1
Abstract--In long distribution feeders, Step Voltage Regulators
(SVRs) with the Line Drop Compensation (LDC) have been
widely implemented to control voltage profiles. After integration
of photovoltaic (PV) systems, reactive power support from PV
inverters can also be utilized in voltage regulation. Although both
SVR and reactive power support can be effective to manage
system voltage without coordination, problems such as large
voltage variations and excessive SVR tap operations still exist in
some strong PV power fluctuating days. In order to solve these
issues, SVR and reactive power support should be assigned to
different voltage regulation tasks according to their voltage
regulation characteristics. Specifically, in a distribution system,
an SVR should mainly deal with slowly changing quantities (e.g.
load, upstream voltage), while the limited reactive power support
should be used to counter fast fluctuating PV power. In this
paper, the power factor droop parameters applied on PV
inverters are optimally selected to achieve such coordination, so
that voltage problems and excessive SVR tap operations can be
successfully mitigated. The effectiveness of the proposed method
is demonstrated via case studies. Future PV integration project in
weak distribution systems can benefit from the innovative and
practical methodology proposed in this paper.
Index Terms--photovoltaic (PV), reactive power, power factor
droop curve, coordination, optimization, distribution systems.
I. INTRODUCTION
ARGE variations in photovoltaic (PV) generation can be
caused by fast moving clouds [1], which can easily lead to
serious voltage fluctuations in distribution systems.
Traditionally, if On-Load Tap-Changer (OLTC) transformers
or Step Voltage Regulators (SVRs) are properly set, they can
successfully control the system voltage. However, as the PV
penetration increases, new challenges (e.g. large voltage
fluctuations, excessive SVR tap changes) arise [2, 3]. So far, a
variety of voltage regulation methods have been proposed to
solve these challenges. Most of these methods belong to
reactive power support schemes.
Some optimal power flow (OPF) methods have been
reported to optimally control reactive power support in voltage
regulation. Centralized OPF problems are formulated in [4-7]
to coordinate all the voltage regulation devices in power
systems and provide optimal reactive power set points in
Corresponding author Ruifeng Yan is with the Global Change Institute,
The University of Queensland, Brisbane, QLD 4072, Australia (e-mail:
ruifeng@itee.uq.edu.au).
Licheng Wang and Tapan Kumar Saha are with the School of Information
Technology and Electrical Engineering, The University of Queensland,
Brisbane, QLD 4072, Australia (e-mail: l.wang8@uq.edu.au,
saha@itee.uq.edu.au).
different time-scales (hourly or 15-minute intervals). Different
from the centralized OPF methods, distributed OPF algorithms
[8, 9] can decompose an overall optimization problem into
small sub problems and solve them in parallel. However, full
observability of the whole power system in real time is needed
in these OPF based methods, which are usually impractical
especially in distribution systems. In addition, considering fast
fluctuations of PV power due to the cloud transient effect,
computation speed is another concern. The results from OPF
methods may not be regarded as optimum any longer if large
PV power has been changed during the computation intervals.
Compared with the OPF based methods, local reactive
power control with predefined parameters are more popular in
real life applications. These methods have fast response speed
and can be easily implemented. In [10], a reactive
power(voltage) - Q(V) droop curve is used for local voltage
regulation in a 9.4MWp photovoltaic plant, which is
connected to a transmission system in Romania. Moreover,
power factor (PF) set point can be given by the PV plant
operators to control the reactive power output. In [11], a
reactive power(active power) - Q(P) curve is proposed using
the German Grid Codes (GGC) to improve voltage profiles
through reactive power support from PV inverters. On the
basis of the GGC, a modified Q(P) curve is developed in [12],
where a voltage sensitivity matrix is utilized to coordinate all
the PV inverters in a distribution system with only local
measurements. According to the analysis in [13], for voltage
regulation, Q(V) control can have better performance
compared with Q(P) control. In [14, 15], different reactive
power compensation methods are compared, and allowable
PV hosting capacities are estimated. A piecewise Q(P) curve
is proposed in [16], whose parameters can be updated through
a central optimization processor every 15 minutes. However,
so far, few investigations have been reported considering the
coordination between reactive power support and existing
voltage regulation devices (e.g. SVRs).
In real life applications, there is indeed a need for such
coordination. For the PV project of the University of
Queensland (UQ) Gatton campus, a new established
3.15MWp PV plant is integrated into a weak distribution
system, where an SVR is used to regulate the voltage profile.
According to the Negotiated Customer Connection Contract
[17], the PV plant power factor should always be within the
range from 0.9 inductive to 0.9 capacitive. Therefore, a
predefined power factor droop curve, namely PF(V) curve, is
applied to provide reactive power support [18] in this PV
plant. As shown in Fig. 1, the power factor of the PV plant
Voltage Management for Large Scale PV
Integration into Weak Distribution Systems
Licheng Wang, Student Member, IEEE, Ruifeng Yan, Member, IEEE, Tapan Kumar Saha, Senior
Member, IEEE
L
L. Wang, R. Yan (Corresponding Author) and T. K. Saha, “Voltage Management for Large Scale PV Integration into Weak Distribution Systems”,
IEEE Transactions on Smart Grid, Vol. 9, No. 5, pp. 4128-4139, September, 2018. DOI: 10.1109/tsg.2017.2651030
© 201
8 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,
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2
will vary according to its connection point voltage.
Consequently, the PV plant can adaptively adjust its reactive
power generation with local voltage, while remains its power
factor within an allowable range (0.9 inductive to 0.9
capacitive). However, four parameters (V
low
, V
m1
, V
m2
, V
high
) of
this PF(V) curve are empirically selected currently (0.96pu,
0.98pu, 0.996pu and 1.01pu), which may not coordinate well
with the existing upstream SVR. As a result, excessive SVR
tap operations and significant voltage variations may occur in
large PV power fluctuating days.
The main contribution of this paper lies in the optimal
selection of power factor droop parameters for the PV plant
based on a novel approach of using the proposed voltage-PV
generation curve. Under such development, the inverter
reactive power support can be well coordinated with the
existing SVR without the need of communication.
Specifically, with this coordination established by the
proposed method, limited reactive power support restricted by
power factor (0.9 leading to 0.9 lagging) is properly utilized to
counter strong PV power fluctuations, while SVR is only used
to compensate slow changing quantities as it was originally
designed. As a result, the issues of serious voltage variations
and excessive SVR tap changes can be successfully alleviated
in strong PV power fluctuating days. Future large scale PV
integration projects in weak distribution systems can benefit
from the valuable experience obtained in this research.
Power Factor
Voltage
PF=0.9 Lag
Capacitive
PF=0.9 Lead
Inductive
V
low
V
high
V
m1
V
m2
Fig. 1 Power factor droop curve.
II. BACKGROUND DESCRIPTION
A. Investigated System
The UQ Gatton Campus is located in a fringe of the grid,
which is expensive to upgrade. As in a rural area, the large
scale PV plant can easily gain access to the low price land, but
at the same time, it has to face the voltage regulation
challenges in such a weak distribution network. The real
Gatton distribution system topology is shown in Fig. 2, in
which the 11kV feeder forks to two directions at the Point A
after around 3km away from the Gatton zone substation.
These two sub feeders are regulated by SVR A and SVR B
respectively. The newly established 3.15MWp PV plant is
connected at the end of the sub feeder that is regulated by
SVR A. Replacing the sub feeder with SVR B by an
equivalent load, the Gatton distribution system can be
simplified as Fig. 3. In this distribution system, except for the
existing SVR, reactive power support from the PV plant also
can be utilized in voltage regulation. The power factor of this
PV plant is limited within the range from 0.9 inductive to 0.9
capacitive by the local utility [17, 18].
Fig. 2 Map of Gatton Campus of the University of Queensland [3].
UG
150m
Racoon
2620m
Moon
1680m
1 2 3
4
SVR
5
Moon
1000m
Moon
1200m
UG
800m
6 7
8
Gatton
Zone
Substation
3.15 MWp
PV Array
Campus
Load
Load
Fig. 3 Schematic figure of the 11kV Gatton network [3].
B. Problem Description
PV generation profile can be different from day to day due
to variable weather conditions. The daily variability index
(DVI) is adopted as in (1) to quantitatively describe the extent
of PV power fluctuations [19]. As in Fig. 4, large DVI values
are corresponding to days with strong PV power fluctuations,
while small DVI values imply PV power fluctuations are
insignificant.
(1)
Fig. 4 PV power profiles with different DVI.
Before the PV plant was integrated into this distribution
system, no serious voltage fluctuation existed under the
regulation of the SVR. After integration of the PV plant, the
SVR and PV inverters equipped with the power factor droop
curve (Fig. 1) can still successfully regulate the PV connection
point voltage for the majority of days. However, this power
factor droop curve with empirically selected parameters and
the independently running SVR cannot effectively control
voltage variations during the days with large DVIs. For
example, October 16th, 2015 (DVI =11.3) is a typical day with
3
strong PV power fluctuations. Under the regulation of the
SVR and the reactive power support, the amount of relative
voltage variations larger than 1.6%, 1.3%, 1.0%, 0.8% during
that day were 8, 18, 37, 57 respectively, which exceed the
maximum allowable occurrences of the perceptibility standard
as in Table I [20]. The relative voltage variation is defined as
the ratio of voltage deviation between consecutive
measurements (with a resolution of one minute) to its nominal
value. For example, and are two consecutive
measurements, and the relative voltage variation can be
expressed as
(2)
where
represents nominal value of the voltage. In addition,
the total amount of SVR tap operations during this day was as
high as 50 times, which implies SVR tap operations can be
frequently triggered by large PV power fluctuations.
Fig. 5 shows the DVI distribution in October, 2015 (data
available for 29 days), where PV power fluctuating levels are
classified as serious, moderate and mild according to the
levels of DVI. As in Fig. 5, serious days (DVI>10) like
October 16th, 2015 can account for around 20% of total days
and this proportion can be larger in summer. Therefore, it is
necessary to improve the voltage regulation performance and
mitigate excessive SVR tap operations in large PV power
fluctuating days. Voltage regulation performance and the
amount of SVR tap operations in one day with different DVIs
are compared in Table II.
Fig. 5 DVI distribution of October.
TABLE I
THE PERCEPTIBILITY STANDARD [20]
Relative voltage variation thresholds
0.8%
1.0%
1.3%
1.5%
Maximum occurrences allowed per day
50
30
10
5
TABLE II
COMPARISONS OF VOLTAGE REGULATION PERFORMANCE AND AMOUNT OF
SVR TAP CHANGES IN DAYS WITH DIFFERENT DVI VALUES
PV Power Profiles
∆V>0.8%
∆V>1.3%
Tap Changes
Oct 16
th
, DVI=11.3 (serious)
57
18
50
Oct 22
th
, DVI=7.7 (moderate)
17
6
36
Oct 11
th
, DVI=3.8 (mild)
10
2
10
III. PARAMETER RESELECTION FOR THE POWER FACTOR
DROOP CURVE
The characteristics of voltage regulation from an SVR and
the reactive power support are different. On the one hand, the
SVR is designed to compensate slow changes in load and
upstream voltage, but not to counter fast PV power
fluctuations. If the reactive power support from PV inverters
can effectively alleviate voltage variations caused by
intermittent PV power generation, excessive SVR tap changes
can be successfully reduced. On the other hand, although fast
reactive power response is effective to mitigate PV power
fluctuations, its voltage regulation ability is limited to the
power factor range specified by the local utility. If the voltage
profile drifts away too much from the pre-set operational
range of PV inverters due to slow load variations, the reactive
power support will not be as effective as designed. Therefore,
for efficient utilization of limited reactive power capacity
restricted by power factor, the reactive power support also
needs the SVR to compensate slowly changing quantities (e.g.
load, upstream voltage) in a distribution system. In this
section, the following content on the way of achieving such
coordination between upstream SVR and local reactive power
support is organized as follows:
i) The voltage regulation from the SVR is introduced in Part
A. Around the operational range provided by the SVR, an
innovative method of using a voltage-PV generation curve
is established to analyze the voltage response of PV power
with a given power factor droop curve in Part B.
ii) Two PV power fluctuation characteristics can be abstracted
from the statistics of PV power historical data in Part C,
which will be used in the established optimization model in
Part D.
iii) In Part D, based on the voltage-PV generation curve
developed in Part B, power factor droop parameters (V
low
,
V
m1
, V
m2
and V
high
) are optimally reselected according to
the PV power fluctuation characteristics obtained in Part C.
A. Voltage Regulation from the SVR
As shown in Fig. 3, a 32-step SVR controlled by the Line
Drop Compensation (LDC) rule is installed between node 4
and node 5 regulating the remote node voltage. No
communication between SVR and the PV plant is needed. The
simulation network setting are as follow: 1) the voltage of
node 8 (campus load node with a PV plant connected) is
regulated by the SVR; 2) the voltage target
of the SVR
is set to be 0.99pu, with a dead band
of ±0.01pu; 3) the
time delay of SVR tap operations is set to be 2 minutes [21];
Before the beginning of analyzing the voltage regulation
performance from reactive power support, the SVR tap is
assumed to be already on a stable position.
B. Voltage Regulation from Reactive Power Support
If the SVR tap has already switched to a reasonable
position to fit a certain load level and remain unchanged for a
period of time, the voltage response of PV generation can be
described by a voltage-PV generation curve, as shown in Fig.
6. This voltage-PV generation curve can be obtained from the
power factor droop curve as in Fig. 1 with fixed load level and
SVR tap position. Through this voltage-PV generation curve,
PV generation is mapped to the voltage, and four inflection
points on this curve are corresponding to the parameters (V
low
,
V
m1
, V
m2
, V
high
) on the power factor droop curve respectively.
4
As a result, the voltage-PV generation curve in Fig. 6 can be
defined by V
low
, V
m1
, V
m2
, V
high
that reveal the changing rule of
the power factor with respect to voltage. Two dashed lines in
Fig. 6 represent the limits of the power factor which has to be
respected at all times.
V
m1
V
low
V
m2
V
high
V
target
PV Generation Increase
Dashed Line 1
(PF=0.9 lagging)
Dashed Line 2
(PF=0.9 leading)
ΔV
db
Voltage Increase
ΔV
db
Fig. 6 Voltage-PV generation curve.
C. The Characteristics of PV Power Fluctuations
The relationship between PV generation value and the
frequency of PV power fluctuation will be established in this
section. Firstly, a synthetic PV power profile (Fig. 7) is used
as a simple example to explain how to obtain such
relationship.
As in Fig. 7 (a), PV power first increases from 0MW to
2MW, then reduces to 1MW before increases to 2MW again,
and finally, it falls from 2MW to 0MW. Therefore, in this
case, PV power is more likely to fluctuate in the range of
[1MW, 2MW] (4 times) than in the range of [0MW, 1MW] (2
times). Correspondingly, the relationship between PV
generation value and the frequency of PV power fluctuation
can be developed as in Fig. 7 (b). An intuitive insight can be
obtained from Fig. 7 (a) that more PV power plots are
“overlapped” in the range from 1MW to 2MW (4 times)
compared with that of the range from 0MW to 1MW (2
times).
PV Generation (MW)
t
2
1
Frequency of
PV Fluctuation
PV Generation (MW)
4
2
1 2
0
(a) (b)
0
Fig. 7 PV generation profile (a) and the frequency of PV power fluctuation
with PV generations (b).
Similar to Fig. 7 (b), Fig. 8 demonstrates the relationship
between PV generation value and the normalized frequency of
PV power fluctuation with real PV historical data, and a
normal distribution curve is used to fit the original curve. As
expected, the frequency of large power fluctuation is low
when PV generation value approaches to zero or its maximum
(rated) value.
There are two characteristics can be obtained from Fig. 8
that will be used in the latter optimization model:
Characteristic One: Large PV power fluctuations (e.g. PV
power fluctuations larger than 0.4MW will cause significant
voltage variations in the Gatton distribution system) almost
only occur in the range from
to
. As in Fig. 8,
and
satisfy that the normalized frequency of
large PV power fluctuation is lower than (a small positive
value) if PV generation is lower (larger) than
(
);
Characteristic Two: Large PV power fluctuations occur most
frequently in the range [μ-σ, μ+σ]. μ and σ are expectation and
standard deviation of the fitting normal distribution curve.
Fig. 8 Normalized frequency of PV power fluctuation with PV generations.
D. Optimization Model for Parameter Reselection
In this part, Characteristic One and Characteristic Two
obtained in Part C are used to optimally reselect the four
parameters (V
low
, V
m1
, V
m2
,
V
high
) for the power factor droop
curve.
1) Utilization of Characteristic One
As large PV power fluctuations almost only occur in the
range from
to
, a straightforward idea to alleviate
significant voltage variations caused by PV power fluctuations
is trying to reduce the voltage deviation
between these
two extreme PV generation scenarios, namely
(3)
where
and
represent the node voltages when
PV generation is equal to
and
respectively.
Fig. 6 shows the voltage response of PV generation with a
given power factor droop curve, and it is redrawn as in Fig. 9.
In this figure, the voltage-PV generation curve first follows
the Dashed Line 1 (PF=0.9 lagging) when PV generation is
low. Then this curve leaves the Dashed Line 1 after the first
inflection point V
low
as PV generation increases. Finally, this
curve overlaps with the Dashed Line 2 (PF=0.9 leading) after
the last inflection point V
high
. Therefore, the positions of first
and last inflection points of the voltage-PV generation curve
are determined by the setting of V
low
and V
high
respectively.
In Fig. 9, Intersection 1 is defined as the crossing point of
the line
and the Dashed Line 1, so is Intersection
2 of the line
and the Dashed Line 2. If the first
inflection point V
low
and the last inflection point V
high
are
situated within these two intersection points, the voltage
deviation
due to PV power drop from
to
will be almost constant (
in Fig. 9). Conversely, if the first inflection point (V
low2
) is set
to be lower than the Intersection 1, this voltage deviation will
become larger (
). Therefore, for
obtaining a low voltage deviation
between the two
extreme PV generation scenarios, V
low
and V
high
should satisfy
(4).
5
(4)
V
m1
V
low
Intersection 1
V
low2
V
m2
V
high
Intersection 2
[PV
low
,μ-σ]
[μ-σ, μ+σ]
[μ+σ,PV
high
]
PV
high
ΔV
ΔV
PV Generation Increase
Dashed Line 1
Dashed Line 2
PV
low
V
target
ΔV
db
Voltage Increase
ΔV
db
Fig. 9 Voltage deviation between two intersections.
2) Utilization of Characteristic Two
The voltage-PV generation curve in Fig. 9 reflects the
voltage response with respect to PV generation. Consequently,
different curve slopes (voltage vs PV generation) mean that
for the same change of PV generation, different voltage
variations will occur due to different reactive power supported
by PV inverters.
The voltage deviation between two extreme PV generation
scenarios (
and
) will be constant, as long as
constraints in (4) are satisfied. Therefore, a lower slope on one
part of the voltage-PV generation curve will cause a higher
slope on another part of this curve. In other words, slopes on
different parts of the curve have a competing relationship
between each other. Therefore, the strategy is to assign a low
slope to the PV generation range [μ-σ, μ+σ] where large PV
power fluctuations most likely to occur. Consequently, the
objective function can be written as
(5)
where L is the maximum curve slope in the range of [μ-σ,
μ+σ], and slopes between any two points on the voltage-PV
generation curve within this range cannot be larger than L. As
slope varies on the whole voltage-PV generation curve, in
order to simplify calculation, the voltage-PV generation curve
within the range of [μ-σ, μ+σ] is divided evenly into n
segments according to PV generation. And average slope of
each segment i is restrained by L, as
(6)
where V
pv(i)
represents the node voltage when PV generation is
equal to pv(i), and pv(1)=μ-σ, pv(n+1)=μ+σ,
pv(i+1)=pv(i)+2σ/n. pv(i) can be calculated in advance
according to μ, σ and n. The relationship between V
pv(i)
and
pv(i) is given as the constraints in (7) and (8),
(7)
(8)
where f
1
represents the power flow equation set and f
2
represents the relationship between the power factor PF
pv(i)
of
PV inverters and the voltage V
pv(i)
of the PV connection point.
It should be noticed that (8) is the piecewise power factor
droop curve which is characterized by parameters V
low
, V
m1
,
V
m2
, V
high
, as shown in Fig. 1.
Furthermore, the competing relationship for different parts
of the curve mentioned before can be balanced through
limiting the curve slope in the range of [
, μ-σ] as in (9).
The parameter c is the predetermined upper limit of curve
slope. The selection and comparison of different parameter c
will be discussed later in case studies.
(9)
IV. THE VOLTAGE-PV GENERATION CURVE WITH VARIABLE
LOAD AND SVR TAP OPERATIONS
A. Interaction between SVR and Variable Load
In this section, the effectiveness of the predefined voltage-
PV generation curve will be demonstrated with variable load.
The offsetting interaction between SVR tap operation and load
variation will be discussed as follow, which can limit the
movement of the predefined voltage-PV generation curve
caused by load variation to a low level.
Fig. 10 demonstrates that the position of the voltage-PV
generation curve will be changed with different load or SVR
tap position. As shown in Fig. 10, the curve is moved towards
left when load decreases or SVR tap position is stepped up,
while the curve is moved towards right when load increases or
SVR tap position is stepped down.
Compared with fast fluctuating PV power, load variation is
much slower and can be regarded as constant in a short period.
As a result, during this short period, the trajectory of (PV
Generation, Voltage) Node will approximately follow the
voltage-PV generation curve. However, accumulated load
variation will cause movement of the voltage-PV generation
curve as in Fig. 10, until a SVR tap operation is triggered to
offset this impact. Therefore, the movement of the
predesigned voltage-PV generation curve will always be
limited to a low level, due to the offsetting interaction between
SVR tap operation and load variation.
Fig. 11 demonstrates the load and PV data recorded in
Gatton campus for one day as an example. As in Fig. 11, the
load creeps from 1.26MW at early morning (3:30) to 2.79MW
at noon (14:00) with an increment of 120%. Using these real
data, Fig. 12 shows the distribution of (PV Generation,
Voltage) Nodes from 9:00 to 14:00 obtained from power flow
calculations with a resolution of 1 minute. During this period,
the load creeps from 2MW at 9:00 to 2.79MW at 14:00 with
an increment of 40%, and SVR changes its tap positions for 4
times. (PV Generation, Voltage) Nodes are denoted as
pentagrams, triangles, circles, asterisks and dots respectively
corresponding to the variation of SVR tap positions. It can be
seen all nodes gather around the predefined voltage-PV
generation curve, especially in the range of [μ-σ, μ+σ], where
large PV power fluctuations occur most frequently. Therefore,
it is reasonable to decouple the voltage regulation analysis of
reactive power support from the load variation (can be offset
