Clean and corrupted-meter experiments with uncertainty evaluation
- 061,280 retained runs, eight generated figures, and an offline dashboard
- 07Complete project files, calculations, tests, and results in a private GitHub repository
- 08Complete project documentation in PDF and editable Word formats
- 09Setup and usage guide in PDF and editable Word formats
Project record
No information is collected on this page.
- Permanent project ID
- GP-EE-135KKNP
- Catalogued
- 21 Aug 2026
- Completed
- 24 Aug 2026
- Verified
- 24 Aug 2026
- Demonstration
- Included in repository
Handover
After purchase
- 01Payment is confirmed
The project is marked unavailable and cannot be purchased again.
- 02Repository access is granted
The buyer's submitted GitHub account receives access to the private repository.
- 03The purchase record is delivered
The certification sheet is prepared from the reviewed buyer details and sent privately by email.