1

Abstract—Recently, utility-scale photovoltaic (PV) plants in

remote areas are drastically increasing due to abundant and low-

priced land. These remote areas are usually connected to zone

substations through long weak feeders with open-delta step

voltage regulators (SVRs) installed in the middle to regulate

downstream voltages. However, frequent PV and load power

fluctuations can lead to undesirable voltage variations and hence

excessive tap operation issues. Currently, it is not clear about the

percentage of responsibility by load or PV fluctuations to

excessive tap operations. In this paper, a novel method based on

line-to-line voltage sensitivity and time series evaluation is

proposed to respectively quantify the interactions between

PV/load fluctuations and tap operations. The accuracy of this

method is firmly validated with the measured data from a real-

life unbalanced distribution network with high PV penetration.

Further, this proposed method is implemented to statistically

quantify the causes of excessive tap operations with half-year

field data under the support of the local utility and the PV plant

owner. The investigation results can provide valuable insights for

utilities to better manage the voltage profiles and tap

maintenance for remote distribution networks with high PV

penetration.

Index Terms—Open-delta step voltage regulator, unbalanced

distribution network, solar photovoltaic (PV), tap changer,

voltage variation, voltage sensitivity.

I. INTRODUCTION

HOTOVOLTAIC (PV) installation has substantially

increased over the last decade, for example from about

45.72MW in March 2009 to 13.9 GW by September 2019 in

Australia [1]. Recently, there has been a rising tendency for

utility-scale PV plants in rural areas due to low-cost land and

government incentives [2]. However, due to long and weak

electrical connection, new challenges arise with PV

penetration increase in these remote areas, such as voltage

variations [3], excessive tap operations [4-5]and network

unbalance [6-7].

In traditional distribution networks, voltage variations are

mainly introduced by load fluctuations. For long weak feeders,

open-delta step voltage regulators (SVRs) are usually installed

in the middle to deal with voltage variations caused by slow

Corresponding author Ruifeng Yan (e-mail: ruifeng@itee.uq.edu.au).

Feifei Bai, Ruifeng Yan and Tapan Kumar Saha are with the School of

Information Technology and Electrical Engineering, the University of

Queensland, and Energy Queensland, Brisbane, QLD 4072, Australia (e-mail:

f.bai@uq.edu.au, ruifeng@itee.uq.edu.au, saha@itee.uq.edu.au). Daniel

Eghbal is with Energy Queensland (Energex), Brisbane, QLD 4006, Australia

(danieleghbal@energex.com.au).

load changes [8-10]. However, with more PV integrated into

rural areas, PV power fluctuations can lead to considerable

voltage variations due to high R/X ratio in distribution

networks [11], which further result in excessive tap

operations. For utility-scale PV integration, there usually is a

connection agreement to specify the voltage variation range,

which is achieved through the cooperation between utility and

PV owner. As the study in [12], the generation of a megawatt-

scale PV plant can drop more than 80% of its rated capacity

within three minutes due to fast-moving clouds, which can

cause significant voltage variations. Consequently, the PV

owner may be subjected to the penalty due to frequent voltage

violations and the utility may face asset management concerns

due to excessive tap operations. However, these issues may

not be only caused by PV fluctuations but also triggered by

load changes or upstream variations. Therefore, the objective

of this paper is to propose an effective approach to clarify the

responsibility of major impact factors (e.g., PV and load

fluctuations) to voltage variations and excessive tap

operations.

Voltage sensitivity is the bridge to explore the interactions

among power fluctuations, voltage variations and tap changes.

Traditionally, two categories of theoretical approaches are

utilized to calculate voltage sensitivity: adjoint network

method [13-14] and Jacobian matrix approach [15-17]. The

adjoint network method is derived from the Tellegen’s

theorem and the computation of the sensitivity index relies on

adjoint networks with a highly sparse adjoint coefficient

matrix. The second category of voltage sensitivity is obtained

by the inversion of the Jacobian matrix of the power flow

calculation. However, these two categories of approaches can

only provide the relationship between power fluctuations and

line-to-neutral voltage variations or line-to-line voltage

variations with a balanced network. Thus, for the unbalanced

network, none of these sensitivity indices has the capability to

assess the impact of power fluctuations on excessive tap

changes of open-delta SVRs, which regulate the line-to-line

voltages.

Currently, there is no available approach that can quantify

the responsibility of different impact factors to excessive SVR

tap operations. This paper has addressed this issue by

developing an innovative scheme for excessive tap operation

evaluation. The main contributions of this paper are as follows.

1) A theoretical approach is derived for line-to-line voltage

sensitivity identification to unlock the interactions among

Feifei Bai, Member, IEEE, Ruifeng Yan, Member, IEEE, Tapan Kumar Saha, Fellow, IEEE, Daniel

Eghbal, Senior Member, IEEE

An Excessive Tap Operation Evaluation

Approach for Unbalanced Distribution Networks

with High PV Penetration

P

F. Bai, R. Yan (Corresponding Author), T. K. Saha and D. Eghbal, “An Excessive Tap Operation Evaluation Approach for Unbalanced Distribution Networks with High PV Penetration”, IEEE Transactions on Sustainable Energy, April, 2020. DOI: 10.1109/TSTE.2020.2988571

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

2

power fluctuations, voltage variations and excessive tap

operations in unbalanced distribution networks;

2) A new scheme for determining tap operation responsibility

is developed based on line-to-line voltage sensitivity and

time series to quantitatively distinguish the responsibility

of tap changes introduced by different impact factors (e.g.,

PV/load power fluctuations and upstream impact);

3) The effectiveness of the proposed approach is fully

validated through measured data from an actual rural

distribution network with high PV penetration;

4) This research provides comprehensive investigation results

on tap operations to statistically identify the duties of

different impact factors to tap operations with half-year

field data under the support from the local utility and the

PV plant owner.

The proposed evaluation approach for excessive tap

operation can assist the utilities to evaluate the PV integration

impact on existing distribution networks. Moreover, this

research also delivers an efficient method to PV owners for

correctly assessing voltage compliance and consequently

avoiding needless penalties.

II. PROBLEM FORMULATION

A. Studied System

The studied system is a remote distribution network with

3.275MWp PV plant [18] installed at the University of

Queensland (UQ) Gatton campus, Queensland, Australia. As

shown in Fig. 1, both 3.275MWp PV plant and UQ campus

load (1.5MW to 3MW) are connected to the Gatton zone

substation through a 7.45km long 11kV feeder. This feeder is

split at Point A into the North feeder for agricultural load and

the South feeder for campus load. After approximately 1.7km

from Point A in the South feeder, an open-delta SVR (Fig. 2)

is installed to manage the voltage at the point of common

coupling (PCC) of the UQ Gatton campus.

Fig. 1 Single line diagram of the UQ Gatton distribution network[8]

4B

S

SL

L

S

SL

L

4A

4C

5B

5A

5C

4BI

4AI

4CI

5BI

5AI

5CI

ABN _2

ABN _1

CBN _2

CBN _1

(a) Equivalent electrical diagram (b) Voltage regulation diagram

Fig. 2 Voltage regulation mechanism of open-delta SVR [8]

The open-delta SVR configuration (consisting of 2

regulators) has been the preferred option for long rural feeders

due to its low component and installation cost compared with

the closed-delta SVR configuration (consisting of 3

regulators). As shown in Fig. 2, two regulators (Regulator-AB

and Regulator-CB) of the open-delta SVR are managing 𝑉𝐴𝐵

and 𝑉𝐶𝐵 at the PCC to meet the connection agreement for

voltage [0.975pu. to 1.01pu.]. The nominal voltage regulation

range is from –10% to +10% over 32 taps, which means

0.00625pu/tap.

Based on the actual load and PV power output profiles, the

yearly average PV penetration level is around 40%. Thus, the

studied system can be classified as a remote network with high

PV penetration. Hence, this research is not only important for

the studied system itself but also substantially valuable for

other similar PV plant integration projects in remote areas.

B. Excessive Tap Operation Issue

A utility-scale PV system (e.g., Gatton 3.275MWp PV plant)

concentrated in one location is susceptible to the impact of

cloud transients. For example, its power output can drop by 80%

within 3 minutes [19]. Considering the high R/X ratio of the

long weak distribution feeder, such PV power fluctuations can

substantially change the overall downstream power profile and

then lead to significant voltage variations. Furthermore, the

impact may propagate to upstream and consequently increase

upstream SVR tap operations.

The voltage regulation by SVR involves mechanical

movement, which will cause wear and tear of SVR tap

changers. Thus, the scheduling of maintenance for SVRs is

usually based on the number of tap operations. According to

the technical specification of SVR reported by Australia

distribution network service providers (DNSPs) [20],

inspection is required when ap operations reach 500,000. In

order to compare the impact of solar PV fluctuations on the

tap operations, one overcast day with lowest solar PV power

output and one cloudy day with high fluctuating solar PV

power output are selected as shown in Fig. 3. The number of

tap changes is 27 during the daytime (6:00 am to 6:00 pm) in

this overcast day, while the corresponding number in the

cloudy day (high variability day) is 66. In other words, the tap

operations are more than doubled with respect to PV power

output fluctuations. Therefore, the life span of the SVR would

be significantly reduced due to the increased tap operations

after PV plant integration. Moreover, the SVR is an expensive

asset (approximately AUD $225,000 for each open-delta SVR)

and the maintenance cost will be increased substantially with

excessive tap operations. Thus, it will bring a big economic

burden to DNSPs with the increase of SVR maintenance. This

has become a serious concern to utilities for asset management

and hence PV owner may be subjected to the penalty. The

causes for excessive tap changes can be downstream load

variations, PV power fluctuations, upstream on-load tap-

changer (OLTC) operations or capacitor bank switching

actions. However, the contributions from these impact factors

on tap changes are currently unclear and unjustified.

3.275 MWp

PV plant

Gatton zone

substation

33kV/11kV

11kV/415V

North Load

Open-delta SVR

1 2 3 4 5 6 7 8 9

10

UG

150m

Moon

2620m

Moon

1680m

Moon

1000mMoon

1200mUG

800m

Point A

Gatton

Campus load

DownstreamUpstream

4A

Common

Neutral

4B (B5)

C5

A5

θ

σ

β N (N4, N5)

C4

α

Voltage Regulation

Bus 4

Bus 5

3

Fig. 3 Recorded load, PV power and tap operations in UQ Gatton

In order to address the concern from utilities and clarify the

responsibility of PV owners for significant voltage change and

excessive tap operations, this paper will develop a voltage

sensitivity-based approach to quantitatively define the impact

from PV, load and other impact factors on tap operations,

respectively.

III. METHODOLOGY OF PROPOSED EVALUATION APPROACH

The evaluation approach of excessive tap operations was

developed to quantitatively define the impact of PV and load

fluctuations to voltage variations and further to tap operations

of SVRs. Since SVRs are regulating the line-to-line voltage

(𝑉𝐿−𝐿) as shown in Fig.2, the required voltage sensitivity to

evaluate tap operations is between the line-to-line voltage and

the power of PV or load.

A test-based approach[19][21] is employed as the

benchmark to validate the proposed approach. The test-based

method is based on the basic sensitivity definition, which is

the ratio of ∆𝑦 ∆𝑥⁄ . ∆𝑦 is the small change of an independent

variable 𝑦 and ∆𝑥 is the small changes of an independent

variable 𝑥. In this paper, the line-to-line voltage and PV/load

power are corresponding to variables 𝑦 and 𝑥 , respectively.

The test-based approach is the most straightforward way to

obtain the sensitivity. However, it is time-consuming to obtain

all the voltage sensitives through a tremendous set of

independent tests. Therefore, the test-based approach is only

used at the verification stage for the developed method.

With respect to the test-based approach and the theoretical

derivation approach, the following notations are made: M

denotes the total number of buses and

𝑉(𝑙−𝑛)𝑖𝑎𝑏𝑐 , 𝑃𝑖

𝑎𝑏𝑐, 𝑄𝑖𝑎𝑏𝑐 represent the line-to-neutral voltage

magnitudes (𝑉𝑎𝑛𝑖 , 𝑉𝑏𝑛𝑖 𝑎𝑛𝑑 𝑉𝑐𝑛𝑖), active power (𝑃𝑎𝑖 , 𝑃𝑏𝑖 𝑎𝑛𝑑 𝑃𝑐𝑖)

and reactive power (𝑄𝑎𝑖 , 𝑄𝑏𝑖 , 𝑎𝑛𝑑 𝑄𝑐𝑖) in each phase at Bus 𝑖,

respectively. Meanwhile, 𝑉(𝐿−𝐿)𝑖𝐴𝐵𝐶 and ∆𝑉(𝐿−𝐿)𝑖

𝐴𝐵𝐶 indicate the line-

to-line voltage (𝑉𝐴𝐵𝑖 , 𝑉𝐵𝐶𝑖 𝑎𝑛𝑑 𝑉𝐴𝐶𝑖 ) and line-to-line voltage

variations at Bus i, respectively. In addition, ∆𝑆𝑖𝑎𝑏𝑐 is used for

the power fluctuation at Bus 𝑖.

A. Test-based Approach

The test-based approach utilizes the sensitivity of the

relationship between the independent input variables (power

fluctuations) and the corresponding network responses (voltage

variations). This relationship between power fluctuations

∆𝑆𝑖𝑎𝑏𝑐 (input at Bus 𝑖) and voltage variations ∆𝑉(𝑙−𝑙)𝑗

𝑎𝑏𝑐 (output at

Bus j) can be described as an input-output model shown in Fig.

4.

The sensitivity of the output (∆𝑉(𝐿−𝐿)𝑗𝑖𝐴𝐵𝐶 ) with respect to each

input (∆𝑆𝑖) is calculated in (1), where the voltage sensitivity

index matrix (𝑆𝑒𝑛′𝑉(L−L)𝑗𝑖𝐴𝐵𝐶 ) to each input ∆𝑆𝑖 is obtained by

setting other inputs (∆𝑆𝑘) as zero.

𝑆𝑒𝑛′𝑉(L−L)𝑗𝑖𝐴𝐵𝐶 = ∆𝑉(𝐿−𝐿)𝑗𝑖

𝐴𝐵𝐶 ∆𝑆𝑖⁄ |∆𝑆𝑘 = 0, 𝑘 ≠ 𝑖 (1)

abc

iP jABV

jCBVPower

Network

Input Output ( )abc

iS

jACV

( )( )

L L ji

ABCV

orabc

iQ

Test-based voltage sensitivity ( )

( )ABC

L L jiV

Sen

Fig. 4. The schematic diagram for test-based approach

Overall, there are five steps to obtain the test-based

sensitivity index:

Step-1: Analyse the power variation range at the interested

bus to define the realistic power variation range to

be generated.

Step-2: Stochastically generate a data set (e.g., 50 data

points) in the power fluctuation range obtained in

Step-1.

Step-3: Select the input channel 𝑆𝑖 , which can be the

active/reactive power of load or PV at Bus 𝑖. Step-4: Run power flow to obtain all the outputs 𝑉(𝐿−𝐿)𝑗𝑖

𝐴𝐵𝐶 ,

where Bus j is the voltage regulated bus.

Step-5: Sensitivity index of the selected channel with

respect to all the outputs can be obtained by (1).

Step-6: Repeat Step-2 to Step-5 to obtain all the sensitivity

index for all the inputs.

Then, the obtained voltage sensitivity index will be the benchmark for the validation of the derived voltage sensitivity.

B. Proposed Theoretical Derivation Approach

A novel line-to-line voltage sensitivity calculation approach

is proposed based on the line-to-neutral voltage sensitivity and

transformer voltage transformation considering off-normal

ratios.

1) Line-to-Neutral Voltage Sensitivity

4

Based on the power flow calculation model [22], the linear

relationship between power changes (∆𝐏𝑎𝑏𝑐 and ∆𝐐𝑎𝑏𝑐) and

voltage variations (∆𝐕𝑙−𝑛𝑎𝑏𝑐) are described in (2).

[∆𝐏𝑎𝑏𝑐

∆𝐐𝑎𝑏𝑐] =

[ 𝜕𝐏𝑎𝑏𝑐

𝜕𝛅𝑎𝑏𝑐𝜕𝐏𝑎𝑏𝑐

𝜕𝐕𝑙−𝑛𝑎𝑏𝑐

𝜕𝐐𝑎𝑏𝑐

𝜕𝛅𝑎𝑏𝑐𝜕𝐐𝑎𝑏𝑐

𝜕𝐕𝑙−𝑛𝑎𝑏𝑐]

⏟ 𝑇𝑒𝑟𝑚−1

[∆𝛅𝑎𝑏𝑐

∆𝐕𝑙−𝑛𝑎𝑏𝑐] (2)

where ∆𝐏𝑎𝑏𝑐 , ∆𝐐𝑎𝑏𝑐, ∆𝛅𝑎𝑏𝑐 , ∆𝐕𝑙−𝑛𝑎𝑏𝑐 are 𝑀 − 1 variation

matrices for active power, reactive power, phase angles and

voltage magnitudes. The element “Term-1” in (2) is the

Jacobian matrix, which is calculated based on the bus voltages,

voltage phase angles and the admittances of the power

network. The details to calculate the Jacobian matrix are in

[22]. Based on the inversion of the Jacobian matrix, the

sensitivity matrix can be obtained as shown in (3).

𝐉−1 =

[ ∆𝛅𝑎𝑏𝑐

∆𝐏𝑎𝑏𝑐

∆𝛅𝑎𝑏𝑐

∆𝐐𝑎𝑏𝑐

∆𝐕𝑙−𝑛𝑎𝑏𝑐

∆𝐏𝑎𝑏𝑐

∆𝐕𝑙−𝑛𝑎𝑏𝑐

∆𝐐𝑎𝑏𝑐]

(3)

The line-to-neutral voltage sensitivity indexes are elements

of the inversion of the Jacobian matrix as in (4).

𝑆𝑒𝑛𝑉(𝑙−𝑛)𝑃𝑎𝑏𝑐 =

∆𝐕𝑙−𝑛𝑎𝑏𝑐

∆𝐏𝑎𝑏𝑐 and 𝑆𝑒𝑛

𝑉(𝑙−𝑛)𝑄𝑎𝑏𝑐 =

∆𝐕𝑙−𝑛𝑎𝑏𝑐

∆𝐐𝑎𝑏𝑐 (4)

Up to now, the descriptions from (2) to (4) are the basic

process for power flow calculation in a three-phase system.

The result of line-to-neutral voltage sensitivity is essential for

line-to-line voltage sensitivity derivation.

2) Development of Line-to-Line Voltage Sensitivity

The sensitivity obtained by (4) is only for the line-to-neutral

voltage. However, the line-to-line voltage sensitivity is needed

for the evaluation of excessive SVR tap operations. Thus, the

line-to-line voltage sensitivity should be developed.

In the distribution system, load and PV are usually

integrated to feeders through ∆-Yg transformers as shown in

Fig.15 of the APPENDIX. The off-normal ratios on primary and

secondary sides are α and β, respectively. These off-nominal

ratios are usually implemented by utilities to raise the voltage

for compensating line voltage drop. Thus, the final voltage

turn ratio between the secondary side and the primary side is

1 √3⁄ ∙ 𝛽 𝛼⁄ as detailed in the APPENDIX. Thus, the line-to-

neutral voltage sensitivity in (4) can be rewritten as in (5).

{

𝑆𝑒𝑛𝑉(𝑙−𝑛)𝑃𝑎𝑏𝑐 =

∆𝐕𝑙−𝑛𝑎𝑏𝑐

∆𝐏𝑎𝑏𝑐 =

1

√3 𝛽

𝛼∙∆𝐕𝐿−𝐿

𝐴𝐵𝐶

∆𝐏𝑎𝑏𝑐

𝑆𝑒𝑛𝑉(𝐿−𝑛)𝑄𝑎𝑏𝑐 =

∆𝐕𝑙−𝑛𝑎𝑏𝑐

∆𝐐𝑎𝑏𝑐 =

1

√3 𝛽

𝛼∙∆𝐕𝐿−𝐿

𝐴𝐵𝐶

∆𝐐𝑎𝑏𝑐

(5)

Then the line-to-line voltage sensitivity can be obtained as

shown in (6) by the transformation of (5).

{

𝑆𝑒𝑛𝑉(𝐿−𝐿)𝑃𝐴𝐵𝐶 =

∆𝐕𝐿−𝐿𝐴𝐵𝐶

∆𝐏𝑎𝑏𝑐 = √3

𝛼

𝛽∙∆𝑉𝑙−𝑛

𝑎𝑏𝑐

∆𝑃𝑎𝑏𝑐= √3

𝛼

𝛽𝑆𝑒𝑛

𝑉(𝑙−𝑛)𝑃𝑎𝑏𝑐

𝑆𝑒𝑛𝑉(𝐿−𝐿)𝑄𝐴𝐵𝐶 =

∆𝐕𝐿−𝐿𝐴𝐵𝐶

∆𝐐𝑎𝑏𝑐 = √3

𝛼

𝛽∙∆𝑉𝑙−𝑛

𝑎𝑏𝑐

∆𝑄𝑎𝑏𝑐= √3

𝛼

𝛽𝑆𝑒𝑛

𝑉(𝑙−𝑛)𝑄𝑎𝑏𝑐

(6)

In terms of Gatton distribution network, the SVR is

regulating two line-to-line voltages 𝑉𝐴𝐵 and 𝑉𝐶𝐵 . Thus, the

sensitivity indexes for Gatton system are shown in (7), where

all the sensitivity symbols are 3 × 1 matrices. This means each

matrix represents the three-phase sensitivity index.

{𝑆𝑒𝑛𝑉𝐴𝐵𝑃

= √3𝛼

𝛽𝑆𝑒𝑛𝑉𝑏𝑛𝑃

, 𝑆𝑒𝑛𝑉𝐴𝐵𝑄= √3

𝛼

𝛽𝑆𝑒𝑛𝑉𝑏𝑛𝑄

𝑆𝑒𝑛𝑉𝐶𝐵𝑃= √3

𝛼

𝛽𝑆𝑒𝑛𝑉𝑐𝑛𝑃

, 𝑆𝑒𝑛𝑉𝐶𝐵𝑄= √3

𝛼

𝛽𝑆𝑒𝑛𝑉𝑐𝑛𝑄

(7)

The developed line-to-line voltage sensitivity is the key to

calculate voltage variations and conduct excessive tap change

evaluation.

In the validation stage, the mismatch error could be

measured as a function of deviation between voltage

sensitivities obtained by both test-based method and the

proposed voltage sensitivity calculation approach. Mean

square error (MSE) [23] is considered as the accuracy index:

MSE =1

𝑁∑ (𝑆𝑒𝑛′𝑉(L−L)𝑘

𝐴𝐵𝐶 − 𝑆𝑒𝑛𝑉(𝐿−𝐿)𝑘𝐴𝐵𝐶 )2

𝑘=𝑁

𝑘=1 (8)

where N is the number of generated data points for validation,

𝑆𝑒𝑛′𝑉(L−L)𝑘𝐴𝐵𝐶 and 𝑆𝑒𝑛𝑉(𝐿−𝐿)𝑘

𝐴𝐵𝐶 are the voltage sensitivities at the

𝑘𝑡ℎ data point obtained by test-based method and the proposed

voltage sensitivity calculation approach, respectively.

3) Validation for the Proposed Voltage Sensitivity

The proposed theoretical derivation approach is validated

against the benchmark approach – the test-based method.

Extensive power fluctuations are generated to

comprehensively evaluate the effectiveness of the proposed

method. In terms of the studied system, the recorded

maximum active and reactive power changes were around 800

kW and 400 kVar in each phase, respectively. Thus, based on

the stochastic data generation approach mentioned in Section

III-A, a stochastic data set with 50 data points within the

realistic power variation range is used to model these power

fluctuations for both test-based method and the proposed

approach. It needs to mention that only in the validation stage

is necessary to generate stochastic power variation data to

show the generality and effectiveness of the proposed

approach. In the real implementation stage of the proposed

approach, the actual recorded time-series data will be used as

the input of the proposed approach so that there is no need to

generate the test data. Due to the unbalance of the distribution

system, the line-to-line voltage sensitivities for three phases

are verified independently and the verification results are

shown in Fig.5.

(a) Voltage sensitivity index of active power in three-phase

5

(b) Voltage sensitivity index of reactive power in three-phase

Fig. 5. Proposed evaluation index verification

As can be seen from Fig. 5, the evaluation indexes

calculated by the test-based method and proposed theoretical

derivation approach are almost aligned together and the MSEs

of all the validations are less than 1 × 10−13, which means the

proposed approach can effectively estimate the line-to-line

voltage sensitivity in a reasonably accurate range.

It needs to be noted that the test-based method is effective

for the validation of the proposed approach but not convenient

to be applied to the voltage sensitivity calculation of the real

system. The test-based method is like a black-box method

without a clear mathematical explanation of the interaction

between power fluctuations and voltage variations. On the

contrary, the proposed approach not only revealed the internal

mathematical relationship between power fluctuations and

voltage variations but also provided a time-efficient method to

achieve the voltage sensitivities.

4) Line-to-Line Voltage Variation

Once the sensitivity is obtained, the voltage variations

(∆𝑉𝐿−𝐿𝐴𝐵𝐶) introduced by each impact factor 𝑆𝑎𝑏𝑐 (i.e., load/PV

power in each phase) can be calculated by (9).

∆𝑉𝐿−𝐿𝐴𝐵𝐶 = 𝑆𝑒𝑛𝑉𝐿−𝐿

𝐴𝐵𝐶 ∙ ∆𝑆𝑎𝑏𝑐 (9)

In a real network, the voltage variations are caused by the

combined effect of active and reactive power changes. Thus,

for the studied system, the voltage variations subjected to PV

or load should be described as in (10) when considering phase

coupling between different phases.

{

∆𝑉𝐴𝐵𝑃𝑉 = 𝑆𝑒𝑛𝑉𝐴𝐵𝑃

∙ ∆𝑃𝑃𝑉𝑎𝑏𝑐 + 𝑆𝑒𝑛𝑉𝐴𝐵𝑄

∙ ∆𝑄𝑃𝑉𝑎𝑏𝑐

∆𝑉𝐶𝐵𝑃𝑉 = 𝑆𝑒𝑛𝑉𝐶𝐵𝑃∙ ∆𝑃𝑃𝑉

𝑎𝑏𝑐 + 𝑆𝑒𝑛𝑉𝐶𝐵𝑄∙ ∆𝑄𝑃𝑉

𝑎𝑏𝑐

∆𝑉𝐴𝐵𝐿𝑜𝑎𝑑 = 𝑆𝑒𝑛𝑉𝐴𝐵𝑃∙ ∆𝑃𝐿𝑜𝑎𝑑

𝑎𝑏𝑐 + 𝑆𝑒𝑛𝑉𝐴𝐵𝑄∙ ∆𝑄𝐿𝑜𝑎𝑑

𝑎𝑏𝑐

∆𝑉𝐶𝐵𝐿𝑜𝑎𝑑 = 𝑆𝑒𝑛𝑉𝐶𝐵𝑃∙ ∆𝑃𝐿𝑜𝑎𝑑

𝑎𝑏𝑐 + 𝑆𝑒𝑛𝑉𝐶𝐵𝑄∙ ∆𝑄𝐿𝑜𝑎𝑑

𝑎𝑏𝑐

(10)

where all the sensitivity indices are 3 × 1 matrices and the

dimensions of all the power matrices are 1 × 3 to represent

three phases. It needs to be noted that the power

( 𝑃𝑃𝑉𝑎𝑏𝑐, 𝑄𝑃𝑉

𝑎𝑏𝑐 , 𝑃𝐿𝑜𝑎𝑑𝑎𝑏𝑐 𝑎𝑛𝑑 𝑄𝐿𝑜𝑎𝑑

𝑎𝑏𝑐 ) in (10) are time-series data

measured from the power network. ∆P (∆𝑃𝑃𝑉𝑎𝑏𝑐, ∆𝑃𝐿𝑜𝑎𝑑

𝑎𝑏𝑐 ) and

∆𝑄 (∆𝑄𝑃𝑉𝑎𝑏𝑐 , ∆𝑄𝐿𝑜𝑎𝑑

𝑎𝑏𝑐 ) are the difference of the measured power

at 𝑡 + 1 and t in three phases. These calculated voltage

variations will be the bridge to evaluate the responsibility of

PV and load power fluctuations with respect to tap operations.

C. Tap Change Evaluation based on Time Series

Time series data are used to clarify the contribution of PV

and load power fluctuations to excessive tap changes. The

time-series data include measured three-phase PV/load power

and tap change incidents. Each tap change incident is assessed

by cumulative voltage variation to determine the causes for the

tap change. This process is illustrated in Fig.6 to show how

such time series evaluation is conducted.

As shown in Fig.6, based on (9), the voltage variation

introduced by load and PV is calculated cumulatively from 𝑡0

to 𝑡2 as in (11) with a time window ∆𝑇2 . During the

calculation, the cumulative voltage variation violates the

deadband −𝑉𝐷 at 𝑡1, and then the violation continues over a

period of ∆𝑇1 until the tap change occurs at 𝑡2. The time delay

∆𝑇1 reduces tap change sensitivity and prevents tap operation

from transients or short-time changes. ∆𝑇2 is the time between

two tap change incidents. For the studied system, ∆𝑇1 = 130𝑠.

0

(pu.)

Time (s)

Cumulative voltage variation

Dead-band

( )CL LV

Corrected

by tap

0t

DV

DV

2T

1t

1T

2t Fig. 6. Tap operation evaluation

After the tap change action, the voltage will be within the

dead-band range, and the cumulative voltage variation will be

set as in (12).

∆𝑉(𝐿−𝐿)𝐶𝐴𝐵𝐶 = ∑ (𝑆𝑒𝑛(𝑉𝐿−𝐿)𝑡 ∙ ∆𝑆𝑡

𝑎𝑏𝑐)𝑡2𝑡0

𝑡0 ≤ t ≤ 𝑡2 (11)

∆𝑉(𝐿−𝐿)𝐶𝐴𝐵𝐶 = 𝑆𝑒𝑛(𝑉𝐿−𝐿)𝑡 ∙ ∆𝑆𝑡

𝑎𝑏𝑐 t ≥ 𝑡2 or t ≤ 𝑡0 (12)

where ∆𝑉(𝐿−𝐿)𝐶𝐴𝐵𝐶 are the cumulative voltage variations,

meanwhile, 𝑆𝑒𝑛(𝑉𝐿−𝐿)𝑡 and ∆𝑆𝑡𝑎𝑏𝑐 are the line-to-line voltage

sensitivity and power fluctuations at time t, respectively.

The cumulative voltage variations subjected to load and PV

are calculated by (11). If the combined cumulative voltage

variation by load and PV violates the deadband for a time

duration of ∆𝑇1 (shown in Fig.6) and consequently trigger tap

changes, then the percentages of tap changing responsibility

by the load, PV and upstream fluctuations will be calculated

based on their contribution to voltage variations. The time

series calculation will be conducted over a long period of time

to achieve statistical significance for the determination of the

tap changing responsibilities. The details for clarifying the

responsibility of tap changes are shown in the following

pseudocode.

Pseudocode Determination of tap change responsibility

Input: Tap change, active/reactive power of load and PV

in each phase

Output: tap change responsibility by PV, load or upstream

Determination of tap change responsibility:

( ) ( ) ( )

( )

( ) ( )( / )

C PV load C PV C load

C PV load

C PV C PV load

L L L L L L

L L D

PV L L L L

V V V

if V V

Tap Tap V V

6

( ) ( )( / )C load C PV loadload L L L L

upstream

upstream upstream

PV PV

load load

Tap Tap V V

else

Tap Tap

end

Tap Tap

Tap Tap

Tap Tap

D. Scheme for Tap Change Responsibility Determination

The schematic diagram of the proposed scheme for

identifying the tap operation responsibility is shown in Fig. 7.

First, tap operations, PV and load power in each phase needs

to be measured as the inputs. Secondly, the line-to-line voltage

sensitivity index (𝑆𝑒𝑛𝑉𝐿−𝐿𝐴𝐵𝐶) should be calculated through the

Jacobian matrix and the Y-∆ transformation by (5)-(7). Then,

the instant voltage variation can be obtained based on (9)-(10).

Afterwards, the cumulative voltage variations introduced by

PV and load will be assessed via (11)-(12) based on tap

operation mechanisms (Fig. 6) and their contribution to

voltage variations through time series analysis. In the end, the

tap operations caused by different impact factors (PV, load

and upstream) will be identified, which are the outputs of the

scheme.

Fig. 7. Flowchart for the proposed approach

To fully prove that the proposed approach can be

implemented to a real system, validation has been carried out

with field recorded data. Then, under the support from the

local utility and PV plant owner, the developed approach is

further applied to the studied system for responsibility

determination of excessive tap operations.

E. Verification with Field Data

In Fig. 8, PV and load power profiles of each phase on 19th

April 2017 are selected to validate the effectiveness of the

proposed approach. In terms of PV power output, 6:00 am to

10:00 am and 10:00 am to 3:00 pm are the hours with a clear

sky and fast-moving clouds, respectively.

Fig. 8. Power profiles on 19th April 2017

The tap operations are shown in Fig. 9. As can be seen,

there are 47 tap changes are recorded in this day. In order to

solidly prove the effectiveness of the proposed approach, two

tap operating incidents (Incident-1 and Incident-2 as shown in

Fig. 9) caused by load and PV power fluctuations are selected

as examples for the demonstration.

Fig. 9. Measured and calculated voltage variations

As presented in Fig. 10, both PV active and reactive power

were zero. Thus, the Gatton load fluctuation was the only

impact factor from the downstream. As it can be seen, the

calculated cumulative voltage changes by the load (based on

the proposed method in Part C of this section) were aligned

with the measured voltage changes, and two tap changes were

triggered by load variations after 130s time delay. After the

tap operation, the voltage was adjusted back to the allowable

range.

Fig. 10. Tap and voltage changes by the load for incident-1

As shown in Fig. 11, there was a PV power drop before the

tap change. The cumulative voltage variations caused by load

were close to zero and the cumulative voltage variations from

PV fluctuations were aligned with the measured voltage

variations. Thus, the PV power fluctuation was the dominant

impact factor for these two tap changes. After the tap

adjustment, the voltage was within the allowable range.

7

Fig. 11 Tap and voltage changes by PV for incident-2

Overall, the proposed approach can accurately track the

voltage variations and tap changes. Thus, the proposed

theoretical approach will be used to quantitatively evaluate the

impact of load and PV power fluctuations on excessive tap

changes.

F. Applications of the Developed Approach

Half-year data (Jan. 1, 2017 to June 30, 2017, time period of

each day is from 6:00 am to 6:00 pm) is used to quantitatively

evaluate the influence of power changes on tap operations. In

the following statistical analysis, all the days in this half-year

period have been divided into four typical categories to

represent four typical daily weather scenarios.

1) Typical Day Analysis

As shown in Fig. 12, the four typical days are categorised as

Cloudy Day, Partially Cloudy Day, Clear Sky Day and

Overcast Day based on the method proposed in[12].

(a) Cloudy day (b) Partially cloudy day

(c) Clear sky day (d) Overcast day

Fig. 12. Active power profiles of four typical days

Based on the proposed scheme in Part D of this section, the

tap operations are calculated and analyzed for these four days

as summarized in Table I. As can be seen from Table I, the tap

changes caused by PV power fluctuations were relatively

minor in the Overcast Day, and moderate in the Partially

Cloudy Day. The number of the corresponding tap changes in

the Clear Sky Day was somewhere between that in the

Overcast Day and the Partially Cloudy Day. However, the tap

changes from PV power fluctuations had remarkably increased

in the Cloudy Day when compared with the other three days,

which made it comparable to the number of tap changes by the

load. Thus, the total tap operations in the Cloudy Day almost

doubled those in the Overcast Day. In addition, some tap

changes were also subjected to the upstream impact (e.g.

capacitor bank switching actions and OLTC tap changes) as

revealed in the last column of Table I.

TABLE I OPEN-DELTA SVR TAP OPERATIONS IN TYPICAL DAYS

Scenarios

Total

Tap

Change

Downstream Impact Up-

stream

Impact by PV by Load

Cloudy

(Jan.30, 2017) 50 24 23 3

Partially Cloudy

(Feb. 20, 2017) 30 8 20 2

Clear Sky

(May. 29, 2017) 26 3 21 2

Overcast

(March 30, 2017) 26 1 20 5

2) Statistical Analysis with Half-year Data

As shown in Table II, the largest proportion of days (up to

70.72%) were Partially Cloudy Days, which is more than

seven-fold of Clear Sky Days. While there were 14.37%

Cloudy Days and 4.97% Overcast Days (the minimum). In this

half-year, the total tap operations were 5935, among which

59% of tap operations were mainly triggered by load

variations and 26% of tap operations were associated with PV

power fluctuations. Other 15% was related to upstream

variations.

TABLE II PERCENTAGE OF DIFFERENT DAYS AND IMPACT FACTORS

Four Typical Days in a half year (181days)

Day Type Cloudy Partially cloudy Clear sky Overcast

Percentage 14.37% 70.72% 9.94% 4.97%

Tap Operations by Different Impact Factors in a half year

Impact Factors PV Load Upstream

Percentage 26% 59% 15%

In order to compare the impact of PV and load fluctuations

on tap operations, this paper conducted a statistical analysis of

half-year tap operations and calculated the average daily tap

operations in different cloud coverage conditions. The

investigation results are presented in Fig. 13. As can be seen

from Fig. 13, the load variation is the dominant impact factor

for tap operations. The tap changes subjected to PV power

fluctuations are similar to those caused by the load in the

Cloudy Day. However, the tap operations associated with PV

are much fewer than those related to the load in Clear Sky Day

and Overcast Day. Especially in Overcast Day, the tap

operation by PV is close to zero, which means that the PV

impact on voltage in Overcast Day can be neglected due to the

minor PV power injection. As shown in the blue curve in Fig.

13, the average total tap operations in each typical day are

increased from 20 to 51 corresponding to four typical days

from Overcast Day to Cloudy Day. In addition, besides the tap

variations caused by PV and load, other tap operations

8

induced by upstream cannot be ignored, as it also brings 889

tap changes in this half-year period.

Fig. 13. Comparison of average daily tap operations caused by different

impact factors in different weather conditions

To compare the overall impact of PV, load and upstream on

tap operations in different weather conditions, this paper

investigated the average tap operations and the results are

shown in Fig. 14. As can be seen, the tap operations by PV

and load are comparable in Cloudy Day at 22. While load

variations are responsible to the majority of tap operations in

other three typical days, and the tap changes by the load are

from 15 to 19 during the daytime. In contrast, the tap changes

by PV have significantly decreased in Partially Cloudy Day (7

times), Clear Sky Day (3 times) and Overcast Day (1 time). In

addition, tap operations by the upstream impact are very

consistent (between 4-6 times) in all types of the days –

Cloudy Day, Partially Cloudy Day, Clear Sky Day, and

Overcast Day.

Fig. 14. Comparison of average daily tap operations

Overall, the contribution of different impact factors to

excessive tap operations can be quantitatively distinguished

via the developed method.

IV. CONCLUSIONS

This paper proposes an innovative theoretical approach to

evaluate voltage variations and excessive SVR tap changes in

distribution networks with high PV penetration. It leverages

the voltage sensitivity and voltage transformation of Delta-

grounded Wye transformers to determine the relationship

between power fluctuations and line-to-line voltage variations.

Furthermore, an evaluation strategy for tap operations is

developed based on time series (i.e., measured voltage, PV

power, load, and tap operations) and the line-to-line voltage

sensitivity to determine the responsibility of different impact

factors (e.g., PV, load, and upstream) to excessive tap

operations in unbalanced networks. Moreover, its accuracy

and practicability are firmly verified with field data. Further,

the developed method has been applied for statistical analysis

with the measured data over a half-year period to quantify the

contribution of different factors to excessive tap changes.

For the studied system, the results show that PV fluctuations

can cause more tap changes than those induced by load

variations during a Cloudy Day. The tap changes by PV

fluctuations in the Partially Cloudy Day are around one-third

of the tap changes in the Cloudy Day. While PV power

fluctuations in the other two types of days (i.e., Clear Sky Day

and Overcast Day) have minor impacts on tap operations. In

addition, upstream factors (e.g. capacitor bank switching

actions and OLTC tap changes) also have certain influences

on SVR tap operations. All of these results will be critically

important for assessing future SVR maintenance responsibility

and PV plant integration impacts on distribution feeders.

This research provides substantial benefits not only for

distribution network operators but also for PV plant owners.

Network operators can apply this method to quantitatively

evaluate the impact of the PV integration on the distribution

networks, which helps to identify the root causes of the

voltage violations and excessive tap operations, improve SVR

maintenance scheduling, and plan PV installations in the

specific feeder without bringing significant impacts on the

feeder. Furthermore, PV plant owners can also implement the

proposed approach to clarify their responsibility to voltage

violations and excessive tap changes, which will assist in

better understanding of voltage and SVR compliance issues

and consequently avoid unnecessary penalties.

APPENDIX

In the distribution system, load and PV are usually

integrated to feeders through ∆-Yg transformers as shown in

Fig. 15.

gz

1R

2R

1L

1L

1L

2L

2L 2L1R

1R

2R

2R

Tap

Ratio

:1

Tap

Ratio

1:

A

Primary Side Secondary Side

nn

B

C

A

B

C

a

bc

a

b

c

Fig. 15. Equivalent structure of a ∆-Yg transformer with off-nominal ratios

In the per-unit system, the effective turn ratio of ∆-Yg

transformer from the secondary side to the primary side is

1 √3⁄ [24]. Thus, the voltage relationship between the

secondary side and primary side can be described as in (A1).

𝑉𝑏′𝑛′ = 1

√3𝑉𝐴′𝐵′；𝑉𝑐′𝑛′ =

1

√3𝑉𝐶′𝐵′；𝑉𝑎′𝑛′ =

1

√3𝑉𝐶′𝐴′ (A1)

As illustrated in Fig. 15, the off-normal ratios on primary

and secondary sides are α and β , respectively. These off-

nominal ratios are usually implemented by utilities to raise the

voltage for compensating line voltage drop. For example, in

Australia, the voltage bases are taken as 11kV and 415V on

the primary and secondary sides, respectively. However, ∆-Yg

transformers are usually set to 11kV/433V or 10.725kV/433V.

9

In the studied system, the off-normal ratios are 𝛼 =

10725/11000 and 𝛽 = 433/415 . The voltage relationship

can be expressed as in (A2).

{

𝑉𝑎𝑛 = 𝛽𝑉𝑎′𝑛′

𝑉𝑏𝑛 = 𝛽𝑉𝑏′𝑛′

𝑉𝑐𝑛 = 𝛽𝑉𝑐′𝑛′ and {

𝑉𝐴𝐵 = 𝛼𝑉𝐴′𝐵′𝑉𝐶𝐵 = 𝛼𝑉𝐶′𝐵′

𝑉𝐶𝐴 = 𝛼𝑉𝐶′𝐴′ (A2)

Thus, the voltage relationship used for line-to-line voltage

sensitivity derivation can be obtained by substituting (A2) into

(A1) as represented in (A3).

𝑉𝑏𝑛 =1

√3 𝛽

𝛼∙ 𝑉𝐴𝐵；𝑉𝑐𝑛 =

1

√3 𝛽

𝛼∙ 𝑉𝐶𝐵；𝑉𝑎𝑛 =

1

√3 𝛽

𝛼∙ 𝑉𝐶𝐴 (A3)

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Feifei Bai (S’13, M’16) received her B.S. and PhD

degree in Power System and its Automation from

Southwest Jiaotong University, China, in 2010 and

2016, respectively. She was a joint-PhD student at

the University of Tennessee at Knoxville, USA,

from 2012 to 2014. She is currently a research

fellow in the School of Information Technology

and Electrical Engineering, University of

Queensland, Australia. Her research interests are

solar energy integration into power grid and PMU

applications in power grid.

Ruifeng Yan (S’09, M’12) received the B. Eng.

degree in Automation from University of Science

and Technology, China, in 2004, the M. Eng

degree in Electrical Engineering from the

Australian National University, Australia, in 2007

and PhD degree in Power and Energy Systems

from the University of Queensland, Australia, in

2012. He is currently a senior lecturer in the School

of Information Technology and Electrical

Engineering, University of Queensland, Australia.

His research interests include power system operation and analysis and

renewable energy integration into power networks.

Tapan Kumar Saha (M’93, SM’97, F’19)

received his B. Sc. Engineering (electrical and

electronic) in 1982 from the Bangladesh

University of Engineering & Technology,

Bangladesh, M. Tech in 1985 from the Indian

Institute of Technology, India and PhD in 1994

from the University of Queensland, Australia.

Tapan is currently a professor in the School of

Information Technology and Electrical

Engineering, University of Queensland, Australia.

His research interests include condition monitoring of electrical plants, power

systems and power quality.

Daniel Eghbal (S’05, M’10) received the B.S.

degree in electrical engineering from Ferdowsi

University of Mashhad, Iran, in 1998, the M.S.

degree in power system engineering from Tarbiat

Modares University, Iran, in 2001, and the PhD

degree from Hiroshima University, Japan, in 2009.

He is a senior engineer at Energy Queensland,

Australia. His research interest lies in PV integration,

demand response and distribution planning.