Study on the accuracy and stability of distributed photovoltaic customer load forecasting based on hybrid modeling

With the social and economic development as well as people’s growing demand for global energy, realizing sustainable development has become a common goal for the development of power systems in all countries around the world, and the intelligentization of power grids has also become an inevitable trend in the development of power grid technology [1-3]. The concept of smart grid was first put forward by the Obama government energy related person in charge, and then promoted and applied all over the world. Different countries have different national characteristics, the smart grid in Europe and the United States focuses on intelligence, mainly distributed power storage, access to new energy sources, and the application of smart meters, etc., while the smart grid in China focuses on meeting the demand of power loads, ensuring the safety, reliability and energy saving of power supply, and then accessing new energy sources and ensuring the quality of power [4-6].

Driven by the goal of “dual-carbon”, the construction of a new power system with new energy as the main body is a major deployment made by China to achieve sustainable development, and it has an important guiding significance for the future development of China’s energy and power transition, and the development of new energy consumption strategies is closely related to the user-side of the power consumption behavior [7-9]. In addition, with the deepening of China’s power market reform, various market players such as load aggregators, virtual power plants, and power sales companies have sprung up. Accurately grasping the demand for electricity from customers is the basis for such power companies to carry out the business of purchasing and selling electricity, and the key to dealing with deviation assessment and improving economic returns, which also directly motivates the active participation of these market players in the interaction of power market transactions [10-11]. Therefore, accurate customer load forecasting is not only extremely important for fine demand side management in the context of the new power system, assisting peak shaving and valley filling, and helping new energy consumption, but also guides power companies such as power sales companies and industrial large users to participate in the power market to declare the amount of electricity and improve economic returns [12-13]. However, with the increasing proportion of new energy access, the nonlinearity and volatility of the power generation side have increased significantly, as well as external objective factors such as climatic conditions, relevant policies, and internal factors such as users’ individualized power consumption habits, which make the customer power load highly variable, nonlinear, and uncertain, and present a stronger volatility and randomness than the system-level loads, which results in the customer load forecasting facing a huge challenges [14-16].

As an important part of the smart grid, load forecasting is of great reference significance for the smart grid to provide high quality service for users and improve the quality of power supply. There exists a large amount of time series data in the smart grid, especially the time series data of user load represented by smart meter data, and fully exploiting the potential user information in the user’s load time series data can be used as an important basis for load forecasting [17-18]. According to the different time of predicted load, load prediction can be categorized into long-term, medium-term, short-term load prediction and ultrashort-term load prediction, in which ultrashort-term load prediction is an important basis for the smart grid to carry out preventive control and emergency treatment under the state of security monitoring, as well as real-time scheduling of the power grid and resource allocation, etc. [19-20].

In this paper, a simplified model of distributed photovoltaic power is established based on the structure of a distributed photovoltaic power system. Then on the basis of the deep learning prediction model, a hybrid neural network model based on CNN-LSTM is proposed to realize the prediction method of load data in the new type of distribution network, which in turn predicts the load electricity consumption and PV power curve. For the voltage problem after PV grid-connection in the new distribution network, the influence of distributed PV grid-connection in mixed mode on the distribution network voltage and its principle of voltage change, the method of voltage control in the distribution network, and the stability of the voltage are theoretically analyzed by adopting the continuous tidal current method and the time series prediction model. Finally, the analysis of the impact of distributed PV grid-connection on grid voltage is verified by comparing the changes of voltage distribution at each node of the distribution grid under different distributed PV grid-connection scenarios through the arithmetic example.

2

Hybrid modeling-based distributed photovoltaic power generation system construction

2.1

Modeling of Distributed Photovoltaic Power Generation System

2.1.1

Basic Principles of Photovoltaic Cells

The basic form of power generation by photovoltaics is the direct conversion of solar energy into electrical energy by utilizing the photoelectric effect of certain substances. The reason why photovoltaic cells can convert solar energy into electrical energy is due to the formation of floating currents by a small number of nonequilibrium carriers in the photovoltaic cell under the action of the electric field in the PN section.

Distributed photovoltaic [21] power generation is one of the more typical DCs, which is mainly formed by the series-parallel connection of PV modules. Its current-voltage characteristics are as follows: (1) $V_{p v} = \frac{N_{s} n k T_{j}}{q} \ln (\frac{\frac{N_{p} I_{s c} I_{r}}{100} - I_{p v}}{N_{p} I_{0}} + 1)$

Where, T_j is the operating temperature of the PV panel, I_r is the light intensity, N_s and N_p are the number of units of series-parallel PV panels, respectively, n is the idealization factor, k_tc is Boltzman’s constant, q is the charge of the electrons, I_sc is the short-circuit current, and I₀ is the saturation current.

2.1.2

Composition and Classification of Distributed Photovoltaic Power Generation Systems

Photovoltaic power generation systems are generally composed of photovoltaic arrays, storage batteries, power control systems, inverters and other equipment. Which through the smaller capacity of the single series-parallel configuration of a single PV module, if the required capacity needs to be further increased, the PV module can then through the series-parallel configuration of larger capacity PV arrays.

Distributed PV power generation systems can be categorized into three forms from the perspective of power supply mode: independent power supply, grid-connected, and hybrid. Next, this paper selects the hybrid model of distributed PV to complete this experiment. The structure of the hybrid PV power generation system is shown in Fig. 1. The hybrid PV power generation system improves the reliability of PV power generation by adding a standby generator set.

2.2

Modeling of Distributed Photovoltaic Power

Distributed photovoltaic grid-connected compared to centralized access to large-scale photovoltaic power station has its own very significant advantages, the most prominent advantage is that the distributed photovoltaic power can be installed as a decorative and above the building, both beautiful and save the area. Secondly, the capacity of distributed PV power supply is relatively small, the impact of start and stop on users and systems is relatively small, and the normal operation of the power grid to alleviate the load pressure and improve power quality has a certain regulatory role. Therefore, distributed PV grid-connected power has been rapidly developed at home and abroad. Distributed photovoltaic grid-connected power generation systems can be divided into single-stage grid-connected and two-stage grid-connected forms from the perspective of energy conversion. The two-stage grid-connected power generation system adds a DC/DC converter module compared with the single-stage grid-connected system, which makes the DC side and AC side of the grid-connected system realize independent control, with stronger reliability and adaptability, and more widely used.

2.2.1

DC/DC converter control strategy

It can be seen from the current-voltage characteristics of the PV plant that the output voltage of the PV plant is affected by factors such as light. The control strategy for maximum power tracking control is an important module in PV grid integration. The most widely used methods are conductivity increment method, and the basic principles are as follows:

Since the PV array P–U curve is a first-order continuously derivable curve with a maximum value, the following method can be used to find its extreme value: (2) $d P = U d I + I d U$ (3) $d P / d U = I + U d I / d U d P = I d U + U d I$

Let dP/dU = 0, can be obtained: (4) $d I / d U = - I / U$

The above equation is the condition that should be satisfied when the PV array emits maximum power. The method determines the direction of change of the reference voltage based on the amount of change in the output current-voltage and the magnitude of the instantaneous current-voltage, which is analyzed in detail below: 1)

When the working point of the photovoltaic cell is on the left side of the maximum power point, P–U the curve becomes monotonically increasing trend, dP/dU > 0, it can be calculated by the push to calculate the formula (2)~(4), at this time dI/dU > –I/U, then the reference value of the output voltage should be increased.

2)

Similarly, when the operating point of the photovoltaic cell is to the right of the maximum power point, dP/dU < 0, dI/dU < –I/U, then the reference value of the output voltage should be reduced.

3)

When the operating point of the photovoltaic cell is on or near the maximum power point, dP/dU = 0, it means that there is no need to change the output reference voltage at this point, and the photovoltaic array is operating at the maximum power point.

2.2.2

Control strategy for DC/AC inverter

Generally, the control strategy of DC/AC inverters adopts double-loop control, which mainly includes voltage outer-loop control and current inner-loop control. However, sometimes only voltage outer-loop control is used. The voltage controller mainly regulates and controls the voltage in the outer loop, and the tracking control is used to compare the desired output signals of the voltage and current instantaneous values with the actual signals in the inner loop, so that the desired signals are used as the reference standard, and the actual signals are used as the feedback to track the desired signal changes. The current inner loop control mainly consists of the current controller module, SPWM modulation module, LC filter module, and current feedback module.

In order to ensure the normal operation of DC/AC, the following four requirements must be met as much as possible: 1)

The inverter should have a high dynamic response speed to ensure that the inverter current’s have stability and reliability;

2)

Requirements for the inverter must ensure that the current connected to the grid and the system voltage of the same frequency and phase, the voltage output is a standard sinusoidal quantity;

3)

The DC side of the inverter is required to have a wide range of acceptance for the size of the input voltage to ensure that the inverter can still work normally and stably when the voltage on the AC side or the load changes drastically resulting in drastic voltage changes;

4)

The inverter should try to meet the practical requirements of small size and low cost.

The DC/AC inverters of PV power plants are usually connected to the system by voltage source converters, and their controllers are mainly controlled by pulse width modulation control (PWM).

The grid-side DC/AC voltage source converter control strategy is shown in Fig. 2, where the proportional and integral controllers are regulated and controlled in accordance with the Wacha signal.

Based on the schematic of the control strategy, the second-order differential equation at the grid-side DC/AC voltage source converter can be written: (5) ${\dot{X}}_{p} = K_{i P} (P_{p s r e f} - P_{p s})$ (6) ${\dot{X}}_{Q} = K_{i Q} (Q_{p s r e f} - Q_{p s})$

2.2.3

Simplified mathematical model of distributed PV grid connection

The differential equations satisfied by the capacitor current and capacitor voltage between the DC/DC converter [22] and the DC/AC converter are as follows: (7) ${\dot{V}}_{d c} = \frac{1}{C_{d c}} (I_{d c 1} + I_{d c 2})$

According to the DC/AC converter control strategy, an expression for the current injected into the power system by the PV plant can be obtained: (8) $I_{p s q} = K_{p P} (P_{p s r e f} - P_{p s}) + X_{P}$ (9) $I_{p s d} = K_{p Q} (Q_{p s r e f} - Q_{p s}) + X_{Q}$

According to the control strategy of the DC/DC converter, an expression for the PV power side current is obtained: (10) $I_{p v} = K_{p P 1} (P_{p v r e f} - P_{p v}) + X_{P 1}$

Orienting the PV plant bus voltage and performing the dq transformation, an expression for the active reactive power injected into the power system by the PV plant can be obtained: (11) $P_{p s} = V_{p s q} I_{p s q}$ (12) $Q_{p s} = V_{p s q} I_{p s d}$

Neglecting the active losses of the PV plant incorporated into the system, an expression for the current at the capacitor can be obtained: (13) $I_{d c 1} = \frac{V_{p v} I_{p v}}{V_{d c}}$ (14) $I_{d c 2} = \frac{P_{p s}}{V_{d c}}$

The active power output of the PV cell is as follows: (15) $P_{p v} = V_{p v} I_{p v}$

2.3

Hybrid CNN-LSTM based prediction models

2.3.1

Time-Series Prediction Model

The problem of load forecasting in power systems based on artificial intelligence methods is to select the input information from the given information, and after obtaining the prediction model through data-driven training, the mapping relationship between the input data and the output predicted values can be obtained, and the time-series data prediction model can be represented by the following equation: (16) $Y_{t + 1 : t + n}^{'} = h (X_{t - k z})$

Where, X_t−k:t is the input quantity, k is the input time length, generally for a certain time length of univariate or multivariate; $Y_{t + 1 z + n}^{'}$ is the prediction quantity, n is the prediction time length, which can be divided into two kinds of value prediction and probability prediction; h(·) is the prediction model constructed based on the artificial intelligence method.

Meanwhile, when training the AI prediction model h(·), the loss function L[h(X_t)(x),Y_t+1:t+n] of the model is usually specified, which is used to measure the error between the predicted value h(X_t·k:t) and the true value Y_t+1:t+n, and optimization algorithms are implemented to minimize the loss function to find the appropriate network parameters, and common optimization algorithms, such as gradient descent, Adam, SGD, etc., are used to obtain the prediction model.

2.3.2

Overall model structure

In the field of power load forecasting, there have been more studies verifying the superiority of LSTM model for data temporality and nonlinear learning, and experiments have proved that CNN structure can significantly improve the nonlinear feature extraction effect of load data. Therefore, in this section, we choose to realize the prediction of load data in a new type of distribution network through the hybrid neural network model of CNN-LSTM [23-24], and we will briefly analyze the network structure of LSTM, CNN, and the hybrid neural network model of CNN-LSTM, and at the same time, we will verify the effectiveness of this prediction model through the arithmetic examples.

1)

LSTM neural network structure

LSTM neural network belongs to the development of RNN a obtained variant network structure. Due to the chain structure of RNN, it has certain advantages in learning time series data, and is mostly applied in the field of time series prediction. However, RNN will have the problem of gradient disappearance and gradient explosion when dealing with longer sequences, and LSTM network proposes that cell state and gating unit can further screen the transmission information, which in turn solves the weakness of RNN for the mastery of long time sequences.

The basic structure of LSTM includes forgetting gate, input gate and output gate. The inputs of LSTM cell include: t moment input variable x_t,t–1 moment forgetting gate reads hidden layer state h_t−1,t–1 moment cell state C_t+1. The principle and steps are as follows:

Step 1: The forgetting gate reads the hidden layer state h_t−1 and the input variable x_t and outputs a value between 0-1 to decide how much information needs to be forgotten in the cell state C_t−1, the closer to 1 means the more data and information is kept and the closer to 0 means the more data and information is discarded, as shown below: (17) $F_{t} = σ (W_{F} [h_{t - 1}, x_{t}] + b_{F})$ where F_t is the oblivious gate state at moment t, σ is the sigmoid activation function, W_F is the oblivious gate weight matrix, b_F is the corresponding bias term, and [h_t−1,x_t] denotes the merging of h_t−1,x_t into a new vector.

Step 2: The input gate reads the input variables x_t at moment t and generates the temporary state $C_{i}^{'}$ by the tanh function, and finally updates the output new cell state C_i as follows: (18) $\begin{array}{l} I_{t} = σ (W_{t} [h_{t - 1}, x_{t}] + b_{t}) \\ C_{t}^{'} = \tanh (W_{C} [h_{t - 1}, x_{t}] + b_{C}) \\ C_{t} = F_{t} ⊙ C_{t - 1} + I_{t} ⊙ C_{t}^{'} \end{array}$ where W_C,W_I is the input gate weight matrix, b_C,b_I is the corresponding bias term, $⊙$ is the matrix dot product, and tanh is the double by tangent activation function.

Step 3: The output gate reads the hidden layer state h_t−1 and the input variable x_t, which can decide the priority output of the neuron state that contains important information, and computes the output value of the unit by the product of the tanh layer and the sigmoid layer h_t, and proceeds to complete the computation of the next LSTM layer as follows: (19) $O_{t} = σ (W_{o} [h_{t - 1}, x_{t}] + b_{o})$ (20) $h_{t} = O_{t} ⊙ \tanh (C_{t})$ where W_o is the output gate weight matrix and bo is the bias term.

2)

CNN network structure

CNN is one of the main network structures belonging to deep learning, and its structural composition includes input layer, convolutional layer, pooling layer, fully connected layer and output layer, and the complete CNN network structure is obtained through the connection of each layer, in which, it is the convolutional layer and pooling layer that can make the network have better performance in extracting data features, the convolutional layer extracts the nonlinear features of the loaded data through the filter, and the pooling layer can filter more important features through the under The pooling layer filters more important features through downsampling compression, which can improve the computational speed and prevent overfitting. In this section, more effective feature extraction is mainly realized by CNN.

3)

CNN-LSTM hybrid neural network model

The structure of the CNN-LSTM hybrid neural network model used in this section is shown in Fig. 3, which is mainly divided into two parts, CNN and LSTM. Firstly, the input time-series dataset is passed into the CNN to extract the data features through multi-layer convolution and pooling, and then flattened to obtain a one-dimensional feature vector, and then fed into the LSTM network connecting multi-layers to improve the prediction accuracy, and then finally linked to the fully-connected layer to realize the load prediction, and ultimately the output of predicted data.

For the short-term user load and distributed photovoltaic output prediction problem in this paper, combined with the structural characteristics of the distribution network, the input dataset of the distribution network has electric power data and environmental meteorological data, including the measurement time, active power, current, voltage, ambient temperature, ambient humidity, ambient wind speed and the total horizontal radiation value, taking into account to ensure the completeness of the low-voltage user load data and to maintain the uniformity of the data, the above input variables Considering to ensure the integrity of the low voltage customer load data and to maintain data uniformity, the above input variables are selected as hourly data density.

In the CNN-LSTM hybrid prediction model used in this paper, the CNN network part of the structure consists of two 1D convolutional layers, a pooling layer and a fully connected layer, where the size of the convolutional kernel is 3*3, the number of parallel filters is 64, and the activation function is ReLu, and the input dataset is feature-extracted by the CNN network, while a pooling layer with a maximum pooling window of 2 is used for the extraction of key features. In addition, the LSTM network part of the structure consists of 2 LSTM layers, a fully connected layer and an output layer, where the first LSTM layer has 64 neurons and an activation function of ReLu, the second LSTM layer has 128 neurons and an activation function of ReLu, and the fully connected layer has 64 neurons and an activation function of ReLu. The length of the model input variable is 72, the length of the output variable is 1, the number of iterations is set to 200, the number of batch processing is 64, and the optimization algorithm is adam, so as to achieve a single-step prediction of the input data, and in turn, with a moving step of 1, the prediction value is merged into the input data iteratively to get the final prediction result of a single day at 24 points.

2.4

Voltage Stability Analysis Methods

The analysis method of system static voltage stability is basically based on the continuous tidal current equation of the system to gradually increase the generator load in order to measure and estimate the degree of change of voltage stability of the current system operation state, and usually take the state of the system generator operation of the power network transmission limit power as the state of the limit of voltage stability of the nonlinear static system. The main methods used to analyze the stability of a nonlinear static system include continuous tidal current method, singular value decomposition method, sensitivity method, nonlinear planning method, collapse point method, and others.

2.4.1

Continuous flow method

The continuous tidal current method can also be called the extension method of voltage stabilization, and its basic idea is the method of continuously predicting and correcting the operating point of the system at the initial operating point of the system according to the PV curves of the system operation until the limit of voltage stabilization is obtained. The method introduces the continuous parameter in the practical application, which makes the problem of non-convergence of Jacobi matrix at the voltage divergence point solved, and makes the calculation of voltage stabilization point more accurate and practical.

The continuous tidal current method is one of the core methods of voltage stability analysis, and its advantage is that the model is relatively simple and has strong universality. Because the critical point of voltage stabilization is gradually approaching from the initial operating point of the system, the selection of the calculation step size is particularly important. If the step size is too small, the number of iterations will increase, slowing down the computational speed of the whole algorithm; if the step size is too large, it will lead to a decrease in the computational accuracy and the results will not converge. Therefore, the control of the step size has become an important research direction of voltage stabilization, how to determine the calculation step size, so that the algorithm can maximize the speed and accuracy requirements, that is, the ultimate goal of this research direction.

2.4.2

Voltage stability

In the process of trend calculation Jacobi matrix is an important characterizer of voltage stability, when it is close to singular, the voltage stability of its corresponding system is also close to the critical point, using this property of Jacobi matrix can be discerned voltage stability, i.e., singular value decomposition method. The core of this method is to take the minimum singular value of Jacobi matrix as the voltage stability index of the whole system to reflect the voltage stability of the whole system.

Let the current equation of the n-node system be: (21) ${\begin{array}{l} P (θ, U) = 0 \\ Q (θ, U) = 0 \end{array}$

θ is the phase of the node voltage and U is the node voltage magnitude. Then the current equation in polar coordinate representation of the system is: (22) $[\begin{matrix} Δ P \\ Δ Q \end{matrix}] = J [\begin{matrix} Δ θ \\ Δ U \end{matrix}] = [\begin{matrix} J_{P θ} & J_{P U} \\ J_{Q θ} & J_{Q U} \end{matrix}] [\begin{matrix} Δ θ \\ Δ U \end{matrix}]$

The singular value decomposition of the Jacobi matrix yields: (23) $J = U Σ V^{T} = \sum_{i = 1}^{m} u_{i} δ_{i} ν_{i}^{T}$

In the above equation, both U and V are mst order unit orthogonal square matrices, the left and right singular vectors u_i and v_i are the column vectors in the matrices U and V, respectively, Σ is the diagonal array, and δ_i is the corresponding singular value. When the minimizer of the singular values is greater than 0, there is the following relation: (24) $[\begin{matrix} Δ θ \\ Δ U \end{matrix}] = U Σ^{- 1} V^{T} [\begin{matrix} Δ P \\ Δ Q \end{matrix}] = \sum_{i = 1}^{m} δ_{i}^{- 1} u_{i}^{T} ν_{i} [\begin{matrix} Δ P \\ Δ Q \end{matrix}]$

It can be seen that the Jacobi matrix singularity of the current operation of the system can reflect the distance from that point of operation to the voltage stability limit, and in general the smallest singularity value reflects the best. When the minimum singular value is close to 0, a small perturbation can be a huge state change of the whole system, thus voltage stability can be measured by the singular value.

3

User load forecasting accuracy and stability results and analysis

3.1

Forecasting of consumer loads

3.1.1

Load power time series

The CNN-LSTM prediction model is applied to predict the load change of the coming day based on the 7-day user electricity load statistics. Based on the electricity consumption status of different users in different time periods, the frequency of appliance use of each user in each time period is statistically analyzed, thus determining the peaking potential of each user as a prerequisite for the development of active load control strategies. Using the load forecasting method, the SPSS software, first of all, a user community in city A, building 23, 7 days of load data to do time-series analysis. 7 days of load power time-series graph results are shown in Figure 4. It can be seen that the data is a seasonal smooth series, that is, the seasonal difference D takes the value of 1. The autocorrelation function and partial autocorrelation function of the load series show that the function value after the 1st order tends to be 0 obviously, and is trailing, so q can be taken as 1. The partial autocorrelation shows that the function value of the 1st order is significantly less than 0 and is trailing, so p is taken as 1. It can be seen that both the autocorrelation function and the partial autocorrelation function exhibit a trailing nature. Therefore, the CNN-LSTM cell load model can be built.

3.1.2

Analysis of residential electricity load forecasts

According to the proposed model, seven consecutive days of customer loads are used as samples to predict the load sequence on the 8th day. The comparison of actual load, fitted curve, and predicted load is depicted in Fig. 5. The graph depicts the actual load sequence, the fitted sequence of the model, and the predicted load on day 8. From the graphical proximity, it can initially be inferred that the model is more reasonable.

The residual sequence graphs are autocorrelation and partial autocorrelation sequence graphs about the residuals, as can be seen, both graphs do not have significant trend characteristics (trailing or truncated tail), so it can be judged that the model is appropriate. The CNN-LSTM model is used to predict the user load, and the one-week load data of a single distribution transformer in a neighborhood is input, and the CNN-LSTM model parameters can be obtained through the calculation of SPSS software. The CNN-LSTM model parameters are shown in Table 1. The results indicate that the t-distribution test of the CNN-LSTM model parameters has a significance level of less than 0.001, which indicates that the resulting parameters are appropriate. Thus, the expression for the user load sequence fitting model is: (25) $Δ_{24} y_{t} = - 5.182 + 0.54 Δ_{24} y_{t - 1} + ε_{t} + 0.885 Δ_{24} ε_{t - 1}$

Table 1.

CNN-LSTM model parameter

CNN-LSTM	Parameter	Estimate	SE	t	Sig.
	Constant	-5.182	0.612	-6.438	0.000
	CNN lag 1	0.540	0.055	7.030	0.000
	Seasonal difference	1
	LSTM seasonal lag 1	0.885	0.054	6.661	0.000

A first-order seasonal difference inverse transform of the above model yields a fitted model of the original series as: (26) $y_{t} = - 5.182 + 1.54 y_{t - 1} - 0.54 y_{t - 25} + ε_{t} + 0.885 ε_{t - 1} - 0.885 ε_{t - 25}$

Applying the above fitting model, the 7-day load data volume is input to predict the forecast load of electricity consumption in the next 1 day. The user load prediction curve is shown in Figure 6. Through the smart meter records uploaded user electricity behavior data, summary analysis can be obtained by different equipment use probability in each time period, and then can be obtained in each time period active load power prediction value.

Since smart meter metering devices were not used in the neighborhood in this case, the probability of using each device was determined based on the literature. The predicted power of each active device load is shown in Figure 7.

3.2

Distributed PV Forecasting in Hybrid Mode

From the CNN-LSTM PV model, it can be seen that the PV power generation is a function about temperature and light intensity, and the prediction data of temperature and light intensity can be obtained through the meteorological bureau, which in turn can predict the distributed PV power generation of a typical user, although the accuracy of this prediction method is poor, but the method is simple and is suitable for the distributed PV power generation prediction scenarios of the power distribution network. The results of predicting distributed PV power generation in hybrid mode are shown in Fig. 8. The results show that the light intensity increases from roughly 6:00 a.m. BST in the morning, peaks at 14:00 p.m. (close to 1000 W/m²), and then begins to decline until it disappears at around 18:00 p.m. The results are shown in Fig. 8. The temperature change of a day is similar to the trend of the change of off light intensity, and its maximum value occurs between 12:00 and 13:00, with a maximum close to 29°C. The trend of power value changes is similar to that of light intensity, with the peak between 12:00 and 14:00 BST.

3.3

Distributed PV customer load stability analysis

3.3.1

No access to DC

This algorithm analyzes the impact of DC access on the static voltage stability of the distribution network by analyzing the changes in voltage before and after the access to DC and the changes in the voltage stability index of each branch. Without access to DC through matlab program, the distribution network without access to DC is used to calculate the current and get the power and voltage distribution of the distribution network. According to the voltage stability index of each branch of the distribution network, the degree of voltage stability of each branch is analyzed.

In order to study the static voltage stability level of the distribution network under different load conditions, on the basis of the load in the original distribution network, the load is gradually increased to improve the load level of the distribution network, and the node voltage distribution of the distribution network and the voltage stability indexes of each branch under different load levels are shown in Fig. 9. The results indicate that as the load level increases, the voltage drop of each branch of the distribution network gradually decreases, resulting in a decrease in static voltage stability. The voltage levels of terminal nodes 16, 17, 32 and 33 of the MV distribution network are lower; the voltage stability of branch circuits 1, 6, 10, 17, 19, 22 and 33 is poorer. In order to highlight the role of distributed power supply so as to facilitate the analysis of the impact of distributed power supply access on the static voltage stability, it is considered that the distributed power supply is accessed at nodes 1, 6, 10, 17, 19, 22, 33 of the MV distribution network and micro-sources are accessed as micro-grids in the LV distribution network connected to node 17.

3.3.2

Access to DC

The simulation analysis of the distribution network with multiple DC access is carried out to obtain the node voltage distribution and branch circuit voltage stability indexes of the multi-source distribution network, and the impact of DC access on the static voltage stability of the distribution network is obtained by comparing with that of the distribution network without DC access. The integration of power output-oriented DC reduces the power circulating on the line, and the trend of the nodal voltage curve is consistent with that before access, but the voltage level of the distribution network nodes has been significantly improved. The voltage stability index of the corresponding line is decreased, but the voltage stability is improved. The places with the largest voltage drop and the largest increase in voltage stability are the nodes where the DCs are connected. The line’s voltage level and stability remain stable without a DC connection. The static voltage stability of the distribution network can be effectively improved by connecting DCs to branches with poorer static stability and improving the voltage stability of the corresponding branches.

Further analyze the effect of parallel access to DCs of different capacities on the degree of improvement in static voltage stability of the distribution network. The voltage stability indexes of the distribution network connected to wind turbines of different capacities are shown in Table 2. Taking the wind turbine as the reference DC, the capacity of the wind turbine is gradually changed to analyze the degree of static voltage stability of the distribution network.

Table 2.

The voltage stability indicator for the power grid of different capacity

Fan capacity(kW)	0	50	100	150	200	250
Voltage stability indicator	0.1338	0.1231	0.1162	0.1199	0.1068	0.1035

The distribution network voltage of wind turbines connected to different capacities is shown in Fig. 10. The results show that accessing different capacities of DC has different degrees of influence on the distribution network voltage. The voltage level and static voltage stability are almost proportional to each other as a result of changing DC access capacity. That is to say, the larger the capacity of DC access, the higher the voltage level of the distribution network, and accordingly, the better the voltage stability of the distribution network. The access of DC brings favorable impact on the node voltage of the distribution network, but the access of DC with too high capacity may lead to the voltage level of the distribution network exceeding the specified range and thus have adverse effects. Therefore, when considering the access of DC, the first step is to determine the range of DC access capacity according to the demand of the network, and within the range, the voltage level of the distribution network can be improved by increasing the penetration rate of DC in the distribution network to enhance the static voltage stability of the distribution network.

4

Conclusion

In this paper, a hybrid model-based distributed PV prediction model is used to predict the consumer load and PV power generation, followed by an arithmetic analysis of the stability control strategy and current-voltage characteristics of the PV converter. The primary conclusions are as follows: 1)

The actual load sequence, the model fitting sequence, and the load prediction value on the 8th day show that the graphical proximity of the prediction model proposed in this paper is extremely high, and the inferred model is more reasonable. The active load power prediction values for each time period can be obtained through the uploaded data of consumers’ electricity consumption behavior from their smart meters.

2)

The quantitative analysis of the static voltage stability of the distribution network before and after DC access reveals that with the gradual increase of the load level, the voltage drop of each branch of the distribution network gradually increases, and the static voltage stability is getting worse and worse. Therefore, when considering the access of DC, the first step is to determine the range of DC access capacity according to the demand of the network, and then increase the penetration rate of DC in the distribution network within the range to improve the voltage level of the distribution network and enhance the static voltage stability of the distribution network. Therefore, when considering the access to DC, the first step is to determine the range of DC accessible capacity according to the demand of the network, and within the range to improve the voltage level of the distribution network by increasing the penetration of DC in the distribution network and enhance the static voltage stability of the distribution network.

Idioma:: Inglés

Calendario de la edición:: 1 veces al año
Temas de la revista:: Ciencias de la vida, Ciencias de la vida, otros, Matemáticas, Matemáticas aplicadas, Matemáticas generales, Física, Física, otros

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Study on the accuracy and stability of distributed photovoltaic customer load forecasting based on hybrid modeling

Hongtao Shen

Bo Feng

Guinan Han

Chao Zhang

Bingyu Zhang

Publicado en línea: 19 mar 2025

Recibido: 17 oct 2024

Aceptado: 10 feb 2025

DOI: https://doi.org/10.2478/amns-2025-0536

Palabras claveDistributed Generation System, Timing Prediction, CNN-LSTM, Continuous Tide Method, Customer Load

© 2025 Hongtao Shen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
Distributed Generation System, Timing Prediction, CNN-LSTM, Continuous Tide Method, Customer Load