# A Comprehensive Survey on Enabling Techniques in Secure and Resilient Smart Grids
## 4 Security and Resilient Architecture
### Power System State Estimation (PSSE)
#### 4.2.4 Dynamic State Estimation (DSE)  
With the development of the distributed energy resources (DERs) infrastructure, especially when renewable energy, electric vehicles, and time-history-related Internet of Things devices are added into the system, the state of the power system is becoming more uncertain and unpredictable [57]. Compared with the SSE, DSE methods will be able to track the dynamic changes of device states and loads throughout time [57]. DSE models usually use current or previous state estimation values combined with the system's physical model to predict future states (\(t+1\)) [51]. However, some research is still based on that the power system is a quasi-static system and has Gaussian distributed noise because of the complexity. Other works focus on reducing the DSE complexity. In [65], the author mentioned that most works use partial measurements and hierarchical and decoupled methods to reduce the DSE model complexity. Some DSE studies are listed in Table 3:  
\begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Cite** & **Contribution** & **Input** & **Algorithm** & **Evaluation** \\ \hline
[26] & Introduce Euclidean detector combined with Kalman filter to detect FDI attacks & DoS attack, Random attack, False data signals. & Kalman filter + Euclidean detector & Compare \(\chi^{2}\) and Euclidean detector under Kalman filter in various attacks. \\ \hline
[66] & Comparing UKF and EKF in non-linear state estimation. & - & UKF, EKF & UKF is more robust and convergence quicker than EKF with similar computational load. \\ \hline
[67] & Extended Kalman filter (EKF) model performance in DSE. & Bus voltage, bus angle, line flows & EKF & EKF performance relatively good under 0.03 s measurement sampling speed, and 30\% noise level. \\ \hline
[68] & Two-stage KF model in DSE: 1. use AKF with InNoVa for static estimation; 2. EKF for DSE & Voltage magnitudes and phase angles, process and measurement noise & AKF with InNoVa EKF & Compare KF, RKF, and AKF with InNoVa estimate performance in stage one under various noise environments \\ \hline
[69] & Iterated EKF combined with Generalised maximum likelihood (GM-IEKF) in DSE. & Voltage magnitudes, phase angles, process and measurement noise & GM estimator + IEKF & Compare GM-IEKF, EKF, UKF under various noise situations (non-Gaussian noise distribution included) in IEEE 39-bus testbed. \\ \hline
[65] & EKF based massively parallel DSE. & - & EKF & In 4992-bus testbed, using parallel iterative and direct linear models, the speed is 15 times faster. \\ \hline
[70] & Use voltage magnitude deviations to identify the radial path from PMUs Phase angle deviations in of-nominal frequency scenarios. & Dynamic generator internal voltages and phase angles & Finite difference difference + Chebyshev Filter to smooth the noise in equivalent generator signal waveforms. \\ \hline
[71] & DSE model combining the power flow equations with load forecasting. & Voltage magnitudes, phase angles. & EKF including load forecast has better accuracy and fewer computational requirements than augmented SSE. \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dynamic state estimation studies with Kalman filters.