A Statistical Approach to Estimate Imbalance-Induced Energy Losses for Data-Scarce Low Voltage Networks

Abstract

Phase imbalance in the UK and European low voltage (415V, LV) distribution networks causes additional energy losses.A key barrier against understanding the imbalanceinduced energy losses is the absence of high-resolution time-series data for LV networks. It remains a challenge to estimate imbalance-induced energy losses in LV networks that only have the yearly average currents of the three phases. To address this insufficient data challenge, this paper proposes a new customized statistical approach, named as the CCRE (Clustering, Classification, and Range Estimation) approach. It finds a match between the network with only the yearly average phase currents (the data-scarce network) and a cluster of networks with time series of phase current data (data-rich networks). Then CCRE performs a range estimation of the imbalance-induced energy loss for the cluster of data-rich networks that resemble the data-scarce network. The Chebyshev's inequality is applied to narrow down this range, which represents the confidence interval of the imbalance-induced energy loss for the data-scarce network. Case studies reveal that, given such few data from the data-scarce networks, more than 80% of these networks are classified to the correct clusters and the confidence of the imbalance-induced energy loss estimation is 89%.

Review of Distribution Network Phase Unbalance: Scale, Causes, Consequences, Solutions, and Future Research Direction

“…W. H. Kersting et al developed a method for computing the currents in the neutral and dirt as well as the associated power losses, which are the consequence of phase unbalance [7]. L. Fang and K. Ma developed a statistical approach to estimate the unbalance-induced energy losses in the neutral and dirt for data-scarce LV networks with data that are only recorded once a year [13]. S. Pajic et al found that for a wide range of conditions, the ratio between the neutral path resistance and the resistance of a transposed three-phase line is approximately given by ≈ ⁄ , where and are the zero and positive sequence resistances of the phase wire, respectively [14].…”

“…A potential solution is to deploy low-cost monitoring devices at a set of representative LV networks and then use machine learning to extrapolate the knowledge from representative data-rich samples to the vast population of datascarce networks. This type of solution can be applied to identifying customers' phase connectivity [31], the estimation of unbalance-induced energy losses [13], the development of re-phasing guidance [51], etc.…”

“…Even if the three phases of a distribution network were balanced when the network was initially constructed, phase unbalance appears and accumulates over K. Ma time with loads being added to and removed from each phase. Phase unbalance causes a number of consequences: 1) additional network investment costs because of the inefficient use of network assets [10], [11], [12]; 2) extra energy losses in the transformer, on the phases and neutral, and in the ground [12], [13], [14]; 3) nuisance tripping [15]; and 4) damages to induction motors [16].…”

Review of Distribution Network Phase Imbalance: Scale, Consequences, Solutions, and Future Research Direction

“…W. H. Kersting et al developed a method for computing the currents in the neutral and dirt as well as the associated power losses, which are the consequence of phase imbalance [7]. L. Fang and K. Ma developed a statistical approach to estimate the imbalance-induced energy losses in the neutral and dirt for data-scarce LV networks with data that are only recorded once a year [13]. S. Pajic et al found that for a wide range of conditions, the ratio between the neutral path resistance and the resistance of a transposed three-phase line is approximately given by ≈ ⁄ , where and are the zero and positive sequence resistances of the phase wire, respectively [14].…”

“…Even if the three phases of a distribution network were balanced when the network was initially constructed, phase imbalance appears and accumulates over time with loads being added to and removed from each phase. Phase imbalance causes a number of consequences: 1) additional network investment costs because of the inefficient use of network assets [10], [11], [12]; 2) extra energy losses in the transformer, on the phases and neutral, and in the ground [12], [13], [14]; 3) nuisance tripping [15]; and 4) damages to K. Ma, L. Fang, and W. Kong are with the University of Bath, Bath, BA2 7AY, UK (Corresponding author: K. Ma; E-mail: K.Ma@bath.ac.uk).…”