an excessive tap operation evaluation approach for
TRANSCRIPT
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: [email protected]).
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:
[email protected], [email protected], [email protected]). Daniel
Eghbal is with Energy Queensland (Energex), Brisbane, QLD 4006, Australia
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.