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Energies 2019, 12, 3384; doi:10.3390/en12173384 www.mdpi.com/journal/energies
Article
Optimal Dispatching of Offshore Microgrid
Considering Probability Prediction of Tidal
Current Speed
Anan Zhang
1,2,
*, Yangfan Sun
1
, Wei Yang
1
, Huang Huang
1
and Yating Feng
1
1
School of Electrical and Information Engineering, Southwest Petroleum University, Chengdu 610500, China
2
School of Engineering, Cardiff University, Cardiff CF24 3AA, UK
* Correspondence: ananzhang@swpu.edu.cn; Tel.: +86-139-818-212-01
Received: 2 July 2019; Accepted: 30 August 2019; Published: 2 September 2019
Abstract: Oceans contain rich tidal current energy, which can provide sufficient power for offshore
microgrids. However, the uncertainty of tidal flow may endanger the operational reliability of an
offshore microgrid. In this paper, a probabilistic prediction model of tidal current is established
based on support vector quantile regression to reduce the influence of uncertainty. Firstly, the
penalty factors and kernel parameters of the proposed prediction model was optimized by the
dragonfly algorithm to predict the tidal speed of any time of a day in different quantiles. Secondly,
combining the above result with the kernel density to predict the probability density function of the
tidal current speed, which is to improve the accuracy of prediction in the absence of information.
Thirdly, an optimal generation dispatching strategy with tidal current generators is proposed to
minimize the fuel consumption of offshore microgrids. Finally, a case study based on the offshore
oil and gas platform in Bohai shows that the mean absolute percent error of the proposed model is
2.8142%, which is better than support vector quantile regression model and support vector
regression model optimized by the genetic algorithm.
Keywords: offshore microgrids; support vector quantile regression; dragonfly algorithm;
probability prediction; optimal operation
1. Introduction
An offshore microgrid is an effective way to provide energy for offshore platforms, which can
deal with the limited fossil resources issues through using renewable energy generators and energy
storage devices [1,2]. At present, offshore renewable energy mainly includes solar energy, wind
energy, ocean temperature difference energy, tidal current energy and so on, among which the tidal
current power has recently received widely concerned due to its vast reserves and high energy
density [3–6]. However, the tide current has strong randomness owing to the wave, sea breeze,
temperature, etc. Therefore, it is essential to establish the prediction model of tidal current speed to
make efficient use of the tidal current energy in that an accurate prediction can achieve sophisticated
strategies to guarantee a stable energy source for offshore microgrids, thereby saving economic cost
[7].
The harmonic analysis method (HAM), which is to decompose complex tidal flow curves into
several harmonic terms, calculate harmonic coefficient changes and the astronomic effect, has been
widely used in tidal current prediction [8,9]. The height of the tidal current is considered as a set of
harmonic components in the HAM. The amplitude and phase of each harmonic component can be
inferred from the historical data of the tidal by the least squares method [10]. Then, the tidal current
speed can be calculated based on the tidal current height [11]. However, the method suffers from
Energies 2019, 12, 3384 2 of 17
two critical drawbacks. (a) They require large historical datasets (several years), and (b) they have
inefficient performances for predicting sudden and aperiodic patterns resulting from weather-based
factors. When the observed tidal current data time interval less than or equal to one hour, there will
exist non-harmonic components in it because of supra-tidal fluctuations. As a result, it cannot be
modeled by conventional harmonic analysis—based on the prediction models. In recent years, to
overcome these barriers and consider the nature of tidal current and the weather-based irregularities,
machine learning-based prediction models have been proposed. Primarily, artificial neural network
(ANN) and support vector machine are widely used, which can reduce the training period
effectively [12–14]. Reference [12] proposed a hybrid model of an ANN and Fourier series model
based on the least squares method (FLSM) to predict the speed and direction of the tidal current.
Reference [13] proposed an accurate hybrid method based on support vector regression (SVR) and
autoregressive integrated moving average (ARIMA) to predict the tidal current speed and direction.
In the proposed hybrid model, the ARIMA model captures the linear component of the tidal current,
and the SVR models the remaining components. A univariate prediction method based on wavelet
transform and SVR was proposed in [14], where tidal current data was decomposed into some
subharmonic components. The Wakeby distribution was also used to capture the probability
characteristics of the tidal current speed. Since the timing of the tidal flow velocity is not taken into
consideration, and the error with the actual data in a short time, this model cannot directly be used
to predict the tidal velocity time series [15–17]. Therefore, the k-means clustering technique and
non-parametric kernel density estimation method were used to model the random components of
the tidal current speed [18–20]. However, the deterministic techniques used in the above literature
do not take into account the timing of the tidal speed, and the single-point prediction may cause
relatively large errors. For example, the Weibull distribution [21] and the Wakeby distribution do
not take into account in the time-series data. Moreover, the single-point prediction using ANN and
support vector machine (SVM) cannot fully reflect the uncertainty of the tidal current power
generation. Furthermore, the tidal data is highly seasonal, containing carious cycles. In other words,
tidal information naturally includes a specific amount of uncertainty, which is produced by its
volatile and random characteristics. Therefore, the probabilistic-prediction was adopted in this
paper to improve the accuracy of the model because it can better describe the possible fluctuation of
future tidal current power generation better. It is conducive to the timely adjustment of the offshore
engineering plan and the optimal scheduling of the offshore microgrid.
Economic dispatch (ED) is to determine the optimal output power of multiple generator sets
and meet the system load demand problem at the lowest cost [22]. In the reference [23,24],
multi-objective optimization scheduling models were established under the environmental and
economic factors. Reference [25] proposed multi-objective optimization problems for solving the
power system using the artificial swarm algorithm. In reference [26], the three-objective optimal
dispatching model was transformed into a single-objective optimal dispatching model, which was
solved by the interior point method to obtain the optimal solution. The dynamic optimization
dispatching model is more suitable for the offshore microgrid with the tidal current because the
power of tidal current generators will change with the tidal current velocity. Therefore, it is
necessary to predict the output of tidal current generators for each time period.
In this paper, we proposed a time-sequential probabilistic prediction model based on support
vector quantile regression (SVQR) and kernel density estimation. By using the dragonfly algorithm,
the parameters of the model are optimized, which not only improved the prediction accuracy but
also obtained the fluctuation range of future tidal current speed. Besides, the optimization model of
an offshore microgrid with tidal current power generation was established by taking into account
indicators such as economic cost and environmental benefits. In order to improve the solving speed
and obtain the globally optimal solution, the dragonfly algorithm was applied. The proposed
method has proven to be efficient and correct when applied to a case of an offshore oilfield
microgrid using tidal current energy.
This paper is organized as follows: The prediction model and the basic theory are introduced in
Section 2, followed by an economic dispatching model of an offshore microgrid based on tidal
Energies 2019, 12, 3384 3 of 17
velocity prediction in Section 3. Section 4 presents the results of the case analysis. Concluding
remarks are given in Section 5.
2. Prediction Models and Basic Theories
The structural diagram of the offshore microgrid is shown in Figure 1. The system mainly
includes renewable energy power generation units, a gas turbine unit, an energy storage unit and an
emergency power unit. Renewable energy refers to the tidal current in this paper.
Figure 1. Structure diagram of the offshore microgrid.
2.1. Support Vector Quantile Regression Based Probablity Prediction Model for Tidal Current Speed
Using the SVM will result in the deviation of single point prediction of tidal current speed due
to the uncertainty of the tidal current energy output and the inherent defects of existing prediction
models. However, compared with the single-point value prediction, the regression analysis under
different quantiles can describe the influence of the distribution characteristics of input variables
more completely. The quantile regression provides powerful theoretical support for probabilistic
predictions. Therefore, useful information can be obtained for more accurate scientific decisions
[27,28]. The quantile regression is based on the conditional quantile of the response variable y to
predict the explanatory variable x, which can reflect the information that the explanatory variable x
affects the position, distribution and shape of the response variable y in different ranges more
closely. It has the following advantages: (1) Robustness, the quantile does not make any assumption
for the distribution of random errors in the model; (2) resistance to outliers data, the quantile
regression can be used from 0 to 1 and (3) parameters estimated by quantile have asymptotic
optimality under large samples.
The main parameters are explained in Table 1:
Table 1. Parameter interpretation.
x, x
i
Explanatory Variables
y, y
i
Response variables
Q
yi
Linear regression estimate
β(τ) Regression coefficient vector
τ Quantile
σ Free parameter of the kernel parameter
C Penalty parameter
Energies 2019, 12, 3384 4 of 17
Assume that the sample set of the tidal current speed and its related historical data can be
represented as
{}
1
(, )
n
ii
i
Gxy
=
=, where xi is the input sample vector containing historical tidal current
rate and is considered as explanatory variables, and yi is the corresponding output sample of the
tidal current speed and is considered as the response variables. Then the linear quantile regression
model of tidal current speed is:
'
01122
(|) () () () () ()
i
ykki
Qx x x xx
τ
β
τ
β
τ
β
τ
β
τ
β
τ
=+ + ++ ≡
. (1)
Here, Qyi(τ|x) is the τ-th conditional quantile of the response variables y under the explanatory
variables x = [x1,x2,…,xi]T. When τ is continuously taken in the interval (0,1), the conditional
distribution of the response variable can be obtained. β(τ) is the regression coefficient vector, it
changes as the quantile changes. The estimation of β(τ) in the above equation can be formulated as
follows:
''
'''
1
min ( ) min (1 )
ii ii
n
ii ii ii
iiy x iy x
yx yx yx
τ
ββ
ββ
ββ
τ
β
τ
β
=≥<
−= −+ − −
.
(2)
The prediction precision of tidal current speed is affected by a variety of complex factors in a
linear or non-linear manner. However, the quantile regression mentioned above is based on linear
regression, which is difficult to solve complex nonlinear functions. Therefore, a semiparametric
method is adopted to optimize the combination of the support vector machine regression (SVR) [29]
and the quantile regression (QR) to obtain the support vector quantile regression (SVQR) model of
tidal current speed. Based on the SVR model, the penalty parameter part is replaced by quantile
regression. As a result, the SVQR model is expressed as follows:
2
,1
1
min ( ( ))
2
I
T
ii
wb i
wC ybwx
ττ
ττττ
ρφ
=
+−−
.
(3)
Here, C is a penalty parameter, wτ and bτ represent the weight and deviation of the τ-th
conditional quantile respectively and φ(x) is a nonlinear mapping function.
According to the theory of structural risk minimization, and satisfying the solution to the
optimization problem, the slack variables
ϑ
and
ϑ
∗ are introduced. The SVM regression model
can be expressed as:
*
,
2*
,, 1
*
*
1
min ( (1 ) )
2
() , 1,2, ,
S.T. ( ) , 1, 2, ,
0; 0
ii
I
ii
wb i
T
ii i
T
iii
ii
C
yxb i N
x
by i N
ττ
τ
ϑϑ
ττ
ττ
ωτϑτϑ
ωϕ ε ϑ
ωϕ ε ϑ
ϑϑ
=
++−
−−≤+=
+−≤+ =
≥≥
.
(4)
To solve the convex quadratic optimization problem of the above formula, the objective
function and Lagrange function constraints are combined to convert the nonlinear programming
problem into a dual problem.
Lagrange function is as follows:
2
***
1
****
111
1
(,,,; , , ,) ( () )
2
( ( ) ) ( (1 ) ) ( )
I
ii i i i i ii i i i
i
III
ii i i i i i ii ii
iii
L
wb w y w x b
yw x b C
τττ τ τττ τ τ τ
ττ ττ
ϑϑ α α ξ ξ α ϑ ϕ
αϑ ϕ τϑ τϑ ξϑ ξϑ
=
===
=− −+ +−
+− − + +− − +
.
(5)
Energies 2019, 12, 3384 5 of 17
Here, Lagrange multipliers at different quantiles are **
,,, 0 (1,2, )
iiii iI
ττττ
ααξξ
≥=, then the
first partial derivative of *
,,,
ii
wb
ττ
ϑϑ
in function Lτ are obtained by formula (6).
*
1
*
1
**
*
0()(),
0( )0,
..
00,
0(1) 0
ii
I
iii
i
I
ii
i
ii
i
i
Lwx
w
L
b
ST LC
LC
ττ
τ
τττ
τ
τ
ττ
τ
τ
ττ
τ
ααϕ
αα
ταξ
ϑ
ταξ
ϑ
=
=
∂
==−
∂
∂=−=
∂
∂
=−−=
∂
∂
=−−−=
∂
.
(6)
The dual optimization problem of the above formula can be obtained by the dual principles, as
follows:
*
** *
,11 1 1
*
1
*
1
max ( )( )(,) () ()
2
()0,
S.T. 0,
0(1)
ij i
ii
i
i
nn I I
ij ijii i
ij i i
I
i
i
i
Kx x y y
C
C
ττ τ
ττ
τ
τ
ττ τ
αα
τ
τ
ααα α α ε α ε
αα
ατ
ατ
== = =
=
−−− +−−−
−=
≤≤
≤≤−
.
(7)
Here,
()
22
exp 2(, ) jij i
xxKx x
σ
−−= is the kernel function, which represents the inner product of
high-dimensional space, i
a
τ
and *
i
a
τ
are Lagrange factors.
Using the kernel function make it easier to calculate nonlinear predictions because it maps the
nonlinear sample data into the higher-dimensional Hilbert space, making them linearly separable.
Therefore, the problem of solving a decision function is transformed into how to select an
appropriate and effective kernel function. The radial kernel function was applied in this paper.
The dual problem above is solved by introducing a kernel function as follows:
*
1
**
1
()()
sgn( ) ( ) ( , )
i
ii
I
ii
i
I
iii i
i
wx
bavera
g
e
y
Kx x
τ
ττ
ττ
τττ
ααϕ
εαα αα
=
=
=−
=−+−−
.
(8)
Therefore, the formula of the SVQR model is as follows:
(|) ( )
T
yi
Qxwxb
τ
ττ
τϕ
=+
. (9)
Here, η = (C, σ) is the hyper-parameter set of SVQR model needed to be optimized, C is the
penalty parameter and σ is the free parameter of the kernel parameter.
Based on the above research, first obtain the different quantiles of the tidal current speed
prediction results Qyτ(τ|x), and then use the quantile at different quantiles as the input value of
kernel density estimation to predict the probability density function. Kernel density estimation is a
non-parametric estimation method with high prediction accuracy that can be used for analysis of
any distribution sample. Assuming v1, v2 … vn are n sample values of tidal current speed, the kernel
density estimation is defined as:
Energies 2019, 12, 3384 6 of 17
1
1
() ( )
n
i
i
vv
fx K
nh h
=
−
=
.
(10)
Here, h is bandwidth and K is the kernel density function.
The accuracy of f(x) depends on the kernel function and the bandwidth coefficient. This paper
adopted the Gaussian kernel function below as follows:
2/2
1
() 2
u
Ku e
π
−
=
.
(11)
When the bandwidth is fixed, the choice of it is essential because the effect of different kernel
functions on probability density function is equivalent. The bandwidth is employed as:
1
5
1.06hn
σ
−
=. (12)
Here, σ is the standard deviation of the random variable x.
2.2. Probablistic Prediction Model of Tidal Current Speed Nased on Dragonfly Algorithm
The dragonfly algorithm (DA) is a novel swarm intelligence optimization algorithm that put
forward by Seyedali Mirjalili in 2015 [30]. Two distinct group behaviors of predation (static
behavior) and migration (dynamic group behavior) of the dragonfly guarantee the stability, fast
speed and global optimization abilities.
In the SVQR model, C is a penalty parameter. The larger C is, the less error of the model is
allowed, and the worse the generalization ability is. σ is also the kernel parameter, which is the
value of the kernel parameter that determines the distribution of the nonlinear input vector that
mapped into a high-dimensional feature space. Therefore, the selection of parameter C and σ
directly affects the regression prediction performance of the SVQR model. Since the dragonfly
algorithm has the advantage of the fast convergence and global optimization, this paper proposed a
DA-SVQR regression prediction model, which improved the accuracy of the prediction model
effectively.
The parameter optimization steps of the DA-SVQR algorithm are as follows:
Step 1: Initialize the parameters. The main parameters of the dragonfly algorithm include the
number of dragonfly individuals, the dimension of the problem and the maximum iteration
number. The main parameters of SVQR model include penalty parameter C, and upper and lower
limits of kernel parameter.
Step 2: Set up the training number sets, training number labels, test sets and test set labels.
Step 3: Initialize dragonfly position. Initialization generates Dragonfly position X0 and
initialization step vector ΔXt. The hyper-parametric η in the SVQR model that needs to be
optimized is taken as the location of the dragonfly solution Xt.
Step 4: Calculate individual weight values. Randomly initialize the neighboring radius (r) and
the inertia weight (w), randomly initialize the weights of five behaviors of a dragonfly individual,
i.e., separation weight (s), alignment weight (a), cohesion weight (c), weight of attraction to food (f)
and weight of distraction from an enemy (e)
Step 5: Calculate the fitness value of the dragonfly. The classification accuracy of the model is
taken as the current fitness value of the individual dragonfly. Whenever a position update is
performed, the current maximum fitness value is calculated and recorded. If the fitness value of the
current dragonfly is higher than the saved fitness value, the former is taken as the optimal one, then
preserves the current optimal value as a corresponding hyper-parametric η, otherwise it retains the
original fitness value and the corresponding hyper-parametric η.
Step 6: Update the resource of food and the enemy position. The Euclidean distance formula is
used to calculate the food source (X+) and enemy position (X−).
Energies 2019, 12, 3384 7 of 17
Step 7: Update the behaviors of the dragonfly. Update the five behaviors of dragonfly
individual: Separation (S), alignment (A), cohesion (C), attraction to food (F) and distraction from
enemies (E).
Step 8: Update position. If there is at least one neighboring dragonfly, then update the step and
position vectors. If there is no neighboring dragonfly, and then update the position vector.
Step 9: Algorithm iteration termination judgment. When the maximum iteration count
appears, the current optimal position vector will be saved and regarded as the optimal
combination. Otherwise, the number of iterations adds up to 1, then go to step 4.
The flow chart of SVQR is shown in Figure 2.
Start
Initialize the
parameters
Initialize
Dragonfly
position and
calculate
Dragonfly
behavior
weight
Calculate the
fitness value of
dragonfly
Update the
positio ns of
food source
and enemy.
Iterative
termination
end
YES
Generating new
superparametric
combinations
NO
Update the
behaviors of
dragonfly
Update
position
N
ij
j=1
N
j
j=1
i
N
j
j=1
i
+
i
-
i
separation
alignment
cohesion
a
S=- X-X
V
A= N
X
C= -X
N
F=X -Xttraction
distraction E = X - X
：
：
：
：
：
t+1
11
(
)+w X
+
ii
iii t
ttt
XsSaA
cC fF eE
step vector
position vec
X
Xtor X
++
Δ= ++
++ Δ
=Δ
：
：
Figure 2. Flowchart of dragonfly algorithm-support vector quantile regression (DA-SVQR).
3. Optimal Dispatching of the Offshore Microgrid with Tidal Current Power Generation
3.1. Objective Function
Since only using tidal current power to generate electricity does not consume ever-decreasing
fossil fuels, the offshore platforms should use tidal current energy firstly to reduce the fuel
consumption of conventional units. Therefore, the objective function is to minimize the combined
operating costs, which includes the cost of unit maintenance, fuel replenishment cost and
environmental protection conversion cost. The operation and maintenance cost of distributed
energy can be considered to be proportional to the electrical energy output. The ratio is Kd, which is
the operation and maintenance cost factor.
2
GT ,
11
min ( )
mk
dGi D D D j iji
iN i j
F
KP C aP bP c F W P
α
∈==
=+++++
.
(13)
1GT
GT GT
CH GT
P
FC
V
η
=
.
(14)
Energies 2019, 12, 3384 8 of 17
Here, N is the total number of distributed generation (DG), Kd is the operating maintenance
coefficient of distributed generation, PGi is the actual output power of DG and CD and CGT are the
prices of emergency diesel engine and gas turbine respectively. a, b and c are the fuel cost
coefficients, αj is the conversion coefficient of class j pollutant, rmb/kg. Wi,j is the pollutant discharge
of the i-th unit, kg/kw, and Pi is the power of the i-th unit. FGT is the fuel replenishment cost of the gas
turbine, VCH is the low calorific value of natural gas and PGT and ηGT are power and efficiency of gas
turbine respectively.
3.2. Constraint Conditions
(1) Power balance constraint:
1
N
Gi load loss BAT
i
P
PPP
=
=++
.
(15)
(2) Distributed power output power constraint:
min max
Gi Gi Gi
PPP<< . (16)
(3) Power constraint of controllable generators on climbing:
G() ()
iGi i
Pt Pt t
γ
−≤Δ
. (17)
(4) Node voltage and line current constraints:
min
max
max
iii
ij ij
UUU
II
≤≤
≤.
(18)
(5) Charging and discharging power constraints of the energy storage system:
min max
()
B
AT BAT BAT
PPtP≤≤
. (19)
When the battery discharges, PBAT(t) ≥ 0. The remaining capacity at time t is:
() ( 1) () / S
SOC SOC BAT D B B
StSt Ptt tDQ
η
=−− ⋅Δ−Δ⋅
. (20)
When the battery charges, PBAT(t) ≤ 0. The remaining capacity at time t is:
min max
() ( 1) () /
S ( )
S
SOC SOC BAT C B B
SOC SOC SOC
StSt Ptt tDQ
StS
η
=−− ⋅Δ−Δ⋅
<< .
(21)
Here, PGi is the output power of various DGs, Pload is the load demand, Ploss is the network loss,
PBAT(t) is the output power of the battery at time t, min
Gi
P
and max
Gi
Pare upper and lower limits of DG
output power respectively, PGi (t) is the active output of the i-th DG at time t, Δt is the scheduling
interval, γi is the maximum climbing rate of the controllable unit, Ui is the voltage of the i-th node.
min
i
U and max
i
U are the lower and upper voltage limits of the i-th node respectively. min
B
AT
P
and max
B
AT
P
are
respectively lower and upper limits of battery output power. SSOC (t) is the remaining capacity of
the battery at time t. min
SOC
S and max
SOC
Sare the minimum and maximum of the remaining capacity of
the battery. ηC and ηD are the charge and discharge efficiencies respectively. DB is the hourly
self-discharge ratio of the battery and S
B
Q is the rated capacity of the battery.
Energies 2019, 12, 3384 9 of 17
4. Case Study
In order to verify the validity and correctness of the above model, this paper selected two
operational modes of an actual microgrid in Bohai for case analysis. The offshore microgrid
includes tidal current generators, gas turbines, emergency engines and batteries.
The offshore microgrid in island operation mode is shown in Figure 3, and the tidal current
generators are located in node 7 and node 22.
G G GG
Transformer
G
Reactor
Load
Gas-Tu rbo Gene rator
1
2
3
4
5
6
7
8
910
11
12
13
14
15 16
17
19
20
21
18
Energy
storage
22
Water
Curren t
Rotor
Drive
train
Generator
Power
Transformer
Fluid Power
Mechanical
Power
Electric Power
Power Take-
off System
Water
Curren t
Rotor
Drive
train
Generator
Power
Transformer
Figure 3. Offshore microgrid in island operation mode.
The tidal current historical data from 24 May 2017 to 24 June 2017 of the offshore microgrid
were selected as the study case, and the selected feature vectors of the tidal current prediction
mainly included actual tidal current speed and direction data, temperature and weather conditions.
Specifically, the tidal current data from 24 May 2017 to 22 June 2017 were taken as the training
input sample, and the data of 23 June 2017 was used as the training output sample. Then, the tidal
current data from 25 May 2017 to 23 June 2017 were used as test input samples to predict the tidal
current on 24 June 2017. The unit of the tidal current speed is knots. All training samples and
prediction data were normalized firstly, and the interval of quantile was [0,1]. The pretreatment
formula is as follows:
*min
max min
xx
x
x
x
−
=−.
(22)
Here, x is the original sample value, xmin and xmax are the maximum sample value and minimum
sample value respectively and x* is the normalized value.
Parameter settings: The population of the dragonfly algorithm is 20, the number of iterations is
100 and the range of the (C, σ) parameters are (0,100).
To verify the accuracy of this method, the mean absolute percent error (MAPE), relative error
(RE) and root mean square error (RMSE) were used to evaluate indicators.
Mean absolute percent error (MAPE):
1
1 100%
nii
ii
yy
MAPE ny
=
−
=×
.
(23)
Relative error (RE):
Energies 2019, 12, 3384 10 of 17
1
100%
nii
ii
yy
RE y
=
−
=×
.
(24)
Root mean square error (RMSE):
2
1
1
100%
n
ii
i
RMSE y y
n=
=−×
.
(25)
Here, i
y
and *
i
y
are the actual value and the predicted value respectively and n is the number
of points of the tidal current collected in one day.
4.1. Analysis of Pradiction Results
As stated above, the DA-SVQR method was used to obtain the tidal current prediction results
including prediction interval and probability density curve on day 24 June 2017. Among them, 99
quantiles from 0.01 to 0.99 were selected with a range of 0.01. Figures 4 and 5 show the prediction
interval (one point every 6 min) of the tidal current speed and tidal current direction, respectively.
Figures 6 and 7 show the predicted relative errors of tidal current speed and tidal current direction,
respectively.
Figure 4. Tidal current speed prediction results.
Figure 5. Tidal current direction prediction results.
0 50 100 150 200 250
Sample
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Tidal Current Speed (knots)
Actual Tidal Data
Upper-bound-test
Lower-bound-test
Mode
Energies 2019, 12, 3384 11 of 17
Figure 6. Tidal current speed prediction relative error.
Figure 7. Tidal current direction prediction relative error.
It can be observed from Figures 4 and 5 that the actual value initially fell within the prediction
interval, and mode (the peak of probability density function) of the prediction result using the
DA-SVQR model was very close to the actual value, which illustrates that the DA-SVQR method
accurately depicts tidal current fluctuations. It can be seen from Figures 6 and 7 that the relative
errors were mostly within 5% indicating that the prediction accuracy was relatively high. Some large
relative errors points might be caused by the tidal current changing dramatically. However, when
the tidal current changed sharply, the prediction method could still track the trend of the tidal
current, which indicates that the proposed method could describe the changes of speed and
direction correctly. In Figure 8, the results of SVQR and SVM based on the classical genetic algorithm
(GA) are presented. It can be seen that the proposed method could capture the change trend of the
actual values better. Figure 9 shows the probability density curves of tidal current speed in the 2nd,
6th, 12th, 16th, 20th and 24th hours respectively. It can be observed that the prediction value of the
tidal current speed by the DA-SVQR all appeared on the probability density curve. This result
further explained the advantages of the probability density prediction methods in quantifying
uncertainty and improving prediction accuracy. In summary, the predicted value and prediction
errors obtained by the proposed method could better provide information for decision-makers,
provide effective guarantee for the reliability and optimal dispatching strategy of offshore microgrid,
and also an effective prediction method for tidal current prediction.
Relative error %
Relative error %
Energies 2019, 12, 3384 12 of 17
Figure 8. Method comparison diagram.
Figure 9. Diagram of the probability density curve.
It is more effective to explain the advantages of the DA-SVQR prediction model and the
advantages of the DA algorithm in solving the optimization operation problem. Table 2 gives the
tidal current speed prediction results of the DA-SVQR, GA-SVQR and GA-SVM methods under the
same conditions for ten times. As shown in Table 2, the MAPE was 2.8142%, and the RMSE was
1.5069% by the proposed method, which was the minimum among all tests. It indicates that the
proposed method had higher stability and higher accuracy against other methods. Moreover, the
DA had a better optimization ability and stronger robustness in comparison with the GA.
Table 2. Prediction error of dragonfly algorithm (DA)-SVQR, genetic algorithm (GA)-SVQR and
GA-support vector regression (SVR) methods.
Method Evaluation Index
MAPE% RMSE%
DA-SVQR 2.8142 1.5069
GA-SVQR 7.2137 2.7217
GA-SVR 10.6869 3.0346
0 50 100 150 200 250
Sample
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.
4
Actual Tidal Data
DA-SVQR
GA-SVQR
GA-SVM
75 80 85 90 95
0
0.1
0.2
205 210 215 220 225
0
0.1
0.2
Energies 2019, 12, 3384 13 of 17
4.2. Analysis of Optimal Dispatching Results
The power output Pout of a tidal current generator can be expressed as (26) [16]:
3
0 0<
0.5
tcutin
out P t cutin t rated
rated rated t
VV
PCAVVVV
PVV
ρ
<
=≤<
≤
.
(26)
Here, Vt, Vcutin and Vrated are the tidal current speed, the cut-in speed and the rated speed of the
tidal current generator respectively. Cp is the energy capture coefficient of the tidal current
generator and ρ is the density of sea water. A is the area swept by the blades of the tidal current
generator and Prated is the rated output power of the tidal current generator.
The parameters of the remaining units of the offshore microgrid are shown in Table 3.
Table 3. Parameters of each unit of the offshore microgrid.
Device Parameter Numerical Value
Energy storage system
Maximum charge and discharge power/kW 50
Charge and discharge efficiency/% 85
Battery sel
f
-discharge ratio/% 10
Battery rated capacity (KW*h) 250
Operation and maintenance cost factor (RMB/KW) 0.02748
Gas turbine
Rated power/KW 200
Climbing rate/(KW/min) 3
Minimum operating power 10
Operation and maintenance cost factor (RMB/KW) 0.03640
Fuel price (RMB/m3) 27.6
Emergency diesel engine
Upper limit of output power (KW) 100
Lower limit of output power (KW) 0
Operation and maintenance cost factor (RMB/KW) 0.0790
Fuel price (RMB/m3) 38.4
Single start cost/RMB 100
The fuel cost of a gas turbine and emergency diesel engine included transportation cost,
storage cost and so on. The fuel prices in the table are the overall prices that take into account the
above fees. The problem of the optimal dispatching model for the microgrid can be classified as a
multi-objective and nonlinear optimization problem. This paper adopted the dragonfly algorithm to
solve the model. Figure 10 shows the power output of each unit in the offshore microgrid in island
operation mode.
It can be seen from Figure 10 that during the island operation of the offshore microgrid, the
system first used tidal energy, followed by the gas turbine. The emergency diesel engine would not
start if there was no special case, which was determined by the economic cost and environmental
protection cost in this paper. Moreover, it can be observed in Figure 10 that under the optimization
of the algorithm, the energy storage system was charged in the electricity valley and discharged at
the electricity consumption peak, which fully reflects the value of cutting peaks, filling the valley
and reducing fluctuations. Figure 11 shows that the dragonfly algorithm converged to the optimal
value when the iteration reached 50 times, which reflected that the dragonfly algorithm had
satisfied convergence speed and less optimization time.
Energies 2019, 12, 3384 14 of 17
Figure 10. Power output curve of units in island operation mode.
Figure 11. Iterative result diagram of dragonfly algorithms in island operation mode.
The offshore microgrid in grid-connected mode was employed to verify the effectiveness and
correctness of the proposed method under different operation modes, as shown in Figure 12, and
the tidal current generators are located in node 21 and node 25. In the dotted frame is a small
circular island microgrid, which is connected to another large offshore microgrid to form an
offshore microgrid with the grid-connected mode.
G G
G
1
2
34
5
G G
6
7
8
9
10
17
16
15 14 13 12
11
Marine cable
Load
Transformer
Gas-turbo generator
Reactor
Water
Current Rotor Drive
train Generator Po wer
Transformer
Fluid Power
Mechanical
Power
Electric Power
Power Take-
off System
19
20
21
22
23
24
25
18
G
G
Water
Current
Rotor
Drive
train
Generator
Power
Transformer
G
G
Figure 12. Offshore microgrid in grid-connected operation mode.
Energies 2019, 12, 3384 15 of 17
Figure 13 shows the power output of each unit in the offshore microgrid under grid-connected
operation mode. It can be seen from Figure 13 that the tidal energy was still the priority power and
then the gas turbine. Figure 14 shows that the dragonfly algorithm converged to the optimal value
when the iteration reached forty-five times. In summary, both in island operation mode or
grid-connected operation mode, the optimal dispatching strategy proposed in this paper could make
the microgrid run in a more effective and environmentally friendly state.
Figure 13. Power output curve of units in grid-connected operation mode.
Figure 14. Iterative result diagram of dragonfly algorithms in grid-connected operation mode.
5. Conclusions
This paper not only proposed a probability prediction method of tidal current based on the
support vector quantile regression but also suggests an optimal dispatching strategy for offshore
microgrids. By taking the offshore microgrid in the Bohai sea as a case to verify the validity and
correctness of the proposed methodology, the following conclusions could be drawn:
It was found that, in all tests, the actual values always fell within the prediction interval
obtained by the DA-SVQR, and the results of this method were consistent with the actual curve
values. Not only could the way depict the volatility of tidal current correctly but also its results
appeared at the mode of the probability density curve with higher probability. The proposed
method was effective in quantifying the uncertainty, which would contribute to the increase of the
forecasting accuracy of the tidal current.
Moreover, this paper established an offshore microgrid optimization scheduling model
considering the tidal current speed prediction, which aimed at minimizing the overall operation cost
of the offshore microgrid. The proposed model may improve the operational technology of offshore
microgrids and enable the microgrids to achieve better economic and environmental outcomes.
Author Contributions: Conceptualization, A.Z. and Y.S.; methodology, A.Z.; software, Y.S.; validation, W.Y.,
and H.H.; writing—original draft preparation, A.Z., Y.S. and Y.F.; writing—review and editing, A.Z. and Y.S.;
supervision, W.Y.
Funding: This work was supported in part by the project of China Postdoctoral Science Foundation under
Grant 2014M562335 and the National Key R&D Project under Grant 2017YFE0112600.
0 5 10 15 20 25
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000 Tidal current
Emergence diesel
Gas turbine
Enger storage system
load
10 20 30 40 50 60 70 80 90 100
Iteration
220
230
240
250
260
270
280 DA
Energies 2019, 12, 3384 16 of 17
Conflicts of Interest: The authors declare no conflict of interest.
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