Quantification of additional reinforcement cost driven by voltage constraint under three-phase imbalance

Three-phase imbalance causes uneven voltage drops across LV transformers and main feeders. With continuous load growth, the lowest phase voltage at the feeder end determines the voltage spare room, which is lower than if the same power were transmitted through balanced three phases. This imbalance causes additional reinforcement cost (ARC) beyond the balanced case. This paper proposes novel ARC models for a typical LV circuit based on primary-side voltage and current measurements. All models except the accurate model not only enable efficient utility-scale ARC calculations with sufficient accuracy but also remove the need for phasor measurements. The ARC models calculate voltage-driven reinforcement costs for the imbalanced case and the benchmark, i.e., the balanced case, where the ARC is the difference between the above values. The models include: an accurate ARC model considering imbalance in both magnitudes and phase angles; a semi-simplified ARC model assuming balanced phase angles; a fully simplified model assuming a purely resistive LV circuit and a unity power factor; and linearized ARC models considering the imbalance degree for two special cases. Test case proves that: the ARC is a monotonically increasing, convex (concave) but close-to-linear function of current (voltage) imbalance; voltage imbalance has a greater impact on ARCs than current imbalance; a higher degree of current imbalance and/or a deteriorating power factor reduce the accuracy of the fully simplified model; and the accuracy of the semi-simplified model is higher in the case of voltage angle imbalance than in the case of current angle imbalance

Utility-Scale Estimation of Additional Reinforcement Cost from 3-Phase Imbalance Considering Thermal Constraints

Widespread three-phase imbalance causes inefficient uses of low voltage (LV) network assets, leading to additional reinforcement costs (ARCs). Previous work that assumed balanced three phases underestimated the reinforcement cost throughout the whole utility by more than 50%. Previous work that quantified the ARCs was limited to individual network components, relying on full sensory data. This paper proposes a novel methodology that will scale the ARC estimation at a utility level, when the data concerning the imbalance of circuits or transformers are scarce. A novel statistical method is developed to estimate the volume of assets that need to be invested by identifying the relationship between the triangular distribution of circuit imbalance and that of circuit utilization. When there are more data available in future, accurate probability distributions can be constructed to reflect the network condition across the whole system. In light of this, two novel generalized ARC estimation formulas are developed that account for generic probability distributions. The developed methodology is applied to a real utility system in the UK, showing that: 1) three-phase imbalance leads to ARCs that are even greater than the reinforcement costs in the balanced case; 2) a 1% increase in the demand growth rate, the maximum degree of imbalance (DIB) and the maximum nominal utilization rate leads to over 10%, approximately 1% and 2% increases in the ARCs, respectively; and 3) the ARC is not sensitive to the minimum DIB values and the minimum nominal utilization rates

Probabilistic impact assessment of phase power imbalance in the LV networks with increasing penetrations of low carbon technologies

Phase imbalances cause a range of network issue, from day-to-day energy losses to long-run capacity wastes that increase investment costs. The impact on low voltage (LV) network from phase imbalance has been investigated independently for losses and investment. However, no research was carried out on the total imbalance-induced cost (TIC) that includes both day-to-day energy losses and long-run capacity wastes, and how the relationship between the two may change with the increasing penetrations of single-phase low carbon technologies (LCTs). Analyzing the TIC is important for distribution network operators (DNOs) as the day-to-day energy loss cost cannot be ignored as it may exceed the long-run network investment cost. This paper develops a new probabilistic framework to investigate the impact of increasing LCT penetration on TIC in the UK's LV distribution networks. Monte Carlo simulations are performed to account for the uncertainties in LCT sizes, connection locations and connection time. Case studies show that the additional energy loss cost exceeds the additional reinforcement cost in urban networks when the LCT penetration level reaches 70%. The key findings will help the DNOs understand the range of TIC and the relationship between imbalance-induced energy losses and capacity wastes under increasing LCT penetrations.</p

Neutrino mixing matrix in the 3-3-1 model with heavy leptons and A4A_4 symmetry

We study the lepton sector in the model based on the local gauge group $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ which do not contain particles with exotic electric charges. The seesaw mechanism and discrete $A_4$ symmetry are introduced into the model to understand why neutrinos are especially light and the observed pattern of neutrino mixing. The model provides a method for obtaining the tri-bimaximal mixing matrix in the leading order. A non-zero mixing angle $V_{e3}$ presents in the modified mixing matrix.Comment: 10 page

Quantification of Additional Reinforcement Cost from Severe 3-Phase Imbalance

This letter is an enhancement to our previous paper that quantifies additional reinforcement costs (ARCs) for low voltage (LV) assets under moderate degree of 3-phase imbalance. The original formulas cause an overestimation of the ARCs under severe imbalance. This letter first quantifies the threshold of the severe degree of imbalance (DIB), below which the original formulas are applicable. Then, the ARC formulas are extended to account for the whole range of DIB. Case studies demonstrate that when the asset loading level is below 33.3% (50%) for a feeder (a transformer), the DIB never exceeds the threshold and the original ARC formulas are applicable; otherwise, the DIB can exceed the threshold and the extended formulas yield correct ARCs

Cost-Benefit Analysis of Phase Balancing Solution for Data-scarce LV Networks by Cluster-Wise Gaussian Process Regression

Phase imbalance widely exists in the UK’s low voltage (415V, LV) distribution networks. The imbalances not only lead to insufficient use of LV network assets but also cause energy losses. They lead to hundreds of millions of British pounds each year in the UK. The cost-benefit analyses of phase balancing solutions remained an unresolved question for the majority of the LV networks. The main challenge is data-scarcity – these networks only have peak current and total energy consumption that are collected once a year. To perform a cost-benefit analysis of phase balancing for data-scarce LV networks, this paper develops a customized cluster-wise Gaussian process regression (CGPR) approach. The approach estimates the total cost of phase imbalance for any data-scarce LV network by extracting knowledge from a set of representative data-rich LV networks and extrapolating the knowledge to any data-scarce network. The imbalance-induced cost is then translated into the benefit from phase balancing and this is compared against the costs of phase balancing solutions, e.g. deploying phase balancers. The developed CGPR approach assists distribution network operators (DNOs) to evaluate the cost-benefit of phase balancing solutions for data-scarce networks without the need to invest in additional monitoring devices

Cost-Benefit Analysis of Phase Balancing Solution for Data-scarce LV Networks by Cluster-Wise Gaussian Process Regression

Phase imbalance widely exists in the UK’s low voltage (415V, LV) distribution networks. The imbalances not only lead to insufficient use of LV network assets but also cause energy losses. They lead to hundreds of millions of British pounds each year in the UK. The cost-benefit analyses of phase balancing solutions remained an unresolved question for the majority of the LV networks. The main challenge is data-scarcity – these networks only have peak current and total energy consumption that are collected once a year. To perform a cost-benefit analysis of phase balancing for data-scarce LV networks, this paper develops a customized cluster-wise Gaussian process regression (CGPR) approach. The approach estimates the total cost of phase imbalance for any data-scarce LV network by extracting knowledge from a set of representative data-rich LV networks and extrapolating the knowledge to any data-scarce network. The imbalance-induced cost is then translated into the benefit from phase balancing and this is compared against the costs of phase balancing solutions, e.g. deploying phase balancers. The developed CGPR approach assists distribution network operators (DNOs) to evaluate the cost-benefit of phase balancing solutions for data-scarce networks without the need to invest in additional monitoring devices

Estimation of voltage-driven reinforcement cost for LV feeders under 3-phase imbalance

Three-phase imbalance causes uneven voltage drops along low voltage (LV) feeders. Under long-term load growth, the phase with the lowest terminal voltage will trigger network reinforcements, which are earlier than if the three phases were balanced. This leads to a higher voltage-driven reinforcement cost (VRC) than the balanced case. Three-phase power flow analyses are not suitable for VRC estimations under serious data deficiency (without customers’ phase connectivity and smart metering data), and are not scalable due to the iterative nature which brings a prohibitively high computation burden on a utility level with millions of feeders. To overcome the challenges, this paper proposes a novel scalable methodology for VRC estimations that is applicable from an individual feeder to millions of feeders where the level of information is insufficient to support accurate three-phase power flow studies. The key is to use five types of load current distributions to represent customers’ phase allocations and individual demands, and to incorporate these distributions into an equivalent impedance matrix which allows a straightforward VRC estimation without iterations. This paper applies this methodology to an individual feeder, showing that: 1) the VRC decreases (increases) with the increase of the K (beta) factor of the trapezoid (triangular-rectangular) distribution, given that other conditions remain the same; 2) the VRC is more sensitive to voltage imbalance than to current imbalance; and 3) if the three phases are balanced, the change of any single variable results in an increase of the VRC, given that all other input variables remain constant

Quantification of additional asset reinforcement cost from three phase imbalance

Uneven load distribution leads to a 3-phase imbalance at the low voltage (LV) substation level. This imbalance has distinct impacts on main feeders and LV transformers: for main feeders, it reduces the available capacity as the phase with the least spare capacity determines the usable capacity; for LV transformers, phase imbalance reduces the available capacity due to additional power along the neutral line. To assess the additional reinforcement cost (ARC) arising from a 3-phase imbalance, this paper proposes two novel costing models for main feeders and LV transformers respectively. Each model involves the derivation of an accurate ARC formula based on the degree of three-phase imbalance and a linearized approximation through Taylor’s expansion to simplify the detailed ARC formula, enabling quantification of future LV investment in scale. The developed models are tested on 4 cases where imbalance ranges from 0 to 10%, and reveals that i) a small imbalance degree may cause a substantial ARC on main feeders; ii) ARC grows exponentially as asset utilization is close to its capacity; and that iii) a main feeder is more sensitive to its respective imbalance degree than a LV transformer under the same condition. The models serve as an effective tool to assist distribution network operators (DNOs) to quantify a key cost (ARC) element from the phase imbalance, allowing DNOs to evaluate their future LV investment in scale

Utility-Scale Estimation of Additional Reinforcement Cost from 3-Phase Imbalance Considering Thermal Constraints

Widespread three-phase imbalance causes inefficient uses of low voltage (LV) network assets, leading to additional reinforcement costs (ARCs). Previous work that assumed balanced three phases underestimated the reinforcement cost throughout the whole utility by more than 50%. Previous work that quantified the ARCs was limited to individual network components, relying on full sensory data. This paper proposes a novel methodology that will scale the ARC estimation at a utility level, when the data concerning the imbalance of circuits or transformers are scarce. A novel statistical method is developed to estimate the volume of assets that need to be invested by identifying the relationship between the triangular distribution of circuit imbalance and that of circuit utilization. When there are more data available in future, accurate probability distributions can be constructed to reflect the network condition across the whole system. In light of this, two novel generalized ARC estimation formulas are developed that account for generic probability distributions. The developed methodology is applied to a real utility system in the UK, showing that: 1) three-phase imbalance leads to ARCs that are even greater than the reinforcement costs in the balanced case; 2) a 1% increase in the demand growth rate, the maximum degree of imbalance (DIB) and the maximum nominal utilization rate leads to over 10%, approximately 1% and 2% increases in the ARCs, respectively; and 3) the ARC is not sensitive to the minimum DIB values and the minimum nominal utilization rates