In the operation of power systems, the knowledge of the system state is required by several fundamental functions, such as security assessment, voltage control and stability analysis. By making reference to the static state of the system represented by the voltage phasors at all the network buses, it is possible to infer the system operating conditions. Until the late 1970s, conventional load flow calculations provided the system state by directly using the raw measurements of voltage magnitudes and power injections. The loss of one measurement made the calculation impossible and the presence of measurement errors affected dramatically the computed state. To overcome these limitations, load flow theory has been combined with statistical estimation constituting the so-called state estimation (SE). The latter consists in the solution of an optimization problem that processes the measurements together with the network model to determine the optimal estimate of the system state. The outputs of load flow and SE are composed of the same quantities, typically the voltage magnitude and phase at all the network buses, but SE uses all the types of measurements (e.g., voltage and current magnitudes, nodal power injections and flows, synchrophasors) and evaluates their consistency using the network model. The measurement redundancy is key to tolerate measurement losses, identify measurement and network parameter errors, and filter out the measurement noise. The foregoing properties of SE allow the system operator to obtain an accurate and reliable estimate of the system state that consequently improves the performance of the functions relying on it.

Chapter Contents:

• 6.1 State estimation measurement and process model
• 6.1.1 Measurement model
• 6.1.1.1 Linear measurement model
• 6.1.1.2 Non-linear measurement model
• 6.1.2 Network observability
• 6.1.3 Process model
• 6.2 Static state estimation: the weighted least squares
• 6.2.1 Linear weighted least squares state estimator
• 6.2.2 Non-linear weighted least squares
• 6.3 Recursive state estimation: the Kalman filter
• 6.3.1 Discrete Kalman filter
• 6.3.2 Extended Kalman filter
• 6.3.3 Kalman Filter sensitivity with respect to the measurement and process noise covariance matrices
• 6.3.4 Assessment of the process noise covariance matrix
• 6.4 Assessment of the measurement noise covariance matrix
• 6.5 Data conditioning and bad data processing in PMU-based state estimators
• 6.6 Kalman filter vs. weighted least squares
• 6.7 Numerical validation and performance assessment of the state estimation
• 6.7.1 Linear state estimation case studies
• 6.7.1.1 Distribution network case study: IEEE 13-bus distribution test feeder
• 6.7.1.2 Transmission system case study: IEEE 39-bus transmission test system
• 6.7.2 Non-linear SE case studies
• 6.8 Kalman filter process model validation
• 6.9 Numerical validation of Theorem 6.1
• Bibliography

Inspec keywords: phasor measurement; optimisation; power distribution reliability; power grids; load flow; statistical analysis; voltage measurement; power transmission reliability; power measurement; power system state estimation

Other keywords: voltage phasor; measurement error; voltage control; SE; optimization problem; distribution power grid; state estimation; voltage magnitude measurement; PMU; power injection measurement; stability analysis; security assessment; power system; reliability; state estimation processing; transmission power grid; statistical estimation; load flow calculation

Subjects: Voltage measurement; Reliability; Other topics in statistics; Power system measurement and metering; Power and energy measurement; Power transmission, distribution and supply