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

Phase imbalance is widespread in the distribution networks in the UK, continental Europe, US, China, and other countries. First, this paper reviews the mass scale of phase imbalance and its consequences. Three challenges arise from phase rebalancing: the scalability, data scarcity, and adaptability (towards changing imbalance over time) challenges. Solutions to address the challenges are: 1) using retrofit-able, maintenancefree, automatic solutions to overcome the scalability challenge; 2) using data analytics to overcome the data-scarcity challenge; and 3) using phase balancers or other online phase rebalancing solutions to overcome the adaptability challenge. This paper categorizes existing phase rebalancing solutions into three classes: 1) load/lateral re-phasing; 2) using phase balancers; 3) controlling energy storage, electric vehicles, distributed generation, and micro-grids for phase rebalancing. Their advantages and limitations are analyzed and ways to overcome the limitations are recommended. Finally, this paper suggests future research topics.


I. INTRODUCTION
HASE imbalance is widespread in distribution networks in the UK, continental Europe, US, China, and other countries.Three-phase current data from a sample of 800 representative low voltage (LV) substations in South Wales, UK, show that more than 50% of these networks suffer from significant phase imbalance [1].For instance, it is common that one phase has a peak current of 300A and another phase only has 150A.Main causes for phase imbalance are: 1) an uneven allocation of single-phase loads/customers across the three phases [2], [3], [4]; 2) random load behavior [2], [5]; 3) network structural asymmetries, e.g. the existence of single-phase laterals [6] and unequal phase impedances [7], [8]; and 4) the occurrence of unbalanced faults [9].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).
This paper performs an in-depth review of the scale of phase imbalance, its consequences, and phase rebalancing solutions.Based on the review, this paper presents the following original analysis and insights: 1) This paper analyzes the dominant consequence out of two imbalance-induced consequences (capacity waste and energy losses) for distribution networks of different loading levels.
2) This paper suggests three directions to address the scalability (towards millions of LV networks), data scarcity, and adaptability (imbalance changes over time) challenges arising from phase rebalancing: i) using retrofit-able, maintenance-free, automatic solutions to overcome the scalability challenge; ii) using data analytics to overcome the data-scarcity challenge; and iii) using phase balancers or other online phase rebalancing solutions to overcome the adaptability challenge.
3) This paper analyzes the advantages and limitations of existing phase rebalancing solutions in terms of: i) the suitability for non-directional phase imbalance; ii) energy losses arising from power electronics devices; iii) impact on power supply reliability; iv) cost and scalability to millions of networks; v) the ability to overcome data scarcity; and vi) adaptability towards changing imbalance conditions.This paper also suggests ways to overcome the above limitations.
4) This paper recommends future research topics.The remainder of this paper is organized as follows: Section II reviews the scale of phase imbalance; Section III summarizes the consequences of phase imbalance; Section IV reviews popular phase rebalancing solutions and analyzes their pros and cons; Section V recommends future research topics.

II. SCALE OF PHASE IMBALANCE
Phase imbalance involves both voltage imbalance and current imbalance.IEEE, IEC, National Electrical Manufacturers Association (NEMA), and CIGRE provided different mathematical definitions for voltage imbalance, using either symmetrical components or the minimum, maximum, and average values [17], [18], [19].IEC defined current imbalance factor as the ratio of the negative sequence component to the positive sequence component [18], [19].As the consequence of voltage and current imbalance, the power values on the three phases are also unbalanced.Different types of imbalance are coupled with each other and they are likely to occur simultaneously.

A. Phase imbalance in the UK
Phase imbalance is widespread in the UK's distribution networks.The University of Bath have time-series phase current data collected from 800 data-rich LV substations throughout a year at an interval of 15 minutes.These substations cover a good mix of geographical areas (urban, suburban, and rural) and customer composition (domestic, commercial, and industrial) in South Wales, UK.For example, Cardiff city center is selected as an urban area with a large number of commercial customers; Monmouthshire is selected as a representative rural area [1].These data show that more than 50% of the 800 LV substations suffer from serious phase imbalance, where the peak current of the "heaviest" phase is greater than that of the "lightest" phase by at least 50%.TNEI, a UK consultancy company, analyzed a total of 89 LV substations with 233 feeders within the business area of Scottish Power Energy Networks (SPEN) in the UK [15].They found that 165 out of these 233 LV feeders suffer from significant phase imbalance, where the mean ratio of the phase current to the average current for all three phases is greater than 1.3 [15].These studies collectively indicate the mass scale of phase imbalance in the UK.The increases of single-phase distributed generation, electric vehicles, and electric heat pumps will likely aggravate phase imbalance in the UK, if they are not properly controlled [20].L. Ochoa et al. concluded that phase imbalance must be considered for the UK's LV distribution networks [21], which have single-phase laterals supplying single-phase customers [6].At the medium voltage (11 kV and 33 kV) level, the assumption of balanced three phases is not realistic but is an acceptable approximation [21].

B. Phase imbalance in continental Europe
Phase imbalance is also widespread in continental Europe.European LV distribution networks are mainly three-phase four-wire networks, where the three phases have uneven load connections [4].For example, in Denmark where domestic customers are mainly supplied with three-phase power, distribution system operators do not have control over which phase each appliance is connected to [22].Electricians make such decisions, which inevitably lead to phase imbalance, because: 1) each appliance demonstrates random load behavior and 2) the phase connection decisions are made locally without coordination with the grid [22].

C. Phase imbalance in the US
The US distribution networks have different layouts from their European counterparts: i) the European distribution networks have three-phase MV/LV transformers with capacities from 300 kVA to 1,000 kVA.Extended from these transformers, three-phase LV main feeders supply either threephase customers or single-phase laterals where single-phase customers are connected [23].ii) On the other hand, the US distribution networks have MV main feeders (the primary system) as the backbone.Extending from the MV main feeders are single-phase laterals that interface the MV feeders with single-phase transformers.These single-phase transformers, normally having capacities less than 100 kVA, supply singlephase customers via very short (typically no more than 80 m) single-phase LV feeders (the secondary system) [23].
Despite the differences in the distribution network layouts, phase imbalance is also widespread in the US distribution networks, especially the MV distribution networks.The causes for phase imbalance are: the existence of single-phase MV laterals (i.e.structural asymmetries of the three phases) serving different number and types of loads; and random behavior of single-phase customers.Furthermore, W. H. Kersting pointed out that the distribution line segments are inherently asymmetrical [7], causing asymmetrical self and mutual impedances and eventually causing widespread current and voltage imbalances in distribution networks [24].In the US, the Department of Energy has identified phase imbalance as the leading cause for the overheating and premature failures of induction motors [25], [26].The fact that motor-driven systems consume more than 50% of the electrical energy (the percentage is 70% for industrial plants) [25], alongside the impacts of phase imbalance on motors, increases the significance of phase imbalance on a whole system level.This also makes phase balancing a key measure to improve motor efficiency [27].

D. Phase imbalance in China
Phase imbalance is rampant in China.The connections of single-phase domestic customers is identified as a major cause for phase imbalance in China's medium and low voltage distribution networks [28], [29].The increase of single-phase loads, especially nonlinear loads, further aggravates phase imbalance [30].J. Wang et al studied the phase imbalance in Jiangsu Province, China [31].Within a ten-day period in 2015, the study recorded a total of 3,762 phase imbalance daily records from 2,432 distribution transformers (a daily record is defined as a day when phase imbalance lasts for more than 6 hours) [31].W. Li et al investigated the causes and characteristics of phase imbalance in a town [28].The study identified correlations between phase imbalance and a variety of factors: the season, time, loading level, and the type of customers [28].

E. Phase imbalance in Australia
In Australia like in other countries, an uneven allocation of single-phase loads causes phase imbalance.The customer side experiences more serious phase imbalance than the substation side [8].

III. CONSEQUENCES OF PHASE IMBALANCE
Four main consequences of phase imbalance are reviewed: 1) Network capacity waste and the associated investment costs A main consequence arising from phase imbalance is a waste of network capacity and the associated cost [11], [32].Phase imbalance wastes the capacity of LV feeders.For a feeder with unbalanced three phases, when the capacity of the heaviest phase is used up, the space capacity of the other two phases cannot be transferred to the heaviest phase, thus resulting in network investment being earlier than if the three phases were balanced [10].Additional investment costs arise from such an imbalance-induced capacity waste.The costs are estimated for both individual networks [10], [33] and the entire business area of a distribution network operator [34].Phase imbalance is a limiting factor for the connection of distributed generation [20].
2) Imbalance-induced energy losses Another main consequence from phase imbalance is additional energy losses, including the additional loss on the phases and that in the neutral and ground (if the neutral is earthed).The additional energy losses occur on both transformers [35], [36] and feeders [37], [38].J Watson et al presented a method for the optimal dispatch of energy storage to minimize power losses on both the phases and the neutral [39].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].This important conclusion facilitates an efficient estimation of the power loss on the neutral path [14].Egwaile et al estimated the imbalance-induced energy loss in distribution transformers [37].The case studies found that rebalancing the loads across the three phases could reduce the transformer energy loss by 6% [37].
3) Imbalance-induced nuisance tripping Nuisance tripping is another consequence from phase imbalance.The ground current caused by phase imbalance may trip the protection devices [32].Phase current imbalance can cause nuisance tripping to a variable-frequency drive (VFD), even when the average phase power is below the VFD current rating [40].

4) Motor overheating and damages
Phase imbalance is widely acknowledged to cause motor overheating and even damages.As explained in Section II -C, the US Department of Energy identified phase imbalance as the leading cause for the overheating and premature failures of induction motors [25], [26].The negative-sequence reactance of an induction motor is only 1/7 to 1/5 of its positive-sequence reactance [41].The consequence is that, a negative-sequence voltage of 1% corresponds to a negative-sequence current of 6%, which causes extra heating to the motor and energy losses.
Fig. 1 shows the causes for and consequences of phase imbalance.

A. Analysis of the dominant type of consequences
This paper compares the imbalance-induced additional reinforcement cost versus the additional energy losses (the latter is calculated for one year) and identifies the dominant one for urban and suburban distribution networks.The degree of phase imbalance for three-phase feeders is defined in [10].The calculation of the additional reinforcement cost is also detailed in [10].With the increase of degree of phase imbalance, the capacity waste, which is represented by additional reinforcement cost (ARC), dominates the main consequence of phase imbalance for urban networks.However, for sub-urban networks, the dominance changes from capacity waste (represented by the ARC) to energy losses.For sub-urban networks with a loading level of 99%, the threshold degree of phase imbalance is 0.14, where the cost of capacity waste is equal to that of extra energy losses.The threshold degrees of phase imbalance are 0.058 and 0.017, respectively, for networks with loading levels of 50% and 25%.For rural LV networks, the conclusion is similar to that for sub-urban networks.The threshold degrees of phase imbalance are 0.11, 0.57 and 0.13, respectively, for networks with loading levels of 99%, 50% and 25%.

IV. SOLUTIONS TO PHASE IMBALANCE
Three challenges arise from phase rebalancing: 1) scalability -millions of LV networks need to be balanced; 2) data scarcity -the majority of the LV networks either do not have any available data or have data that are collected only once a year or at an even lower frequency; 3) adaptability -the phase imbalance condition changes over time with new connections of large single-phase loads such as electric vehicles and heat pumps.
Existing phase rebalancing solutions are classified into three categories and their performance with respect to the above challenges are summarised: 1) Re-phasing of loads and/or laterals This type of solution refers to moving loads/laterals from the heavily loaded phase to the light phase(s) either when energized ("online") or during scheduled power cuts ("offline").Also known as phase swapping, this is a traditional and intuitive way of phase rebalancing.J. Zhu et al formulated the re-phasing problem as an optimal power flow (OPF) problem, where: the control variables are the re-phasing options at each candidate nodes; the objective is to minimize the weighed sum of the rephasing cost and the cost of phase imbalance [11].Simulated annealing was adopted to solve the nonlinear OPF problem [11].In [32], J. Zhu et al developed a mixed-integer optimization model for re-phasing, considering both nodal rephasing and lateral re-phasing.D. Singh et al incorporated the voltage-dependency of loads into an online re-phasing model, which is a mixed-integer nonlinear optimization model [42].W. M. Siti et al developed a combined heuristic and neural network approach, which both reconfigures the feeders and performs customer re-phasing through switching [2].The same authors also developed a combined fuzzy logic and Newton-Raphson method to re-phase customers on the secondary feeder, with fuzzy objectives to minimize a number of phase imbalance indicators [43].C. Lin et al developed an expert system based on heuristics to re-phase laterals and single-phase transformers, with the objective to reduce the neutral current [44].T. H. Chen et al developed a genetic-algorithm-based approach to achieve both phase rebalancing and loss reduction for radial distribution networks, where the control variables are the phase connectivity of the transformers connected to a primary feeder [45].K. Wang et al applied six algorithms to the phase rebalancing problem and identified dynamic programming as a promising algorithm because of its optimality [46].S. H. Soltani et al developed a dynamic re-phasing strategy, which automatically re-phases loads at any time of a day when the degree of imbalance exceeds a threshold through automatic re-phasing switches [47].O. Homaee et al developed a phase balancing approach that optimally re-phases single-phase customers using discrete genetic algorithm [48].
Limitations of re-phasing, challenges, and potential solutions are: i) Only for directional phase imbalance: offline re-phasing is only applicable to phase imbalance with a definite direction, i.e. the existence of a phase that is consistently heavier (or lighter) than the other phases.
ii) Data-scarcity: in LV networks, the time-varying phase imbalance characteristics and customers' phase connectivity are not known.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.
iii) Scalability: digging up roads and re-phasing the cables for each individual LV network are impractical for millions of networks on a utility scale.A potential solution is to identify a small percentage of LV networks with serious phase imbalance out of millions of networks and then only target the identified ones.iv) Adaptability: the random new connections of large singlephase loads (e.g.electric vehicles) can completely change the direction of phase imbalance, invalidate any previous offline rephasing effort, and cause phase imbalance to reappear.Offline re-phasing is unable to address this problem.Online re-phasing is capable of resolving this, but frequent switching increases energy losses as well as wear and tear.
2) Using phase balancers based on power electronics S. M. Fazeli developed an individual-phase decoupled PQ control logic for distributed Static Synchronous Compensator (DSTATCOM) to rebalance the active power and the voltages of the three phases [49], [50].S. Yan et al developed a new three-phase electric spring and its control logic for balancing the three-phase load of a smart building [3].F. Shahnia et al developed optimal placement and control methods for a DSTATCOM to perform phase rebalancing [51]. A. Alsulami et al evaluated the dynamic performance of a Static Var Compensator (SVC) in mitigating the negative sequence component of the network voltage/current [52].H. Chiu et al developed a current-sharing method for a three-phase power factor correction converter to eliminate current imbalance [53].S. Beharrysingh developed a static balancer, which is essentially an interconnected-star autotransformer, for phase rebalancing in LV networks [12].
An advantage of phase balancers is their adaptability towards changing imbalance conditions.In other words, phase balancers rebalances the three phases online in response to changing imbalance conditions.However, they have limitations and they also face challenges: i) Efficiency: phase balancers are based on power electronics that perform high-frequency switches.These devices incur energy losses that cannot be ignored.They typically have an efficiency less than 95% [54], [55], whereas distribution transformers have an efficiency > 97% (the efficiency of liquidimmersed transformers is as high as 99.5%) [55].The more advanced control function and the greater time resolution of phase rebalancing, the more complex the topology of a phase balancer is and the greater losses are incurred.The excess energy losses compared to conventional, mature distribution network assets (e.g.transformers) is a fundamental problem for power electronic devices.The fundamental solution is beyond the power system discipline.It requires a breakthrough to future switching devices (e.g.insulated-gate bipolar transistors) that have a very high efficiency and a high number of lifetime switches -but it can be costly when the technology is at an early stage.An alternative solution to improve efficiency is to reduce the switching frequency, for example, by switching phases only when both the load current and the phase imbalance degree are above predefined thresholds -only the "peak load with a high degree of phase imbalance" case is worth attention.
ii) Reliability: phase balancers connected in series to the grid compromise power supply reliability.The outage of a series-connected phase balancer causes an outage of its downstream network.The outage lasts until either the fault is cleared or the downstream network is reconfigured.Potential solutions are: using phase balancers that are connected in parallel to the grid, maintaining redundancy, using components of a high reliability, and using as simple a hardware structure as possible.However, redundancy adds to the cost.
iii) Cost and scalability: the costs of phase balancers include capital and installation costs, costs of monitoring and communication, and maintenance costs.To reduce the total cost, this paper recommends the deployment of retrofit-able, maintenance-free, automatic phase balancers.They can be retrofitted to the existing network, requires minimal or no maintenance, and performs automatic phase rebalancing.
3) Controlling energy storage (including electric vehicles), distributed generation, and micro-grid for phase rebalancing S Chen et al developed a game theoretic approach for phase balancing, where a non-cooperative game incentivizes plug-in electric vehicles (EVs) to charge in a way that benefits both the grid and EV owners [56].S. Sun et al developed control algorithms for energy storage to balance the three phases under uncertainties [57].T. Hong et al developed centralized operation schemes for DC micro-grids to: i) fully rebalance the three phases of the substation transformer during the peak load period; and ii) partially rebalance the three phases if the microgrid capacity is insufficient [58].P. Lico et al developed a control algorithm which coordinates and controls single-phase EV chargers for phase rebalancing [22].K. H. Chua et al developed a control strategy for energy storage as part of the single-phase photovoltaic system to perform phase rebalancing [59].C. C. Bajo et al developed an individual-phase control strategy for three-phase PV systems to perform phase rebalancing [60].F. Shahnia et al developed a control method for single-phase PV converters to provide reactive power support, thus reducing voltage imbalance [61].E. Vega-Fluentes et al developed a coordination strategy for singlephase EV charging with three-phase power supply: when charging starts, chargers connect EVs to the lightly loaded phase of their feeder [62].This would reduce imbalanceinduced consequences and increases the network capacity to host EVs.
An advantage of this type of solutions is that no additional phase balancer is required.However, their costs and scalability are still a concern: the installation, communication, operation, and maintenance costs for millions of LV networks.
Table I summarizes the phase rebalancing solutions, which not only reduce energy losses but also release extra network capacities that are otherwise wasted by phase imbalance.This
2. Reliability concern: phase balancers connected in series with the grid compromises power supply reliability Use parallel-connected phase balancers, maintain redundancy, use highly reliable components, and use simple, reliable hardware structures

Costly and not scalable to millions of LV networks
Use retrofit-able, maintenance-free, and automatic phase balancers 4. Space limit in MV/LV distribution substations Use small-sized phase balancers 3. Control energy storage, EVs, DG, and micro-grids [56], [57], [58], [22], [59], [60], [61], [62] Adaptive; no new phase balancer required Costs of implementation, operation, and maintenance; scalability issue when applied to millions of LV networks Use mature and low-cost technologies for control and communication.Perform automatic control paper suggests the following directions that will address the scalability, data-scarcity, and adaptability challenges arising from phase rebalancing: 1) use retrofit-able, maintenance-free, automatic solutions to overcome the scalability challenge; 2) use data analytics to overcome the data-scarcity challenge by extrapolating knowledge to data-scarce networks; and 3) use phase balancers or other online phase rebalancing solutions to overcome the adaptability challenge.

V. FUTURE RESEARCH TOPICS
A number of promising future research topics are suggested: 1) Long-term forecast of phase imbalance.It is yet an unresolved question to perform a long-term forecast of the phase imbalance degree for years into the future.Traditional forecast methods are based on historical data [31].However, historical data do not reflect future increases of disruptive single-phase loads such as electric vehicles and electric heat pumps.Therefore, projections solely based on historical data are highly questionable.The key to the long-term phase imbalance forecast is to model in a stochastic way both the overall growth of those disruptive loads and their phase connectivity.The latter refers to the stochastic allocation of disruptive loads across the three phases, given existing phase connectivity information, e.g. the customer mix (domestic, industrial, and commercial customers) of each phase.
Such a long-term phase imbalance forecast will determine the projected costs of phase imbalance for distribution network operators.These costs will be translated into the potential benefits from phase rebalancing and will determine whether it is economically feasible for distribution network operators to invest in phase balancing solutions.
2) Whole-system analysis of the imbalance-induced costs.Whole-system analysis of the costs of phase imbalance, considering the propagation of imbalance from the very root (i.e.customers) to LV, medium voltage (MV), and high voltage (HV) distribution networks.Although the degree of phase imbalance is expected to decrease with the increase of the voltage level because of the load aggregation effect, the imbalance-induced costs cannot be simply ignored at MV and HV distribution levels.This is because two factors counter the degreasing phase imbalance degree: 1) the imbalance-induced network investment costs are proportional to the asset capital costs, which are greater at MV and HV levels than at the LV level.2) The imbalance-induced energy losses and the associated costs are proportional to the power flows.At MV and HV levels, the power flow magnitudes are tens or hundreds of times as much as those at the LV level.Therefore, a wholesystem analysis would reveal a more accurate cost of phase imbalance (also the potential benefit from phase rebalancing) than the analysis solely focusing on the LV level, thus enabling a more accurate cost-benefit analysis of phase rebalancing solutions.This will guide distribution network operators to make informed decisions on whether it is better to leave phase imbalance as it is or to invest in phase rebalancing solutions (as well as the type of solutions).
The key to the whole-system analysis of phase imbalance is to model the upward propagation of phase imbalance, i.e. how quickly phase imbalance diminishes upwards from LV to MV or HV levels for distribution networks that may or may not have sufficient sensory data.
3) Phase imbalance diagnosis for data-scarce LV networks.A promising topic is to diagnose phase imbalance for datascarce LV networks, including the diagnosis of phase imbalance direction and its coincidence with peak loads.
The existence of a phase imbalance direction refers to the existence of a particular phase that is consistently heavier (or lighter) than the other two phases.An example of phase imbalance with a definite direction is: phase a is heavier than the other two phases for 70% of the time and that phase a has an average current greater than that of the other phases.It is important to identify whether a phase imbalance direction exists or not, because the existence of the direction indicates that the loads are unevenly allocated towards a particular phase [63], meaning that offline load re-phasing is a feasible solution, e.g.move loads away from the consistent heavy phase to the other two phases during scheduled power cuts [63].However, not all cases have such a direction, e.g. a network where each phase is the heaviest phase for 1/3 of the time and the three phases have roughly equal average currents.In such cases, random load behavior is the dominant cause for phase imbalance.Solutions other than load re-phasing should be sought for, e.g.deploying phase balancers.
It is also important to diagnose to what extent phase imbalance coincides with the peak demand.If the peak demand coincides with the maximum degree of phase imbalance and if the peak demand is already close to the network capacity, the imbalance-induced capacity waste would be aggravated.Such a coincidence indicates that phase rebalancing is particularly urgent.On the other hand, if the peak demand does not coincide with the peak degree of phase imbalance, the imbalanceinduced energy losses would be a main consequence.
A promising research topic is to develop data-efficient (require a minimal amount of data) methods to diagnose phase imbalance for data-scarce LV networks.Ideally, the methods shall utilize the data that can be easily obtained during lowfrequency (e.g.once a year) inspections of the networks/substations by field engineers.The key is to extract knowledge from representative data-rich networks and extrapolate the knowledge to the data-scarce networks, using a combination of signal processing and data analytics.
4) Techno-commercial solutions to exploit the flexibility from large three-phase customers for phase rebalancing.There is a potential to exploit large three-phase customers (parking lots, building) for phase balancing through appropriate incentive schemes.Making three-phase customers draw balanced three-phase power does not aggravate the existing phase imbalance in the network, but it does not contribute to phase rebalancing either.This paper argues that, by deliberately making the three phases of large customers unbalanced, it can counter the phase imbalance at the substation.For example, a 11kV/415V substation has instantaneous load currents of 150A, 100A, 70A on phases a, b, and c, respectively.At this instance, a three-phase load which interfaces the network with power electronics can be controlled to draw unbalanced three-phase currents that counter the phase imbalance at the substation, e.g.0, 0, and 30A on phases a, b, and c, respectively, at the point of common coupling.This is "better" for the substation in terms of phase balancing, compared to the case where the three-phase load draws a current of 10A on each phase.This requires realtime automatic communication and control between the substation and the customer.The key technical part of the solution includes: 1) developing a control strategy to allocate the substation-side phase rebalancing task among all contracted customers/aggregators in the form of a control objective for each customer/aggregator; and 2) developing a control logic for contracted customers to perform phase current control to meet the control objective mentioned in 1).
The commercial part of the phase rebalancing solution is to develop a commercial arrangement to incentivize large threephase customers to contribute to phase rebalancing.This requires an estimation of the imbalance-induced cost, which is translated into the potential gross benefit from phase rebalancing.The net benefit is the gross benefit less the implementation cost.The distribution network operator needs to share the net benefit among all contributing customers, e.g. in the form of electricity bill discounts.Furthermore, the phase rebalancing service can be integrated with demand-side response services, referred to as "revenue stack up", to relieve the stress and improve operation efficiency for the network.
5) The optimal placement of phase balancers.A phase balancer can be deployed at different candidate locations of a network, e.g. the substation, a feeder node, and the customer side.Deployments at different locations have their respective pros and cons.If a phase balancer is deployed at a three-phase feeder node close to customers or at the three-phase customer's point of common coupling (PCC), it eliminates the imbalance close to its very source, i.e. customers, but new imbalance can emerge upstream of the phase balancer.On the other hand, if a phase balancer is deployed at the MV/LV substation or even at a higher-level substation, it does not reduce any downstream imbalance on the feeders but it effectively prevents the imbalance from propagating upwards.The optimal placement of a phase balancer requires a cost-benefit analysis, which can be formulated as a mixed-integer optimization model, where the decision variable is the optimal location of the phase balancer.
6) The transition from single-phase customers to threephase customers.Unlike in continental Europe, the majority of the UK's existing customers have single-phase supply.A recent study advocated that new customers should be supplied with three-phase power and investigated the feasibility to retrofit three-phase supply to existing single-phase domestic customers [64].The purpose for the change is to increase the supply capacity to accommodate new electric vehicles, electric heat pumps, and photovoltaic generation with a capacity of more than 4 kW.However, the impact of such a transition on phase imbalance needs to be investigated and it depends on how domestic appliances will be allocated across the three phases.

Fig. 1 :
Fig. 1: Causes for and consequences of phase imbalance.

Fig. 2 :
Fig. 2: Comparison of imbalance-induced energy losses and additional reinforcement costs (ARC) for urban networks

TABLE I :
SUMMARY OF PHASE REBALANCING SOLUTIONS 1. Offline re-phasing is only applicable to phase imbalance with a definite direction