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This paper presents a tri-objective Optimal Phasor Measurement Units (PMUs) Placement (OPP) strategy that is focused on the minimization of i) the total number of PMU channels, ii) the maximum state estimation uncertainty based only on high-rate PMU data and iii) the sensitivity of state estimation to line parameter tolerances. The proposed formulation keeps into account system observability with and without contingencies due to single-line and PMU faults. Also, it includes the effect of possible zero-injection buses and a-priori constraints on both the number of PMU channels and the type of PMU measurements performed at each bus. Due to the nonlinear combinatorial nature of the proposed OPP problem, this is solved through a custom implementation of the nondominated sorting genetic algorithm II (NSGA-II). The analysis of the proposed OPP strategy is focused on distribution systems. The placement results obtained using four test systems of different size show that increasing the number of buses instrumented with PMUs and/or the number of PMU channels beyond given thresholds just leads to larger costs with negligible further reductions in both state estimation uncertainty and sensitivity to line parameters tolerances. Moreover, if PMUs with just two three-phase channels are used, we can avoid instrumenting between 30% and 40% of buses with a minor impact on state estimation performance even in the case of contingencies. This percentage can be slightly increased if multi-channel PMUs are used. However, this choice generally is not profitable.

The study of the behavior of smart distribution systems under increasingly dynamic operating conditions requires realistic and time-varying load profiles to run comprehensive and accurate simulations of power flow analysis, system state estimation and optimal control strategies. However, due to the limited availability of experimental data, synthetic load profiles with flexible duration and time resolution are often needed to this purpose. In this paper, a top-down stochastic model is proposed to generate an arbitrary amount of synthetic load profiles associated with different kinds of users exhibiting a common average daily pattern. The groups of users are identified through a preliminary Ward’s hierarchical clustering. For each cluster and each season of the year, a time-inhomogeneous Markov chain is built, and its parameters are estimated by using the available data. The states of the chain correspond to equiprobable intervals, which are then mapped to a time-varying power consumption range, depending on the statistical distribution of the load profiles at different times of the day. Such distributions are regarded as Gaussian Mixture Models (GMM). Compared with other top-down approaches reported in the scientific literature, the joint use of GMM models and time-inhomogeneous Markov chains is rather novel. Furthermore, it is flexible enough to be used in different contexts and with different temporal resolution, while keeping the number of states and the computational burden reasonable. The good agreement between synthetic and original load profiles in terms of both time series similarity and consistency of the respective probability density functions was validated by using three different data sets with different characteristics. In most cases, the median values of synthetic profiles’ mean and standard deviation differ from those of the original reference distributions by no more than ±10% both within a typical day of each season and within the population of a given cluster, although with some significant outliers.

The Interpolated Discrete Fourier Transform (IpDFT) is one of the most popular algorithms for Phasor Measurement Units (PMUs), due to its quite low computational complexity and its good accuracy in various operating conditions. However, the basic IpDFT algorithm can be used also as a preliminary estimator of the amplitude, phase, frequency and rate of change of frequency of voltage or current AC waveforms at times synchronized to the Universal Coordinated Time (UTC). Indeed, another cascaded algorithm can be used to refine the waveform parameters estimation. In this context, the main novelty of this work is a fair and extensive performance comparison of three different state-of-the-art IpDFT-tuned estimation algorithms for PMUs. The three algorithms are: (i) the so-called corrected IpDFT (IpDFTc), which is conceived to compensate for the effect of both the image of the fundamental tone and second-order harmonic; (ii) a frequency-tuned version of the Taylor Weighted Least-Squares (TWLS) algorithm, and (iii) the frequency Down-Conversion and low-pass Filtering (DCF) technique described also in the IEEE/IEC Standard 60255-118-1:2018. The simulation results obtained in the P Class and M Class testing conditions specified in the same Standard show that the IpDFTc algorithm is generally preferable under the effect of steady-state disturbances. On the contrary, the tuned TWLS estimator is usually the best solution when dynamic changes of amplitude, phase or frequency occur. In transient conditions (i.e., under the effect of amplitude or phase steps), the IpDFTc and the tuned TWLS algorithms do not clearly outperform one another. The DCF approach generally returns the worst results. However, its actual performances heavily depend on the adopted low-pass filter.

In the context of smart grids, Distribution Systems State Estimation (DSSE) is notoriously problematic because of the scarcity of available measurement points and the lack of real-time information on loads. The scarcity of measurement data influences on the effectiveness and applicability of dynamic estimators like the Kalman filters. However, if an Extended Kalman Filter (EKF) resulting from the linearization of the power flow equations is complemented by an ancillary prior least-squares estimation of the weekly active and reactive power injection variations at all buses, significant performance improvements can be achieved. Extensive simulation results obtained assuming to deploy an increasing number of next-generation smart meters and Phasor Measurement Units (PMUs) show that not only the proposed approach is generally more accurate and precise than the classic Weighted Least Squares (WLS) estimator (chosen as a benchmark algorithm), but it is also less sensitive to both the number and the metrological features of the PMUs. Thus, low-uncertainty state estimates can be obtained even though fewer and cheaper measurement devices are used.