A photovoltaics-aided interlaced extended Kalman filter for distribution systems state estimation
Introduction
The penetration of renewable-based distributed energy resources is both one of the main opportunities for smart grid evolution and one of the main challenges for its stable operation. Limiting the attention to the Photovoltaics (PV) case, new generators with a total capacity of about 99 GW were connected to the grid in 2017, with a year-on-year increase of almost 30% compared to 2016 [1].
In general, solar generation affects not only the inherent variability of RMS voltage amplitude and phase (regarded as system state variables) at different buses, but also the performance and stability of the algorithms used to estimate these quantities in real-time. As known, PV penetration may lead to violations of the voltage limits established by national or international regulations due to reverse power flows. The American National Standards Institute (ANSI) Standard C84.1-2016 specifies indeed that the voltage magnitude of residential loads has to lie within of the nominal value [2]. According to the European Standard (EN) 50160:2010 instead, Medium- and Low-voltage levels should not exceed of the declared value for more than 5% of a week under normal operating conditions [3]. Besides voltage rises, a large PV penetration may have several other critical consequences on distribution networks, such as voltage fluctuations due to solar power intermittency, voltage and current imbalances, harmonic distortion (mainly caused by PV inverters) and possible safety hazards due to unintentional islanding [4]. Of course, maximizing the hosting capacity (i.e. the amount of PV-based distributed generation for which given operational constraints on a feeder are not violated) is of paramount importance for renewable-based smart grid evolution [5], [6]. Even if a variety of measures (e.g., adjustable switched capacitor banks, on-load tap changers, network topology reconfiguration and above all, VAR-capable PV inverters) exist to mitigate voltage fluctuations and overvoltages, the impact of solar penetration on Distribution System State Estimation (DSSE) could be potentially critical and it has not been deeply investigated yet. In fact, even when the system voltage is kept under control, the combination of: solar generation intrinsic variability, limited system observability and heterogeneous measurement uncertainty contributions may significantly affect state estimation behavior. At the distribution level, this problem is even more critical not only because the number of measurement points and deployed instruments is usually smaller than in transmission systems, but also because the radial structure and the higher R/X ratio of typical distribution systems make them more sensitive to the penetration of distributed energy resources [7], [8]. In this respect, one of the open research challenges of DSSE is the definition and inclusion of models able to exploit (or at least mitigate the impact of) generation variability on state estimation algorithms [9], like in the case of large PV penetration [10], [11]. This paper provides a possible solution to this problem, by proposing a PV-aided Interlaced Extended Kalman Filter (PV-IEKF) conceived to be numerically more robust to zero power injections and able to exploit the available information on solar generation. The key advantage of the proposed approach is that it improves DSSE accuracy and robustness with no need to revolutionize the overall measurement infrastructure. In the rest of this manuscript, the novelty and the benefits of the proposed estimator are highlighted in Section 2 in the context of some related work. Section 3 deals with both models description and PV-IEKF implementation. Section 4 presents two case studies and analyzes the intrinsic variability of state variables due to growing PV penetration and seasonal fluctuations. Finally, in Section 5 the state estimation results obtained with the PV-IEKF using two different measurement setups are reported and compared with those obtained by using a classic state-of-the-art DSSE algorithm.
Section snippets
Related work
In general, the purpose of state estimation algorithms for transmission or distribution systems is to determine the node voltage or branch current phasors at a given time by using only a limited amount of available information, that can be obtained from historical data records (pseudo-measurements), or can be collected through Supervisory Control And Data Acquisition (SCADA) systems, intelligent electronics devices or, more recently, from Phasor Measurement Units (PMUs) [12], [13]. In general,
Models and state estimator description
The state of a distribution systems is usually expressed in terms of either bus voltage or line current phasors expressed either in polar or in rectangular coordinates [32]. In the following, without loss of generality, the state of the system will be expressed in terms of bus voltage amplitude and phase.
Case study description
Two Medium-Voltage (MV) case studies are considered in the rest of the paper, i.e. a simplified and modified version of the IEEE 37-bus radial feeder,1 and the rural 85-bus distribution system reported in [37]. Such distribution systems were selected among others because they both include a significant fraction (i.e. about 30%) of zero-injection buses. In the following subsections, first, the simulation settings for load and PV generation in both
DSSE performance evaluation
In this Section, the performance of the PV-IEKF estimator is analyzed in the case studies described in Section 4. In the following, first the state estimator settings as well as two possible measurement setups for DSSE implementation are described. Then, the state estimation results in the 37-bus and 85-bus case studies are reported and compared with those obtained with a classic WLS estimator in the very same experimental conditions. In the WLS case, the zero-injections are regarded as
Conclusions
In this paper, a study about the potential benefits of the use of PV generation data for distribution system state estimation (DSSE) is reported. In particular, a PV-aided Interlaced Extended Kalman Filter (PV-IEKF) is proposed. The advantage of the PV-IEKF is twofold. First, the state estimation uncertainty is generally lower than the uncertainty achievable with a classic WLS algorithm, which is still the most common approach adopted at the distribution level. Second, compared to a standard
CRediT authorship contribution statement
Grazia Barchi: Methodology, Formal analysis, Validation, Resources, Writing. David Macii: Conceptualization, Software, Writing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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