# A Comprehensive Survey on Enabling Techniques in Secure and Resilient Smart Grids
## 4 Security and Resilient Architecture
### Power System State Estimation (PSSE)
#### 4.2.5 Distribution System State Estimation (DSSE)  
Compared to centralised PSSE, DSSE is more robust, and decentralised estimators are able to provide decentralised information from different system hierarchies divided according to geographical, topological, and measurement points [53; 72]. Especially when the new generations of digital devices start to join the power grid, the study of DSSE is necessary.  
In [73], [PERSON] points out that DSSE nowadays shares some similar features: 1. radial or weakly meshed topology, 2. high R/X ratios, 3. few real-time measurements, and 4. asymmetric construction and unbalanced loads. Lack of network observability (unless using pseudo measurements) makes the DSSE processes even harder to implement.  
[PERSON] and [PERSON] proposed two main types of WLS state estimation methods: node-voltage estimator (NV-DSSE) and branch-current estimator (BC-DSSE) [74; 75]. The differences mainly exist in the state variables, the simplifications of estimation, and the incorporation of heterogeneous measurements [53]. In NV-DSSE, voltage magnitudes and phase angles are usually used as the state vector. In BC-DSSE, pseudo measurements of power injections, power flows, and sometimes the slack bus voltage magnitudes are included in the state vector. However, because of the voltage measurements, the derivations of branch current are non-zero Jacobian terms, which makes the BC-DSSE method compute slower than NV-DSSE [53]. Some DSSE studies are listed in Table 4:  
\begin{table}
\begin{tabular}{c l l l l} \hline \hline
**Cite** & **Contribution** & **Input** & **Algorithm** & **Evaluation** \\ \hline
[73] & The proposed & Analog real-time & WLS & Test in modified IEEE \\  & three-phase DPSSE & current & & 34-bus testbed. \\  & model reduces the & magnitude, active & But cannot perform \\  & dimension of state & and reactive & & well in systems that \\  & estimation processes. & power & & lack telemetered \\  & & measurements; & power and \\  & & Historical & magnitude \\  & & loads/AMI/AMR & measurements, \\  & & information as & & and bad data in load. \\  & & pseudo & measurements. & \\ \hline
[76] & Do not need local & 14-bus: 6 power & WLS + WAU & The algorithms based \\  & observability of all & injection, 16 & (rule-based) & on WLS can perform \\  & control areas. In DC & power flow & & estimation on both \\  & SE, the linear power & measurements; & & AC/DC system in \\  & flow model & 118-bus: 49 power & & IEEE 14-bus and \\  & converges to a & injection, 129 & & 118-bus testbeds. \\  & centralised WLS & power flow & & \\  & model. In AC SE, use & measurements & & \\  & distributed WAU & & & \\  & (wait-and-update) & & & \\  & rule-based & & & \\  & algorithms. & & & \\ \hline
[77] & Divided the DPSSE & Voltage & WLS & Test on a substation \\  & processes into two & magnitudes, & with two parallel \\  & stages: (1) Decouple & transformers & transformers, which \\  & the manner of & power flows & includes 69-bus and \\  & multiple WLS & & & 85-bus systems. \\  & subproblems; & & & \\  & (2) Coordinate each & & & \\  & substation using & & \\  & linear WLS. & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Distribution system state estimation algorithms.