CN107404118A - Electrical interconnection system probability optimal load flow computational methods based on stochastic response surface - Google Patents

Abstract

The invention discloses a probabilistic optimal power flow calculation method for an electrical interconnection system based on the stochastic response surface method. The invention first establishes models of an electric power system and a natural gas system, and the electric power system and the natural gas system are coupled through a gas turbine to form an electric-gas interconnection system. Then, taking the minimum total operating cost of the interconnected system as the objective function, the operating constraints of the power system and the natural gas system are considered. In the optimization process, the influence of random factors such as electricity and gas loads, wind power, and light energy are considered, and the probability optimal power flow is solved by the particle swarm optimization algorithm to obtain the probability statistics information of the objective function and its state variables.

Description

Probabilistic Optimal Power Flow Calculation Method for Electrical Interconnection System Based on Stochastic Response Surface Method

technical field

The invention relates to a probabilistic optimal power flow calculation method for an electrical interconnection system based on a stochastic response surface method, and belongs to the technical field of multi-energy uncertainty analysis.

Background technique

Energy is the basis and important guarantee for human survival and the lifeline of the national economy. How to ensure sustainable energy supply while reducing environmental pollution is the focus of common concern in today's society. my country's long-term energy consumption structure dominated by fossil energy such as coal and petroleum has caused enormous environmental pressure. Therefore, improving energy utilization efficiency and developing clean, efficient, and pollution-free clean energy have become an inevitable choice to solve the increasingly prominent energy problems and environmental protection in the process of human society development. The electrical interconnection system uses gas turbines to establish the coupling of the power system and the natural gas system, and uses natural gas, which is cleaner than coal, to generate electricity, relieving energy pressure and reducing environmental pollution.

Compared with other primary energy sources, natural gas has less impact on the environment, is economical, has abundant reserves, and is easy to store. It can be used for emergency peak regulation and can be used for the coordination of random and indirect renewable energy; With the increasing proportion of the group on the power generation side, the coupling between the power system and the natural gas system will be further deepened, and the electrical interconnection system will become the main form of the future integrated energy network.

Optimal power flow (OPF) is an important tool for power system network planning and operation analysis. As the proportion of gas turbines in the power system gradually increases, the operation of the natural gas system will inevitably affect the results of OPF, but the traditional OPF does not consider the coupling between the power network and the natural gas network. The existing research on electrical interconnection systems is basically based on deterministic models, and there are few studies on the uncertainty of power systems and natural gas systems under the background of new energy access.

Contents of the invention

Purpose of the invention: The technical problem to be solved by the present invention is to adopt the stochastic response surface method to solve the uncertainty of electrical interconnection system under the connection of electricity, gas load and new energy, and the power generation cost is the lowest under the probability optimal power flow.

Technical solution: a probabilistic optimal power flow calculation method for electrical interconnection systems based on the stochastic response surface method, which is implemented in the following steps:

1) Obtain the parameter information of the power system for steady-state modeling. The parameter information includes: the topology of the transmission line network, the resistance and reactance of the π-type equivalent circuit, the conductance and susceptance of the parallel connection to the ground, the transformation ratio and impedance of the transformer, each Node load and generator output active and reactive power constraints, voltage constraints of each node;

2) Obtain the parameter information of the natural gas network for steady-state modeling. The parameter information includes: the topological structure of the gas pipeline, transmission efficiency and other parameter information, the topological structure of the booster station, the gas load of each node, and the natural gas output information of the gas source point , the pressure constraints of each node;

3) Obtain the coupling of the electrical interconnection system with various parameters and constraints of the gas turbine;

4) To establish the probability information of load, wind speed, and light for the uncertainty of load forecast, wind speed forecast, and light forecast;

5) The output response is expressed as a chaotic polynomial with known coefficients on the basis of the known input random variable probability distribution through the stochastic response surface method, and the undetermined coefficients in the polynomial are determined by the sampling points selected by the optimal point method, and then get the probability distribution of the estimated output response

6) According to the probability distribution of each variable, with the cost as the objective function, the cost value under the probability optimal power flow is obtained;

7) Output the probability statistics information of the state variables.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention;

Fig. 2 is a schematic diagram of a pressurization station driven by a gas turbine of the present invention;

Fig. 3 is a structural diagram of the electrical interconnection system of the present invention;

Figure 4 is a probability distribution diagram of power generation costs;

Fig. 5 is a probability distribution diagram of the voltage amplitude of the No. 7 node of the power system;

Fig. 6 is a probability distribution diagram of the pressure of the No. 4 node of the natural gas system.

detailed description

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

1 Steady-state modeling of power system

In the Cartesian coordinate system of the power system, the active power and reactive power of each point can be calculated according to the node voltage, P _i is the injected active power of the PQ node and the PV node, Q _i is the injected reactive power of the PQ node, U _i is the PV node voltage size. For node i in the power network:

In the formula: e _i , f _i are the real part and imaginary part of the voltage _vector of node _i respectively;

2 Steady-state modeling of natural gas system

The steady-state modeling of the natural gas system actually involves various components and is related to many factors. The present invention mainly performs steady-state modeling on the two main components of the natural gas pipeline and the pressurization station.

2.1 Pipe flow equation:

The flow equation of a natural gas pipeline is related to many factors including the pressure at both ends of the pipeline. Under ideal conditions, for a completely turbulent high-pressure gas network, the mn flow equation of the pipeline is:

in:

In the formula: f _kmn is the pipeline flow value; π _m is the pressure value of node m; π _n is the pressure value of node n; ε is the pipeline efficiency factor; T ₀ is the standard temperature value; D _k is the inner diameter of the pipeline k; π ₀ is the standard pressure value; Air is 1, natural gas is 0.6; L _k is the length of pipeline k; T _ka is the average gas temperature of pipeline k; Z _a is the average gas compression coefficient.

2.2 Energy Consumption Equation of Compressor

Due to the frictional resistance in the pipeline, the loss of natural gas will inevitably be caused. In order to compensate for the loss of natural gas, a pressurization station will be added to the system to increase the pressure of natural gas. The pressurization station increases the pressure through the compressor, which needs to consume additional energy. This energy can be provided by the equivalent gas load of the pressurization station, or it can be driven by electricity. This invention considers the equivalent gas load and considers it as natural gas load on the network.

in:

In the formula: f _k is the gas flow rate through the compressor; π _m is the gas injection compressor pressure; π _n is the gas output compressor pressure; Z _ki is the gas compression factor at the inflow end of the compressor; T _ki is the natural gas intake point of the compressor temperature; α is the adiabatic index; η _k is the efficiency of the pressurization station.

The flow of natural gas consumed to drive the pressurization station:

In the formula: α _Tk , β _Tk , and γ _Tk are conversion coefficients of consumed natural gas flow rate.

2.3 Natural gas flow balance equation

Similar to the node power equation in the power system, the natural gas flow conservation means that the inflow flow of each node is equal to the outflow flow, which can be expressed in the form of a matrix:

(A+U)f+w-Tτ＝0

in:

In the formula: f is the branch flow value vector; w is the gas injection vector of each node; τ is the consumption flow value vector of each compressor, matrix A is the line-node correlation matrix, which represents the connection between the pipeline and the node; the matrix U is the unit-node association matrix, which represents the connection between the unit and the node. T is the compressor consumption and node association matrix, which represents the connection between the gas turbine and the node.

3 Coupling between electric power system and natural gas system

The natural gas input of the gas turbine is regarded as the gas load of the natural gas system, and the power output of the natural gas consumed by the gas turbine is regarded as the power supply of the power system, so that the gas turbine couples the power system and the natural gas system, and the coupling relationship is:

In the formula: H _g,i is the input heat value of the gas turbine; _PG,i is the output power of the gas turbine to the power system node i; α _g,i , β _g,i , and γ _g,i are determined by the heat consumption rate curve of the gas turbine; Enter the gas flow rate of the gas turbine for the natural gas system; GHV=1015BTU/SCF, which is the high calorific value.

4 Probabilistic Optimal Power Flow of Electrical Interconnection System

According to the above model, the power system and the natural gas system are coupled through gas turbines to form an electrical interconnection system. Taking the total energy cost as the objective function, considering various constraints of power network, natural gas network and gas turbine, a probabilistic optimal power flow model of electrical interconnection system is established.

4.1 Objective function

The present invention takes the total energy cost of the system as the objective function:

In the formula: P _G is the set of non-gas turbines; a _i , b _i , _ci are the cost coefficients of generators; P _i is the active output of generators, _NS is the set of gas source points; g _i is the cost coefficient of natural gas; w _{g, i} is the natural gas supply.

4.2 Constraints

equality constraints

1) Power system equation constraints:

ΔP _i =P _G,i +P _W,i -P _L,i -P _i

ΔQ _i ＝Q _G,i -Q _L,i -Q _i

In the formula: ΔP _i , ΔQ _i is the unbalanced amount of active and reactive power of node i; P _G,i , Q _G,i are the active and reactive output of generator i respectively; P _W,i are the active output of gas turbine i; P _L,i , Q _L,i are the active and reactive loads of node i, respectively.

2) Natural gas system equality constraints:

Δw _i =w _g,i -w _L,i -F _i =0

In the formula: Δw _i is the unbalanced flow value of each node in the natural gas network; w _g,i is the gas injection volume of the gas source point to node i; w _L,i is the gas load of node i, and F _i is the gas load of node i injection volume.

inequality constraints

1) Power system inequality constraints:

P _Gmin,i ≤P _G,i ≤P _Gmax,i

Q _Gmin,i ≤Q _G,i ≤Q _Gmax,i

In the formula: P _Gmax,i , P _Gmin,i are the upper limit and lower limit of the active power generated by the generator; Q _Gmax,i , Q _Gmin,i are the upper limit and lower limit of the reactive power generated by the generator; are the upper and lower limits of the square of the node voltage amplitude.

2) Natural gas network inequality constraints:

w _gmin,i ≤w _g,i ≤w _gmax,i

π _min,i ≤π _i ≤π _max,i

In the formula: w _gmax,i , w _gmin,i are the upper limit and lower limit of the gas supply of each gas source point in the natural gas network; π _max,i , π _min,i are the upper limit and lower limit of the pressure value of each node; R _{max ,i} , R _min,i are the upper and lower limits of the pressurization ratio of the pressurization station respectively.

5 Analysis of Uncertain Factors

In actual production, both electrical load and gas load are random. Similarly, with the access of new energy sources such as wind power and photovoltaics, the randomness of wind speed and light intensity will also affect the system. The load, wind farm, and solar power plant are analyzed below.

5.1 Randomness of load

The loads of the electrical interconnection system include electrical loads and gas loads. A lot of practice has proved that the probability distribution of the load satisfies the normal distribution, namely:

In the formula: E _L is (electricity, gas) load power; Respectively, the mathematical expectation and standard deviation of the load power; f(E _L ) is the probability density function of the load power.

5.2 Randomness of wind farm output

The output of wind turbines is related to wind speed, and the uncertainty of wind speed leads to the uncertainty of wind turbine output. The two-parameter Weibull curve can well describe the probability density function of wind speed, namely:

In the formula: v _w is the wind speed variable; k _w is the shape parameter of Weibull distribution; c _w is the scale parameter of Weibull distribution.

According to the relationship between wind speed and wind generator output active power _Pw can be expressed as:

in:

Where: P _N is the rated power of the fan; v _ci is the cut-in wind speed; v _N is the rated wind speed; v _co is the cut-out wind speed.

Practice shows that the wind speed is generally maintained between v _ci and v _N , so the linear function relationship between P _w and v _w can be approximated, so the probability density of active power of wind power generation is as follows:

The active power of a wind farm can be considered as a three-parameter Weibull distribution, which can be expressed as a standard normal distribution variable:

In the formula: ξ represents a standard normal distribution variable.

The wind farm generator is simplified to PQ node processing, assuming that the wind farm adopts constant power factor control, the output reactive power of the wind farm is:

In the formula: is the power factor angle.

5.3 Randomness of photovoltaic power generation output

The output of solar photovoltaic power plants is related to the light intensity. The randomness of light intensity leads to the uncertainty of the output of solar photovoltaic power plants. The light intensity is often described by Beta distribution, namely:

In the formula: r is the light intensity; r _max is the maximum light during this period; α, β are the shape parameters of the Beta distribution.

For a solar photovoltaic power generation system, the total output active power of a solar cell array is:

P _p =rAη

In the formula: A is the total area of the square array, and η is the total photoelectric transfer efficiency of the square array.

It can be obtained that the probability density function of the output power of the photovoltaic cell square array also presents a Beta distribution, namely:

Where: P _pmax =r _max Aη is the maximum output power of the square array.

The photovoltaic active power variable can be expressed as a normal distribution variable:

In the formula: f ^-1 is the inverse function of the probability density function of the output power of the photovoltaic cell square array.

Similar to wind farms, photovoltaic power plants are also simplified to PQ node processing, and the constant power factor of photovoltaic cells is basically constant:

In the formula: is the power factor angle.

6 Random response surface method

The stochastic response surface method expresses the output response as a chaotic polynomial with known coefficients on the basis of the known probability distribution of the input random variable, and determines the undetermined coefficients in the polynomial through a small number of samples, and then obtains the estimated probability distribution of the output response . The specific operation is as follows:

(1) Input the information of the electrical interconnection system, and determine the number n and the probability distribution of random input variables X in the system. According to the principle of probability transformation, all input variables are unitized, that is, all input variables are represented by a set of functions of standard normal distribution random variables Z, namely:

x _i ＝F _i ^-1 (Φ(z _i ))

In the formula: x _i is an input variable; z _i is the corresponding standard normal distribution variable; Φ is the probability distribution function of z _i ; F _i is the probability distribution function of x _i .

(2) Construct the second-order chaotic polynomial corresponding to the output variable, namely

In the formula: Y is the output variable; _ξi is n uncorrelated random variables with standard normal distribution, corresponding to n input variables; a is the coefficients of the second-order chaotic polynomial.

Among them, the number of coefficients to be determined is

(3) Configuration points of parameter standard normal distribution random variable group ξ. There are 3 ⁿ candidate points for the configuration points that use the roots of Hermite polynomials with a higher order (that is, 3rd order) to combine candidate points. Using the most optimal point method, select a suitable configuration point C _pi (i=1,...,N). The output variable samples X _{pi ( i =} ¹ , .

(4) Substitute the sample point X _pi into the power flow equation as a disturbance variable, use the particle swarm optimization algorithm to calculate the deterministic optimal power flow, and use the calculated output variable Y _i to form the output vector Y. Use the selected output configuration point C _pi to form the Hermite coefficient matrix H by row, let A be the vector composed of the chaotic polynomial coefficients to obtain a linear equation system, solve the chaotic polynomial coefficients, and obtain the chaotic polynomial of the variable That is, the variable is represented by a set of n standard normal distribution random variables;

(5) The probability density function and probability distribution function of the variable are estimated by kernel density estimation method.

Case analysis

The electrical interconnection system of the present invention is composed of a modified IEEE 14-node system and a natural gas 14-node system through two gas turbines, and its structure is shown in Figure 3 of the appendix. It is assumed that the four pressurization stations are all driven by gas turbines; it is assumed that the generators connected to 2 and 3 in the IEEE14 node system are gas turbines, which are respectively connected to nodes 14 and 12 of the natural gas 14 node system; the connection capacity of IEEE14 node system at node 9 is 15MW The wind farm is connected to the 8MW solar power plant at node 14; the standard deviation of all electric and gas loads is 5% of the expected value. The stochastic response surface method is used for the electrical interconnection system, and the objective function is to minimize the cost of power generation, and the optimal power flow calculation is carried out with the particle swarm optimization algorithm. The probability curve of power generation cost is shown in Figure 4, the voltage amplitude probability distribution curve of No. 7 node of the power system is shown in Figure 5, and the pressure probability distribution curve of No. 4 node of natural gas is shown in Figure 6.

Claims (6)

1. A probabilistic optimal power flow calculation method for electrical interconnection systems based on stochastic response surface method, characterized in that it is realized in the following steps: 1) Obtain the parameter information of the power system for steady-state modeling. The parameter information includes: the topology of the transmission line network, the resistance and reactance of the π-type equivalent circuit, the conductance and susceptance of the parallel connection to the ground, the transformation ratio and impedance of the transformer, each Node load and generator output active and reactive power constraints, voltage constraints of each node; 2) Obtain the parameter information of the natural gas network for steady-state modeling. The parameter information includes: the topological structure of the gas pipeline, transmission efficiency and other parameter information, the topological structure of the booster station, the gas load of each node, and the natural gas output information of the gas source point , the pressure constraints of each node; 3) Obtain the coupling of the electrical interconnection system with various parameters and constraints of the gas turbine; 4) To establish the probability information of load, wind speed, and light for the uncertainty of load forecast, wind speed forecast, and light forecast; 5) The output response is expressed as a chaotic polynomial with known coefficients on the basis of the known input random variable probability distribution through the stochastic response surface method, and the undetermined coefficients in the polynomial are determined by the sampling points selected by the optimal point method, and then obtain the probability distribution of the estimated output response; 6) According to the probability distribution of each variable, with the cost as the objective function, the cost value under the probability optimal power flow is obtained; 7) Output the probability statistics information of the state variables. 2. the electrical interconnection system probabilistic optimal power flow calculation method based on stochastic response surface method as claimed in claim 1, is characterized in that, Power system steady-state modeling: For node i in the power network: <mrow><msub><mi>P</mi><mi>i</mi></msub><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>&amp;lsqb;</mo><msub><mi>e</mi><mi>i</mi></msub><mrow><mo>(</mo><msub><mi>G</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>e</mi><mi>j</mi></msub><mo>-</mo><msub><mi>B</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>f</mi><mi>j</mi></msub><mo>)</mo></mrow><mo>+</mo><msub><mi>f</mi><mi>i</mi></msub><mrow><mo>(</mo><msub><mi>G</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>f</mi><mi>j</mi></msub><mo>+</mo><msub><mi>B</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>e</mi><mi>j</mi></msub><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow> <mrow><msub><mi>Q</mi><mi>i</mi></msub><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>&amp;lsqb;</mo><msub><mi>f</mi><mi>i</mi></msub><mrow><mo>(</mo><msub><mi>G</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>e</mi><mi>j</mi></msub><mo>-</mo><msub><mi>B</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>f</mi><mi>j</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>e</mi><mi>i</mi></msub><mrow><mo>(</mo><msub><mi>G</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>f</mi><mi>j</mi></msub><mo>+</mo><msub><mi>B</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>e</mi><mi>j</mi></msub><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow> <mrow><msubsup><mi>e</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>f</mi><mi>i</mi><mn>2</mn></msubsup><mo>=</mo><msubsup><mi>U</mi><mi>i</mi><mn>2</mn></msubsup></mrow> In the formula: e _i , f _i are the real part and imaginary part of the voltage vector of node i respectively; P _i , Q _i are the active power and reactive power of node i in the power network respectively; G _ij , B _ij are the node admittance The real part and imaginary part of the element in row i, column j of the matrix; is the voltage of node i. 3. the electrical interconnection system probabilistic optimal power flow calculation method based on stochastic response surface method as claimed in claim 1, is characterized in that, Pipe flow equation: For the completely turbulent flow in the high-pressure gas network, the mn flow equation of the pipeline is: <mrow><msub><mi>f</mi><mi>k</mi></msub><mo>=</mo><msub><mi>f</mi><mrow><mi>k</mi><mi>m</mi><mi>n</mi></mrow></msub><mo>=</mo><msub><mi>M</mi><mi>k</mi></msub><msub><mi>S</mi><mrow><mi>m</mi><mi>n</mi></mrow></msub><msqrt><mrow><msub><mi>S</mi><mrow><mi>m</mi><mi>n</mi></mrow></msub><mrow><mo>(</mo><msubsup><mi>&amp;pi;</mi><mi>m</mi><mn>2</mn></msubsup><mo>-</mo><msubsup><mi>&amp;pi;</mi><mi>n</mi><mn>2</mn></msubsup><mo>)</mo></mrow></mrow></msqrt></mrow> in: <mrow><msub><mi>M</mi><mi>k</mi></msub><mo>=</mo><mi>&amp;epsiv;</mi><mfrac><mrow><mn>18.73</mn><msub><mi>T</mi><mn>0</mn></msub><msubsup><mi>D</mi><mi>k</mi><mrow><mn>8</mn><mo>/</mo><mn>3</mn></mrow></msubsup></mrow><mrow><msub><mi>&amp;pi;</mi><mn>0</mn></msub><msqrt><mrow><msub><mi>GL</mi><mi>k</mi></msub><msub><mi>T</mi><mrow><mi>k</mi><mi>a</mi></mrow></msub><msub><mi>Z</mi><mi>a</mi></msub></mrow></msqrt></mrow></mfrac></mrow> In the formula: f _kmn is the pipeline flow value; π _m is the pressure value of node m; π _n is the pressure value of node n; ε is the pipeline efficiency factor; T ₀ is the standard temperature value; D _k is the inner diameter of the pipeline k; π ₀ is the standard pressure value; Air is 1, natural gas is 0.6; L _k is the length of pipeline k; T _ka is the average gas temperature of pipeline k; Z _a is the average gas compression coefficient; The energy consumption equation of the compressor: <mrow><msub><mi>H</mi><mi>k</mi></msub><mo>=</mo><msub><mi>B</mi><mi>k</mi></msub><msub><mi>f</mi><mi>k</mi></msub><mo>&amp;lsqb;</mo><msup><mrow><mo>(</mo><mfrac><msub><mi>&amp;pi;</mi><mi>m</mi></msub><msub><mi>&amp;pi;</mi><mi>n</mi></msub></mfrac><mo>)</mo></mrow><mrow><msub><mi>Z</mi><mrow><mi>k</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mfrac><mrow><mi>&amp;alpha;</mi><mo>-</mo><mn>1</mn></mrow><mi>&amp;alpha;</mi></mfrac><mo>)</mo></mrow></mrow></msup><mo>-</mo><mn>1</mn><mo>&amp;rsqb;</mo></mrow> in: <mrow><msub><mi>B</mi><mi>k</mi></msub><mo>=</mo><mfrac><mrow><mn>3554.58</mn><msub><mi>T</mi><mrow><mi>k</mi><mi>i</mi></mrow></msub></mrow><msub><mi>&amp;eta;</mi><mi>k</mi></msub></mfrac><mrow><mo>(</mo><mfrac><mi>&amp;alpha;</mi><mrow><mi>&amp;alpha;</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>)</mo></mrow></mrow> In the formula: f _k is the gas flow rate through the compressor; π _m is the gas injection compressor pressure; π _n is the gas output compressor pressure; Z _ki is the gas compression factor at the inflow end of the compressor; T _ki is the natural gas intake point of the compressor temperature; α is the adiabatic index; η _k is the efficiency of the pressurization station; The flow of natural gas consumed to drive the pressurization station: <mrow><msub><mi>&amp;tau;</mi><mi>k</mi></msub><mo>=</mo><msub><mi>&amp;alpha;</mi><mrow><mi>T</mi><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>&amp;beta;</mi><mrow><mi>T</mi><mi>k</mi></mrow></msub><msub><mi>H</mi><mi>k</mi></msub><mo>+</mo><msub><mi>&amp;gamma;</mi><mrow><mi>T</mi><mi>k</mi></mrow></msub><msubsup><mi>H</mi><mi>k</mi><mn>2</mn></msubsup></mrow> In the formula: α _Tk , β _Tk , and γ _Tk are conversion coefficients of consumed natural gas flow rate; Natural gas flow balance equation: The natural gas flow conservation is that the inflow flow of each node is equal to the outflow flow, which can be expressed in the form of matrix: (A+U)f+w-Tτ＝0 in: In the formula: f is the branch flow value vector; w is the gas injection vector of each node; τ is the consumption flow value vector of each compressor, matrix A is the line-node correlation matrix, which represents the connection between the pipeline and the node; the matrix U T is the unit-node correlation matrix, which represents the connection between the unit and the node; T is the compressor consumption and node correlation matrix, which represents the connection between the gas turbine and the node. 4. The probabilistic optimal power flow calculation method for electrical interconnected systems based on the stochastic response surface method as claimed in claim 1, wherein the coupling between the power system and the natural gas system: The natural gas input of the gas turbine is regarded as the gas load of the natural gas system, and the power output of the natural gas consumed by the gas turbine is regarded as the power supply of the power system, so that the gas turbine couples the power system and the natural gas system, and the coupling relationship is: <mrow><msub><mi>H</mi><mrow><mi>g</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>=</mo><msub><mi>&amp;alpha;</mi><mrow><mi>g</mi><mo>,</mo><mi>i</mi></mi>mrow></msub><mo>+</mo><msub><mi>&amp;beta;</mi><mrow><mi>g</mi><mo>,</mo><mi>i</mi></mrow></msub><msub><mi>P</mi><mrow><mi>G</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>+</mo><msub><mi>&amp;gamma;</mi><mrow><mi>g</mi><mo>,</mo><mi>i</mi></mrow></msub><msubsup><mi>P</mi><mrow><mi>G</mi><mo>,</mo><mi>i</mi></mrow><mn>2</mn></msubsup></mrow> <mrow><msubsup><mi>F</mi><mrow><mi>g</mi><mi>a</mi><mi>s</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>i</mi></mrow></msubsup><mo>=</mo><msub><mi>H</mi><mrow><mi>g</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>/</mo><mi>G</mi><mi>H</mi><mi>V</mi></mrow> 2 In the formula: H _g,i is the input heat value of the gas turbine; _PG,i is the output power of the gas turbine to the power system node i; α _g,i , β _g,i , and γ _g,i are determined by the heat consumption rate curve of the gas turbine; Enter the gas flow rate of the gas turbine for the natural gas system; GHV=1015BTU/SCF, which is the high calorific value. 5. the electrical interconnection system probabilistic optimal power flow calculation method based on stochastic response surface method as claimed in claim 1, is characterized in that, uncertainty factor analysis: A. Load randomness The load of the electrical interconnection system includes electrical load and gas load; generally, a normal distribution is used to represent the uncertainty of the load forecast error; B. Randomness of wind farm output The output of wind turbines is related to the wind speed, and the uncertainty of wind speed leads to the uncertainty of the output of wind turbines; the two-parameter Weibull curve can well describe the probability density function of wind speed. C. The randomness of photovoltaic power generation output The output of solar photovoltaic power plants is related to the intensity of light. The randomness of light intensity leads to the uncertainty of the output of solar photovoltaic power plants. Beta distribution is often used to describe the light intensity. 6. The probabilistic optimal power flow calculation method for electrical interconnection systems based on the stochastic response surface method as claimed in claim 1, wherein the stochastic response surface method expresses the output response on the basis of the known input random variable probability distribution For a chaotic polynomial with known coefficients, the undetermined coefficients in the polynomial are determined by sampling, and then the probability distribution of the estimated output response is obtained; According to the simulation results of the stochastic response surface method, the probability distribution of the cost under the probability optimal power flow and the probability distribution of each state quantity of the electrical interconnection system are output.