A statistical methodology to identify imbalance-induced capacity wastes for LV networks

Highlights

• Not considering single-phase peak current would underestimate imbalance induced additional reinforcement costs (ARCs).

• Adopting a probability study of ARC promotes its credibility on making investment decisions of phase balancing.

• With the increase of the average load for LV networks, their ARCs do not continuously increase.

Abstract

Phase imbalance (i.e., load imbalance among the three phases) causes inefficient use of three-phase distribution assets, resulting in additional reinforcement costs (ARCs) compared to if the three phases were balanced. However, two problems remain unresolved when calculating the ARC: 1) previous ARC formulas assume that the three-phase total peak and the single-phase peak current occur simultaneously, thus causing an underestimation of the ARC; and 2) previous formulas calculate ARC as a point value, using one year's peak load. However, the point value is not credible in supporting making investment decisions on phase balancing. This is because the growth of the yearly peak load is inconsistent over the years – the growth could be positive or negative over the years for low voltage (415 V, LV) networks. To address the above problems, this paper originally develops 1) an updated ARC formula; and 2) a customised approach, named as the cluster-wise probability assessment, to deliver a distribution and confidence range of ARCs for any given LV network. This approach only requires the yearly average current and single-phase peak current, making it applicable to the majority of the LV networks that have a minimal amount of data. Case studies also identify a counterintuitive finding of how the yearly single-phase peak current and the yearly average phase current impact the ARCs.

Introduction

Phase imbalance is a widespread and long-outstanding problem in the UK, where customers are single-phase connected to the LV network. According to our data from Western Power Grid [1], more than 50% of LV networks suffered from significant phase imbalance, where the load on the “heaviest” phase exceeded that of the “lightest” phase by 50% most of the time. Further, TNEI, a UK consultancy, delivered a phase imbalance assessment report [2] for Scottish power, indicating that more than 70% of their sampled LV networks performed noticeable phase imbalance, where the greatest phase current exceeded the average phase current by 30% most of the time. In continental Europe, where customers are three-phase connected to the LV network, such as Denmark, phase imbalance is also a problem for distribution network operators [3]. Moreover, reference [4] presented 2% of MV networks in the USA have an undesirable degree of phase imbalance.

Phase imbalance wastes network capacity because of the inefficient use of network assets [5]. When the heaviest phase of a network asset is overloaded, the capacity margins on the other two phases cannot be transferred to the heaviest phase to relieve the overload. This is effectively an imbalance-induced capacity waste, resulting in an additional reinforcement cost (ARC) compared to if the three phases were balanced [5]. In the industry, the ARC serves as a vital indicator for making investment decisions on phase balancing solutions, e.g. phase swapping [6], deploying power-electronic-based phase balancer [7],[8], and so forth.

A number of references identified the imbalance-induced capacity waste qualitatively [8],[9]. References [5],[10], quantified the costs of imbalance-induced network capacity wastes in terms of ARCs. It assumed that the single-phase peak current coincides with the three-phase total peak, thereby taking the utilization rate and the degree of phase imbalance during the three-phase total peak as the inputs when calculating the ARC. However, the above assumption is not consistent with reality, and it causes an underestimation of the ARC. This is because the single-phase peak current and the three-phase total peak current do not occur simultaneously in reality, i.e., there is a time mismatch between the two peaks. Fig. 1 shows an example of why the previous ARC formula produces an underestimated ARC result.

In Fig. 1, the imbalance-induced capacity waste is 33A during the three-phase total peak period. However, because the actual single-phase peak current is greater than the maximum phase current during the three-phase total peak period by 40A, the actual imbalance-induced capacity waste is 73A. The previous ARC formulation only considers the capacity waste during the three-phase total peak, resulting in underestimating the ARC.

Besides, the previous formulation calculates ARC as a point value, using one year's peak data [5],[10]. However, for an LV network, the single-phase peak current and the three-phase total peak may not grow at the same rate [11],[12]: 1) the growth of the former can be negative, although the latter significantly increases in the next year; or 2) the growth of the former can be positive although the latter significantly decreases in the next year. This situation can be exacerbated if there is a mass penetration of heavy loads (e.g. electric vehicles and heat pumps) in future LV networks. Under this circumstance, the ARC value, calculated only from one year's peak data, is not credible to support investment decisions on phase balancing. One solution to addressing this problem is to use the yearly peak data of multiple years, e.g. 20 years, to obtain the distribution of ARC. However, this solution is too ideal to be implemented on a large scale. This is because: 1) LV networks can suffer from severe phase imbalance under peak load, requiring network reinforcement well before the required total number of years for generating the distribution. The data up to the point of reinforcement are therefore insufficient to generate a credible ARC distribution. 2) The majority of the LV networks only have the single-phase peak current and average phase current available in field works, whereas the three-phase total peak is not collected. The above insufficient data problem hinders the calculation of ARC value and its distributions.

Given the above problems, a gap therefore remains: there is a lack of an accurate, data-efficient, and credible ARC assessment approach that can support making investment decisions on phase balancing for a mass scale of LV networks that have a minimal amount of data. To this end, this paper makes the following original contributions:

This paper develops a new updated ARC formula that considers the mismatch between the three-phase total peak and the single-phase peak load and delivers an accurate calculation of the ARC.

Compared to the previous ARC formula that produces point estimations, this paper develops a customised approach, named as the cluster-wise probability assessment. This approach delivers a more credible ARC assessment, including a probability distribution and a confidence range of the ARCs. The results are significant economic indicators, supporting DNOs to improve network planning approaches and to make phase balancing investment decisions.

In this customised approach, the clustering stage firstly divides a set of data-rich LV networks, as training samples, into several groups. Then, the ARC values within each group are used to form a probability distribution, as well as a confidence range of ARC. Thirdly, for any network that is not used as a training sample in the clustering stage, if it has similar features to one of the derived groups, this group's confidence range and distribution of ARC are used as those for the LV network in question.

The developed approach is data-efficient, evidenced by the following perspectives: 1) this approach only requires time-series data from a small number of LV networks and the size of the required data does not have to cover multiple years. The lower-bound of data size is one year's time-series data; 2) this approach only requires the yearly single-phase peak currents and the yearly average phase currents for LV networks. The three-phase total peaks that are not collected by the majority of LV networks are not required.

The remainder of this paper is organized as follows: Section II develops an accurate formula to calculate the additional reinforcement costs; Section III presents the cluster-wise probability approach for ARC assessments; Section IV performs the case studies; and Section V concludes this paper.