Overvoltage prediction method integrating the model-driven
and data-driven
techniques
The improved DT-based method proposed in Section 2 realizes reliable
prediction accuracy and strong adaptability to high-risk scenarios.
However, for data-driven methods, the lack of theoretical analysis and
the potential over-fitting phenomenon due to insufficient training
samples should be taken into account. Furthermore, the interpretability
of prediction results are crucial for decision-making in power system
operation. To further address the above issues,
this section proposes an
overvoltage analysis method integrating the model-driven and data-driven
techniques, and the integration framework of two methods is presented.
Model-driven overvoltage analysis method
The transient overvoltage mechanism and an analytical expression on
transient overvoltage peak value are studied, and key influencing
factors leading to overvoltage problems are extracted. The proposed
model-driven method has the potential for online application, which
provides the effective support for the integration with data-driven
methods.
(1) Transient overvoltage mechanism
The equivalent circuit of a typical wind-thermal-bundled HVDC
transmission system is shown in Fig. 3.
Fig.3 Typical two-terminal AC/DC hybrid system model
When the AC/DC hybrid system is operating normally, . The active and
reactive powers should be balanced, which can be expressed as:
Where the subscript N indicates the normal operating condition,QdrN is the reactive power consumption of the
converter station, QCrN ,Qac 1N ,QwN denote the reactive output of reactive power
compensation device, sending AC system, and wind farm, respectively. A
short-circuit fault which occurs in the receiving AC system may lead to
CF. For the sending AC system, the voltage is directly related to the
reactive power, and the transient overvoltage of converter bus can be
expressed as follows.
Where ∆Qr is the reactive surplus of converter
station, Scr is the short circuit capacity of
converter station. During the CF, the reactive power consumed by the
converter is dynamic. Therefore, the ∆Qr in can
be expressed as follows.
Combining with , the transient overvoltage level under different DC
faults can be obtained.
(2) Expression of transient overvoltage level
According to the dynamic characteristic of reactive power compensation
device, can be derived from .
Combining and , the transient overvoltage of converter bus can be
derived.
According to [28], the Qdr can be calculated
as follows.
Where Udr andUdr 0 are DC voltage and no-load
DC voltage of the rectifier bus, respectively;Idr is the DC current. It is obvious that theIdr is always greater than 0 during the CF.
According to , the Qdr is greater than 0, which
indicates that the rectifier and inverter only absorb reactive power.
Furthermore, the derivative of Qdr is shown as
follows.
When a CF occurs, the DC voltage of the inverter will directly plummets
to 0, and the DC current will rapidly increase. Then, the DC current
will reach I min (I min is
depending on VDCOL), and the rectifier constant current controller will
escalate the firing angle to reduce the DC current. Consequently, the DC
current will increase first and then decrease toI min, and the Ud will also
decrease to Udr min. Make
dQdr /dt =0, then
whenUdr =Ud minandIdr =Id rmin,
is satisfied, and the rectifier will absorb the minimum reactive power.
The Udr min can be calculated as
follows.
Substituting into , the Qdr can be expressed as:
Therefore, the transient overvoltage of converter bus can be calculated
as follows.
It can be seen from that the crucial factors which contribute to
overvoltage issues are the short-circuit capacity, the reactive output
of the AC system during normal operation, and the reactive power
consumption of the converter station during the fault. Therefore,
alternative transient overvoltage control measures can be summarized as
follows: reducing reactive-voltage sensitivity [29] and suppressing
reactive surplus source [30,31].
Framework of the integrated methodThe proposed theoretical analysis method for calculating the
overvoltage peak value of converter buses achieves the compatibility
of computation speed and accuracy for online application, providing
effective support for the integration with data-driven method.
Specifically, as shown in , the theoretical overvoltage values can be
obtained efficiently by utilizing the equivalent parameters of AC
system and the operation parameters of DC system.
To avoid the over-fitting phenomenon caused by improper feature
selection and enhance the interpretability of regression prediction
results, the theoretical analysis results are regarded as additional
input features to the original training samples for the data-driven
method. The detailed integration mode between model-driven and
data-driven overvoltage analysis methods is depicted in Fig. 4. The
objective of improved DT model is transformed from massive data
relationship mining to association pattern revealing between the
theoretical evaluation values and the true values. Therefore, for
typical fault scenarios, the key electrical quantities and
corresponding theoretical overvoltage values are selected as input
features, and the overvoltage peak values obtained by the time domain
simulation method are taken as the output. The DT model is trained by
the improved samples to achieve fast error correction.
Fig.4 Integrated prediction network structure
Specific procedure of overvoltage level predictionThe specific procedure of overvoltage peak value prediction is
depicted in Fig. 5, which is comprised of offline training and online
prediction.
Fig.5 Specific procedure of overvoltage level prediction
In the stage of offline training, typical fault scenarios are simulated
in PSASP software, taking into account factors such as load levels,
renewable energy penetration rates, and active power transmitted by the
DC link. From the simulation results, characteristic quantities related
to overvoltage levels are extracted to form the sample set. The input
features of the sample set consist of key electrical quantities and
corresponding overvoltage peak values calculated by theoretical analysis
method, while the output labels are the overvoltage peak values obtained
by time domain simulation method. The tree growing and pruning
procedures are then carried out based on the sample sets, and the
splitting rules of each node are determined according to the prediction
performance to obtain the optimal overvoltage level prediction model. In
the stage of online application, when a fault occurs in the actual power
grid, key electrical quantities are collected by WAMS, and the
corresponding theoretical overvoltage peak value is obtained through .
The combined input features are then fed into the well-trained improved
DT model, which accurately predicts the overvoltage level and guides the
secure and stable operation of power systems.
Case study
In this section, the Northwest China local region hybrid AC/DC power
grid depicted in Fig. 6 is adopted as the test system to verify the
accuracy and effectiveness of the proposed method. The test system is
constructed based on 750kV grid structure. Qingyu DC transmission
projects are adopted to achieve the transmission of renewable energy
electricity in Northwest China region, forming a typical hybrid AC/DC
power grid.
Fig.6 Northwest China local region hybrid AC/DC power
grid
Performance of improved DT model
(1) Evaluation indices
Performance evaluation indices, containing the mean absolute error
(MAE), mean absolute percentage error (MAPE), root-mean squared error
(RMSE) and coefficient of determination (R2), are
adopted in this paper to evaluate the overvoltage prediction effect of
different models, and calculation formulas are shown as:
where m is the number of testing samples,y ’i is the predicting value,yi is the actual value, and ỹ is the mean
value of yi .
(2) Improved DT model training
Taking the operating mode and fault type of power systems into account,
the simulation software PSASP is adopted to establish a dataset of
overvoltage under large disturbances. For the operating mode, the output
of traditional power stations and renewable energy stations are adjusted
under the load levels of 90%, 100% and 110%. In addition, the DC
transmission is adjusted in increments of 10% within the range of 60%
to 100%. As for the fault type, CF is set at the rectifier station,
including single and double pole faults. The number of times that CF
occurs is set as 1, 2 and 3, respectively. In addition, the duration of
CF ranges from 0.15s to 0.25s. The simulation time is 20s, and the rated
frequency of the test system is 50Hz. For each DT, the total number of
samples is 4480, where 60% of the samples is selected as the training
data set, and the remaining 40% are used for the testing dataset.
The key electrical characteristics are selected as the input features,
and the overvoltage peak value of Qingnan 750kV bus is collected as the
output. As a common approach for modelling and verifying model
parameters, the ‘10-fold cross-validation’ [32] is adopted to
determine the depth of DT model. With the increasing of DT depth, the
prediction effect of testing set are depicted in Fig. 7. Considering the
coordination between calculation efficiency and prediction accuracy, the
optimal DT depth is determined as 11.
Fig.7 Prediction effect under different DT depth
During the training process, as the number of samples increases, the
RMSE and R2 of training set and testing set are
depicted in Fig. 8 and 9, respectively. The consistency of prediction
accuracy between training set and testing set is demonstrated, verifying
the effectiveness and generalization capability of the integrated
method.
Fig.8 RMSE of training and testing set
Fig.9 R 2 of training and testing
set
(3) Prediction effect and visualization of improved DT model
Fig. 10 and 11 depict the MAPE index of traditional DT model and
improved DT model under different ranges of actual overvoltage peak
values. It can be concluded from the prediction effect of the
traditional integrated method that the MAPE for testing samples with
high actual peak values is considerably higher than those with low
actual peak values. Hence, modifying the DT algorithm is expected to
reduce the MAPE for cases with high actual peak values. After modifying
the common DT algorithm, the overall prediction effect in testing
samples is improved, especially in the cases with high actual peak
values.
In detail, to evaluate the efficacy of the improved DT algorithm, four
regions have been delineated based on overvoltage levels, namely region
1 with less than 1.34 p.u., region 2 ranging from 1.34 p.u. to 1.38
p.u., region 3 ranging from 1.38 p.u. to 1.42 p.u., and region 4 with
more than 1.42 p.u.. The corresponding MAE and MAPE indices for each of
these regions are presented in Tables 1 and 2. It can be seen that the
maximum improvement in both MAE and MAPE indices, amounting to 6.9% and
34.3%, respectively, occurs in region 4. These findings indicate that
the proposed approach has more significant enhancement in high-risk
scenarios.
Table 1 MAE (p.u.) of four overvoltage regions