CN109995031B - Probability power flow deep learning calculation method based on physical model - Google Patents

Abstract

The invention discloses a probability load flow deep learning calculation method based on a physical model, which mainly comprises the following steps: 1) acquiring power system data; 2) establishing a loss function of the probabilistic load flow analysis deep neural network, and updating a coding parameter theta of the deep neural network; 3) deep learning is carried out on the probability trend of the power system by utilizing a deep neural network; 4) establishing a probability trend deep learning calculation model; the method solves the problem that huge calculation cost and calculation precision are difficult to balance when solving the probability load flow by combining the data driving technology and the physical mechanism in the power field.

Description

Probability power flow deep learning calculation method based on physical model

Technical Field

The invention relates to the field of electric power systems and automation thereof, in particular to a probabilistic power flow deep learning calculation method based on a physical model.

Background

In recent years, renewable power generation has rapidly developed on a global scale. Not to be neglected, the uncertainty of the power system increases dramatically with the massive access of intermittent renewable energy sources. The rapid increase of uncertainty can have great influence on various departments of the power system, and threatens the safe and stable operation of the power grid. The probabilistic power flow is an important tool for uncertainty analysis of the power system, various random factors can be fully considered, and comprehensive and important reference information is provided for planning and operating the power system. However, the probability load flow involves a large number of high-dimensional complex nonlinear equations, and the existing solving algorithm is difficult to effectively balance the calculation cost and the calculation precision of the probability load flow. Therefore, efficient solutions to probabilistic power flows have become an urgent problem in high-proportion renewable energy power systems.

Disclosure of Invention

The present invention is directed to solving the problems of the prior art.

The technical scheme adopted for achieving the purpose of the invention is that the probability power flow deep learning calculation method based on the physical model mainly comprises the following steps:

1) power system data is acquired. The power system data mainly includes wind speed, photovoltaic power and load.

2) And establishing a loss function of the probability trend analysis deep neural network, and updating a coding parameter theta and a parameter r of the deep neural network.

The method mainly comprises the following steps of establishing a loss function of the probabilistic power flow analysis deep neural network:

2.1) determining the objective function loss, namely:

where m is the number of training samples per training round L is the number of layers Y_outIs the output characteristic vector of the power system probability power flow. X_inIs an input feature vector of the power system probability power flow.

Representing the first layer encoding function.

Representing the L th layer encoding function loss represents the loss function.

Wherein, when i is 1, 2, 3 …, L-1, the i-th layer coding function

As follows:

in the formula, R_iIs a function of activation of layer i neurons. Weight matrix w_iIs n_i+1×n_iAnd (4) matrix. Partial vector b_iIs n_i+1A dimension vector. n is_iIs the ith^thThe number of neurons in a layer. X is the input to the encoding function.

When i is L, the i-th layer coding function

As follows:

in the formula, R_LAs a function of activation of layer L neurons weight matrix w_LIs n_L+1×n_LAnd (4) matrix. Partial vector b_LIs n_L+1A dimension vector. n is_LIs L th^thThe number of neurons in a layer.

When i is 1, 2, 3 …, L-1, the i-th layer activation function R_iAs follows:

in the formula, x is the input of the neuron, i.e., the input data of the power system.

When i is L, the i-th layer activation function R_iAs follows:

R_i(x)＝R_L(x)＝x。 (5)

2.2) preprocessing input data and output data of the power system probability power flow, namely:

v_outinput data or output data vectors representing the preprocessed power system probabilistic power flow. v represents the raw input data or output data vector of the power system probabilistic power flow. v. of_meanAnd v_stdMean and standard deviation, respectively, of the vector v.

2.3) updating the parameter theta of the deep neural network based on the target function loss, namely:

in the formula (I), the compound is shown in the specification,

for the objective function loss at t^thThe partial derivative of the theta variable when changing ⊙ is the hamiltonian r is the attenuation factor p and is a constant η is the learning rate of the neural network.

3) And deep learning is carried out on the probability trend of the power system by utilizing a deep neural network.

The method for deep learning the probability trend of the power system by using the deep neural network comprises the following main steps:

3.1) determining the probability power flow of the power system, namely establishing a reactive power equation and an active power equation of the probability power flow of the power system.

Wherein, the ith in the power system^thBus to jth^thBranch active power P of bus_ijAs follows:

P_ij＝G_ij(V_i ²-V_iV_jcosθ_ij)-B_ijV_iV_jsinθ_ij。 (8)

in the formula, V_iIs the voltage amplitude of the bus i. Theta_ijThe voltage phase angle difference between bus i and bus j. G_ijAnd B_ijAre respectively the ith^thA bus and a jth bus^thConductance and susceptance between the buses. V_jIs the voltage amplitude of bus j.

Ith in power system^thBus to jth^thBranch reactive power Q of bus_ijAs follows:

Q_ij＝-B_ij(V_i ²-V_iV_jcosθ_ij)-G_ijV_iV_jsinθ_ij。 (9)

3.2) determining a training target loss by taking the node voltage of the power system as an output vector_newNamely:

in the formula (I), the compound is shown in the specification,

and (4) an active power equation of a branch of the power system.

And (4) a reactive power equation of a branch of the power system. loss_newIs an updated loss function.

Active power equation of branch of electric power system

As follows:

in the formula (I), the compound is shown in the specification,

is normalized active power. P_outThe active power of the branches of the standardized power system is obtained. | | represents a norm.

In the formula (I), the compound is shown in the specification,

is normalized active power. Q_outThe active power of the branches of the standardized power system is obtained.

3.3) update the weight w with back propagation, i.e.:

w_(i,T+1)＝w_(i,T)-Δw_(i,T)。 (13)

in the formula,. DELTA.w_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe amount of change in the weight matrix of the layer. w is a_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer. w is a_(i,T+1)Is the (T +1)^thUpdating of individual parametersFrom the i-th^thLayer to i +1^thThe weight of the layer.

T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ w of weight matrix of layer_(i,T)As follows:

in the formula, R_(i,T)Is the T th^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable.

R_(i,T)＝ρ*R_(i,T-1)+(1-ρ)*dw_(i,T)⊙dw_(i,T)。 (15)

In the formula, dw_(i,T)Is the amount of weight change. R_(i,T-1)Is the first (T-1)^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable.

Weight change amount dw_(i,T)As follows:

where r is the serial number of the initial sample in the batch, and m is the sample size of the batch. k is an arbitrary sample sequence.

3.4) update bias b with back propagation, i.e.:

b_(i,T+1)＝b_(i,T)-Δb_(i,T)。 (17)

in the formula,. DELTA.b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe amount of change in the bias matrix of the layer. b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers. b_(i,T+1)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers.

T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ b of bias matrix of layer_(i,T)As shown below：

In the formula (II), R'_(i,T)Is the T th^thThe learning rate decays the variable as the secondary bias is iteratively updated.

R′_(i,T)＝ρ*R′_(i,T-1)+(1-ρ)*db_(i,T)⊙db_(i,T)。 (19)

In the formula db_(i,T)Is the amount of change in the bias. R'_(i,T-1)Is the T-1^thThe learning rate decays the variable as the secondary bias is iteratively updated.

Bias change db_(i,T)As follows:

3.5) determining the original loss function loss and the updated loss function loss_newThe difference equation d (L) of (c) is as follows:

d(L)＝d₁+d₂+d₃。 (21)

in the formula (d)₁、d₂、d₃Is a difference equation.

d(i)＝d(i+1)w_i,T-1⊙max(0,y_i)。 (22)

In the formula, y_iAnd outputting data for the deep neural network. w is a_(i,T-1)Is the first (T-1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer.

Weight change amount dw_(i,T)As follows:

dw_(i,T)＝d(i)^Ty_i/m。 (23)

in the formula (I), the compound is shown in the specification,

is the output of the deep neural network. Y is

The denormalized value of (a).

In the formula, Y is an output vector of the probability power flow.

Is the output of the deep neural network; y is

The denormalized value of (a). And P is the active power of the power system.

The estimation value of the active power of the deep neural network on the power system is obtained. And Q is reactive power of the power system.

And the estimation value of the reactive power of the deep neural network on the electric power system is obtained.

Equation of difference d₂And difference equation d₃The contribution weights to the output feature vector of the deep neural network are respectively as follows:

in the formula (d)_θ[L]、d_1,θ、d_2,θAnd d_3,θIs denoted by d_θ[L]Equation of difference d₁Equation of difference d₂And difference equation d₃The medium voltage phase angle outputs a vector. d_v[L]、d_1,v、d_2,vAnd d_3,vIs denoted by d_v[L]Equation of difference d₁Equation of difference d₂And difference equation d₃Intermediate voltage magnitude output vector d L]Is the equation of difference d₂And difference equation d₃The total contribution weight of. d_θ[L]Express difference equation d₂And difference equation d₃Weight of contribution to the voltage phase angle output vector of the deep neural network. d_v[L]Express difference equation d₂And difference equation d₃A weight of contribution to a voltage magnitude output vector of the deep neural network.

The empirical value α and the empirical value β are respectively as follows:

in the formula, max is a function that returns the maximum value, and abs is a function that returns the absolute value.

4) And establishing a probabilistic power flow deep learning calculation model.

The method for establishing the probabilistic power flow deep learning calculation model mainly comprises the following steps:

4.1) establishing a power system power flow probability equation as shown in the formulas 29 to 34 respectively.

In the formula, V_iIs the voltage amplitude of the bus i. Theta_ijIs the voltage phase angle difference between bus i and bus j. G_ijAnd B_ijAre respectively the ith^thA bus and a jth bus^thConductance and susceptance between the buses.

4.2) removing voltage amplitude data in the flow input data of the deep neural network.

4.3) removing the phase angle data in the reactive power input data of the deep neural network.

4.4) based on the steps 4.1 to 4.3, establishing a probabilistic power flow deep learning calculation model, which mainly comprises the following steps:

4.4.1) determining the weight of the probability trend deep learning calculation model, namely:

wherein d is_1,θAnd difference equation d (L) are respectively as follows:

in the formula (I), the compound is shown in the specification,

is an estimate of the parameter theta by the neural network. Theta is a neural network coding parameter.

d(L)＝d₁。 (37)

4.4.2) establishing a probabilistic power flow deep learning calculation model, namely:

5) and calculating the probability load flow of the power system to be measured by utilizing the probability load flow deep learning calculation model.

The technical effect of the present invention is undoubted. The invention realizes the effective combination of a physical model and a data-driven deep learning technology, provides a model-based deep learning simplification method according to the physical characteristics of the power transmission network of the power system, and can effectively combine the advantages of model driving by light-weight calculation. The method solves the problem that huge calculation cost and calculation precision are difficult to balance when solving the probability load flow by combining the data driving technology and the physical mechanism in the power field.

Drawings

FIG. 1 is a process flow diagram.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

referring to fig. 1, the probabilistic power flow deep learning calculation method based on the physical model mainly includes the following steps:

1) and acquiring data of the power system and establishing a physical model of the power system. The power system data mainly includes wind speed, photovoltaic power and load.

2) And establishing a loss function of the probabilistic power flow analysis deep neural network, and updating a parameter theta of the deep neural network.

The method mainly comprises the following steps of establishing a loss function of the probabilistic power flow analysis deep neural network:

2.1) determining the objective function loss, namely:

where m is the number of training samples per training round L is the number of layers Y_outIs the output characteristic vector of the power system probability power flow. X_inIs an input feature vector of the power system probability power flow.

Representing the first layer encoding function.

Represents the L th layer encoding function loss represents the square loss function.

Wherein, when i is 1, 2, 3 …, L-1, the i-th layer coding function

As follows:

in the formula, R_iIs a function of activation of layer i neurons. Weight matrix w_iIs n_i+1×n_iAnd (4) matrix. Partial vector b_iIs n_i+1A dimension vector. n is_iIs the ith^thThe number of neurons in a layer. X is the input to the encoding function. When i is 1, X is X_in. When the value of i is 2, the ratio of i to i is,

and so on.

When i is L, the i-th layer coding function

As follows:

in the formula, R_LAs a function of activation of layer L neurons weight matrix w_LIs n_L+1×n_LAnd (4) matrix. Partial vector b_LIs n_L+1A dimension vector. n is_LIs L th^thThe number of neurons in a layer.

When i is 1, 2, 3 …, L-1, the i-th layer Re L U activates the function R_iAs follows:

in the formula, x is the input of the neuron, i.e., the input data of the power system.

When i is L, the i-th layer activation function R_iAs follows:

R_i(x)＝R_L(x)＝x。 (5)

2.2) in order to improve the training efficiency of DNN, the input data and the output data of PPF should be preprocessed to eliminate the adverse effect of singular samples and numerical problems on the training process. Outliers can be efficiently processed by normalizing the samples using the z-score method and only the mean and standard deviation of the historical statistics are required. Furthermore, it can preserve the distribution characteristics more efficiently than other pre-processing methods (such as the min-max method).

Preprocessing input data and output data of the power system probability power flow, namely:

v_outinput data or output data vectors representing the preprocessed power system probabilistic power flow. v represents the raw input data or output data vector of the power system probabilistic power flow. v. of_meanAnd v_stdMean and standard deviation, respectively, of the vector v.

2.3) this example uses the RMSProp method as the learning algorithm. It divides the training samples into several batches. Each batch of samples is trained to update parameters in turn. The RMSProp method adaptively updates the learning rate for each parameter by keeping a moving average of the gradient squared, reducing the training burden and avoiding local minimization. The deep neural network parameters are updated by the RMSProp algorithm.

Updating the deep neural network parameter theta based on the target function loss, namely:

in the formula (I), the compound is shown in the specification,

for the objective function loss at t^thThe partial derivative of the theta variable when changing ⊙ is the hamiltonian r is the attenuation factor rho and is a constant η is the learning rate of the neural network rho 0.99 η 0.001 1 × 10^-8。

For the objective function loss at t^thPartial derivative of the theta variable when changing. Theta^tIs at the t^thUpdated parameter, θ^t-1Is the t-1^thUpdated parameter, r^tIs at the t^thUpdated parameter, r^t-1Is the t-1^thThe updated parameters.

3) And deep learning is carried out on the probability trend of the power system by utilizing a deep neural network. The goal of deep learning is to obtain optimal parameters for DNN (deep neural network)

The method for deep learning the probability trend of the power system by using the deep neural network comprises the following main steps:

3.1) determining the probability power flow of the power system, namely establishing a reactive power equation and an active power equation of the probability power flow of the power system.

Wherein, the ith in the power system^thBus to jth^thBranch active power P of bus_ijAs follows:

P_ij＝G_ij(V_i ²-V_iV_jcosθ_ij)-B_ijV_iV_jsinθ_ij。 (8)

in the formula, V_iIs the voltage amplitude of the bus i. Theta_ijThe voltage phase angle difference between bus i and bus j. G_ijAnd B_ijAre respectively the ith^thA bus and a jth bus^thConductance and susceptance between the buses. V_jIs the voltage amplitude of bus j.

Ith in power system^thBus to jth^thBus bar supportRoad reactive power Q_ijAs follows:

Q_ij＝-B_ij(V_i ²-V_iV_jcosθ_ij)-G_ijV_iV_jsinθ_ij。 (9)

3.2) taking the node voltage of the power system as an output vector, and adding a branch load flow equation as a penalty term into a training target loss by combining the physical mechanism and the field knowledge of electrical engineering, so that the training target loss_newAs follows:

in the formula (I), the compound is shown in the specification,

and (4) an active power equation of a branch of the power system.

And (4) a reactive power equation of a branch of the power system. loss_newIs an updated loss function.

Active power equation of branch of electric power system

As follows:

in the formula (I), the compound is shown in the specification,

is normalized active power. P_outThe active power of the branches of the standardized power system is obtained. | | represents a norm.

In the formula (I), the compound is shown in the specification,

is normalized active power. Q_outThe active power of the branches of the standardized power system is obtained.

3.3) update the weight w with back propagation, i.e.:

w_(i,T+1)＝w_(i,T)-Δw_(i,T)。 (13)

in the formula,. DELTA.w_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe amount of change in the weight matrix of the layer. w is a_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer. w is a_(i,T+1)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer.

T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ w of weight matrix of layer_(i,T)As follows:

in the formula, R_(i,T)Is the T th^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable.

R_(i,T)＝ρ*R_(i,T-1)+(1-ρ)*dw_(i,T)⊙dw_(i,T)。 (15)

In the formula, dw_(i,T)Is the amount of weight change. R_(i,T-1)Is the first (T-1)^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable.

Weight change amount dw_(i,T)As follows:

where r is the serial number of the initial sample in the batch, and m is the sample size of the batch. k is an arbitrary sample sequence.

3.4) update bias b with back propagation, i.e.:

b_(i,T+1)＝b_(i,T)-Δb_(i,T)。 (17)

in the formula,. DELTA.b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe amount of change in the bias matrix of the layer. b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers. b_(i,T+1)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers.

T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ b of bias matrix of layer_(i,T)As follows:

in the formula (II), R'_(i,T)Is the T th^thThe learning rate decays the variable as the secondary bias is iteratively updated.

R′_(i,T)＝ρ*R′_(i,T-1)+(1-ρ)*db_(i,T)⊙db_(i,T)。 (19)

In the formula db_(i,T)Is the amount of change in the bias. R'_(i,T-1)Is the T-1^thThe learning rate decays the variable as the secondary bias is iteratively updated.

Bias change db_(i,T)As follows:

3.5) determining the original loss function loss and the updated loss function loss_newThe difference equation d (L) of (c) is as follows:

d(L)＝d₁+d₂+d₃。 (21)

in the formula (d)₁、d₂And d₃Is a difference equation.

d(i)＝d(i+1)w_i,T-1⊙max(0,y_i)。 (22)

Wherein d (i +1) is the (i +1) th^thLayer difference equation. max (×) indicates taking the maximum value. y is_iAnd outputting data for the deep neural network. w is a_(i,T-1)Is the first (T-1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer.

Weight change amount dw_(i,T)As follows:

dw_(i,T)＝d(i)^Ty_i/m。 (23)

in the formula, superscript T denotes transpose.

In the formula (I), the compound is shown in the specification,

is the output of the deep neural network. Y is

The denormalized value of (a).

In the formula, Y is an output vector of the probability power flow.

Is the output of the deep neural network. Y is

The denormalized value of (a). And P is the active power of the power system.

The estimation value of the active power of the deep neural network on the power system is obtained. Q is electric powerAnd (5) system reactive power.

And the estimation value of the reactive power of the deep neural network on the electric power system is obtained.

As can be seen from equations (13) - (26), the proposed objective function (9) will increase the update step size of the parameter w when the update direction decreases with both voltage and power calculation errors. This may facilitate training convergence speed. In addition, when the parameter update directions of (24) and (25) and (26) are different, the branch power constraint added in the loss function is expected to reduce or prevent the deep neural network from over-fitting the node voltage.

As can be seen from equations (21) - (26), the parameter update direction can be guided by (25) and (26), since

The error of (2) can be very large. In fact, this strategy is commonly referred to as normalization in the deep learning field. From the perspective of deep learning, the update direction of the core target (high-precision voltage) of the present embodiment should be dominant. The output of the deep neural network contains the voltage amplitude and phase angle (i.e., Y)_out＝[V,θ])。d₂+d₃The contribution to the output feature vector should not be greater than d₁This may disturb or diverge the DNN training. d₂+d₃Should be slightly less than d₁The contribution of (c). Thus, the present invention proposes d₂And d₃Two contribution weights to the output feature vector.

Equation of difference d₂And difference equation d₃The contribution weights to the output feature vector of the deep neural network are respectively as follows:

in the formula (d)_θ[L]、d_1,θ、d_2,θAnd d_3,θIs denoted by d_θ[L]Equation of difference d₁Equation of difference d₂And difference equation d₃The medium voltage phase angle outputs a vector. d_v[L]、d_1,v、d_2,vAnd d_3,vIs denoted by d_v[L]Equation of difference d₁Equation of difference d₂And difference equation d₃Intermediate voltage magnitude output vector d L]Is the equation of difference d₂And difference equation d₃The total contribution weight of. d_θ[L]Express difference equation d₂And difference equation d₃Weight of contribution to the voltage phase angle output vector of the deep neural network. d_v[L]Express difference equation d₂And difference equation d₃A weight of contribution to a voltage magnitude output vector of the deep neural network.

The empirical value α and the empirical value β are respectively as follows:

in the formula, max is a function that returns the maximum value, and abs is a function that returns the absolute value.

4) And establishing a probabilistic power flow deep learning calculation model.

The method for establishing the probabilistic power flow deep learning calculation model mainly comprises the following steps:

4.1) establishing a power system power flow probability equation as shown in the formulas 29 to 34 respectively.

In the formula, V_iIs the voltage amplitude of the bus i. Theta_ijIs the voltage phase angle difference between bus i and bus j. G_ijAnd B_ijAre respectively the ith^thA bus bar and the j^thConductance and susceptance between the individual busbars.

4.2) removing voltage amplitude data in the flow input data of the deep neural network.

Deep neural networks mine the non-linear characteristics or relationships of the probability trend by quantifying the effects of input changes. In power systems, the voltage amplitude typically fluctuates at ± 5% p.u. However, under operating conditions, the range of nodal phase angle variation can reach 30 ° or more. Therefore, voltage amplitude is easier to learn than phase angle, which also requires guidance from a physical model. Furthermore, since the standard deviation of the voltage magnitude is much smaller than the standard deviation of the phase angle, it can be found in (25) and (26) that the model guides the influence on the voltage magnitude much smaller than the influence on the phase angle.

The guidance of the voltage amplitude is computationally expensive compared to the phase voltage in view of the respective computational complexity. From equations (29) - (34), if the guidance of the voltage amplitude is not removed, all equations (23) - (27) need to be performed, it can be seen that the calculation cost of the voltage amplitude guidance is about twice the voltage phase angle.

Therefore, the guidance of the voltage amplitude is removed in the general model-based deep learning method according to numerical analysis and computational complexity comparison.

4.3) removing the phase angle data in the reactive power input data of the deep neural network.

In a power transmission network, conductance and susceptance have the following relationship:

although the node phase angle may vary drastically with operating conditions, the phase angle difference of two nodes will typically not vary much. Thus, we can have:

sinθ_ij＜cosθ_ij； (36)

from equations (35) and (36), it can be easily deduced that the absolute value of equation (30) is much smaller than equation (29). In addition to this, the present invention is,

is generally less than

Absolute value of (a). The absolute value of std (p) is usually smaller than the absolute value of std (q), since in practice the active load demand is higher than the reactive load demand. Therefore, it can be concluded from (23) - (27) that the reactive branch power has a much smaller impact on the training process than the active power flow. Therefore, the present embodiment eliminates reactive guidance of the phase angle. std (×) represents the standard deviation.

4.4) based on the steps 4.1 to 4.3, establishing a probabilistic power flow deep learning calculation model, which mainly comprises the following steps:

4.4.1) determining the weight of the probability trend deep learning calculation model, namely:

wherein d is_1,θAnd difference equation d (L) are respectively as follows:

in the formula (I), the compound is shown in the specification,

is an estimate of the parameter theta by the neural network.

d(L)＝d₁。 (37)

4.4.2) establishing a probabilistic power flow deep learning calculation model, namely:

5) and calculating the probability load flow of the power system to be measured by utilizing the probability load flow deep learning calculation model.

Example 2:

the probability power flow deep learning calculation method based on the physical model mainly comprises the following steps:

1) the system state is sampled. And randomly extracting random input variables of the system, including wind speed, photovoltaic power and load.

2) Inputting the system operating conditions (random input variables in step 1) and directly mapping the voltage amplitude and phase angle of all unresolved samples by the deep neural network, and directly solving power information by the amplitude phase angle. Iterative computation is not needed in the whole process, so that the computation speed of the probability load flow can be remarkably increased.

3) And (3) calculating and analyzing a probability power flow index based on the result of the step (2), wherein the probability power flow index comprises the average value, the standard deviation and the probability density function of all output variables.

Example 3:

a probabilistic load flow deep learning calculation method based on a physical model, mainly as in embodiment 2, wherein the main steps of establishing a loss function of a probabilistic load flow analysis deep neural network are as follows:

1) determining the objective function loss, namely:

where m is the number of training samples per training round L is the number of layers Y_outIs the output characteristic vector of the power system probability power flow. X_inIs an input feature vector of the power system probability power flow.

Representing the first layer encoding function.

Represents the L th layer encoding function loss represents the square loss function.

Wherein, when i is 1, 2, 3 …, L-1, the i-th layer coding function

As follows:

in the formula, R_iIs a function of activation of layer i neurons. Weight matrix w_iIs n_i+1×n_iAnd (4) matrix. Partial vector b_iIs n_i+1A dimension vector. n is_iIs the ith^thThe number of neurons in a layer. X is the input to the encoding function.

When i is L, the i-th layer coding function

As follows:

in the formula, R_LAs a function of activation of layer L neurons weight matrix w_LIs n_L+1×n_LAnd (4) matrix. Partial vector b_LIs n_L+1A dimension vector. n is_LIs L th^thThe number of neurons in a layer.

When i is 1, 2, 3 …, L-1, the i-th layer Re L U activates the function R_iAs follows:

in the formula, x is the input of the neuron, i.e., the input data of the power system.

When i is L, the i-th layer activation function R_iAs follows:

R_i(x)＝R_L(x)＝x。 (5)

2) in order to improve the training efficiency of DNN, the input data and the output data of PPF should be preprocessed to eliminate the adverse effect of singular samples and numerical problems on the training process. Outliers can be efficiently processed by normalizing the samples using the z-score method and only the mean and standard deviation of the historical statistics are required. Furthermore, it can preserve the distribution characteristics more efficiently than other pre-processing methods (such as the min-max method).

Preprocessing input data and output data of the power system probability power flow, namely:

v_outinput data or output data vectors representing the preprocessed power system probabilistic power flow. v represents the raw input data or output data vector of the power system probabilistic power flow. v. of_meanAnd v_stdMean and standard deviation, respectively, of the vector v.

3) The present embodiment adopts the RMSProp method as a learning algorithm. It divides the training samples into several batches. Each batch of samples is trained to update parameters in turn. The RMSProp method adaptively updates the learning rate for each parameter by keeping a moving average of the gradient squared, reducing the training burden and avoiding local minimization. The deep neural network parameters are updated by the RMSProp algorithm.

Updating the deep neural network parameter theta based on the target function loss, namely:

in the formula (I), the compound is shown in the specification,

for the objective function loss at t^thThe partial derivative of the theta variable when changing ⊙ is the hamiltonian r is the attenuation factor rho and is a constant η is the learning rate of the neural network rho 0.99 η 0.001 1 × 10^-8。

Example 4:

a deep learning calculation method of probability power flow based on a physical model, mainly as shown in embodiment 2, wherein the deep learning of the probability power flow of a power system by using a deep neural network mainly comprises the following steps:

1) and determining the probability power flow of the power system, namely establishing a reactive power equation and an active power equation of the probability power flow of the power system.

Wherein, the ith in the power system^thBus to jth^thBranch active power P of bus_ijAs follows:

P_ij＝G_ij(V_i ²-V_iV_jcosθ_ij)-B_ijV_iV_jsinθ_ij。 (8)

in the formula, V_iIs the voltage amplitude of the bus i. Theta_ijThe voltage phase angle difference between bus i and bus j. G_ijAnd B_ijAre respectively the ith^thA bus bar and the j^thConductance and susceptance between the individual busbars.

Ith in power system^thBus to jth^thBranch reactive power Q of bus_ijAs follows:

Q_ij＝-B_ij(V_i ²-V_iV_jcosθ_ij)-G_ijV_iV_jsinθ_ij。 (9)

2) determining a training target loss by taking the node voltage of the power system as an output vector_newNamely:

in the formula (I), the compound is shown in the specification,

and (4) an active power equation of a branch of the power system.

And (4) a reactive power equation of a branch of the power system. loss_newIs an updated loss function.

Active power equation of branch of electric power system

As follows:

in the formula (I), the compound is shown in the specification,

is normalized active power. P_outThe active power of the branches of the standardized power system is obtained.

In the formula (I), the compound is shown in the specification,

is normalized active power. Q_outThe active power of the branches of the standardized power system is obtained.

3) Update the weights w with back propagation, i.e.:

w_(i,T+1)＝w_(i,T)-Δw_(i,T)。 (13)

wherein Δ w: (_i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe amount of change in the weight matrix of the layer. w is a_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer. w is a_(i,T+1)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer.

T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ w of weight matrix of layer_(i,T)As follows:

in the formula, R_(i,T)Is the T th^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable.

R_(i,T)＝ρ*R_(i,T-1)+(1-ρ)*dw_(i,T)⊙dw_(i,T)。 (15)

In the formula, dw_(i,T)Is the amount of weight change.

Weight change amount dw_(i,T)As follows:

where r is the serial number of the initial sample in the batch, and m is the sample size of the batch.

4) Update bias b with back propagation, i.e.:

b_(i,T+1)＝b_(i,T)-Δb_(i,T)。 (17)

in the formula,. DELTA.b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe amount of change in the bias matrix of the layer. b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers. Δ b_(i,T)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers.

T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ b of bias matrix of layer^(l,T)As follows:

in the formula (II), R'_(i,T)Is as follows.

R′_(i,T)＝ρ*R′_(i,T-1)+(1-ρ)*db_(i,T)⊙db_(i,T)。 (19)

In the formula db_(i,T)Is the amount of change in the bias.

Bias change db_(i,T)As follows:

5) determining an original loss function loss and an updated loss function loss_newThe difference equation d (L) of (c) is as follows:

d(L)＝d₁+d₂+d₃。 (21)

in the formula (d)₁、d₂、d₃Respectively, are shown.

d(i)＝d(i+1)w_i,T-1⊙max(0,y_i)。 (22)

In the formula, y_iAnd outputting data for the deep neural network.

Weight change amount dw_(i,T)As follows:

dw_(i,T)＝d(i)^Ty_i/m。 (23)

in the formula (I), the compound is shown in the specification,

is the output of the deep neural network. Y is

The denormalized value of (a).

d₂And d₃The contribution weights to the output feature vector of the deep neural network are respectively as follows:

in the formula (d)_θ[L]、d_1,θ、d_2,θAnd d_3,θIs denoted by d_θ[L]、d₁、d₂And d₃The medium voltage phase angle outputs a vector. d_v[L]、d_1,v、d_2,vAnd d_3,vIs denoted by d_v[L]、d₁、d₂And d₃The medium voltage magnitude output vector.

The empirical value α and the empirical value β are respectively as follows:

in the formula, max is a function that returns the maximum value, and abs is a function that returns the absolute value.

Example 5:

a probabilistic power flow deep learning calculation method based on a physical model, mainly as in embodiment 2, wherein the method for establishing the probabilistic power flow deep learning calculation model mainly comprises the following steps:

1) and establishing power flow probability equations of the power system, which are respectively shown in equations 29 to 34.

In the formula, V_iIs the voltage amplitude of the bus i. Theta_ijIs the voltage phase angle difference between bus i and bus j. G_ijAnd B_ijAre respectively the ith^thA bus and a jth bus^thConductance and susceptance between the buses.

2) And removing voltage amplitude data in the flow input data of the deep neural network.

3) Removing phase angle data in the reactive power input data of the deep neural network.

4) Based on the steps 1 to 3, a probabilistic load flow deep learning calculation model is established, and the method mainly comprises the following steps:

4.1) determining the weight of the probability trend deep learning calculation model, namely:

wherein d is_1,θAnd difference equation d (L) are respectively as follows:

d(L)＝d₁。 (37)

4.2) establishing a probabilistic power flow deep learning calculation model, namely:

example 6:

a method for verifying probability load flow deep learning calculation based on a physical model mainly comprises the following steps:

1) in this embodiment, simulation was performed using IEEE30, an IEEE118 standard system, and a 661-node system. A Monte-Carlo simulation method of a Newton-Raphson algorithm is used as a reference of the probability power flow.

2) The following methods were compared to verify the effectiveness of the method disclosed in example 1.

M1: DNN of the designed learning method was applied.

M2 introduction of the proposed model-based general deep learning method on the basis of the M1 method.

M3: on the basis of M2. However, the guidance of the voltage amplitude is removed.

M4: on the basis of M3. However, the guidance of the reactive power phase angle is removed.

The above method has the same hyper-parameters under each calculation. The hyper-parameters and the number of training samples of the deep neural network under different examples are shown in table 1. The number of validation samples and test samples was 10000. If the deep neural network satisfies the early stopping method or the number of iteration rounds reaches a threshold, the training process is stopped. All simulations were performed on a PC equipped with Intel (R) core (TM) i7-7500U CPU @2.70GHz 32GB RAM.

TABLE 1 hyper-parameter settings of deep neural networks under different examples

Examples of the design	Hidden layer	Number of training samples
			Case 30	[100 100 100]	10000
Case 118	[200 200 200]	20000
			Case 661	[500 500 500 500 500]	70000

3) Validation of the proposed method:

table 2 comparison of performance of M1 and M2 under the same iteration round

Table 3 compares the performance of M1 and M2 when meeting the accuracy requirements

Tables 2 and 3 are used to verify the validity of the proposed model-based general deep learning method for probabilistic power flow problems.

When the number of iterations is fixed, it can be seen from table 2 that the proposed method M2 can make all the indicators meet the accuracy requirement (< 5%), while one or two accuracy indicators cannot be met by the method M1.

From the results shown in table 3, it can be seen that N of M1 can be converted by the proposed method M2 on the premise that the accuracy requirement is met_epochThe reductions of 68.7%, 71.7% and 61.3% were found in three cases, Case30, Case118 and Case661, respectively. Further, it is noted that, in case661, P is caused to be P by the M1 method_pfIncreases with the number of iteration rounds between tables 1 and 2. This phenomenon may be referred to as "overfitting". Without the guidance of the physical model, the accuracy of the branch power cannot be guaranteed even if the values of most node voltages are well approximated by M1. Further, P calculated from M2 in Case661_pfThe value of (A) was 3.4%, which is an improvement of only 1.6% over 5%. However, it is almost impossible to achieve a 1.6% improvement in DNN by M1.

In conclusion, the method realizes perfect combination of the physical model and the data-driven deep learning technology. The proposed method can significantly accelerate the convergence efficiency and can reduce or prevent overfitting of the deep neural network to the node voltages.

TABLE 4 comparison of Performance between M1 and M3 when accuracy requirements are met

Table 4 shows a comparison of the properties between M1 and M3. It can be observed that method M3 still has a greater advantage than M1. Comparing table 4 and table 3, it can be observed that the number of iterations in M3 that meet the accuracy requirements is less than in cases 118 and 661 (indicated by arrows) for M2. In Case30, the number of iteration rounds is rising from 507 to 576, which is absolutely tolerable in the Case of small scales. Therefore, it is effective to remove the guidance of the voltage amplitude.

TABLE 5 comparison of Performance between M1 and M4 when accuracy requirements are met

The phase angle response guidance was further eliminated and the numerical simulation results are shown in table 5. As can be seen from Table 5, N of M4 is compared with M1_epochThe decrease or increase tendency of (c) is the same as that of (M3). However, in Case661, N of M4 was compared to M3_epochFurther reduction; and N of M1_epochThe reduction can be 74.1%. In Case661, the phase angle guidance can be significantly reduced by removing the reactive power.

In summary, it is reasonable to remove the guiding of the voltage amplitude and the guiding of the reactive power of the phase angle, and compared with the general deep learning method based on the model, the simplified deep learning method based on the model can obtain a comparable result, even better.

Calculating time comparison:

TABLE 6 comparison of computation time for each iteration under different methods

Cases	tM1(s)	tM2(s)	tM3(s)	tM4(s)
					Case 30	0.13	0.26	0.21	0.20
Case 118	0.68	1.64	1.25	1.09
					Case 661	35.21	51.53	45.07	43.18

Table 6 shows the computation time for each iteration using different methods. In all cases, the simplified methods M3 and M4 take less time than the general deep learning method M2 based on the basic model. In the Case30 and Case118 standard examples, there was not much difference in the calculation time using the different methods. However, for a large practical power system, the difference is very significant.

For a real 661 bus system, method M3 may reduce the computation time per iteration by 6.64 seconds compared to M2 by removing the steering of the voltage amplitude. By removing the reactive guidance of the phase angle M4, the calculation time of M2 can be further reduced by 8.35 seconds.

In conclusion, the proposed model-based simplified deep learning method M4 can significantly reduce the computational stress while maintaining high performance, compared to the model-based general deep learning method M2.

In conclusion, the invention realizes the effective combination of the physical model and the data-driven deep learning technology, and provides the model-based deep learning simplification method according to the physical characteristics of the power transmission network of the power system, and the advantage of the effective combination of the model drive can be calculated in a light weight manner. The results of the simulation analysis also verify the accuracy and validity of the proposed method. Therefore, the method can provide technical support for high-precision and rapid calculation of the probability load flow of the power system.

Claims (2)

1. The probability power flow deep learning calculation method based on the physical model is characterized by mainly comprising the following steps of:

1) acquiring power system data;

2) establishing a loss function of the probabilistic load flow analysis deep neural network, and updating a parameter theta of the deep neural network;

the method mainly comprises the following steps of establishing a loss function of the probabilistic power flow analysis deep neural network:

2.1) determining the objective function loss, namely:

where m is the number of training samples per training round, L is the number of layers, Y is_outIs an output characteristic vector of the power system probability power flow; x_inIs an input feature vector of the power system probability power flow;

representing a first layer encoding function;

representing the L th layer encoding function, loss representing the loss function;

wherein, when i is 1, 2, 3 …, L-1, the i-th layer coding function

As follows:

in the formula, R_iIs an activation function for layer i neurons; weight matrix w_iIs n_i+1×n_iA matrix; partial vector b_iIs n_i+1A dimension vector; n is_iIs the ith^thThe number of neurons in a layer; x is the input of the coding function;

when i is L, the i-th layer coding function

As follows:

in the formula, R_LAs a function of the activation of the layer L neurons, a weight matrix w_LIs n_L+1×n_LA matrix; partial vector b_LIs n_L+1A dimension vector; n is_LIs L th^thThe number of neurons in a layer;

when i is 1, 2, 3 …, L-1, the i-th layer activation function R_iAs follows:

in the formula, x is input of a neuron, namely input data of a power system;

when i is L, the i-th layer activation function R_iAs follows:

R_i(x)＝R_L(x)＝x； (5)

2.2) preprocessing input data and output data of the power system probability power flow, namely:

in the formula, v_outInput data or output data vectors representing the preprocessed power system probabilistic power flow; v represents the original input data or output data vector of the power system probability power flow; v. of_meanAnd v_stdMean and standard deviation of the vector v, respectively;

2.3) updating the deep neural network parameter theta based on the target function loss, namely:

in the formula (I), the compound is shown in the specification,

is the target function loss at t-1^thPartial derivative of theta variable in variation, ⊙ Hamiltonian, r attenuation factor, rho sum constant, η learning rate of neural network, ▽_θloss is the objective function loss at t^thPartial derivatives of the theta variable as it changes;

3) the deep neural network is used for deep learning of the probability trend of the power system, and the method mainly comprises the following steps:

3.1) determining the probability power flow of the power system, namely establishing a reactive power equation and an active power equation of the probability power flow of the power system;

wherein, the ith in the power system^thBus to jth^thBranch active power P of bus_ijAs follows:

in the formula, V_iIs the voltage amplitude of bus i; theta_ijThe voltage phase angle difference between bus i and bus j; g_ijAnd B_ijAre respectively the ith^thA bus and a jth bus^thConductance and susceptance between the individual buses; v_jIs the voltage amplitude of bus j;

ith in power system^thBus to jth^thBranch reactive power Q of bus_ijAs follows:

3.2) determining a training target loss by taking the node voltage of the power system as an output vector_newNamely:

in the formula (I), the compound is shown in the specification,

an active power equation of a branch of the power system;

a reactive power equation of a branch of the power system; loss_newIs an updated loss function;

active power equation of branch of electric power system

As follows:

in the formula，

For the deep neural network pair P_outAn estimated value of (d); p_outThe method comprises the steps of (1) providing standard power system branch active power; | | represents a norm;

in the formula (I), the compound is shown in the specification,

for the deep neural network pair Q_outAn estimated value of (d); q_outThe branch reactive power of the standardized electric power system is obtained;

3.3) update the weight w with back propagation, i.e.:

w_(i,T+1)＝w_(i,T)-Δw_(i,T)； (13)

in the formula,. DELTA.w_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAn amount of change in the weight matrix of the layer; w is a_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer; w is a_(i,T+1)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer;

t th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAmount of change Δ w of weight matrix of layer_(i,T)As follows:

in the formula, R_(i,T)Is the T th^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable;

R_(i,T)＝ρ*R_(i,T-1)+(1-ρ)*dw_(i,T)⊙dw_(i,T)； (15)

in the formula, dw_(i,T)Is the weight change amount; r_(i,T-1)Is the first (T-1)^thWhen the secondary weight is updated iteratively, the learning rate attenuates the variable;

weight change amount dw_(i,T)As follows:

wherein r is the serial number of the initial sample in the batch, and m is the sample size of the batch; k is an arbitrary sample sequence;

3.4) update bias b with back propagation, i.e.:

b_(i,T+1)＝b_(i,T)-Δb_(i,T)； (17)

in the formula,. DELTA.b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thAn amount of change in the bias matrix of the layer; b_(i,T)Is the T th^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers; b_(i,T+1)Is the (T +1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thBiasing of the layers;

t th^thWhen each parameter is updated, from the ith^thLayer to (i +1)^thAmount of change Δ b of bias matrix of layer_(i,T)As follows:

in the formula (II), R'_(i,T)Is the T th^thWhen the secondary bias is updated in an iterative manner, the learning rate attenuates the variable;

R'_(i,T)＝ρ*R'_(i,T-1)+(1-ρ)*db_(i,T)⊙db_(i,T)； (19)

in the formula db_(i,T)Is a bias change amount; r'_(i,T-1)Is the T-1^thWhen the secondary bias is updated in an iterative manner, the learning rate attenuates the variable;

bias change db_(i,T)As follows:

3.5) determining the original loss function loss and the updated loss function loss_newThe difference equation d (L) of (c) is as follows:

d(L)＝d₁+d₂+d₃； (21)

in the formula (d)₁、d₂And d₃Is a difference equation;

wherein, the ith^thThe layer difference equation d (i) is shown below:

d(i)＝d(i+1)w_(i,T-1)⊙max(0,y_i)； (22)

wherein d (i +1) is the (i +1) th^thA layer difference equation; max (×) represents taking the maximum value; y is_iOutputting data for the deep neural network; w is a_(i,T-1)Is the first (T-1)^thWhen each parameter is updated, from the ith^thLayer to i +1^thThe weight of the layer;

based on the formula (21) and the formula (22), the weight change amount dw_(i,T)Satisfies the following formula:

dw_(i,T)＝d(i)^Ty_i/m； (23)

in the formula, superscript T represents transposition;

difference parameter d₁A difference parameter d₂And a difference parameter d₃Respectively as follows:

wherein Y is the probability trendThe output vector of (1);

is the output of the deep neural network; y is

The denormalized value of (a); p is the active power of the power system;

an estimated value of the active power of the deep neural network to the power system; q is reactive power of the power system;

an estimate of the reactive power of the electrical power system for the deep neural network;

equation of difference d₂And difference equation d₃The contribution weights to the output feature vector of the deep neural network are respectively as follows:

in the formula (d)_θ[L]、d_1,θ、d_2,θAnd d_3,θIs denoted by d_θ[L]Equation of difference d₁Equation of difference d₂And difference equation d₃A medium voltage phase angle output vector; d_v[L]、d_1,v、d_2,vAnd d_3,vIs denoted by d_v[L]Equation of difference d₁Equation of difference d₂And difference equation d₃Medium voltage amplitude output vector d L]Is the equation of difference d₂And difference equation d₃The total contribution weight of (c); d_θ[L]Express difference equation d₂And difference equation d₃A contribution weight to a voltage phase angle output vector of the deep neural network; d_v[L]Express difference equation d₂And difference equation d₃A contribution weight to a voltage magnitude output vector of the deep neural network;

the empirical value α and the empirical value β are respectively as follows:

where max is a function that returns the maximum value and abs is a function that returns the absolute value;

4) the method comprises the following steps of establishing a probabilistic tidal current deep learning calculation model:

4.1) establishing a power flow probability equation derivation formula of the power system, wherein the derivation formula is shown as formulas (29) to (34);

in the formula, V_iIs the voltage amplitude of bus i; theta_ijIs the voltage phase angle difference between bus i and bus j; g_ijAnd B_ijAre respectively the ith^thA bus and a jth bus^thConductance and susceptance between the individual buses; theta_iIs the voltage phase angle, θ, of the bus i_jIs the voltage phase angle of bus j; v_jIs the voltage amplitude of bus j;

4.2) removing the guide of the physical model to the voltage amplitude in the deep neural network learning process;

4.3) removing guidance of reactive power to a voltage phase angle in the deep neural network learning process;

4.4) based on the steps 4.1) to 4.3), establishing a probabilistic power flow deep learning calculation model, which mainly comprises the following steps:

4.4.1) determining the weight of the probability trend deep learning calculation model, namely:

wherein the calculation of d (L) is simplified as follows:

in the formula (I), the compound is shown in the specification,

an estimated value of the parameter theta for the neural network;

d(L)＝d₁； (37)

wherein d (L) is the equation of difference;

4.4.2) establishing a probabilistic power flow deep learning calculation model: establishing a probabilistic power flow deep learning calculation model based on physical model driving according to the formula (2) to the formula (3), the formula (13) to the formula (15), the formula (17) to the formula (19), the formula (36) to the formula (37);

5) and calculating the probability load flow of the power system to be measured by utilizing the probability load flow deep learning calculation model.

2. The physical model-based probabilistic power flow deep learning calculation method according to claim 1, wherein the power system data mainly comprises wind speed, photovoltaic power and load.

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