A Low Voltage Prediction Based on LSTM-BP Combined Model for Distribution Station Areas

The timely management of low voltage issues in the distribution network relies heavily on accurate predictions of voltage in the station areas. Many current methods for voltage prediction require complex data collection involving power grid topology parameters and electricity information. However, these methods suffer from drawbacks such as the need for extensive data, limited real-time performance, and significant prediction errors. Hence, this study proposes an approach to voltage prediction utilizing a combined LSTM-BP model. Initially, an analysis of the mechanism of low voltage formation in the station areas reveals that the primary factor influencing node points voltage is the power consumption of users. Subsequently, the LSTM neural network is employed to forecast short-term load curves in the distribution station areas, while the self-learning capability of the BP neural network is utilized to establish the correlation between users’ power and their corresponding voltage levels. By effectively combining the above two neural network models, the historical load’s data can be used to accurately and quickly predict the future low voltage situation in the station areas. Finally, taking station areas as the research object and comparing the actual voltage data with the voltage data predicted in this paper, the results show that within the 1V error range, the prediction accuracy is 99.8%. In contrast to the conventional voltage prediction approach, the method put forward in this research paper enables instantaneous and precise anticipation of low voltage levels without relying on details such as station configuration, line characteristics, or user voltage information.


Introduction
The voltage conformity rate is a crucial measure of electricity consumption quality.China generally exhibits a voltage conformity rate below 95%, whereas advanced countries worldwide achieve rates exceeding 99% [1].Among them, the issue of reduced voltage in the Low-Voltage (LV) distribution station vicinity stands out as the primary contributor to China's LV conformity rate.The extended supply radius, suboptimal wire conditions, and dispersed loads associated with LV distribution networks make them susceptible to voltage reductions.Additionally, the current loss of an intelligent in-line voltage detection way further exacerbates the situation, often leading to delayed identification of LV concerns within the station areas and haphazard repair efforts [2].Consequently, for prompt addressing of station areas' voltage issues, it becomes imperative to employ a straightforward and accurate online prediction approach for such occurrences.
Due to the intricacy of power systems, it is very challenging to achieve exact online voltage forecasting for distribution stations.Artificial intelligence algorithms are now widely used in the field of power forecasting, thereby providing decisions for grid operation and dispatch.Compared to traditional methods, AI algorithms have significant advantages in solving such non-linear problems.There are currently many studies on LV prediction, both nationally and internationally.[3] analyzed the factors influencing LV in station areas, such as holidays, seasons, daily time periods, and climate, based on the electricity consumption habits of customers, and established a machine learning-based model for estimating customer voltage based on its relationship with customer voltage.However, the method requires a large amount of sample data and is not supported by the relevant mathematical mechanism for LV calculation, making its practicality hard to guarantee.[4] proposed the notion of the node points loads torque and the mapping between node points loads torque and node points voltage was set up by using BP neural network.However, the loads moment calculation of this method is complicated, and it is difficult to complete the loads moment calculation quickly and accurately in the case of user power changes, so it is difficult to achieve rapid prediction of LV online.
With the popularity of intelligent meters, the large amount of voltage and load data from customers in the station areas provides a realistic basis for data mining [5].In this article, by analyzing the landing mechanism of electrical voltage in distribution station areas, we find that there is a certain objective connection between station areas' user voltage and electricity loads, and propose an LV prediction method for distribution station areas under a combined LSTM-BP model.Firstly, the LSTM neural network is used to fully learn the characteristics of different intervals and levels of loads time series data to complete the construction of the load's prediction model.Secondly, the powerful data-fitting ability of BP NeuroNetwork is used to fit the mapping relations between the customer load power and the voltage per node point in the station areas.Thus, a combined nodal voltage prediction model is established with the electricity loads data as input to achieve voltage prediction in the distribution station areas.Last, the proposed model is verified to be able to predict LV in the distribution station areas, which facilitates early action on LV problems.

Voltage drop calculations
As the distribution lines in low-voltage distribution areas are usually 220 V overhead lines, in this article, voltage drop analysis and calculations will be carried out using overhead lines as a model.For LV distribution areas the 220 V on-air line can be explained by a Π-type equal circuit with centralized distribution dates [1], as shown in Figure 1.

Equal circuit of airlines
As the rated voltage of the 220 V overhead line is very low and its current level is ignorable, the equal loop can be far more simplistic than a string resistive loop.The electrical voltage land produced by the overhead line equal loop is in two components: a perpendicular component and a level component.As only the numerical value of the voltage-land is required for the voltage calculation in this paper, the level elements of the voltage land can be neglected, so the voltage land from the initial end voltage to the terminal voltage of the stand-off line is approximated as [1][4]: where  and  are the active and reactive power at the first end of the cable. is the voltage at the first coda of the line. and  are the line resistance and reactance. is the length of the cable. and  are for the line unit resistance and unit reactance. is the user power factor.

Analysis of key influences on voltage-drop
Formula (1) shows that factors of a section of the line voltage landing factors are line first power, line length, line unit impedance, and energy factors. Line head power and voltage.Under Formula (1), it can be seen that the line voltage landing is proportional to the line first power and inversely proportional to the first voltage. Line duration.Formula (1) shows that the line voltage landing and line length are proportional.
However, for the station area, the line length is a given amount and is not a time-dependent variable. Line unit resistance, energy factor.Line unit resistance is dependent on the type of cable, so for the established station areas, its unit resistance and reactance are for a fixed value, where the overhead line unit inductance X 0 is usually 0.35 Ω/km or so.As for 220 V LV distribution areas for residential use, the likeness of the residential load makes the power factor value of the area higher and less volatile, with a range of 0.8 to 0.98, resulting in a range of 0.75 to 0.2 for tan.Therefore, when the value of  is around 0.35, the multiplication of energy factor and unit reactance has an insignificant value, so the effect of unit reactance and energy factors on voltage drop is ignorant.

Feature selection
It is very hard to make an exact online real-time prognosis of low power in station areas, because, for the same station areas, there are several factors that affect its voltage landing, such as line head power and voltage, line duration.,line unit obstacle, and energy factors.Traditional numerical ways such as the backward/forward sweep method and the Newton-Raphson technique require a large amount of underlying data for the station areas, have a complex calculation process, and do not fit today's demands [6].And machine learning has been proposed to provide ideas to solve this aspect of the challenge.However, although the existing machine learning-based voltage estimation methods have solved the problems of computational difficulties and complexity in these areas, they still require part of the station areas data, such as the precise topology of the station areas, operating parameters, or the electricity usage habits of users under the influence of time and climate [3][4][7] [8], which not only makes this type of method have certain prerequisite difficulties in data acquisition but also reduces the advantage in prediction time advantage and cannot meet the real-time requirements of voltage prediction.In addition, as the user voltages are coupled with each other, the electricity loads of any user in the station areas will affect the voltage quality of other users, and at the same time there is a certain randomness in the users' electricity consumption characteristics, so direct user LV prediction will lead to an increase in the accumulation of errors.Since among the influencing factors for voltage reduction, line length, and line unit resistances are a fixed value for a given station area, the effect of the power factor is ignorable.At the same time, as the electrical loads are independent of each other, it is sufficient to just analyze the objective and rational relationship between customer voltage and customer power in the distribution desk areas.In this paper, the station areas' customer power is selected as the key characteristic quantity, and the under-voltage prediction model is established using the electricity loads data as input to achieve under-voltage prediction for the power supply station areas.

LSTM-BP Combined model
This paper introduces a method for predicting low-voltage using a combined LSTM-BP model.The method utilizes an LSTM NeuroNetwork to learn the characteristics of different time intervals and load levels in time series data.By constructing a load prediction model and leveraging the powerful data fitting capabilities of deep learning, a BP NeuroNetwork-based voltage estimation method is proposed.This method establishes a mapping relationship between loads and voltage, allowing for the creation of a combined model for predicting node points' voltage.The user loads data to serve as input to this model, enabling voltage prediction.The process of building the LSTM-BP combined model is illustrated in Figure 2. , by which the previous information is judged to have an effect on the cell memory at this time [10], as shown in Figure 3. (2) The input gate is utilized to compute the information that is stored in the state unit, comprising two components of information.One part corresponds to the amount of current input information that should be saved in the unit state.The other part, denoted as  , stands for new messages created by the actual input that needs to be included in the unit status.These two components combine to form a fresh memory state.The equations are expressed as follows: As a result, the cell state at the current moment is the product of the forgot gate input and the previous moment state plus the product of the two parts of the input gate.The equation is expressed as:   *   *  .(4) The state of the output gate is used to calculate the degree to which the information is output at the current moment, while the output gate is used to calculate the output value of the LSTM unit at time t.The equation is expressed as:    ℎ ,   ℎ  * ℎ  . (5)

Model parameters configuration
To build an LSTM network prediction model to forecast the electricity loads of distribution station areas, some parameters of the model need to be set and debugged, such as the number of neurons, the dimension of input and output layers, the number of layers of hidden layers, and the time step, etc.Since loads prediction belongs to serial prediction, the input feature quantity is the historical loads of station users, and the output feature quantity is the predicted loads of station users, and the input and output dimensions can be determined as one-dimensional.After repeated experiments, the prediction model is set as an LSTM network with three hidden layers, the number of neurons in the first hidden layer network is 288, the number of neurons in the second hidden layer is 100, and the number of neurons in the third hidden layer is 50.In this paper, the Adam optimizer was chosen as the optimization method for the LSTM network market.The Adam optimizer has the merits of fast aggregation and simple realization The Adam optimizer has the merits of fast aggregation, simple realization, and high calculation efficiency, and is commonly used for NeuroNetwork models.In addition, the gradient threshold of the model is set to 1, the initial learning rate is specified to be 0.005, while the training number is set to 250, and after 125 rounds of practice, the learning rate is reduced by multiplying it by a factor of 0.2.

Select the indicator function
The loss function is a reflection of how well the model fits the data, i.e., the distinction between the model's actual value and predicted value; the better the model fits, the smaller the loss function is.In this paper, the Mean Squared Error (MSE) is selected as the loss function of the model, which is calculated as follows [11].Root mean square error (R MSE ): Coefficient of determination (R-square, R 2 ); where  is the predicted value of user loads in the station areas,  is the true value of user loads in the station areas,  is the mean value of the true value of user loads in the district, and n is the number of samples.The root mean square error reflects the deviation of the predicted value from the true value, and represents the general reliability of the forecast; the smaller the value is, the smaller the forecast variance is, i.e., the more reliable the overall forecast.The coefficient of determination takes a range of [0,1], and a larger value indicates a better fit of the model.

BP Neural Networks
BP neural networks can be used in a framework for data drive to learn the intrinsic logic and non-linear mathematical models between data using abstraction while performing data fitting to establish mapping relationships between data.As shown in Figure 4, the BP neural network framework consists of three components: the input layer, the implicit layer, and the output layer.In the figure , 𝑋1

Input layer
Hidden layers Output layer .. .

Determining feature quantities and input and output dimensions
Since a logical mapping relationship must exist among the input and output quantities, it is clear from the analysis in the first section of this paper that there is a certain amount of realistic logical linkage between the user power and the user voltage in the distribution station areas, so that the user energy in the distribution network areas can be used as input characteristic quantities and the user voltage as output characteristic quantities, thus enabling LV prediction in the distribution network areas.In addition, this paper studies the problem of fast voltage prediction in station areas.Since the topology of station areas does not generally change once it is determined, its system feature quantity dimension does not need to change either.The number of user power node points in the station areas in the sample data is taken as the input dimension and the number of all node points in the station areas is taken as the output dimension, and based on actual measurements and experience, a demand NeuroNetwork framework can be built to meet the demand.

Selection of activation function and training algorithm
Based on the analysis of experience, a feed-forward neural network with sufficient learning potential to represent sufficiently complex non-linear mapping relations is chosen as the network framework.The hidden layer activation function is a Rectified Linear Unit (ReLU) with strong non-linear representation and robustness [12][13].
In the case of the output layer, the Sigmoid function is the activation function, which is defined by the following equation: The derivative of this equation for X can be expressed by itself: From the above equation can be seen, when the input value of the sigmoid function tends to positive or negative infinity, the gradient is going to converge to zero, and then the definition of its equation shows that the value range of the function is (0,1), and the information handling purpose and results of this article are consistent, so the sigmoid function is chosen as the function of the activation of the output layers.
Furthermore, while depth learning is able to estimate arbitrary sequential functions theoretically, to avoid effective disadvantages such as its slow rate of convergence, the tendency to slip into local optima and low stability, this paper chooses Levenberg-Marquardt (L-M) which is a method of estimation for least-squares estimation of regression data in nonlinear regression as its trainer algorithm [13].
If W(k) is the kth iteration of the vector of weights and thresholds, then the result of the +1st iteration is: 1     .(10) And in the L-M algorithm, the incremental vector ∆of weights and thresholds is calculated by the following rule: is the Jacobian matrix,   is the error vector,  is the adaptive learning element and  is the unit matrix.
From the above analysis, it is evident that when μ = 0, the method is a Gauss-Newton method; the higher the value of μ is, the nearer the method is to a gradient method.This makes the L-M method have the benefits of both the Newton and Gradient algorithms, so the choice of this algorithm will clearly increase the computational rate and overall property.

Voltage prediction process based on combined LSTM-BP model
In this paper, we propose an LSTM-BP based prediction model for LV combinations in distribution stations, the implementation process of which is shown in Figure 5 and consists of the following steps: Step 1: We obtain historical voltage and power data from the station areas and pre-process the data to divide it into training samples and test samples.
Step 2: We input the historical loads' data from the training sample into the LSTM model for training, build a loads prediction model based on LSTM, and input the test sample for model validation.The training samples are also input to the BP model for training to establish a non-linear mapping relationship between node points' voltage and user power and input to the test samples for validation analysis.
Step 3: The LSTM model BP model is effectively combined to establish a combined LSTM-BP based LV prediction model for the distribution station areas.
Step 4: On-line voltage prediction for the distribution station areas.The real-time load data is input into the LSTM-BP combined prediction model to get the voltage prediction results and compare them with the actual voltage data to verify the model's accuracy and feasibility.

Data Acquisition
In this paper, LV power distribution stations are used as the studied object, and the line data and path architecture are displayed in Figure 6.A model of simulation is established using SIMULINK and a sensible range of stochastic variables of each is established to make it consistent with the engineering reality.The model was run to obtain voltage and power data for the node points in this station area for 24 hours per day and one quarter, i.e., 2160 sets of power and voltage data, and the first 90% of them were used as a trainer and the remaining 10% as proof of comparison.

Forecast results and analysis
A node point in the station areas is randomly selected, and the first 90% of the power data of this node point is used as the training sample.The LSTM loads prediction network model built in this paper is used to predict loads of the station areas, and the predicted load's data is obtained and compared with the remaining 10% of theload'ss data.Its load prediction results are shown in Figure 7.
As can be seen from Figure 7, the curve fluctuation trend between the predicted and actual values of this node points loads is consistent and the degree of agreement is high.Based on simulation validation results, the root mean square error of the prediction results of this method is approximately 0.1, which is a high prediction accuracy, indicating that the prediction effect of this LSTM network model on the node points loads of the distribution station areas is very considerable, which provides a guarantee for achieving reliable prediction of the station areas voltage.
The load prediction data of the node points in the station areas in the above section are fed into the BP network model built in the article to obtain the voltage prediction results for the whole station area and compare them with the actual voltage data.At the same time, to better analyze the voltage situation of the node points, the voltage data values are scalarized in this paper.With branch 2 as an example, the voltage prediction results are shown in Figure 8.As can be seen from the figure, the estimated and actual numeric of the voltage at each node points nearly coincide, indicating that the BP network has a good fitting effect on the loads and voltage of the node points in the distribution station areas.Meanwhile, based on the simulation validation results, the voltage prediction accuracy of the way is up to 100% within a voltage error of 1 V, which meets the actual engineering requirements.Meanwhile, according to China's technical standards, the allowable deviation of 220 V single-phase supply voltage is limited to +7% and -10%.Therefore, when the user voltage is less than 90% of the rated voltage, then it is LV [1].According to the simulation results, on branch 2, the voltage of the users before node point 5 is in the normal range, while the users located at node point 5 start to have a few test samples with the LV phenomenon.After node point 5 the users are always in the under-voltage range, the voltage of node points 8 at the end of the line drops to 82% of the normal voltage, only 180 V, which seriously affects the normal use of electricity by users.The voltage estimation method was also compared with other statistics in the literature on the number of features to be counted, and the sophistication of the computational and comparative errors of the machine learning-based voltage estimation method.The results of which are shown in Through contrast, it can be discovered that the voltage online forecast measure under deep learning introduced in this paper, without a large number of operating parameters, can get the voltage value for the whole topological structure of the station areas under the power data of the user node points alone, and the calculation process is easy and the results of the evaluation are exact.Meanwhile, the values and range of LV users in the station areas can be effectively monitored, and the degree of LV users can be quickly responded to in real time, with its very practical features.

Conclusion
This paper proposes an LV forecasting way under a combined LSTM-BP model.The LSTM neural network model is utilized to predict the nodal loads of the distribution station areas, and then the BP neural network is utilized to make a customer voltage prediction model using the predicted load's data as input to achieve voltage prediction for the transmission station areas.Practical examples show that the method proposed in this paper can predict the voltage of all node points in distribution station areas without requiring information on the station areas topology, line parameters, and customer voltage, achieve universal access online prediction of the voltage in transmission station areas, and obtain the number of LV customers and LV range of the station areas in real time.This provides an effective way to monitor and manage LV in LV distribution areas.

Figure 2 .
Figure 2.The establishment process of the LSTM-BP model 3.2.Constructing LSTM loads prediction models 3.2.1.LSTM neural network LSTM (Long-Short Term Memory) the NeuroNetwork was first presented by Hochreiter et al. and enhanced by Graves on the basis of RNN (Recurrent neural network) to solve the gradient extinction problem that tends to occur in RNN[9].LSTM cells are made up of input gates, forget gates, output gates, and cell states, where the forget gate indicates that the input has the hidden state ℎ of the previous sequence with the present sequence of data  .The output  of the forget gate is obtained through the sigmoid activation function, i.e., by which the previous information is judged to have an effect on the cell memory at this time[10], as shown in Figure3.

Figure 3 .
Figure 3.LSTM unit structure diagram W f and b f are the coefficients and bias coefficients of the linear relationship and X is the sigmoid function of activation.The equation is expressed as:    ℎ ,   .(2)The input gate is utilized to compute the information that is stored in the state unit, comprising two components of information.One part corresponds to the amount of current input information that should be saved in the unit state.The other part, denoted as  , stands for new messages created by the actual input that needs to be included in the unit status.These two components combine to form a fresh memory state.The equations are expressed as follows:   ℎ ,    ℎ  ℎ ,   .(3)

Figure 5 .
Figure 5. Voltage prediction process based on the LSTM-BP combination model

Figure 6 .Figure 7 .
Figure 6.The topological structure of an LV distribution areas

Table 1 .
Comparison results of different voltage prediction methods