CN105528674A - Grid planning method based on stochastic dual dynamic theory - Google Patents

Abstract

The present invention provides a grid planning method based on the stochastic dual dynamic theory. The method comprises the steps of establishing a grid planning mathematical model, selecting a grid operation scene, solving a grid planning mathematical model, checking the grid operation scene, and using the stochastic dual dynamic theory to optimize the grid planning mathematical model. According to the invention, a load uncertainty and a renewable energy uncertainty are considered, the renewable energy utilization rate is considered, thus a renewable energy access requirement can be satisfied by a planning scheme, the feasibility of the grid planning in different scenes is considered, thus the planning scheme has strong robustness, the N-k safety verification is considered comprehensively, the safety operation requirement can be satisfied by the planning scheme, the SDDP theory is used to establish a grid planning mathematical model under the circumstance of uncertainty, the Bender decomposition method is employed to solve the grid planning mathematical model, and the solving difficulty is reduced.

Description

Power grid planning method based on random dual dynamic theory

Technical Field

The invention belongs to the technical field of power grid planning, and particularly relates to a power grid planning method based on a random dual dynamic theory.

Background

As the load and the power generation capacity increase year by year, the power grid needs to be reinforced to improve the transmission capacity, optimize the line investment cost and meet certain operation safety constraints, which is a problem to be solved in power grid planning. With the large scale access of renewable energy sources, it is necessary to transport renewable energy sources far from the load center to the load center in a long-distance transportation manner. Due to the intermittency of renewable energy sources and the difficulty of long-distance transportation, the complexity of power grid planning is increased.

In existing power grid planning studies, more and more studies are taking into account load uncertainty and renewable energy uncertainty in power grid planning. Various methods are used to resolve uncertainties in power grid planning, including Stochastics Dual Dynamic Programming (SDDP). The uncertainty in the power generation planning is investigated with SDDP in the literature "generationexplanationplanning undivided with the properties quotas" (electrical power systems research,2014, vol.114, pp.78-85); the transmission-generation planning problem was studied using the SDDP method in the document "power systems investments planning storage dual dynamic programming" (docorof philiosophy, electrocaland computing engineering, university of cantury, 2008); the thermal-hydro power scheduling problem was investigated using the SDDP method in the literature "sampling and training boiler and boiler system" learning and boiler system "engineering and boiler.

In the existing power grid planning research, N-k safety verification is not considered enough. Most processing methods are to perform N-k verification at the final stage of planning, and if the N-k verification is not satisfied, the relevant lines are reinforced. Such processing methods may not result in an optimal planning solution.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a power grid planning method based on a stochastic dual dynamic theory.

In order to achieve the purpose of the invention, the invention adopts the following technical scheme:

the invention provides a power grid planning method based on a random dual dynamic theory, which comprises the following steps:

step 1: establishing a power grid planning mathematical model;

step 2: selecting a power grid operation scene;

and step 3: solving a power grid planning mathematical model;

and 4, step 4: checking a power grid operation scene;

and 5: and optimizing a power grid planning mathematical model by adopting a random dual dynamic theory.

In the step 1, the uncertainty of the load and the renewable energy is considered, a power grid planning mathematical model is established by taking the sum of the line investment cost and the expected operation cost as a target, and an objective function F is expressed as:

the corresponding constraints of the objective function F are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(2\right)$

$\begin{array}{cc}-B_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(3\right)$

$\begin{array}{cc}{B}_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(4\right)$

$\begin{array}{cc}-{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(5\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(6\right)$

$\begin{array}{cc}\mathrm{\σ}\·\underset{w}{\Σ}{\stackrel{\‾}{p}}_{w,d}^t\left(\mathrm{\ξ}\right)\≤\underset{w}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)& \∀d,\∀t,s\∈S_0,\∀\mathrm{\ξ}\∈\mathrm{\Λ}\end{array}---\left(7\right)$

$\begin{array}{cc}0\≤p_{w,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_{w,d}^t\left(\mathrm{\ξ}\right)& \∀w,\∀d,\∀t,\∀s\∈S,\∀\mathrm{\ξ}\end{array}---\left(7\right)$

$\begin{array}{cc}0\≤q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(9\right)$

$\begin{array}{cc}\underset{i\∈B}{\Σ}{q}_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\mathrm{\ϵ}}_{\left|s\right|}{D}_d^t\left(\mathrm{\ξ}\right)& \∀s,\∀d,\∀t,\∀\mathrm{\ξ}\∈\mathrm{\Λ}\end{array}---\left(10\right)$

$\begin{array}{cc}{x}_e^t=1& \∀e\∈E_0,\∀t\end{array}---\left(11\right)$

$\begin{array}{cc}{x}_e^{t-1}\≤x_e^t,x_e^t\∈\{0,1\}& \∀e\∈E\backslash E_0,\∀t\end{array}---\left(12\right)$

wherein r is^t-1The swelling rate in the t-1 year is shown, t is 1,2, …, NT and NT show the planned years; e denotes the set of all lines, E₀Representing an existing set of lines;indicating the state of the line e in the t year; ND represents the number of load time segments divided per year, d is 1,2, …, ND; Δ d represents the number of hours per time period; c_gRepresents the power generation cost of the generator G, G is 1,2, … and G_t，G_tRepresents the generator set of the t year;denotes a calculated expected value, ξ denotes samples of random variables, and ξ∈ xi, xi denote a set of samples of all random variables;representing the generated power of the generator G under a sample ξ when the generator G normally operates in the tth period of the year_i,tRepresenting a set of generators at node i of the t year;representing the power generation power of the generator g under the accident s and the sample ξ in the tth period of the t year_·iRepresenting a set of lines ending in node i, E_i·Representing a line set with a starting end as a node i;represents the transmission power of line e at the d-th time period of the year, incident s, sample ξ;represents the generated power of renewable energy source W under the d-th time period accident s and the sample ξ in the t year, wherein W is 1,2, … and W_i,t，W_i,tRepresenting a set of renewable energy sources on node i in the t year;representing the load shedding amount of node i at the tth period accident s, sample ξ in the t year;representing the load on node i at the d-th time period of year t, sample ξ, B_eRepresents the reactance of line e; i.e. i_eAnd j_eRespectively representing a starting node and a tail end node of a line e;represents the initial node i under the d period accident s and the sample ξ in the t year_eThe phase angle of (d);represents the end node j under the d period accident s, sample ξ of the t year_eThe phase angle of (d); m_eRepresents a constant;indicating the state of the line e under the accident s,taking 0 indicates normal operation, which takes1 represents exiting the run;represents the maximum capacity of line e under accident s;representing the power generation capacity of the generator g in the t year;the method comprises the steps of obtaining a total power of renewable energy sources w under a sample ξ in the ith time period of the t year, wherein the total power is the maximum power generation power of the renewable energy sources w under the sample ξ;_|s|indicating the allowable load shedding proportion under the accident s; s represents all accident sets; s₀Λ denotes a given sample set of random variables, ξ∈Λ;representing the load under the sample ξ at the d-th period of the year t, B representing the set of nodes, inv_eRepresents the annual investment cost of line e, expressed as:

inv_e＝C_e·r(1+r)^y/((1+r)^y-1)(13)

wherein, C_eRepresents the total investment cost of the line e, r represents the percent swelling, and y represents the line cost recovery years.

In the step 2, the selection of the power grid operation scene comprises the following two conditions:

1) under the conditions of large load and small power generation power of renewable energy sources, the power grid can output the traditional power generation power to the load;

2) when the load is large and the power generated by the renewable energy source is large, the power grid can transmit the power generated by the renewable energy source to the load.

In the step 3, the power grid planning stage is firstly decomposed into a power grid planning main stage and a power grid planning sub-stage by adopting a Benders decomposition method, and the power grid planning mathematical model is solved in the power grid planning main stage and the power grid planning sub-stage respectively.

Solving the power grid planning mathematical model in the main power grid planning stage, wherein the solving comprises the following steps:

the objective function f is used for minimizing the sum of the line investment cost and the expected operation cost in the main stage of power grid planning₁Expressed as:

$\begin{array}{cc}\min & f_1=\underset{t=1}{\overset{NT}{\Σ}}{r}^{t-1}\underset{e\∈E}{\Σ}(x_e^t-x_e^{t-1})C_e\end{array}---\left(14\right)$

wherein,representing the state of the line e in the t-1 year;

objective function f₁The corresponding constraints are equations (11) and (12).

In a power grid planning sub-stage, according to different accident quantities, the sub-stage of power grid planning is divided into k +1 classes, wherein s is 0,1,2, …, k and k represent the level of N-k safety check to be considered; the following two cases are specifically distinguished:

1) dividing SP-0 into SP-0(t, d, ξ), and taking the minimum sum of load shedding amount and renewable energy utilization amount as the target function f₂Expressed as:

$\begin{array}{cc}Min& f_2=\underset{i\∈B}{\Σ}{q}_{i,d}^{t,0}\left(\mathrm{\ξ}\right)+j_d^t\left(\mathrm{\ξ}\right)\end{array}---\left(15\right)$

objective function f₂The corresponding constraints are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,0}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,0}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i\end{array}---\left(16\right)$

$\begin{array}{cc}-B_e({\mathrm{\θ}}_{i_e,d}^{t,0}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,0}\left(\mathrm{\ξ}\right))\≤-f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)-M_e(1-{\tilde{x}}_e^t)& \∀e\end{array}---\left(17\right)$

$\begin{array}{cc}{B}_e({\mathrm{\θ}}_{i_e,d}^{t,0}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,0}\left(\mathrm{\ξ}\right))\≤f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)+M_e(1-{\tilde{x}}_e^t)& \∀e\end{array}---\left(18\right)$

$\begin{array}{cc}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^0{\tilde{x}}_e^t& \∀e\end{array}---\left(19\right)$

$\begin{array}{cc}-f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^0{\tilde{x}}_e^t& \∀e\end{array}---\left(20\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g\end{array}---\left(21\right)$

$\mathrm{\σ}\·\underset{w}{\Σ}{\stackrel{\‾}{p}}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)\≤\underset{w}{\Σ}{p}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)+j_d^t\left(\mathrm{\ξ}\right)---\left(22\right)$

wherein,indicating node ξ under sample operating normally during the tth period of timei load shedding amount;representing the amount of renewable energy w utilization at sample ξ for normal operation at the tth period of time in year t;represents the transmission power at sample ξ for line e operating normally during the tth period of the year;represents the generated power of renewable energy source w under sample ξ in the normal operation of the tth time period of the t year;represents the starting node i under the sample ξ for the d period of normal operation in the t year_eThe phase angle of (d);represents the end node j under sample ξ for the d-th period of the t-th year in normal operation_eThe phase angle of (d);representing the state of a circuit e in the t year in power grid planning;represents the maximum capacity of line e for normal operation;represents the maximum generated power of the renewable energy source w under the sample ξ in the ith time period of the t year;

2) when the power grid is in an accident state, | s | ═ k, recorded as SP-k, and dividing SP-k intoTarget function f with minimum load shedding amount as target₃Expressed as:

$\begin{array}{cc}Min& f_3=\underset{i\∈B}{\Σ}{q}_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\end{array}---\left(23\right)$

objective function f₃The corresponding constraints are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i\end{array}---\left(24\right)$

$\begin{array}{cc}-B_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e\end{array}---\left(25\right)$

$\begin{array}{cc}{B}_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e\end{array}---\left(26\right)$

$\begin{array}{cc}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^e(1-{\tilde{h}}_e^s)& \∀e\end{array}---\left(27\right)$

$\begin{array}{cc}-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e\end{array}---\left(28\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g\end{array}---\left(29\right)$

$\begin{array}{cc}0\≤p_{w,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_{w,d}^t& \∀w\end{array}---\left(30\right)$

$\begin{array}{cc}0\≤q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤D_{i,d}^t& \∀i\end{array}---\left(31\right)$

wherein,represents the maximum generated power of the renewable energy source w in the d-th time period of the t year;representing the load on node i at the d-th time period of year t.

The step 4 specifically comprises the following steps:

step 4-1: load shedding and renewable energy utilization rate verification are carried out; the method specifically comprises the following steps:

the method comprises the following steps that SP-0(t, d, xi) exists in a normal operation state of a power grid, if the sum of load shedding amount and renewable energy utilization amount is larger than 0 in the normal operation state of the power grid, it is indicated that the load shedding amount and the renewable energy utilization amount do not reach a corresponding proportion, namely the load shedding amount and the renewable energy utilization rate do not pass verification;

step 4-2: carrying out N-k security check; the method specifically comprises the following steps:

in the event of an accident in the power grid, there areAnd if the minimum load capacity of the power grid in the accident state is larger than the allowed load shedding capacity, the N-k safety check is not passed.

The step 5 specifically comprises the following steps:

step 5-1: setting the iteration number ll to 0 and setting the power gridRun cost estimate at the ll-th iteration in the planning sub-phaseIs 0;

step 5-2, selecting samples ξ of N random variables₁,ξ₂,...,ξ_N；

Step 5-3: increasing the iteration number ll +1, and calculating the minimum value z of the sum of the construction cost and the expected operation cost, wherein the minimum value z comprises the following steps:

wherein,representing the estimated value of the operation cost in the ll-1 iteration in the sub-stage of the power grid planning, c representing the line construction cost, c^TDenotes the transpose of c, x denotes the variable; intermediate volume Represents n₁A line state set of stages, wherein A represents a matrix and b represents a vector;

then updating the line state x_llSetting a lower limit z of z_l；

Step 5-4, from ξ₁,ξ₂,...,ξ_NIn which samples ξ of M random variables are selected₁,ξ₂,...,ξ_MFor the current solution x_ll∈% for calculating the function in the network planning sub-stageThe corresponding constraint condition is Tx + Wy ═ h, wherein q and h are vectors, and q is^TThe transpose of q is represented by,w, T is matrix, y is variable, and y is more than or equal to 0;

recording function in power grid planning sub-phaseThe optimal solution under the samples of different random variables is theta_jAnd is andy_jdenotes the j-th variable, j-1, 2, …, M,denotes q_jTranspose of (q)_jRepresents the jth vector;

calculating the upper limit z of z_uAnd standard deviation σ_uThe method comprises the following steps:

$z_u=c^{T}x+\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\θ}}_j---\left(33\right)$

${\mathrm{\σ}}_u=\sqrt{\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{(c^{T}x+{\mathrm{\θ}}_j)}^2-z_u^2}---\left(34\right)$

if it is notIf true, stopping forward estimation, wherein gamma_α/2Quantile of (1- α) for a standard normal distribution;

step 5-5: backward estimation, including:

for the current solution x_ll∈ χ, and optionally ξ ═ ξ_jj 1.. N, calculating a function in a network planning sub-stageAnd a functionDual function of (2) The corresponding constraint is Tx + Wy-h,corresponding constraint is W^TPi is less than or equal to q, pi, h and q represent vectors, pi^TTranspose of π, W, T TableDisplay matrix, W^TIs the transposition of W, y is variable and is more than or equal to 0;

in the sub-stage of power grid planningAndare respectively solved asAnd represents T_jTranspose of (1), T_jDenotes the jth vector, π_jRepresents the jth vector;

make an intermediate amountIntermediate volume ${\mathrm{\ρ}}_{ll}(x-x_{ll})=-\frac{1}{N}\underset{j=1}{\overset{N}{\Σ}}{T}_j^T{\mathrm{\π}}_j,$ ComputingComprises the following steps:

and returning to the step 5-3.

Compared with the prior art, the invention has the beneficial effects that:

1) the invention considers the load uncertainty and the renewable energy uncertainty, and considers the renewable energy utilization rate, so that the planning scheme can meet the renewable energy access requirement;

2) the feasibility of power grid planning under different scenes is considered, so that the planning scheme has high robustness;

3) according to the method, N-k safety check is comprehensively considered, so that a planning scheme can meet the requirement of safe operation;

4) the method adopts an SDDP theory to establish a power grid planning mathematical model under the uncertain condition;

5) the method adopts a Bender decomposition method to solve the power grid planning mathematical model, and reduces the solving difficulty.

Drawings

FIG. 1 is a flow chart of a mathematical model for optimizing power grid planning using stochastic dual dynamics theory according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

The invention provides a power grid planning method based on a random dual dynamic theory, which comprises the following steps:

step 1: establishing a power grid planning mathematical model;

step 2: selecting a power grid operation scene;

and step 3: solving a power grid planning mathematical model;

and 4, step 4: checking a power grid operation scene;

and 5: and optimizing a power grid planning mathematical model by adopting a random dual dynamic theory.

In the step 1, the uncertainty of the load and the renewable energy is considered, a power grid planning mathematical model is established by taking the sum of the line investment cost and the expected operation cost as a target, and an objective function F is expressed as:

the corresponding constraints of the objective function F are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(2\right)$

$\begin{array}{cc}-B_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(3\right)$

$\begin{array}{cc}{B}_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(4\right)$

$\begin{array}{cc}-{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(5\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(6\right)$

$\begin{array}{cc}\mathrm{\σ}\·\underset{w}{\Σ}{\stackrel{\‾}{p}}_{w,d}^t\left(\mathrm{\ξ}\right)\≤\underset{w}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)& \∀d,\∀t,s\∈S_0,\∀\mathrm{\ξ}\∈\mathrm{\Λ}\end{array}---\left(7\right)$

$\begin{array}{cc}0\≤p_{w,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_{w,d}^t\left(\mathrm{\ξ}\right)& \∀w,\∀d,\∀t,\∀s\∈S,\∀\mathrm{\ξ}\end{array}---\left(8\right)$

$\begin{array}{cc}0\≤q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(9\right)$

$\begin{array}{cc}\underset{i\∈B}{\Σ}{q}_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\mathrm{\ϵ}}_{\left|s\right|}{D}_d^t\left(\mathrm{\ξ}\right)& \∀s,\∀d,\∀t,\∀\mathrm{\ξ}\∈\mathrm{\Λ}\end{array}---\left(10\right)$

$\begin{array}{cc}{x}_e^t=1& \∀e\∈E_0,\∀t\end{array}---\left(11\right)$

$\begin{array}{cc}{x}_e^{t-1}\≤x_e^t,x_e^t\∈\{0,1\}& \∀e\∈E\backslash E_0,\∀t\end{array}---\left(12\right)$

wherein r is^t-1The swelling rate in the t-1 year is shown, t is 1,2, …, NT and NT show the planned years; e denotes the set of all lines, E₀Representing an existing set of lines;indicating the state of the line e in the t year; ND represents the number of load time segments divided per year, d is 1,2, …, ND; Δ d represents the number of hours per time period; c_gRepresents the power generation cost of the generator G, G is 1,2, … and G_t，G_tRepresents the generator set of the t year;denotes a calculated expected value, ξ denotes samples of random variables, and ξ∈ xi, xi denote a set of samples of all random variables;representing the generated power of the generator G under a sample ξ when the generator G normally operates in the tth period of the year_i,tRepresenting a set of generators at node i of the t year;representing the power generation power of the generator g under the accident s and the sample ξ in the tth period of the t year_·iRepresenting a set of lines ending in node i, E_i·Representing a line set with a starting end as a node i;represents the transmission power of line e at the d-th time period of the year, incident s, sample ξ;represents the generated power of renewable energy source W under the d-th time period accident s and the sample ξ in the t year, wherein W is 1,2, … and W_i,t，W_i,tRepresenting a set of renewable energy sources on node i in the t year;representing the load shedding amount of node i at the tth period accident s, sample ξ in the t year;representing the load on node i at the d-th time period of year t, sample ξ, B_eRepresents the reactance of line e; i.e. i_eAnd j_eRespectively representing a starting node and a tail end node of a line e;represents the initial node i under the d period accident s and the sample ξ in the t year_eThe phase angle of (d);represents the end node j under the d period accident s, sample ξ of the t year_eThe phase angle of (d); m_eRepresents a constant;indicating the state of the line e under the accident s,taking 0 for normal operation and 1 for quitting operation;represents the maximum capacity of line e under accident s;representing the power generation capacity of the generator g in the t year;the method comprises the steps of obtaining a total power of renewable energy sources w under a sample ξ in the ith time period of the t year, wherein the total power is the maximum power generation power of the renewable energy sources w under the sample ξ;_|s|indicating the allowable load shedding proportion under the accident s; s represents all accident sets; s₀Λ denotes a given sample set of random variables, ξ∈Λ;represents the load at sample ξ at the tth time period of year t;b represents a node set; inv_eRepresents the annual investment cost of line e, expressed as:

inv_e＝C_e·r(1+r)^y/((1+r)^y-1)(13)

wherein, C_eRepresents the total investment cost of the line e, r represents the percent swelling, and y represents the line cost recovery years.

In the step 2, the selection of the power grid operation scene comprises the following two conditions:

1) under the conditions of large load and small power generation power of renewable energy sources, the power grid can output the traditional power generation power to the load;

2) when the load is large and the power generated by the renewable energy source is large, the power grid can transmit the power generated by the renewable energy source to the load.

In the step 3, the power grid planning stage is firstly decomposed into a power grid planning main stage and a power grid planning sub-stage by adopting a Benders decomposition method, and the power grid planning mathematical model is solved in the power grid planning main stage and the power grid planning sub-stage respectively.

Solving the power grid planning mathematical model in the main power grid planning stage, wherein the solving comprises the following steps:

the objective function f is used for minimizing the sum of the line investment cost and the expected operation cost in the main stage of power grid planning₁Expressed as:

$\begin{array}{cc}\min & f_1=\underset{t=1}{\overset{NT}{\Σ}}{r}^{t-1}\underset{e\∈E}{\Σ}(x_e^t-x_e^{t-1})C_e\end{array}---\left(14\right)$

wherein,representing the state of the line e in the t-1 year;

objective function f₁The corresponding constraints are equations (11) and (12).

In a power grid planning sub-stage, according to different accident quantities, the sub-stage of power grid planning is divided into k +1 classes, wherein s is 0,1,2, …, k and k represent the level of N-k safety check to be considered; the following two cases are specifically distinguished:

1) under the normal operation state of the power grid, | s | ═ 0, marked as SP-0, and load shedding and the utilization rate of renewable energy can meet the requirements under the given scene needing to be verified; will be provided withSP-0 is divided into SP-0(t, d, ξ), and the objective function f is used to minimize the sum of load shedding amount and renewable energy utilization amount₂Expressed as:

$\begin{array}{cc}Min& f_2=\underset{i\∈B}{\Σ}{q}_{i,d}^{t,0}\left(\mathrm{\ξ}\right)+j_d^t\left(\mathrm{\ξ}\right)\end{array}---\left(15\right)$

objective function f₂The corresponding constraints are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,0}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,0}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i\end{array}---\left(16\right)$

$\begin{array}{cc}-B_e({\mathrm{\θ}}_{i_e,d}^{t,0}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,0}\left(\mathrm{\ξ}\right))\≤-f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)-M_e(1-{\tilde{x}}_e^t)& \∀e\end{array}---\left(17\right)$

$\begin{array}{cc}{B}_e({\mathrm{\θ}}_{i_e,d}^{t,0}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,0}\left(\mathrm{\ξ}\right))\≤f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)+M_e(1-{\tilde{x}}_e^t)& \∀e\end{array}---\left(18\right)$

$\begin{array}{cc}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^0{\tilde{x}}_e^t& \∀e\end{array}---\left(19\right)$

$\begin{array}{cc}-f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^0{\tilde{x}}_e^t& \∀e\end{array}---\left(20\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g\end{array}---\left(21\right)$

$\mathrm{\σ}\·\underset{w}{\Σ}{\stackrel{\‾}{p}}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)\≤\underset{w}{\Σ}{p}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)+j_d^t\left(\mathrm{\ξ}\right)---\left(22\right)$

wherein,represents the load shedding amount of node i under sample ξ for the normal operation at the tth period in the t year;representing the amount of renewable energy w utilization at sample ξ for normal operation at the tth period of time in year t;represents the transmission power at sample ξ for line e operating normally during the tth period of the year;represents the generated power of renewable energy source w under sample ξ in the normal operation of the tth time period of the t year;represents the starting node i under the sample ξ for the d period of normal operation in the t year_eThe phase angle of (d);indicating that the d th period of the t year is positiveEnd node j under constant run, sample ξ_eThe phase angle of (d);representing the state of a circuit e in the t year in power grid planning;represents the maximum capacity of line e for normal operation;represents the maximum generated power of the renewable energy source w under the sample ξ in the ith time period of the t year;

2) when the power grid is in an accident state, | s | ═ k, recorded as SP-k, and dividing SP-k intoTarget function f with minimum load shedding amount as target₃Expressed as:

$\begin{array}{cc}Min& f_3=\underset{i\∈B}{\Σ}{q}_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\end{array}---\left(23\right)$

objective function f₃The corresponding constraints are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i\end{array}---\left(24\right)$

$\begin{array}{cc}-B_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e\end{array}---\left(25\right)$

$\begin{array}{cc}{B}_e({\mathrm{\θ}}_{i_e,d}^{t,s}\left(\mathrm{\ξ}\right)-{\mathrm{\θ}}_{j_e,d}^{t,s}\left(\mathrm{\ξ}\right))\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e\end{array}---\left(26\right)$

$\begin{array}{cc}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^e(1-{\tilde{h}}_e^s)& \∀e\end{array}---\left(27\right)$

$\begin{array}{cc}-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e\end{array}---\left(28\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g\end{array}---\left(29\right)$

$\begin{array}{cc}0\≤p_{w,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_{w,d}^t& \∀w\end{array}---\left(30\right)$

$\begin{array}{cc}0\≤q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤D_{i,d}^t& \∀i\end{array}---\left(31\right)$

wherein,represents the maximum generated power of the renewable energy source w in the d-th time period of the t year;representing the load on node i at the d-th time period of year t.

The step 4 specifically comprises the following steps:

step 4-1: load shedding and renewable energy utilization rate verification are carried out; the method specifically comprises the following steps:

the method comprises the following steps that SP-0(t, d, xi) exists in a normal operation state of a power grid, if the sum of load shedding amount and renewable energy utilization amount is larger than 0 in the normal operation state of the power grid, it is indicated that the load shedding amount and the renewable energy utilization amount do not reach a corresponding proportion, namely the load shedding amount and the renewable energy utilization rate do not pass verification;

step 4-2: carrying out N-k security check; the method specifically comprises the following steps:

in the event of an accident in the power grid, there areAnd if the minimum load capacity of the power grid in the accident state is larger than the allowed load shedding capacity, the N-k safety check is not passed.

As shown in fig. 1, the step 5 specifically includes the following steps:

step 5-1: setting the iteration number ll to be 0, and setting the estimated value of the running cost in the ll iteration in the sub-stage of the power grid planningIs 0;

step 5-2, selecting samples ξ of N random variables₁,ξ₂,...,ξ_N；

Step 5-3: increasing the iteration number ll +1, and calculating the minimum value z of the sum of the construction cost and the expected operation cost, wherein the minimum value z comprises the following steps:

wherein,representing the estimated value of the operation cost in the ll-1 iteration in the sub-stage of the power grid planning, c representing the line construction cost, c^TDenotes the transposition of c, x denotes the variationAn amount; intermediate volume Represents n₁A line state set of stages, wherein A represents a matrix and b represents a vector;

then updating the line state x_llSetting a lower limit z of z_l；

Step 5-4: forward estimation, including:

from ξ₁,ξ₂,...,ξ_NIn which samples ξ of M random variables are selected₁,ξ₂,...,ξ_MFor the current solution x_ll∈% for calculating the function in the network planning sub-stageThe corresponding constraint condition is Tx + Wy ═ h, wherein q and h are vectors, and q is^TRepresenting the transposition of q, wherein W, T is a matrix, y is a variable and is more than or equal to 0;

recording function in power grid planning sub-phaseThe optimal solution under the samples of different random variables is theta_jAnd is andy_jdenotes the j-th variable, j-1, 2, …, M,denotes q_jTranspose of (q)_jRepresents the jth vector;

calculating the upper limit z of z_uAnd standard deviation σ_uThe method comprises the following steps:

$z_u=c^{T}x+\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{\mathrm{\θ}}_j---\left(33\right)$

${\mathrm{\σ}}_u=\sqrt{\frac{1}{M}\underset{j=1}{\overset{M}{\Σ}}{(c^{T}x+{\mathrm{\θ}}_j)}^2-z_u^2}---\left(34\right)$

if it is notIf true, stopping forward estimation, wherein gamma_α/2Quantile of (1- α) for a standard normal distribution;

step 5-5: backward estimation, including:

for the current solution x_ll∈ χ, and optionally ξ ═ ξ_jj 1.. N, calculating a function in a network planning sub-stageAnd a functionDual function of (2) The corresponding constraint is Tx + Wy-h,corresponding constraint is W^TPi is less than or equal to q, pi, h and q represent vectors, pi^TIs a transposition of π, W, T denotes the matrix, W^TIs the transposition of W, y is variable and is more than or equal to 0;

in the sub-stage of power grid planningAndare respectively solved asAnd represents T_jTranspose of (1), T_jDenotes the jth vector, π_jRepresents the jth vector;

make an intermediate amountIntermediate volume ${\mathrm{\ρ}}_{ll}(x-x_{ll})=-\frac{1}{N}\underset{j=1}{\overset{N}{\Σ}}{T}_j^T{\mathrm{\π}}_j,$ ComputingComprises the following steps:

and returning to the step 5-3.

Finally, it should be noted that: the above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person of ordinary skill in the art can make modifications or equivalents to the specific embodiments of the present invention with reference to the above embodiments, and such modifications or equivalents without departing from the spirit and scope of the present invention are within the scope of the claims of the present invention as set forth in the claims.

Claims (8)

1. A power grid planning method based on a random dual dynamic theory is characterized in that: the method comprises the following steps:

step 1: establishing a power grid planning mathematical model;

step 2: selecting a power grid operation scene;

and step 3: solving a power grid planning mathematical model;

and 4, step 4: checking a power grid operation scene;

and 5: and optimizing a power grid planning mathematical model by adopting a random dual dynamic theory.

2. The power grid planning method based on the stochastic dual dynamics theory according to claim 1, wherein: in the step 1, the uncertainty of the load and the renewable energy is considered, a power grid planning mathematical model is established by taking the sum of the line investment cost and the expected operation cost as a target, and an objective function F is expressed as:

the corresponding constraints of the objective function F are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(2\right)$

$\begin{array}{cc}-B_e\left({\mathrm{\θ}}_{i_e,d}^{t,s}\right(\mathrm{\ξ})-{\mathrm{\θ}}_{j_e,d}^{t,s}(\mathrm{\ξ}\left)\right)\≤-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(3\right)$

$\begin{array}{cc}{B}_e\left({\mathrm{\θ}}_{i_e,d}^{t,s}\right(\mathrm{\ξ})-{\mathrm{\θ}}_{j_e,d}^{t,s}(\mathrm{\ξ}\left)\right)\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(4\right)$

$\begin{array}{cc}-{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(5\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(6\right)$

$\begin{array}{cc}\mathrm{\σ}\·\underset{w}{\Σ}{\stackrel{\‾}{p}}_{w,d}^t\left(\mathrm{\ξ}\right)\≤\underset{w}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)& \∀d,\∀t,s\∈S_0,\∀\mathrm{\ξ}\∈\mathrm{\Λ}\end{array}---\left(7\right)$

$\begin{array}{cc}0\≤p_{w,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_{w,d}^t\left(\mathrm{\ξ}\right)& \∀w,\∀d,\∀t,\∀s\∈S,\∀\mathrm{\ξ}\end{array}---\left(8\right)$

$\begin{array}{cc}0\≤q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i,\∀d,\∀t,\∀s,\∀\mathrm{\ξ}\end{array}---\left(9\right)$

$\begin{array}{cc}\underset{i\∈B}{\Σ}{q}_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\mathrm{\ϵ}}_{\left|s\right|}{D}_d^t\left(\mathrm{\ξ}\right)& \∀s,\∀d,\∀t,\∀\mathrm{\ξ}\∈\mathrm{\Λ}\end{array}---\left(10\right)$

$\begin{array}{cc}{x}_e^t=1& \∀e\∈E_0,\∀t\end{array}---\left(11\right)$

$\begin{array}{cc}{x}_e^{t-1}\≤x_e^t,x_e^t\∈\{0,1\}& \∀e\∈E\backslash E_0,\∀t\end{array}---\left(12\right)$

wherein r is^t-1The swelling rate in the t-1 year is shown, t is 1,2, …, NT and NT show the planned years; e denotes the set of all lines, E₀Representing an existing set of lines;indicating the state of the line e in the t year; ND represents the number of load time segments divided per year, d is 1,2, …, ND; Δ d represents the number of hours per time period; c_gRepresents the power generation cost of the generator G, G is 1,2, … and G_t，G_tRepresents the generator set of the t year;denotes a calculated expected value, ξ denotes samples of random variables, and ξ∈ xi, xi denote a set of samples of all random variables;representing the generated power of the generator G under a sample ξ when the generator G normally operates in the tth period of the year_i,tRepresenting a set of generators at node i of the t year;representing the power generation power of the generator g under the accident s and the sample ξ in the tth period of the t year_·iRepresenting a set of lines ending in node i, E_i·Representing a line set with a starting end as a node i;represents the transmission power of line e at the d-th time period of the year, incident s, sample ξ;represents the generated power of renewable energy source W under the d-th time period accident s and the sample ξ in the t year, wherein W is 1,2, … and W_i,t，W_i,tRepresenting a set of renewable energy sources on node i in the t year;representing the load shedding amount of node i at the tth period accident s, sample ξ in the t year;representing the load on node i at the d-th time period of year t, sample ξ, B_eRepresents the reactance of line e; i.e. i_eAnd j_eRespectively representing a starting node and a tail end node of a line e;represents the initial node i under the d period accident s and the sample ξ in the t year_eThe phase angle of (d);represents the end node j under the d period accident s, sample ξ of the t year_eThe phase angle of (d); m_eRepresents a constant;indicating the state of the line e under the accident s,taking 0 for normal operation and 1 for quitting operation;represents the maximum capacity of line e under accident s;representing the power generation capacity of the generator g in the t year;the method comprises the steps of obtaining a total power of renewable energy sources w under a sample ξ in the ith time period of the t year, wherein the total power is the maximum power generation power of the renewable energy sources w under the sample ξ;_|s|indicating the allowable load shedding proportion under the accident s; s represents all accident sets; s₀Λ denotes a given sample set of random variables, ξ∈Λ;representing the load under the sample ξ at the d-th period of the year t, B representing the set of nodes, inv_eRepresents the annual investment cost of line e, expressed as:

inv_e＝C_e·r(1+r)^y/((1+r)^y-¹)(13)

wherein, C_eRepresents the total investment cost of the line e, r represents the percent swelling, and y represents the line cost recovery years.

3. The power grid planning method based on the stochastic dual dynamics theory according to claim 2, wherein: in the step 2, the selection of the power grid operation scene comprises the following two conditions:

1) under the conditions of large load and small power generation power of renewable energy sources, the power grid can output the traditional power generation power to the load;

2) when the load is large and the power generated by the renewable energy source is large, the power grid can transmit the power generated by the renewable energy source to the load.

4. The power grid planning method based on the stochastic dual dynamics theory according to claim 3, wherein: in the step 3, the power grid planning stage is firstly decomposed into a power grid planning main stage and a power grid planning sub-stage by adopting a Benders decomposition method, and the power grid planning mathematical model is solved in the power grid planning main stage and the power grid planning sub-stage respectively.

5. The power grid planning method based on the stochastic dual dynamics theory according to claim 4, wherein: solving the power grid planning mathematical model in the main power grid planning stage, wherein the solving comprises the following steps:

the objective function f is used for minimizing the sum of the line investment cost and the expected operation cost in the main stage of power grid planning₁Expressed as:

$\begin{array}{cc}\min & f_1=\underset{t=1}{\overset{NT}{\Σ}}{r}^{t-1}\underset{e\∈E}{\Σ}(x_e^t-x_e^{t-1})C_e\end{array}---\left(14\right)$

wherein,representing the state of the line e in the t-1 year;

objective function f₁The corresponding constraints are equations (11) and (12).

6. The power grid planning method based on the stochastic dual dynamics theory according to claim 5, wherein: in a power grid planning sub-stage, according to different accident quantities, the sub-stage of power grid planning is divided into k +1 classes, wherein s is 0,1,2, …, k and k represent the level of N-k safety check to be considered; the following two cases are specifically distinguished:

1) dividing SP-0 into SP-0(t, d, ξ), and taking the minimum sum of load shedding amount and renewable energy utilization amount as the target function f₂Expressed as:

$\begin{array}{cc}Min& f_2=\underset{i\∈B}{\Σ}{q}_{i,d}^{t,0}\left(\mathrm{\ξ}\right)+j_d^t\left(\mathrm{\ξ}\right)\end{array}---\left(15\right)$

objective function f₂The corresponding constraints are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,0}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,0}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i\end{array}---\left(16\right)$

$\begin{array}{cc}-B_e\left({\mathrm{\θ}}_{i_e,d}^{t,0}\right(\mathrm{\ξ})-{\mathrm{\θ}}_{j_e,d}^{t,0}(\mathrm{\ξ}\left)\right)\≤-f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)-M_e(1-{\tilde{x}}_e^t)& \∀e\end{array}---\left(17\right)$

$\begin{array}{cc}{B}_e\left({\mathrm{\θ}}_{i_e,d}^{t,0}\right(\mathrm{\ξ})-{\mathrm{\θ}}_{j_e,d}^{t,0}(\mathrm{\ξ}\left)\right)\≤f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)+M_e(1-{\tilde{x}}_e^t)& \∀e\end{array}---\left(18\right)$

$\begin{array}{cc}{f}_{e,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^0{\tilde{x}}_e^t& \∀e\end{array}---\left(19\right)$

$\begin{array}{cc}-f_{e,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^0{\tilde{x}}_e^t& \∀e\end{array}---\left(20\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,0}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g\end{array}---\left(21\right)$

$\mathrm{\σ}\·\underset{w}{\Σ}{\stackrel{\‾}{p}}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)\≤\underset{w}{\Σ}{p}_{w,d}^{t,0}\left(\mathrm{\ξ}\right)+j_d^t\left(\mathrm{\ξ}\right)---\left(22\right)$

wherein,represents the load shedding amount of node i under sample ξ for the normal operation at the tth period in the t year;representing the amount of renewable energy w utilization at sample ξ for normal operation at the tth period of time in year t;represents the transmission power at sample ξ for line e operating normally during the tth period of the year;represents the generated power of renewable energy source w under sample ξ in the normal operation of the tth time period of the t year;represents the starting node i under the sample ξ for the d period of normal operation in the t year_eThe phase angle of (d);represents the end node j under sample ξ for the d-th period of the t-th year in normal operation_eThe phase angle of (d);representing the state of a circuit e in the t year in power grid planning;represents the maximum capacity of line e for normal operation;represents the maximum generated power of the renewable energy source w under the sample ξ in the ith time period of the t year;

2) when the power grid is in an accident state, | s | ═ k, recorded as SP-k, and dividing SP-k intoTarget function f with minimum load shedding amount as target₃Expressed as:

$\begin{array}{cc}Min& f_3=\underset{i\∈B}{\Σ}{q}_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\end{array}---\left(23\right)$

objective function f₃The corresponding constraints are as follows:

$\begin{array}{cc}\underset{g\∈G_{i,t}}{\Σ}{p}_{g,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{e\∈E_{\·i}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-\underset{e\∈E_{i\·}}{\Σ}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+\underset{w\∈W_{i,t}}{\Σ}{p}_{w,d}^{t,s}\left(\mathrm{\ξ}\right)+q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)=D_{i,d}^t\left(\mathrm{\ξ}\right)& \∀i\end{array}---\left(24\right)$

$\begin{array}{cc}-B_e\left({\mathrm{\θ}}_{i_e,d}^{t,s}\right(\mathrm{\ξ})-{\mathrm{\θ}}_{j_e,d}^{t,s}(\mathrm{\ξ}\left)\right)\≤-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)-M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e\end{array}---\left(25\right)$

$\begin{array}{cc}{B}_e\left({\mathrm{\θ}}_{i_e,d}^{t,s}\right(\mathrm{\ξ})-{\mathrm{\θ}}_{j_e,d}^{t,s}(\mathrm{\ξ}\left)\right)\≤f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)+M_e(1-x_e^t+{\tilde{h}}_e^s)& \∀e\end{array}---\left(26\right)$

$\begin{array}{cc}{f}_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e\end{array}---\left(27\right)$

$\begin{array}{cc}-f_{e,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{f}}_e^s{x}_e^t(1-{\tilde{h}}_e^s)& \∀e\end{array}---\left(28\right)$

$\begin{array}{cc}0\≤p_{g,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_g^t& \∀g\end{array}---\left(29\right)$

$\begin{array}{cc}0\≤p_{w,d}^{t,s}\left(\mathrm{\ξ}\right)\≤{\stackrel{\‾}{p}}_{w,d}^t& \∀w\end{array}---\left(30\right)$

$\begin{array}{cc}0\≤q_{i,d}^{t,s}\left(\mathrm{\ξ}\right)\≤D_{i,d}^t& \∀i\end{array}---\left(31\right)$

wherein,represents the maximum generated power of the renewable energy source w in the d-th time period of the t year;representing the load on node i at the d-th time period of year t.

7. The power grid planning method based on the stochastic dual dynamics theory according to claim 6, wherein: the step 4 specifically comprises the following steps:

step 4-1: load shedding and renewable energy utilization rate verification are carried out; the method specifically comprises the following steps:

the method comprises the following steps that SP-0(t, d, xi) exists in a normal operation state of a power grid, if the sum of load shedding amount and renewable energy utilization amount is larger than 0 in the normal operation state of the power grid, it is indicated that the load shedding amount and the renewable energy utilization amount do not reach a corresponding proportion, namely the load shedding amount and the renewable energy utilization rate do not pass verification;

step 4-2: carrying out N-k security check; the method specifically comprises the following steps:

in the event of an accident in the power grid, there areAnd if the minimum load capacity of the power grid in the accident state is larger than the allowed load shedding capacity, the N-k safety check is not passed.

8. The power grid planning method based on the stochastic dual dynamics theory according to claim 1, wherein: the step 5 specifically comprises the following steps:

step 5-1: setting the iteration number ll to be 0, and setting the estimated value of the running cost in the ll iteration in the sub-stage of the power grid planningIs 0;

step 5-2, selecting samples ξ of N random variables₁,ξ₂,...,ξ_N；

Step 5-3: increasing the iteration number ll +1, and calculating the minimum value z of the sum of the construction cost and the expected operation cost, wherein the minimum value z comprises the following steps:

wherein,representing the estimated value of the operation cost in the ll-1 iteration in the sub-stage of the power grid planning, c representing the line construction cost, c^TDenotes the transpose of c, x denotes the variable; intermediate volume Represents n₁A line state set of stages, wherein A represents a matrix and b represents a vector;

then updating the line state x_llSetting a lower limit z of z_l；

Step 5-4: forward estimation, including:

from ξ₁,ξ₂,...,ξ_NIn which samples ξ of M random variables are selected₁,ξ₂,...,ξ_MFor the current solution x_ll∈% for calculating the function in the network planning sub-stageThe corresponding constraint condition is Tx + Wy ═ h, wherein q and h are vectors, and q is^TRepresenting the transposition of q, wherein W, T is a matrix, y is a variable and is more than or equal to 0;

recording function in power grid planning sub-phaseThe optimal solution under the samples of different random variables is theta_jAnd isy_jDenotes the j-th variable, j-1, 2, …,M，denotes q_jTranspose of (q)_jRepresents the jth vector;

calculating the upper limit z of z_uAnd standard deviation σ_uThe method comprises the following steps:

$z_u=c^{T}x+\frac{1}{M}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\θ}}_j---\left(33\right)$

${\mathrm{\σ}}_u=\sqrt{\frac{1}{M}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{(c^{T}x+{\mathrm{\θ}}_j)}^2-z_u^2}---\left(34\right)$

if it is notIf true, stopping forward estimation, wherein gamma_α/2Quantile of (1- α) for a standard normal distribution;

step 5-5: backward estimation, including:

for the current solution x_ll∈ χ, and optionally ξ ═ ξ_jj 1.. N, calculating a function in a network planning sub-stageAnd a functionDual function of (2) The corresponding constraint is Tx + Wy-h,corresponding constraint is W^TPi is less than or equal to q, pi, h and q represent vectors, pi^TIs a transposition of π, W, T denotes the matrix, W^TIs the transposition of W, y is variable and is more than or equal to 0;

in the sub-stage of power grid planningAndare respectively solved asAnd represents T_jTranspose of (1), T_jDenotes the jth vector, π_jRepresents the jth vector;

make an intermediate amountIntermediate volume ${\mathrm{\ρ}}_{ll}(x-x_{ll})=-\frac{1}{N}\underset{j=1}{\overset{N}{\Σ}}{T}_j^T{\mathrm{\π}}_j,$ ComputingComprises the following steps:

and returning to the step 5-3.