In Table 2.13, note that the best estimates are provided by the QC and LMR estimators, while the performance of the LTS procedure is poor. Note that this conclusion is withdrawn considering only one measurement scenario, a particular metering configuration, and a small 4‐bus system. In order to obtain statistically sound conclusions, the following section provides a detailed analysis of both the numerical and computational behaviors of the aforementioned algorithms, considering 100 measurement scenarios, different measurement configurations, and a large system.
2.5.10 Case Study
In this section, the performance of the mathematical programming estimation procedures described above is analyzed from both numerical and computational perspectives. These state estimation methods are applied to a realistic 118‐bus system. This system corresponds to the IEEE 118‐bus network, which represents a significant area of the American Electric Power system.
For statistical consistency, each analysis is carried out by considering 100 measurement scenarios. Each measurement scenario is synthetically generated from the solution of a converged power flow by adding Gaussian‐distributed random errors to the corresponding true values.
Each scenario involves:
1 A random active/reactive power consumption level.
2 Random locations of voltage and active/reactive power meters (ensuring observability of the whole system).
3 A random redundancy level.
4 Gaussian‐distributed random errors in all measurements (standard deviations of 0.01 and 0.02 p.u. for voltage and power measurements, respectively).
The computational analysis of this chapter has been performed using MINOS [11] and SBB [31] solvers under GAMS [12, 30] on a Linux‐based server with four processors clocking at 2.9 GHz and 64 GB of RAM.
2.5.10.1 Estimation Assessment
This subsection analyzes the performance of the estimators described in this chapter: WLS, LAV, QC, QL, LMS, LTS, and LMR.
To compare the accuracy provided by each estimator with regard to the true values for each scenario ω, the metrics
(2.47)
where
2.5.11 Results
The estimation problems previously mentioned are solved by using optimization software and by considering that parameters M and T are set to 100 and 2, respectively. The maximum number of iterations and the duality gap for MINLP problems is set to 1000 and 1%, respectively.
In order to remove mathematical unfeasibilities, the solutions to LMS and LTS mathematical problems are obtained by imposing that the set of measurements whose residuals are smaller than ∣yν( x )∣ provides whole system observability. This observability is achieved by forcing some binary variables to be equal 1 (i.e. bi = 1). These fixed variables correspond to a set of voltage and active power flow measurements that make the system observable.
Both numerical accuracy and computation performance are analyzed and compared. Tables 2.14 and 2.15 and Figures 2.13–2.15 provide results regarding estimation accuracy and computational performance:
Table 2.14 provides the mean and standard deviation of metrics and for each estimator considered.
Table 2.15 provides the minimum, mean, maximum, and standard deviation for the CPU time required (measured in seconds) for each estimator.
Figure 2.13 depicts the histogram of voltage magnitude absolute error for each estimator considered.
Figure 2.14 likewise shows the histogram of voltage angle estimation accuracy (measured in terms of absolute
