This article has been accepted for publication in a future issue of this journal, but has not been

fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2020.3024069, IEEE
Transactions on Industrial Informatics

Delay-tolerant Predictive Power Compensation

Control for Photovoltaic Voltage Regulation
Zhanqiang Zhang, Student Member, IEEE, Yateendra Mishra, Member, IEEE, Dong Yue, Senior Member, IEEE,
Chunxia Dou, Member, IEEE, Bo Zhang, Student Member, IEEE, and Yu-Chu Tian, Senior Member, IEEE

Abstract—Voltage regulation is imperative for the successful NN Neural network

operation of electricity distribution networks, especially with PCC Power compensation control
a high penetration level of photovoltaic (PV) systems. Power PM Power mutation
compensation control (PCC) that uses both reactive power
compensation and active power curtailment has shown promising PV Photovoltaic
results in alleviating voltage rise problems. It crucially relies on RPC Reactive power compensation
real-time communications among distributed PV systems. Howev-
er, the transmission of state measurements and control signals in
PCC is hampered by inevitable communication delays. Therefore, I. I NTRODUCTION
it is important to not only estimate the maximum tolerable
communication delay (MTCD) but also develop an alternative
technique for PCC under abnormal communication delay (ACD)
conditions. This paper presents a delay-tolerant predictive PCC
V OLTAGE profile along a feeder is an important criterion
to accommodate a high penetration level of photovoltaic
(PV) systems [1]. The recent rapid growth in the installations
for voltage regulation in distribution feeders. After estimating of PV systems results in an overvoltage problem along feeders
the MTCD based on voltage and power mutation, it uses normal due to reverse power flow. The overvoltage issue becomes
PCC for effective operation when communication delay is within
severer especially during mid-day periods with high PV power
MTCD, or switches to predictive PCC under ACD conditions. An
accurate prediction is achieved using a double neural network injection but low load demand. It not only restricts the power
with on-line adjustment of weights and samples. Simulations on injection from the PV systems but also limits the scope of any
a sample distribution network demonstrate the effectiveness of further integration of PV in electricity distribution systems.
our presented approach. The conventional methods of voltage regulation such as
Index Terms—Voltage regulation, power compensation control, reconductoring of feeders, installation of capacitors and on-
communication delay, double neural network. load tap changers have some deficiencies due to their slow
response, discrete feature, and high cost [2]. Power com-
A BBREVIATIONS AND ACRONYMS pensation control (PCC) is usually used with reactive power
ACD Abnormal communication delay compensation (RPC) and active power curtailment (APC)
APC Active power curtailment to mitigate voltage rise problems. The rapid shift in power
BESS Battery energy storage system exchanges using PCC allows continuous voltage regulation. It
BP Back-propagation has shown a significant voltage regulation capability even in
DNNP Double neural network prediction a low-voltage system with a high Resistance/Inductance ratio.
MTCD Maximum tolerable communication delay An typical distribution system is shown in Fig. 1, where each
bus is equipped with a PV, a battery energy storage system
This work is supported in part by the National Key Research and De- (BESS), and a load. Each of the PV and BESS components is
velopment Project of China under Grant 2018YFA0702200, the National
Natural Science Foundation of China under Grant 61833008, the Australian connected to the feeder via a separate inverter. Because RPC
Research Council (ARC) through Discovery Project Scheme under Grant and APC are respectively attained by PV and BESS inverters,
DP170103305, the Natural Science Foundation of Jiangsu Province of China a coordinated PCC has been proposed [3]. PCC acquires the
under Grant BK20171445, the Postgraduate Innovation Foundation Project
of Hebei Province of China under Grant CXZZBS2019057, and the China information of system states via a communication network and
Scholarship Council (CSC). (Corresponding authors: D. Yue, C. Dou and Y.- determines the power control references for the individual PV
C. Tian) and BESS inverters to achieve coordinated operations.
Z. Zhang is with the School of Electrical Engineering, Yanshan University,
Qinhuangdao 066044, China, and also with the School of Electrical Engi- The transmission of state measurements and control signals
neering and Robotics, Queensland University of Technology, GPO Box 2434, in PCC is hampered by inevitable communication delays. This
Brisbane QLD 4001, Australia (e-mail: zhanqiangzhangysu@163.com). paper aims to develop a delay-tolerant PCC for voltage regula-
Y. Mishra is with the School of Electrical Engineering and Robotics,
Queensland University of Technology, GPO Box 2434, Brisbane QLD 4001, tion. Large power mutation (PM) during communication delay
Australia (e-mail: yateendra.mishra@qut.edu.au) causes overvoltage to reappear, necessitating minimal delays
D. Yue and C. Dou are with the Institute of Advanced Technology, Nanjing for effective PCC operation. In this paper, the upper bound of
University of Posts and Telecommunications, Nanjing 210023, China (e-mails:
medongy@vip.163.com, cxdou@ysu.edu.cn). this time-varying delay is defined as the maximum tolerable
B. Zhang is with the School of Electrical Engineering, Yanshan University, communication delay (MTCD). Any delay over MTCD is
Qinhuangdao 066044, China (e-mail: zb516869613@163.com). considered as an abnormal communication delay (ACD) [4].
Y.-C. Tian is with the School of Computer Science, Queensland Uni-
versity of Technology, GPO Bx 2434, Brisbane 4001, Australia (e-mail: Reducing communication delays has been studied from
y.tian@qut.edu.au) various perspectives, e.g., distributed control [5], [6], event-

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Transactions on Industrial Informatics

the voltage regulation through PCC. This is followed by an

1
approach to estimate the MTCD in Section III. Section IV in-
troduces DNNP-based predictive PCC under ACD. Simulation
experiments are conducted in Section V. Finally, Section VI
No
Prediction concludes the paper.
Yes
 1 ?
Evaluation MTCD
II. VOLTAGE R EGULATION T HROUGH C OORDINATED PCC
PCC Let Ph (t) and Qh (t) denote active and reactive power
2 M injections at the hth bus, respectively. They are described as:
h k 
PM
Ph (t) = Vh (t) Vk (t) (Ghk cos θhk +Bhk sin θhk )


Fig. 1. A distribution network with high levels of PV systems. k=1 (1)
M
P
Qh (t) = Vh (t) Vk (t) (Ghk sin θhk −Bhk cos θhk )


k=1
triggered control [7], [8], and sparse communication [9]. Ref-
erence [10] analyzed the impact of delay on voltage stability. where Vh (t) and Vk (t) are voltages at the hth and kth
A few methods were developed to mitigate the impact, such buses, respectively; Ghk and Bhk are the real and imaginary
as gain scheduling [11], phase-shifting [12], and adaptive parts of segment admittance between the hth and kth buses,
delay compensator [13]. Also, voltage stability within MTCD respectively; θhk is the voltage angle difference between the
from the perspectives of small-signal analysis [11], [14], hth and kth buses; and M is the total number of buses.
[15] and Lyapunov-Krasovskii theory [5], [7], [16], [17] has Voltage change ∆Vk (t) at the kth bus is expressed as:
been investigated. Nevertheless, a quantitative method is still M M
X ∂Vk (t) X ∂Vk (t)
missing for the estimation of MTCD. ∆Vk (t) = ∆Ph (t) + ∆Qh (t) (2)
When a PV/BESS inverter does not receive a PCC signal ∂Ph (t) ∂Qh (t)
h=1 h=1
within the MTCD, i.e. under ACD conditions, a predictive
where ∆Ph (t), ∆Qh (t) are the PV PMs at the hth bus; and
control becomes necessary. Predictive compensation methods
∂Vk (t)/∂Ph (t), ∂Vk (t)/∂Qh (t) are the voltage sensitivities at
have been proposed over the years. Examples are generalized
the kth bus to the powers at the hth bus. Sensitivities can be
predictive control [18], model predictive control and Smith
obtained by solving the partial derivatives of voltage to powers
predictor [19], and neural network (NN) prediction [20]. Due
in Eq. (1). When h 6= k, the mutual sensitivities are given as:
to the complexity in the configuration of control parameters, a 
direct prediction of PCC signals shows large uncertainties [18],  ∂Vk (t) = V −1 (t) (Ghk cos θhk + Bhk sin θhk )−1
∂Ph (t) h
[19], [20]. However, a method for accurate PCC prediction (3)
under ACD conditions is not found in the literature.  ∂Vk (t) = V −1 (t) (Ghk sin θhk − Bhk cos θhk )−1
∂Qh (t) h
Hence, this paper presents a delay-tolerant PCC for voltage
regulation in distribution feeders. Voltage sensitivity is used for For h = k, the self-sensitivities are expressed as:
estimating MTCD based on allowable voltage and PM. After −1
 M
 ∂Vk (t) =
 P
determining the MTCD, it uses normal PCC for effective oper-

 ∂Pk (t) V h (t) (Ghk cosθ hk +B hk sinθhk )+V k (t)Gkk
ation when communication delay is within MTCD, or switches h=1
M
−1
to predictive PCC under ACD conditions. This is realized by ∂V (t)
 P
 ∂Qkk (t) = Vh (t) (Ghk sinθhk −Bhk cosθhk )−Vk (t)Bkk


using a double NN prediction (DNNP) with multiple data pre- h=1
processing, on-line adjustment of samples and weights of NN. (4)
The main contributions of the paper include: According to [21], the nearest PV inverter and BESS are
selected to perform PCC for overvoltage buses. RPC and APC
1) a delay-tolerant PCC framework for voltage regulation;
are obtained based on the voltage sensitivities in Eqs. (3) and
2) an approach to estimate the MTCD with consideration
(4). An effective PCC is achieved by limiting the voltage rise
of the maximum allowable PM; and
within a certain percentage, say 5% of the nominal value:
3) an NN-based predictive PCC under ACD conditions.
M
Embedded with a quantitative estimation of MTCD, the X ∂Vk (t)
presented approach is unique and effective compared to the Vk (t) + ak qh δQh (t)
∂Qh (t)
methods reported in [14]-[17]. By optimizing the DNNP on- h=1
M
line, the predictive PCC is still effective for the continuous X ∂Vk (t)
PM under ACD conditions, which is different from the delay +bk ph δPh (t) − Vk,n ≤ 5% · Vk,n (5)
∂Ph (t)
h=1
compensation methods in [11]-[13]. For an individual PV,
its historical power data is used to train NN for optimized where Vk,n is the nominal voltage of the kth bus; δQh (t) and
weights, and the trained NN is then used for predictive PCC. δPh (t) are PCC signals at the hth bus; ak = 1 for RPC, qh = 1
Unlike the direct predictions in [18]-[20], this indirect manner for RPC at the hth bus; bk = 1 for APC; and ph = 1 for APC
contributes an accurate prediction. at the hth bus. For all other cases, ak = 0, qh = 0, bk = 0
This paper is organized as follows: Section II describes and ph = 0.

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III. Q UANTITATIVE E STIMATION O F MTCD t1 t1  i1 s t2 t2  i2 s tr tr  ir s

Delay
A. The impacts of communication delay on voltage regulation
PCC
Considering a communication network with variable de-  11  21  r1
Delay
lays, an event-triggered mechanism is used for data trans-
mission [22]. If there is a significant change from the last  12 t1   1  22 t2   2  r 2 tr   r
transmission instant, data at the minimal sampling instant
is transmitted. The transmission of sampled data x(t), i.e. Fig. 2. Example of data sampling and transmission.
voltage, power, and PCC signal, occurs at the time instant:
 k
tr+1 = tr + min {ir s}

s

Acceptable Overvoltage
T Ckp,max
s.t. [x(tr + ir s) − x(tr )] Ω [x(tr + ir s) − x(tr )] (6)
 T
> σx (tr + ir s)Ωx(tr + ir s)

Pk ,max
where tr+1 , tr are the (r + 1)th and rth transmission instants;
PV power
ir ∈ N is the number of sampling between tr+1 and tr ; s is the Bus voltage
5%  Vk ,n
sampling interval; Ω is a positive definite weighting matrix;  kr Before regulation
After regulation
and σ ∈ [0, 1). The transmission manner becomes periodic
Vk ,n
when σ = 0. Effective voltage regulation Invaild voltage regulation
The sampling and transmission of data are shown in Fig. 2.
With a communication delay τ , the PCC signals received by Fig. 3. Voltage regulation through PCC with communication delay.
PV are δQh (t − τ ) and δPh (t − τ ). The impacts of inevitable
communication delay on voltage regulation are demonstrated PM of PVs in one region obeys the capacity ratio, we have
in Fig. 3. PM causes extra voltage rises at sampling instants the following relationship from Eq. (2):
during τ . A PCC signal with the maximum limit in voltage rise
M
still leads to acceptable voltages at smaller sampling instants X p ∂Vk (t)
∆Vk (t) ≈ rhk ∆Pk (t) (9)
under allowable PM. When PM increases with τ , it becomes ∂Ph (t)
h=1
insufficient for voltage regulation at larger sampling instants. p
Overvoltage exists until an opportune PCC signal is received where rhk is the generation capacity ratio between PVs at the
at t. Eq. (5) with communication delay is expressed as: hth and kth buses.
Substituting Eqs. (2) and (8) into Eq. (9) gives the allowable
M
X ∂Vk (t) range of PM during communication delay:
Vk (t) + ak qh δQh (t) #−1
∂Qh (t) " M
X p ∂Vk (t)
h=1
M
! |∆Pk (t)| ≤ 5% · Vk,n rhk (10)
X ∂Vk (t) ∂Ph (t)
+bk ph δPh (t) − Vk,n − 5% · Vk,n h=1
∂Ph (t) In Fig. 3, when the total PM during communication delay
h=1
× (τkr − τ̄kr ) ≥ 0 (7) is allowable, the communication delay is tolerable. When it is
more than the threshold given in Eq. (10), the communication
where t ∈ [tr + τkr , tr+1 + τkr+1 ], τkr is the communication delay is relatively long for voltage regulation. If PM slope
delay at tr , and τ̄kr is the MTCD at tr . remains constant at sampling instants during data transmis-
It is seen from Eq. (7) that communication delay has two sion, the MTCD is equal to the ratio between the maximum
impacts on voltage regulation. Without communication delay, allowable PM and its slope. Since PV power changes with
voltage meets Eq. (5) regardless of PV PM. When PM increas- solar intensity, the PM slope varies at sampling instants.
es with communication delay, voltage gradually deteriorates. Let ∆Pk,max denote the maximum allowable PM. Also,
As long as communication delay is within MTCD, voltage let Pk (tr ) denote the initial PV power injection at tr . Let
rise is contained. When it exceeds MTCD, PCC becomes p
Ck,max (t) represent the maximum PV PM slope at sampling
insufficient for voltage regulation due to the extra voltage rise. instants tr + ir s. Then, for t ∈ [tr + τkr , tr+1 + τkr+1 ], we
This will be verified later in our theorems. can use the maximum PM slope to obtain the minimal upper
bound of MTCD at the kth bus:
B. Estimation of MTCD  P −1
τ̄kr = [∆Pk,max − Pk (tr s)] × Ck,max (t)
To ensure effective voltage regulation with communication " M #−1
X p ∂Vk (t)
delay, the maximum allowable voltage change at the kth bus 5% · Vk,n rhk − Pk (tr )
caused by PM is limited to 5% of the nominal value, i.e., ∂Ph (t)
h=1
= (11)
|∆Vk (t)| = |Vk (t) − Vk,n | ≤ 5% · Vk,n (8) max {∆Pk (tr + ir s)/s}
ir ∈N&[0,ir,max ]

Generally, PV power is associated with solar intensity and where ∆Pk (tr + ir s) = Pk (tr + (ir + 1)s) − Pk (tr + ir s) is
generation capacity. Since active power is dominant with a the total PM between tr + ir s and tr + (ir + 1)s, and ir,max
power factor close to 1, reactive PM is negligible. Considering is the maximum number of sampling between tr and tr+1 .

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Theorem 1: For any communication delay within τ̄kr , volt- Proof: In accordance with Eq. (12), the voltage at the kth
age regulation in Eq. (7) is always effective under PV PM. bus at tr + (ir,max + 1)s is expressed as follows:
Proof: Assume PV PM keeps increasing. For ∀tr + ir s ∈
[tr , tr + τ̄kr ] and ir ∈ [0, ir,max ], the largest integer ir,max is Vk (tr + (ir,max + 1)s)
not greater than τ̄kr /s. The voltage at the kth bus at tr +ir,max s M
X ∂Vk (tr )
 ir,max +1
X 
p
with a larger rise than other sampling instants is expressed as: = Vk,n + rhk Pk (tr ) + ∆Pk (tr + ir s)
∂Ph (tr ) i =1
h=1 r
Vk (tr + ir,max s) (17)
M ir,max
X ∂Vk (tr ) X For (ir,max + 1)s > τ̄kr , the total PM between tr and tr +
= Vk (tr ) + ∆Ph (tr + ir s)
∂Ph (tr ) i =1 (ir,max + 1)s is expressed as follows:
h=1 r

M  ir,max 
p ∂Vk (tr ) ir,max +1 ir,max +1
X X
= Vk,n + rhk Pk (tr )+ ∆Pk (tr + ir s) X X ∆Pk (tr + ir s)
∂Ph (tr ) ∆Pk (tr + ir s) = (ir,max + 1)s
h=1 i =1 r
ir =1 i =1
(ir,max + 1)s
r
(12)
ir,max +1
Because ir,max s ≤ τ̄kr , for a given τ̄kr and varying
X ∆Pk (tr + ir s)
> τ̄kr (18)
∆Pk (tr + ir s) /s at tr + ir s ∈ [tr , tr + ir,max s], the total ir =1
(ir,max + 1)s
PM between tr and tr + ir,max s is described as:
Substituting Eq. (11) into Eq. (18) yields:
ir,max ir,max
X X ∆Pk (tr + ir s)
∆Pk (tr + ir s) = ir,max s ir,max +1
ir,max s
X ∆Pk,max − Pk (tr )
ir =1 i =1 r ∆Pk (tr + ir s) >
ir,max ir =1
max {∆Pk (tr + ir s)/s}
X ∆Pk (tr + ir s) ir ∈N&[0,ir,max ]
≤ τ̄kr (13) ir,max +1
ir,max s X ∆Pk (tr + ir s)
i =1
r × (19)
ir =1
(ir,max + 1)s
Substituting Eq. (11) into Eq. (13) leads to:
ir,max
X ∆Pk,max − Pk (tr ) Then, substitute Eq. (16) into Eq. (19) to derive the total PM
∆Pk (tr + ir s) ≤ between tr and tr + (ir,max + 1)s as follows:
ir =1
max {∆Pk (tr + ir s)/s}
ir ∈N&[0,ir,max ]
ir,max +1
ir,max X
X ∆Pk (tr + ir s) ∆Pk (tr + ir s) > ∆Pk,max − Pk (tr ) (20)
× ≤ ∆Pk,max − Pk (tr ) (14)
i =1
ir,max s ir =1
r

Substituting Eqs. (11) and (14) into Eq. (12) gives the voltage By substituting Eqs. (11) and (20) into Eq. (17), the voltage
at tr + ir,max s as: at tr + (ir,max + 1)s is expressed as follows:
M M
X p ∂Vk (tr ) X p ∂Vk (tr )
Vk (tr + ir,max s) ≤ Vk,n + ∆Pk,max rhk Vk (tr + (ir,max + 1)s) > Vk,n + ∆Pk,max rhk
∂Ph (tr ) ∂Ph (tr )
h=1 h=1
= (1 + 5%) · Vk,n (15) = (1 + 5%) · Vk,n (21)

Eq. (15) indicates that the maximum voltage is acceptable, Eq. (21) means that for a given total PM in Eq. (16), the
showing the effectiveness of voltage regulation within the voltage regulation is invalid under any ACD over the bound
delay bound τ̄kr . This completes the proof. τ̄kr . This completes the proof.
Remark 1: If PV PM does not keep increasing, the bus Remark 2: It is known from Theorems 1 and 2 that τ̄kr
voltage at a sampling instant such as tr + ir s reaches the is the minimal upper bound of MTCD. Eqs. (15) and (21)
maximum. Then, it will drop at least once during rise. It is indicate that the impacts of communication delay on voltage
found that tr +ir s ≤ tr +ir,max s ≤ tr + τ̄kr . Use the same ap- regulation can be written as Eq. (7).
proach with this Proof to derive Vk (tr +ir s) ≤ (1+5%)·Vk,n .
Hence, Theorem 1 is also proven.
Theorem 2: For the voltage at a sampling instant with ACD IV. P REDICTIVE PCC U NDER ACD C ONDITIONS
such as tr + (ir,max + 1)s > tr + τ̄kr , voltage regulation in Predictive PCC is used to enhance the voltage regulation
Eq. (7) is invalid if there is a total PM between tr + ir,max s under ACD conditions. Since PCC signal depends on bus
and tr + (ir,max + 1)s meeting: voltage and PV power, there is a one-to-one correspondence as
∆Pk (tr + (ir,max + 1)s) ≥ max {∆Pk (tr + ir s)} shown in Fig. 4. Hence, a new DNNP with data preprocessing
ir ∈N&[0,ir,max ] and on-line optimization of weight is designed. If PV power
ir,max is derived by performing a weighted sum of historical power
X
× (ir,max + 1)s − ∆Pk (tr + ir s) (16) data, an accurate PCC signal is predicted by performing a sum
ir =1 of historical PCC signal data with the same weights.

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S V S with the smallest difference between the mean of each cluster

S̄k [i] = {S̄k [i|1], . . . , S̄k [i|ni ]} and S̄k [0], i.e.,
ni
_ 1 X
S̄k [ i ] = arg min S̄k [0] − S̄k [i|l] (24)
ni
l=1

t t t
B. DNNP for PCC signal
Fig. 4. One-to-one correspondence of PV power, voltage, and PCC signals. To obtain precise PCC signals with optimal data weights,
the NN is trained by the back-propagation (BP) algorithm. As
shown in Fig. 5, the NN includes input, hidden, and output
A. Preprocessing of historical PV power data layers. It adopts a multi-layer feed-forward design. The inputs
Due to the intermittence of PV generation, there are several of NN are respectively the ni historical PV power data from
_
historical power data unavailable for prediction. It is necessary S̄k [ i ] in the first round. In the second round, they are the
to extract available samples for NN training. While this causes ni corresponding historical PCC signal data. The respective
the loss of some data, the remaining data is still enough to en- outputs of NN are the predictive PV power and the predictive
sure the predictive accuracy. Since the data with a wide range PCC signal. Power prediction in the first round is to get the
will reduce convergence rate and predictive accuracy [23], the optimal data weights. The second round uses the weights to
min-max method is used to normalize N original data to [0,1]: get the final predictive PCC signal.
 The numbers of neurons in the input, hidden, and output
Sk [l] − Sk,min
S̄k [l] = layer are p, q, and 1, respectively. In accordance with the

Sk,max − Sk,min (22)
Kolmogorov theorem, we set the number of neurons in the
s.t. |Sk [l] − Sk [0]| ≤ αSk [0], τk [l] ≤ τ̄k ; l ∈ N

hidden layer as q = 2p + 1 [23], [25]. Neurons in different
where Sk = Pk + jQk represents apparent power; Sk [l] is the layers are interconnected by synaptic whose weight is adjusted
lth historical power; Sk,max and Sk,min are the maximum and by the BP algorithm until the difference between predictive PV
minimal values, respectively; τk [l] is communication delay; power and S̄k [0] is very small. This contains the data forward
and α is a constant to regulate the threshold. The smaller the propagation in two rounds and the error back propagation in
value of α, the closer the historical PV power will be to the the first round.
current value S̄k [0] in Eq. (22). This improves the similarity of In the forward propagation, the power of neuron is obtained
available historical data and the accuracy of entire prediction. by performing a biased weighted sum of input data and passing
The K-means algorithm is used to select the historical PV an activation function such as Sigmoid function. In the back
power data with a similar value and classify them into a cluster. propagation, the weight of synaptic is adjusted through a feed-
Current PV power S̄k [0] is used as the clustering benchmark. forward error signal until it is smaller than the threshold.
The procedures of the K-means algorithm are to randomly For data forward propagation in the first round, the predic-
select K cluster centers and classify the available historical tive PV power is obtained as follows:
power data to the nearest cluster according to the Euclidean q X p  !
X _
distance. Cluster centers are updated by computing the mean 0 hi in hi ou
S̄k [0] = f wm1 f wom S̄k [ i |l] − bm −b1 (25)
value of each cluster. It is iterative to recompute the Euclidean m=1 o=1
distance and update each cluster center. The corresponding −x −1
objective function and constraints are exprssed as: where f (x) = (1 + e ) is the activation function example;
in hi
wom and wm1 are the weights of synaptic connecting the oth
2
input neuron, mth hidden neuron, and output neuron; and bhi
 ni
P
 K P ni wli S̄k [l] m
and bou

1 are the biases of the mth hidden neuron and output
P l=1
F = arg min wli S̄k [l]− P


 ni
i=1 l=1
l=1
wli neuron, respectively.
For error back propagation in the first round, if the pre-
(
0, if S̄k [l]−Ce[i] > S̄k [l] − Ce[j]



s.t. ∀j 6= i, wli =
 dictive PV power significantly deviates from S̄k [0], the BP
1, if S̄k [l]−Ce[i] ≤ S̄k [l] − Ce[j]

algorithm will process an error signal e to be back-propagated:
Pni
Pni (23)
2
where Ce[i]= l=1 wli S̄k [l] / l=1 wli is the ith cluster center, e = 0.5 · S̄k0 [0] − S̄k [0] (26)
ni is the ith cluster size, and wli is a binary weight. With this in hi
objective function, the computation process is repeated until The gradient descent method is used to adjust wom and wm1
the variation of clustering center or objective function is ac- to minimize e. By computing its partial derivatives to neurons
in hi
ceptable or the maximum number of iteration is reached [24]. at hidden and output layers, wom and wm1 are updated as:
( _ hi
For given total N historical data PKin Eq. (22) and K clusters wm1 = wm1 hi
 hi
− η∂e ∂wm1 , if e > ē
in Eq. (23), we obtain that N = i=1 ni . The greater the total _ in
 in (27)
in
number of clusters, the smaller the average cluster size. For the wom = wom − η∂e ∂wom , if e > ē
data in each cluster, their values should be highly similar. To where ē is the threshold of e, and η is the learning rate. If
extract the most similar available historical data to S̄k [0], an the learning rate is too small, the convergence is very slow.
_ _ _
optimal cluster S̄k [ i ] = {S̄k [ i |1], . . . , S̄k [ i |ni ]} is selected However, a large learning rate will cause oscillating output

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Transactions on Industrial Informatics

Historical Hidden layer

Preprocessing of historical data PV power Historical b1hi
Input layer 1
1 PCC signal
Min-max Sk [i |1] f
method 1
 Sk [i |1] b2hi
1
Cluster Sk [i | 2] 2 Output layer
2 2 f
K-means ..  Sk [i | 2]  Sk [0]
3
.. ..

...
algorithm Cluster . .. 1 f
Cluster 2 . bmhi .
Optimal data S k [i | l ] .
o f b1ou
3
Available data ..
.  S k [i | l ] .. m Sk [0]
Means .. . Sk [0]
comparison Original data Sk [i | ni ] . bqhi ..
p .
 Sk [i | ni ] f
q Eq. (26)
in
wom wmhi1
Samples Weights Weights
adjustment Eq. (27) On-line adjustment adjustment ee?
Yes No

Fig. 5. Predictive PCC by using a DNNP with data preprocessing.

results. We use the common exponential decay method in [26] 5 0.8km 4

to design η = η0 ∗ e−rd nite , where η0 is the initial learning
rate, rd is the decay rate, and nite is the number of iterations. 0.2km
After the optimal weight of synaptic is obtained, the inputs PV5 PV4
of NN are changed to ni corresponding historical PCC signals 380V
in the second round. By performing the forward propagation
0 1.0km 1 0.6km 2 0.4km 3
process once again, the predictive PCC signal is obtained
below as the final NN output:
q p
X  !
_ hi _ in _ PV1 PV2 PV3
X
0 hi ou
δSk [0] = f wm1 f wom δSk [ i |l]−bm −b1 (28)
m=1 o=1
Fig. 6. A distribution system in simulation experiments.
V. S IMULATION R ESULTS AND D ISCUSSIONS
2.50
A sample distribution network with PV systems is shown
Power injection

2.00
(kW, kvar)

in Fig. 6. The distribution feeders are modelled as the RL 1.50 Active power
impedance (1 km = 0.642 Ω + 0.841 mH). PV inverters have 1.00
the same reactive power capacity 2.5 kvar. Power factor is set Reactive power
0.50
as 0.9487. Voltages are presented in per unit value (pu) and
0.00
the nominal voltage is 380 V. All simulations are performed 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (a)
in MATLAB/Simulink. 1.12
1.10 V1 Overvoltage
Bus voltage

V2
1.08 V3
A. Results under coordinated PCC
(pu)

1.06 V4
The initial power injection (P and Q) from individual PV 1.04 V5
is shown in Fig. 7 (a), where all PVs are assumed to inject the 1.02
1.00
same amount of power into the grid. The bus voltages without 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (b)
any coordinated PCC is shown in Fig. 7 (b). It is seen that
bus5 has the maximum rise in voltage. At t=1.1s, it reaches the Fig. 7. Results without using PCC.
peak value 0.11pu. The overvoltage problem appears during
peak generation periods: 0.4s-0.7s and 1.0s-1.3s.
When PCC is used to mitigate voltage rise, bus5 is selected of other buses become acceptable during 0.4s-0.7s and 1.0s-
as the primary regulation bus. According to the voltage sen- 1.3s. The results indicate the effectiveness of PCC in voltage
sitivities of bus5, powers Q5 , Q4 , Q3 , Q2 , Q1 , P5 , P4 , P3 , regulation for all PV buses.
P2 , P1 are successively curtailed. The results of power control
are shown in Fig. 8 (a). PCC is performed during 0.4s-0.7s
and 1.0s-1.3s. RPC reaches the maximum, i.e., the reactive B. Results under communication delay
power absorption of all PV inverters reach the limited capacity The estimation of MTCD is shown in Fig. 9. From Eq. (10),
2.5kvar. The APC of some PVs is performed during 0.5s-0.6s the maximum allowable PV PMs are obtained as 1.444kW,
and 1.0s-1.3s. The corresponding results of voltage regulation 1.094kW, 1.003kW, 1.032kW, and 0.926kW, respectively. In
are shown in Fig. 8 (b). By curtailing PV power injection, the Fig. 9 (a), the consistent PM slopes reach the maximum value
bus5 voltage is regulated to 1.00pu-1.05pu. Also, the voltages 9.00kW/s at t=1.1s, and the minimal value 1.50kW/s at t=0.1s,

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Transactions on Industrial Informatics

3.00 3.00
P1 Q1 1,2,3 P1 Q1 1,2,3
Power injection

Power injection
2.00 1,2,3
P_ 2.00 1,2,3,4
P_
P2 Q2 P2 Q2
(kW, kvar)

(kW, kvar)
1.00 4 4 1.00 4,5
5 5 5
0.00 0.00
P3 Q3 1,2 1,2,3,4 P3 Q3 1 1,2,3,4 1,2,3
-1.00 P4 Q4 3,4,5 5 Q_ -1.00 P4 Q4 2,3,4,5 5 Q_ 1,2,3,4,5
-2.00 P5 Q5 1,2,3,4,5 -2.00 P5 Q5 4,5

-3.00 -3.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (a) Time (s) (a)
1.06 1.06
1.05 V1 1.05 V1
Bus voltage

Bus voltage
V2 V2
1.04 V3 1.04 V3
(pu)

(pu)
1.03 V4 1.03 V4
1.02 V5 1.02 V5
1.01 1.01
1.00 1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (b) Time (s) (b)

Fig. 8. Results from PCC without communication delay. Fig. 10. Results from PCC with 0.05s communication delay.

10.00 3.00
P1 Q1

Power injection
2.00 1,2,3
PV PM slope

8.00 P2 Q2 P_

(kW, kvar)
1,2,3 4
1.00
(kW/s)

5
6.00 4
5
Same PM slope 0.00
4.00 P3 Q3 1,2 1,2,3,4 1,2,3,4,5
-1.00 P4 Q4 Q_
3,4,5 5
2.00 -2.00 P5 Q5
0.00 -3.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (a) Time (s) (a)
1.00 1.12
 V1 Overvoltage
Delay threshold

0.80  1 1.10
Bus voltage

V2
2
1.08 V3
0.60
(pu)
(s)

1.06 V4
0.40  3 1.04 V5

0.20  4 1.00
5
0.00 1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (b) Time (s) (b)

Fig. 9. MTCD estimation. Fig. 11. Results from PCC with 0.25s communication delay.

respectively. The delay thresholds obtained from Eq. (11) are C. Results under predictive PCC
shown in Fig. 9 (b). Each PV has different delay thresholds When the predictive PCC with data preprocessing is used at
at all instants. PV1 is always the maximum, and PV5 has t=0.4s, 0.5s, 0.6s, 1.0s, 1.1s, and 1.2s, the corresponding result-
the minimal. Their respective minimal values 0.144s, 0.109s, s are shown in Figs. 12-16. The results of data preprocessing
0.100s, 0.103s, and 0.093s at t=1.1s are the MTCDs of PVs. are shown in Fig. 12. Optimal data with a high similarity to
To study the impacts of communication delay on voltage PV power at these instants (1.15kW, 1.78kW, 1.33kW, 1.30kW,
regulation, we tested PCC under communication delays of 2.20kW, 1.75kW) are extracted from original historical data.
0.05s and 0.25s. The results are shown in Figs. 10 and 11. The data with large differences are removed.
It is seen from Fig. 9 (b) that 0.05s communication delay is The predictive results of direct NN prediction and DNNP
acceptable for all instants. When compared with Fig. 8 (a), are shown in Fig. 13. As shown in Fig. 13 (a) and (b), by using
there are no significant changes in PV power control in Fig. the NN to predict PCC signal, we can obtain the maximum and
10 (a). It is observed from Fig. 8 (b) and Fig. 10 (b) that minimal predictive errors as 11.93% and 8.15%, respectively.
although the voltage regulation amplitude changes with the When using the DNNP without data preprocessing, the predic-
delayed PCC, all bus voltages are still within 1.05pu under tive error is reduced to the range of 5.89%-9.22% in Fig. 13
the allowable 0.05s communication delay. (c) and (d). With data preprocessing, the results of DNNP are
However, 0.25s communication delay exceeds the thresholds shown in Fig. 13 (e) and (f). It allows the predictive error to
at t=0.4s, 0.5s, 0.6s, 1.0s, 1.1s, and 1.2s in Fig. 9 (b). Because be further reduced to 1.17%-2.94%, and thus is more accurate.
of the significant changes in PV power control in Fig. 11 (a), The corresponding PCC results are shown in Figs. 14-16.
there are obvious voltage rises over 0.05pu at these instants in Light-colored curves are the desired results by using current
Fig. 11 (b). The maximum value reaches 0.11pu at t=1.1s. It PCC signals without communication delay at above instants.
has no significant difference from the value in Fig. 7 (b). In In Fig. 14, the bus3 voltage is still over 1.05pu at t=1.1s after
addition to showing an effective MTCD estimation, the results being regulated by PCC with a large direct prediction error.
indicate that voltage regulation is effective within MTCD but For the DNNP without data preprocessing, it is seen from Fig.
becomes invalid under ACD conditions. 15 that although the voltages of all buses are within 1.00pu-

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Transactions on Industrial Informatics

1.40 1.40 3.00

preprocessing (kW)

preprocessing (kW)
P1 Q1 1,2,3

Power injection
Historical data

Historical data
1.30 1.90 2.00 1,2,3
P_
P2 Q2

(kW, kvar)
1.00 4 4
1.20 1.80 5 5
0.00
1.10 1.70 P3 Q3 1,2 1,2,3,4
-1.00 P4 Q4 3,4,5
1.00 1.60 -2.00 P5 Q5 Q_ 5
1,2,3,4,5

0.90 1 2 3 4 5 1.50 1 2 3 4 5 -3.00

PV PV PV PV PV(a) PV PV PV PV PV(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (a)
t=0.4s t=0.5s
1.60 1.60 1.06
preprocessing (kW)

preprocessing (kW)
V1 1.052
1.05
Historical data

Historical data
1.50 1.50 1.050

Bus voltage
V2
1.04 V3
1.40 1.40

(pu)
1.03 V4
1.30 1.30 1.02 V5
1.20 1.20 1.01
1.10 1 2 3 4 5 1.10 1 2 3 4 5 1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
PV PV PV PV PV(c) PV PV PV PV PV(d) Time (s) (b)
t=0.6s t=1.0s
2.40 1.40
preprocessing (kW)

preprocessing (kW)
Historical data

Historical data

2.30 1.90 Fig. 14. Results from direct NN prediction.

2.20 1.80
3.00
2.10 1.70 P1 Q1 1,2,3

Power injection
2.00 1,2,3
P_
P2 Q2

(kW, kvar)
2.00 1.60 1.00 4 4
5 5
1.90 1 2 3 4 5 1.50 1 2 3 4 5 0.00
PV PV PV PV PV(e) PV PV PV PV PV(f) P3 Q3 1,2 1,2,3,4
t=1.1s t=1.2s -1.00 P4 Q4 3,4,5
-2.00 P5 Q5 Q_ 5
1,2,3,4,5

Fig. 12. Results of data preprocessing. -3.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (a)
1.06
0.00 12.00 1.05 V1
Predictive error of

Bus voltage
signal (kW, kvar)

V2
PCC signal (%)
Predictive PCC

-0.60 10.00 1.04 V3

(pu)

8.00 1.03 V4
-1.20 V5
6.00 1.02
-1.80 1.01
4.00
-2.40 2.00 1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
-3.00 0.00 Time (s) (b)
0.4 0.5 0.6 1.0 1.1 1.2 0.4 0.5 0.6 1.0 1.1 1.2
Time(s) (a) Time(s) (b)
0.00 10.00 Fig. 15. Results from DNNP without data preprocessing.
Predictive error of
signal (kW, kvar)

PCC signal (%)

Predictive PCC

-0.60 8.00
-1.20 6.00 3.00
P1 Q1 1,2,3
Power injection

-1.80 4.00 2.00 1,2,3

P_
P2 Q2
(kW, kvar)

1.00 4 4
-2.40 2.00 5 5
0.00
-3.00 0.00 P3 Q3 1,2 1,2,3,4
0.4 0.5 0.6 1.0 1.1 1.2 0.4 0.5 0.6 1.0 1.1 1.2 -1.00 P4 Q4 3,4,5
Time(s) (c) Time(s) (d) -2.00 P5 Q5 Q_ 5 1,2,3,4,5
0.00 3.00
Predictive error of
signal (kW, kvar)

-3.00
PCC signal (%)
Predictive PCC

-0.70 2.40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Time (s) (a)
-1.40 1.80 1.06
1.05 V1
Bus voltage

-2.10 1.20 V2
1.04 V3
(pu)

-2.80 0.60 1.03 V4

-3.50 0.00 1.02 V5
0.4 0.5 0.6 1.0 1.1 1.2 0.4 0.5 0.6 1.0 1.1 1.2
Time(s) (e) Time(s) (f) 1.01
1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Fig. 13. Results from direct NN prediction (a,b), DNNP without data Time (s) (b)
preprocessing (c,d) and with data preprocessing (e,f), respectively.
Fig. 16. Results from DNNP with data preprocessing.

1.05pu, there are still significant deviations in PCC. With a

VI. C ONCLUSION
larger PM, some voltages may exceed the acceptable range.
For a small prediction error of DNNP with data preprocessing, Predictive PCC has been studied in this paper for voltage
the power and voltage are very close to the desired results in regulation under communication delay in distribution networks
Fig. 16. An accurate prediction for PCC is necessary for an with a high penetration level of PV systems. The delay-tolerant
effective voltage regulation and is independent of amount of PCC estimates the MTCD based on the maximum allowable
communication delays. The results indicate that our approach PM of PV. It operates in normal mode when communication
can realize an accurate predictive compensation for PCC under delay is within MTCD and switches to predictive mode under
ACD conditions. ACD conditions. A DNNP with data preprocessing is adopted

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Transactions on Industrial Informatics

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He was a recipient of the National Scholarship for
microgrids,” IEEE Trans. Smart Grid, vol. 9, no. 3, pp. 2192–2202, May
Graduate students, the State Scholarship for Overseas Studies, and the Beijing
2018.
Environment Foundation for Young Talents.
[11] S. Liu, X. Wang, and P. X. Liu, “Impact of communication delays on His current research interests include microgrid control, photovoltaic power
secondary frequency control in an islanded microgrid,” IEEE Trans. Ind. system control, distribution system optimization, and communication security.
Electron., vol. 62, no. 4, pp. 2021–2031, Apr. 2015.
[12] S. S. Yu, T. K. Chau, T. Fernando, and H. H.-C. Iu, “An enhanced
adaptive phasor power oscillation damping approach with latency com-
pensation for modern power systems,” IEEE Trans. Power Syst., vol. 33,
no. 4, pp. 4285–4296, Jul. 2018.
[13] L. Cheng, G. Chen, W. Gao, F. Zhang, and G. Li, “Adaptive time delay
compensator (ATDC) design for wide-area power system stabilizer,”
IEEE Trans. Smart Grid, vol. 5, no. 6, pp. 2957–2966, Nov. 2014.
[14] E. A. Coelho, D. Wu, J. M. Guerrero, J. C. Vasquez, T. Dragicevi, Yateendra Mishra (M’09) received the Ph.D. de-
C. Stefanovi, and P. Popovski, “Small-signal analysis of the microgrid gree from the University of Queensland, Brisbane
secondary control considering a communication time delay,” IEEE QLD, Australia, in 2009. He is currently a Senior
Trans. Ind. Electron., vol. 63, no. 10, pp. 6257–6269, Oct. 2016. Lecturer and Advanced QLD Research Fellow with
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no. 3, pp. 1662–1673, Sept. 2017. QLD, Australia.
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islanded microgrids,” IEEE Syst. J., vol. 13, no. 2, pp. 1851–1860, Jun. stability and control, and their applications in smart
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optimal control of DC microgrids with communication delays,” IEEE
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Transactions on Industrial Informatics

10

Dong Yue (SM’08) received the Ph.D. degree in

control theory and application from the South Chi-
na University of Technology, Guangzhou, China,
in 1995. He was a Changjiang Professor with the
Department of Control Science and Engineering,
Huazhong University of Science and Technology,
Wuhan, China. He is currently a professor and dean
of the Institute of Advanced Technology, Nanjing U-
niversity of Posts and Telecommunications, Nanjing,
China.
His research interests include analysis and syn-
thesis of networked control systems, multi-agent systems, optimal control of
power systems, and internet of things.

Chunxia Dou (M’19) received the B.S. and M.S.

degrees in automation from the Northeast Heavy
Machinery Institute, Qiqihaer, China, in 1989 and
1994, respectively, and the Ph.D. degree in electrical
engineering from Yanshan University, Qinhuangdao,
China, in 2005. In 2010, she joined the Department
of Engineering, Peking University, Beijing, China,
where she was a Postdoctoral Fellow for two years.
From 2005 to 2019, she was a Professor in the
School of Electrical Engineering, Yanshan Univer-
sity, China. Since 2019, she has been a Professor
in the Institute of Advanced Technology, Nanjing University of Posts and
Telecommunications, Nanjing, China.
Her current research interests include MAS-based control, event-triggered
hybrid control, distributed coordinated control, multi-mode switching control,
and their applications in power systems and smart grid.

Bo Zhang (S’19) received the B.S. degree in elec-

trical engineering and automation from Yanshan
university, Qinhuangdao, China, in 2016, where he
is currently pursuing the Ph.D. degree in control
science and engineering.
He was a recipient of the National Scholarship
for Graduate students, and the Beijing Environment
Foundation for Young Talents.
His current research interests include microgrid
control, distribution system optimization, and com-
munication security.

Yu-Chu Tian (SM’19, M’00) received the Ph.D. de-

gree in computer and software engineering from the
University of Sydney, Sydney NSW 2000, Australia,
in 2009, and the Ph.D. degree in industrial automa-
tion from Zhejiang University, Hangzhou 310027,
China, in 1993.
He is currently a Professor of Computer Science
with the School of Computer Science, Queensland
University of Technology, Brisbane QLD, Australia.
His research interests include big data computing,
distributed computing, cloud computing, computer
networks and communications, cyber-physical system security, artificial intel-
ligence and machine learning, large-scale optimization, control systems, and
smart grid communications and control.

1551-3203 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Authorized licensed use limited to: Auckland University of Technology. Downloaded on October 29,2020 at 21:47:53 UTC from IEEE Xplore. Restrictions apply.