CN111799799A - Alternating current-direct current hybrid power distribution network interval power flow calculation method based on interval Taylor expansion method - Google Patents

Abstract

The invention relates to an alternating current-direct current hybrid power distribution network interval power flow calculation method based on an interval Taylor expansion method. The method considers the influence of the voltage and power fluctuation of the nodes in the direct-current power distribution network on the power flow and modulation ratio in the voltage source converter and the alternating-current power distribution network under a master-slave control strategy and an equivalent control strategy, adopts an interval Taylor expansion method to avoid interval iteration and nonlinear programming, has extremely high sparsity of a Jacobian matrix and a Hessian matrix based on an augmented rectangular coordinate power flow model, and carries out interval power flow calculation in an alternating-current and direct-current hybrid power distribution network system expanded by an IEEE33 node, and the result shows that the time spent in the augmented rectangular coordinate is 0.0814 seconds, the time spent in the rectangular coordinate is 0.4757 seconds, and the calculation efficiency can be obviously improved.

Description

Alternating current-direct current hybrid power distribution network interval power flow calculation method based on interval Taylor expansion method

Technical Field

The invention relates to the technical field of power systems, in particular to an alternating current-direct current hybrid power distribution network interval power flow calculation method based on an interval Taylor expansion method.

Background

With the increasing importance of renewable energy resources in various countries in the world, wind power generation and photovoltaic power generation technologies are gradually mature, and a large power grid is successfully connected to participate in system operation. Wind power and photoelectricity are greatly influenced by weather factors, the output of wind power generation power mainly depends on wind speed, and the output of photovoltaic power generation power mainly depends on illumination intensity. Because the weather randomness is strong, the generated power output is uncertain, the actual generated power output is deviated from a predicted value, when the deviation exceeds a certain value, voltage fluctuation is caused when the power is input into a large power grid, the power quality is reduced, and further the operation of equipment is influenced. In addition, voltage fluctuation is caused when a fluctuating load is connected into a power grid, so that uncertain power flow calculation of the power grid is very necessary for acquiring voltage fluctuation information in advance.

With the development of an alternating current-direct current hybrid network, the research focus of an uncertain power flow algorithm is changed from an alternating current network to the alternating current-direct current hybrid network, the research is limited to the constraint of multiple control modes of a voltage source converter, the current research on the uncertain algorithm of the alternating current-direct current hybrid network is not many, the current research mainly comprises a nonlinear optimization method and a deterministic equivalence method, the nonlinear optimization method is long in calculation time, the deterministic equivalence can not independently complete calculation, the nonlinear optimization method needs to be combined at the voltage source converter, and meanwhile, the boundary value of a node voltage phase angle cannot be obtained.

The node voltage and the node injection current in the augmented rectangular coordinate power flow model are both state quantities, so that a power equation is converted from a fully-coupled nonlinear equation into a linearly-coupled quadratic equation, based on the characteristic, most elements in the Jacobian matrix are constants, repeated calculation is not needed in iterative calculation, meanwhile, the sparsity rate of the Jacobian matrix and the Hessian matrix is greatly improved, and the power flow calculation efficiency is improved.

Disclosure of Invention

In view of the above, the invention aims to provide an improved interval power flow algorithm of an alternating current-direct current hybrid power distribution network based on an interval taylor expansion method, which avoids interval iteration and nonlinear optimization, adopts an extended rectangular power flow model, has extremely high sparsity of a jacobian matrix and a hessian matrix, and carries out interval power flow calculation in an alternating current-direct current hybrid power distribution network system expanded by an IEEE33 node, and the result shows that the time spent in the extended rectangular power flow model is 0.0814 seconds, and the time spent in the extended rectangular power flow model is 0.4757 seconds, so that the calculation efficiency can be obviously improved.

The invention is realized by adopting the following scheme: an alternating current-direct current hybrid power distribution network interval power flow calculation method based on an interval Taylor expansion method comprises the following steps:

step S1: respectively determining a control mode corresponding to each VSC according to a master-slave control strategy and an equivalent control strategy of the alternating-current and direct-current hybrid power distribution network, combining multiple control modes of the VSCs with an interval power flow algorithm, analyzing node voltages of the direct-current power distribution network under different control modes in the interval power flow, and analyzing node injection currents and active power transmission fluctuation conditions between the direct-current power distribution network and the VSCs;

step S2: providing a voltage relation formula which is required to be met by a VSC modulation ratio in the interval tide, VSC internal node voltage and direct-current distribution network node voltage, determining a voltage fluctuation variable in the direct-current distribution network, and analyzing the influence of the voltage fluctuation variable on the VSC internal node voltage, the alternating-current distribution network node voltage and the modulation ratio; (DC side also AC side)

Step S3: writing a Jacobian matrix and a Hessian matrix under an augmented rectangular coordinate according to a node voltage equation, a power equation and a voltage relational column in the alternating-current and direct-current hybrid power distribution network;

step S4: selecting a load power fluctuation node and a photovoltaic power generation and wind power generation access node, determining a node power fluctuation amount and an interval central value by adopting an interval algorithm, and establishing a fluctuation variable matrix;

step S5: the method comprises the steps that an alternating current-direct current decoupling load flow algorithm is adopted, interval load flow calculation of a direct current power distribution network is firstly carried out, node voltage of the direct current power distribution network is obtained, a first derivative and a second derivative of a node injection current interval variable to a fluctuation variable are obtained, and interval values of the node voltage, the node current and node injection power of the direct current power distribution network are calculated;

step S6: the method comprises the steps of obtaining node voltage and node injection power interval values of the direct-current power distribution network, considering influences of power value fluctuation of the direct-current power distribution network input to the alternating-current power distribution network and voltage fluctuation conditions of the direct-current power distribution network on the alternating-current power distribution network, selecting load power fluctuation nodes of the alternating-current power distribution network, and carrying out interval load flow calculation on the alternating-current power distribution network.

Further, the specific content of step S1 is:

the control strategy of the alternating current-direct current hybrid power distribution network mainly comprises a master-slave control strategy and an equivalent control strategy, wherein under the master-slave control strategy, one VSC is used as a master station and adopts a constant direct current voltage control mode to stabilize a direct current voltage value, and other VSCs adopt constant power control modes to control an active power transmission value; under an equivalent control strategy, all converter stations adopt a droop control mode, and the node voltage of the direct-current power distribution network and the node injection current active power value are adjusted simultaneously;

for a single VSC, the control modes comprise a constant direct-current voltage, a constant alternating-current voltage, a constant active or reactive power control mode and a droop control mode;

and (3) a constant direct-current voltage control mode:

controlling the voltage value of the node to be a fixed value, wherein the power fluctuation in interval load flow calculation causes the fluctuation of the injection current of the node, so that the injection power of the node is an interval value;

in the above formula

Injecting power into the direct current distribution network node,

is the voltage of the node, and is,

a current is injected for the node and,

the amount of power fluctuation is injected for the node,

injecting a current fluctuation amount into the node; when no other power is injected, the DC distribution network injects the power of VSCA rate of

In the power fluctuation process, when the fluctuation quantity amplitude is high, the power transmission direction can be changed, and the conversion of rectification and inversion states can be realized. Fluctuation of voltage amplitude and phase angle of nodes in the VSC is caused by fluctuation of injection power of nodes of the direct-current power distribution network, and fluctuation of each state quantity in the alternating-current power distribution network is further caused;

constant power control mode:

in a constant power control mode, when the power injection values of other nodes fluctuate, the node voltage and the node injection current slightly fluctuate, and the power fluctuation value calculated by multiplying the node voltage and the node injection current is lower than the convergence precision, so that the node injection power is considered to be a constant value within an allowable error range; because an alternating current-direct current decoupling power flow algorithm is adopted, the fixed active power transmission value is changed into the fixed P_c，P_cThe active power transmission value between the VSC and the direct current power distribution network; value of reactive power transmission Q_sMaintaining a constant value, and setting the fluctuation amount to 0;

the droop control mode is as follows:

when voltage of a node connected with the VSC in the direct-current power distribution network rises or falls, the VSC determines a power value of an injection node according to a voltage deviation value;

in the above formula K_droopAnd

in order to control the parameters of the device,

and

meanwhile, when the power injection values of other nodes fluctuate, the fluctuation of the node voltage and the node injection current can be caused at the same time, so that the node injection power can correspondingly progressMovable part

According to the interval algorithm, the node injection power is as follows:

when no other power is injected, the active power of VSC injected into the direct current power distribution network is

Constant alternating voltage control mode:

under the augmented rectangular coordinate, the constant alternating voltage control mode maintains the voltage amplitude of the node i to be 1 constantly, and the following control mode is adopted:

e_i＝1 f_i＝0 (5)

in the above formula e_iIs the real part of the node voltage, f_iIs the node voltage imaginary part; there is no power fluctuation variable in the fixed AC voltage equation, and only the relation e in the Jacobian matrix_iTherefore, the node voltage amplitude can be kept constant at 1 in the interval power flow calculation, namely the voltage amplitude U_i＝1。

Further, the specific content of step S2 is:

combining an interval Taylor expansion method and a control mode of the AC/DC hybrid power distribution network to obtain a power flow model adopting the interval Taylor expansion method in the AC/DC hybrid power distribution network, wherein voltage relation equations required to be satisfied on two sides of the VSC are as follows

In the above formula, M_kAdopting per unit value and reference value for the voltage modulation ratio of the kth VSC

Wherein the content of the first and second substances,

e_i,f_ithe real part and the imaginary part of the voltage of the internal node of the kth VSC are provided, each VSC comprises an internal node,

the node voltage value is connected with the kth VSC in the direct-current power distribution network; when the control mode is constant DC voltage control, the node voltage

Is a constant value; when the control mode is droop control and constant active power control, the node voltage

The node voltage is near to a per unit value of 1 when the direct current distribution network runs under the ground state, so that the node voltage is an interval value

Is interval voltage

The square of the central value, after the square operation of the node voltage interval,

deviation of section center value of

In the ground state tide before power fluctuation, the power distribution network operates

Thus, the formula (7) is defined as

Is unfolded by

The interval represented is no longer a symmetric interval, and therefore

As follows

In the above formula

Voltage fluctuation amount [ delta V ] of node connected with VSC in direct-current power distribution network_lowj,ΔV_hj]For the VSC internal voltage e_i,f_iAnd a voltage modulation ratio M_kAll will have an influence on the internal voltage e of the VSC_i,f_iAnd a voltage modulation ratio M_kThe fluctuation occurs, and then the node voltage and the node injection current of the node connected with the VSC in the alternating current distribution network fluctuate.

Further, the step S3 specifically includes the following steps:

step S31: establishing a power equation, a node voltage equation and a VSC voltage relational expression in the interval tide of the alternating-current and direct-current hybrid power distribution network, carrying out interval Taylor expansion, and establishing three deterministic equations under the uncertain tide;

in an uncertain power flow equation considering the volatility of a distributed power supply such as wind power, photoelectricity and the like and the load volatility, the power fluctuation of a node i in an alternating-current power distribution network is expressed as an interval value:

[P_i]＝P_ic+[-ΔP_i,ΔP_i](9)

[Q_i]＝Q_ic+[-ΔQ_i,ΔQ_i](10)

P_ic,Q_icrespectively the central value of the active power interval and the reactive power interval, delta P_i,ΔQ_iRespectively the active power fluctuation quantity and the reactive power fluctuation quantity;

in an uncertain power flow equation considering the fluctuation of a photovoltaic equal-distribution type power supply and the load fluctuation, the power fluctuation of a node i in a direct-current power distribution network is represented as an interval value;

is the active power interval central value of the direct current distribution network,

is the active power fluctuation amount;

in an uncertain power flow equation considering node voltage fluctuation in the direct-current power distribution network, the voltage fluctuation of a node j connected with a kth VSC in the direct-current power distribution network is represented as an interval value;

in addition, the active power transmission quantity between the direct current distribution network and the VSC is also fluctuated under the influence of voltage fluctuation, and influences are generated on the load flow and the modulation ratio in the VSC and the alternating current distribution network; therefore, fluctuation variables in the uncertainty trend of the alternating current-direct current hybrid power distribution network comprise active power, reactive power and fluctuating load of injection nodes of the distributed power supply, and node voltage fluctuation quantity and active power transmission fluctuation quantity connected with VSC in the direct current power distribution network

In the above formula, the first and second carbon atoms are,_Pi＝[-ΔP_i,ΔP_i]the active power fluctuation quantity of the node is obtained by adding the active power injected by the node and the active power load of the node in intervals,_Qi＝[-ΔQ_i,ΔQ_i]representing the amount of node reactive power fluctuation, reactive powerThe fluctuation amount is obtained by adding the node injection reactive power and the node reactive power load in intervals, wherein i is 1,2, …, n;

representing the node voltage fluctuation quantity of nodes connected with VSC in the direct current distribution network,

the active power transmission fluctuation amount between the direct current distribution network and the VSC is represented, and k is 1 and 2 … L; the expression of the interval between the node voltage equation and the node power equation in the alternating-current power distribution network is as follows:

ΔP_i＝(P_ic+_Pi)-e_i()a_i()-f_i()b_i()＝0 (15)

ΔQ_i＝(Q_ic+_Qi)-f_i()a_i()+e_i()b_i()＝0 (16)

1,2, …, n, and the PV node adopts formula (17) instead of formula (16); the expression of the interval between the node voltage equation and the node power equation in the direct-current power distribution network is as follows:

i is 1,2, …, r; the constant voltage node adopts an equation (20) instead of an equation (19); in the droop control mode, an interval expression of a node j connected with the kth VSC in the direct-current distribution network is as follows:

the kth VSC voltage relational interval expression is as follows:

combining equations (14) - (22), the uncertain power flow equation of the alternating current-direct current hybrid power distribution network is expressed as a matrix equation:

the uncertain power flow matrix equation Δ I (W (), (0) includes equations (14) and (18), Δ P (W (), (0) includes equations (15), (19) and (21), Δ Q (W (), (0) includes equation (16), and Δ U (W (), (0) includes equations (17), (20) and (22). Wherein W is represented as:

W＝[e₁(),f₁(),a₁(),b₁(),e₂(),f₂(),a₂(),b₂()…M₁(),M₂()…V₁ ^d(),I₁ ^d(),V₂ ^d(),I₂ ^d()…]

(24)

the direct-current power distribution network contains 2r state quantities, and the alternating-current power distribution network and the VSC contain 4n + L state quantities;

the system operates under the ground state value before power fluctuation, and the fluctuation variable is equal to_cAnd therefore, performing interval taylor expansion on the power uncertain power flow equation at the system ground state operation value by adopting an interval taylor expansion method, wherein after the power equation only contains node voltage, a second term of a state quantity such as node injection current and the like and a first term of a fluctuation variable, the higher order of the equation is infinitesimal 0 after the equation is expanded to the second order, the node voltage equation only contains the first term of the state quantity, the second derivative of the node voltage equation is 0, and the taylor expansion formula of the function F (W (),) 0 is as follows:

where Δ [ - Δ, Δ ], the above equation is always 0, as long as:

F(W(_c),_c)＝0 (26)

the first derivative formula (27) and the second derivative formula (28) of the function are developed as follows

Therefore, the following three deterministic equations are obtained

F(W(_c),_c)＝0 (31)

In the direct-current power distribution network, x is 2r, and y represents the number of active power fluctuation variables; in an alternating current distribution network and VSC, x is 4n + L, and y represents the number of active, reactive and voltage fluctuation variables;

step S32: expanding the three deterministic equations, and calculating the derivative of the power function to the power fluctuation variable and the derivative of the voltage relational expression in the VSC to the voltage fluctuation quantity in the DC distribution network; formula (31) is a fluctuating variable ═_cPerforming load flow calculation by adopting a cow pulling method when the ground state load flow is 0;

the expansion of equation (32) is as follows:

in the above formula, z is the number of matrix equations F (W (),) ═ 0, in the dc distribution network, z ═ x ═ 2r, and in the matrix equations F₁-F_rAs an equation of node voltage, F_r+1-F_2rIs an active power equation; in an alternating current distribution network and VSC, z is equal to x is equal to 4n + L, and F is in a matrix equation₁-F_2nAs an equation of node voltage, F_2n+1-F_4nIs an active and reactive power equation, F_4n+1-F_4n+LIs a VSC voltage relational equation;

derivative of matrix equation to fluctuation amount

The derivative is 0 when no power fluctuation occurs in the node, and the derivative is 1 when power fluctuation occurs. When the voltage of a node connected with the kth VSC in the direct-current distribution network fluctuates, the derivative of the VSC voltage relational equation (22) to the voltage fluctuation quantity

The values of (a) are as follows:

k is 1,2 … L, the kth VSC voltage relational expression is the 4n + k equation of matrix equation F (W (),) < 0 of the AC distribution network, M_kcThe voltage modulation ratio basic state operation value of the kth VSC is obtained;

the expression of formula (33) is as follows:

due to the need to satisfy the voltage relation (22), compared to a pure ac distribution network,the second derivative of the alternating current distribution network matrix equation connected with the direct current distribution network to the fluctuation quantity increases the matrix

When in use_iIs the i voltage fluctuation quantity and W of a node in a direct current power distribution network_aWhen the modulation ratio of the VSC connected with the node i is the same, the 4n + k equations in the alternating-current power distribution network, namely the second derivative of the voltage relational expression of the kth VSC to the fluctuation quantity

As non-zero elements, the following is specifically calculated:

wherein the modulation ratio M_kIs the 4n + k th element in the state quantity W. The other elements of the matrix are all 0, so the matrix is highly sparse. The first derivative of the state variable to the fluctuation variable is obtained by calculating equations (34), (36)

Second derivative of

The method is substituted into the following formula, and a state quantity interval value is solved;

W_cthe specific values of the state quantities in the ground state are as follows:

step S33: calculating a Jacobian matrix and a Hessian matrix under the augmented rectangular coordinate power flow model, and analyzing the sparsity of the Jacobian matrix and the Hessian matrix adopting the augmented rectangular coordinate power flow model;

about the enlarged right angle in formula (34)Jacobian matrix in coordinates

The specific calculation is as follows:

in the alternating-current distribution network:

the elements of the matrix in equation (40) are as follows:

is a 2 n-order matrix;

in formulae (41) to (43), a_n,b_nInjecting the real part and the imaginary part, e, of the current into the node n of the AC distribution network_n,f_nFor the real and imaginary part of the voltage at node n, G_nn,B_nnFor the real and imaginary parts of the node n admittance, G_1n＝G_n1The real part of the transadmittance of node 1 and node n, which are equal, B_1n＝B_n1Node 1 and node n have equal imaginary parts of transadmittance.

In the formula (44), the reaction mixture is,

respectively being the real part and the imaginary part of the voltage of the 1 st VSC internal node, and the subscript i being the voltage of the node in the alternating currentNode numbers in the network, superscript (1,2i-1) denoting element e_iThe position in the matrix.

Respectively a real part and an imaginary part of the voltage of an internal node of the L-th VSC, subscript j is a node label of the node in the AC network, and superscripts also represent positions;

M₁，M_Lvoltage modulation ratios of 1 st, L VSCs,

node voltage values connected with 1 st VSC and L VSC in the direct-current power distribution network respectively;

in the direct current distribution network:

the direct-current power distribution network comprises r nodes;

the above matrix A_I，A_V，D_I，D_VThe non-diagonal elements in the I are all 0, so the sparsity in the Jacobian matrix is very high; the hessian matrix h (f) in the formula (36) in the augmented rectangular coordinate is specifically calculated as follows:

in the alternating-current distribution network:

the highest order of the node voltage equation is 1 st order, Hessian matrix H (F)₁)-H(F_2n) 0 matrices of 4n + L levels;

hessian matrix H (F) of the nodal power equation_2n+1)-H(F_4n) For sparse matrix, the active power equation for node i Heisen matrix H (F)_2n+2i-1) Is a 4n + L-order matrix, wherein the matrix comprises

The value is 1, other elements are 0, the sparsity of the Hessian matrix of the reactive power equation is the same, and the i is the highestA value of n;

hessian matrix H (F) of VSC voltage relational equation_4n+1)-H(F_4n+L) Are all 4n + L-order matrices, in which

Three non-zero elements in the matrix, all others being 0; m_jFor the modulation ratio of the jth converter station, e_cj,f_cjCompacting an imaginary part for the alternating current side of the jth converter station, wherein the highest value of j is L;

in the direct current distribution network:

node voltage equation hessian matrix H (F)₁)-H(F_r) Is a 0 matrix of 2r order;

node power equation hessian matrix H (F)_r+1)-H(F_2r) All are 2r order matrixes, wherein the active power equation of the node i is in Hessian matrix

The value is 1, the others are all 0, and the highest value of i is r;

further, the specific content of step S4 is:

interval variables in an uncertain power flow equation considering wind power, photoelectric and other distributed generation volatility in the alternating-current power distribution network are power values, wherein the interval value of power injection power of a node i power supply is

The interval variable in the uncertain power flow equation considering the load power fluctuation is a power value, wherein the load power interval value of the node i is

And (3) carrying out interval operation on active and reactive power of the node:

in the formulae (47) to (56),

injecting the central value of the active power interval for the power supply of the node i,

the central value of the load active power interval of the node i,

the node i power supply injects the fluctuation quantity of the active power interval,

the fluctuation amount of the load active power interval of the node i,

the central value of the reactive power interval of the node i load,

injecting the reactive power interval central value for the power supply of the node i,

the fluctuation amount of the reactive power interval of the load of the node i,

injecting a reactive power interval fluctuation quantity into a power supply of a node i;

in the direct-current power distribution network, interval variables in an uncertain power flow equation considering distributed power generation volatility such as photoelectricity are power values, wherein the interval value of power injection power of a node i power supply is

The interval variable in the uncertain power flow equation considering the load power fluctuation is a power value, wherein the load power interval value of the node i is

Performing interval operation on active power of node

Formulas (57) - (61)

For nodes i of DC distribution networkThe power supply injects the central value of the active power interval,

is the central value, delta P, of the active power interval of the node i load_i ^dSInjecting active power interval fluctuation quantity delta P for node i power supply_i ^dLLoading the fluctuation quantity of the active power interval for a node i;

substituting the calculated active power and reactive power fluctuation variables in the AC/DC distribution network into a formula (13), injecting active power into a node, wherein the reactive power fluctuation range is +/-20%, and the power base value is

P_ic，Q_icOn the basis of the node, the active power and the reactive power fluctuation quantity of the node are obtained, and the fluctuation variable is subjected to calculation

_PiAnd_Qiand (5) assigning to obtain a fluctuation variable matrix, and further performing interval load flow calculation on the alternating current and direct current hybrid power distribution network.

Further, the specific content of step S5 is:

active power supply fluctuation nodes and load fluctuation nodes in the direct-current power distribution network are selected, node active power fluctuation amplitude is calculated, node injection power fluctuation amplitude is +/-20%, and the node active power fluctuation amplitude is calculated at a power basic value

Calculating the power fluctuation amount on the basis of the power fluctuation amount; the basic value of the node injection active power is an active power operation value before the node injection active power fluctuates; after obtaining the fluctuation amount of the active power, the fluctuation variable is adjustedAssigning a value to obtain a fluctuation variable matrix, wherein the fluctuation variable matrix only comprises active power fluctuation variables in the direct current power distribution network and has the order of 1 multiplied by r; the interval load flow calculation of the direct current distribution network is carried out, and the direct current distribution network is firstly calculated by a formula (46)The net Jacobian matrix, and further the state quantity is obtained from the equation (34)

For fluctuating variables

The hessian matrix of the direct current distribution network is calculated by the formula (30), and the state quantity V is obtained according to the formula (36)_i ^d,I_i ^dFor fluctuating variables

The second derivative of (2) is obtained by the equation (38) for the node voltage of the dc distribution network, the interval value of the node injection flow.

Further, the specific content of step S6 is:

step S5, acquiring a node injection power interval value of the direct-current power distribution network, and acquiring an interval value of node voltage and node injection current in the direct-current power distribution network through interval load flow calculation of the direct-current power distribution network; therefore, the active power transmission interval value between the direct current distribution network and the VSC is obtained through the formula (3), and the active power transmission fluctuation quantity is calculated according to the formula (9)

Through formulas (7) and (8) for acquiring node voltage fluctuation quantity connected with VSC in direct-current power distribution network

Therefore, considering the influence of the fluctuation of the active power value of the direct-current power distribution network input to the alternating-current power distribution network and the voltage fluctuation condition of the direct-current power distribution network on the alternating-current power distribution network, selecting power fluctuation nodes of the alternating-current power distribution network, wherein the active and reactive injection power fluctuation amplitudes of the nodes are +/-20%, and the power fluctuation nodes are set at a power basic value P_ic，Q_icBased on the calculated active power fluctuation amount_PiAmount of fluctuation of reactive power_Qi(ii) a Therefore, the fluctuation amount of active power transmission between the DC distribution network and the VSC

Node voltage fluctuation amount of direct current power distribution network

Active power fluctuation quantity injected into AC distribution network node_PiAnd node injected reactive power fluctuation amount_QiForming a fluctuation variable matrix of the alternating-current power distribution network, wherein the fluctuation variable matrix is a 1 x (2n +2L) order matrix; firstly, calculating a Jacobian matrix of the alternating current distribution network by using a formula (40), and then solving the node voltage, the node injection current and the voltage modulation ratio fluctuation variable of the alternating current distribution network according to a formula (34)

And_Qithe first derivative of (a); firstly, the Hessian matrix is calculated through the formula (30), and then the node voltage, the node injection current and the voltage modulation ratio fluctuation variable of the alternating current distribution network are solved according to the formula (36)

_PiAnd_Qiand finally, solving the interval values of the node voltage, the node injection current and the voltage modulation ratio of the alternating-current distribution network by the equation (38). Compared with the prior art, the invention has the following beneficial effects:

the invention provides an interval power flow calculation method suitable for solving intermittent power supplies and fluctuating loads in an alternating current-direct current hybrid power distribution network by applying an interval Taylor expansion method to the alternating current-direct current hybrid power distribution network and combining an augmented rectangular coordinate power flow model. The method realizes the interval load flow calculation of the alternating current-direct current hybrid power distribution network under a master-slave control strategy and an equivalent control strategy, and can complete the interval load flow calculation of the large-scale alternating current-direct current power distribution network with higher calculation efficiency by considering the transmission control of the VSC on active power and reactive power and a voltage relation equation which should be satisfied by two sides of the VSC.

Drawings

Fig. 1 is a structural diagram of an ac/dc distribution network according to an embodiment of the present invention.

Fig. 2 is a node voltage amplitude distribution diagram of the direct-current distribution network under master-slave control according to the embodiment of the invention.

Fig. 3 is a distribution diagram of the injection current amplitude of the nodes of the dc distribution network under master-slave control according to the embodiment of the present invention.

Fig. 4 is a direct-current distribution network node injection power distribution diagram under master-slave control according to an embodiment of the present invention.

Fig. 5 is a node voltage amplitude distribution diagram of the ac distribution network under master-slave control according to the embodiment of the present invention.

Fig. 6 is a voltage phase angle distribution diagram of nodes of the ac distribution network under master-slave control according to the embodiment of the present invention.

Fig. 7 is a voltage amplitude distribution diagram of the dc distribution network under peer-to-peer control according to the embodiment of the present invention.

Fig. 8 is a direct current distribution network node injection power distribution diagram under peer-to-peer control according to an embodiment of the present invention.

Fig. 9 is a node voltage amplitude distribution diagram of the ac distribution network under peer-to-peer control according to the embodiment of the present invention.

Fig. 10 is a voltage phase angle distribution diagram of nodes of an ac distribution network under peer-to-peer control according to an embodiment of the present invention.

Detailed Description

The invention is further explained below with reference to the drawings and the embodiments.

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

The embodiment provides an alternating current-direct current hybrid power distribution network interval power flow calculation method based on an interval Taylor expansion method, which comprises the following steps:

step S1: respectively determining a control mode corresponding to each VSC according to a master-slave control strategy and an equivalent control strategy of the alternating-current and direct-current hybrid power distribution network, combining multiple control modes of the VSCs with an interval power flow algorithm, analyzing node voltages of the direct-current power distribution network under different control modes in the interval power flow, and analyzing node injection currents and active power transmission fluctuation conditions between the direct-current power distribution network and the VSCs;

step S2: providing a voltage relation formula which is required to be met by a VSC modulation ratio in the interval tide, VSC internal node voltage and direct-current distribution network node voltage, determining a voltage fluctuation variable in the direct-current distribution network, and analyzing the influence of the voltage fluctuation variable on the VSC internal node voltage, the alternating-current distribution network node voltage and the modulation ratio; (DC side also AC side)

Step S3: writing a Jacobian matrix and a Hessian matrix under an augmented rectangular coordinate according to a node voltage equation, a power equation and a voltage relational column in the alternating-current and direct-current hybrid power distribution network;

step S4: selecting a load power fluctuation node and a photovoltaic power generation and wind power generation access node, determining a node power fluctuation amount and an interval central value by adopting an interval algorithm, and establishing a fluctuation variable matrix;

step S5: the method comprises the steps that an alternating current-direct current decoupling load flow algorithm is adopted, interval load flow calculation of a direct current power distribution network is firstly carried out, node voltage of the direct current power distribution network is obtained, a first derivative and a second derivative of a node injection current interval variable to a fluctuation variable are obtained, and interval values of the node voltage, the node current and node injection power of the direct current power distribution network are calculated;

step S6: the method comprises the steps of obtaining node voltage and node injection power interval values of the direct-current power distribution network, considering influences of power value fluctuation of the direct-current power distribution network input to the alternating-current power distribution network and voltage fluctuation conditions of the direct-current power distribution network on the alternating-current power distribution network, selecting load power fluctuation nodes of the alternating-current power distribution network, and carrying out interval load flow calculation on the alternating-current power distribution network.

In this embodiment, the specific content of step S1 is:

the control strategy of the alternating current-direct current hybrid power distribution network mainly comprises a master-slave control strategy and an equivalent control strategy, wherein under the master-slave control strategy, one VSC is used as a master station and adopts a constant direct current voltage control mode to stabilize a direct current voltage value, and other VSCs adopt constant power control modes to control an active power transmission value; under an equivalent control strategy, all converter stations adopt a droop control mode, and the node voltage of the direct-current power distribution network and the node injection current active power value are adjusted simultaneously;

for a single VSC, the control modes comprise a constant direct-current voltage, a constant alternating-current voltage, a constant active or reactive power control mode and a droop control mode;

and (3) a constant direct-current voltage control mode:

controlling the voltage value of the node to be a fixed value, wherein the power fluctuation in interval load flow calculation causes the fluctuation of the injection current of the node, so that the injection power of the node is an interval value;

in the above formula

Injecting power into the direct current distribution network node,

is the voltage of the node, and is,

a current is injected for the node and,

the amount of power fluctuation is injected for the node,

injecting a current fluctuation amount into the node; when no other power is injected, the power of the direct current distribution network injected with VSC is

In the power fluctuation process, when the amplitude of the fluctuation quantity is higher, the power transmission direction is changedAnd converting the rectification state into the inversion state. Fluctuation of voltage amplitude and phase angle of nodes in the VSC is caused by fluctuation of injection power of nodes of the direct-current power distribution network, and fluctuation of each state quantity in the alternating-current power distribution network is further caused;

constant power control mode:

in a constant power control mode, when the power injection values of other nodes fluctuate, the node voltage and the node injection current slightly fluctuate, and the power fluctuation value calculated by multiplying the node voltage and the node injection current is lower than the convergence precision, so that the node injection power is considered to be a constant value within an allowable error range; because an alternating current-direct current decoupling power flow algorithm is adopted, the fixed active power transmission value is changed into the fixed P_c，P_cThe active power transmission value between the VSC and the direct current power distribution network; value of reactive power transmission Q_sMaintaining a constant value, and setting the fluctuation amount to 0;

the droop control mode is as follows:

when voltage of a node connected with the VSC in the direct-current power distribution network rises or falls, the VSC determines a power value of an injection node according to a voltage deviation value;

in the above formula K_droopAnd

in order to control the parameters of the device,

and

meanwhile, when the power injection values of other nodes fluctuate, the fluctuation of the node voltage and the node injection current can be caused at the same time, and therefore, the node injection power can also fluctuate correspondingly

According to the interval algorithm, the node injection power is as follows:

when no other power is injected, the active power of VSC injected into the direct current power distribution network is

Constant alternating voltage control mode:

under the augmented rectangular coordinate, the constant alternating voltage control mode maintains the voltage amplitude of the node i to be 1 constantly, and the following control mode is adopted:

e_i＝1 f_i＝0 (5)

in the above formula e_iIs the real part of the node voltage, f_iIs the node voltage imaginary part; there is no power fluctuation variable in the fixed AC voltage equation, and only the relation e in the Jacobian matrix_iTherefore, the node voltage amplitude can be kept constant at 1 in the interval power flow calculation, namely the voltage amplitude U_i＝1。

In this embodiment, the specific content of step S2 is:

combining an interval Taylor expansion method and a control mode of the AC/DC hybrid power distribution network to obtain a power flow model adopting the interval Taylor expansion method in the AC/DC hybrid power distribution network, wherein voltage relation equations required to be satisfied on two sides of the VSC are as follows

In the above formula, M_kAdopting per unit value and reference value for the voltage modulation ratio of the kth VSC

Wherein the content of the first and second substances,

e_i,f_ifor the real part and the imaginary part of the voltage of the internal node of the kth VSC, each VSC comprises an internal node，

The node voltage value is connected with the kth VSC in the direct-current power distribution network; when the control mode is constant DC voltage control, the node voltage

Is a constant value; when the control mode is droop control and constant active power control, the node voltage

The node voltage is near to a per unit value of 1 when the direct current distribution network runs under the ground state, so that the node voltage is an interval value

Is interval voltage

The square of the central value, after the square operation of the node voltage interval,

deviation of section center value of

In the ground state tide before power fluctuation, the power distribution network operates

Thus, the formula (7) is defined as

Where it is deployed, mined

Interval of representation is no longerIs a symmetrical interval, therefore

As follows

In the above formula

Voltage fluctuation amount [ delta V ] of node connected with VSC in direct-current power distribution network_lowj,ΔV_hj]For the VSC internal voltage e_i,f_iAnd a voltage modulation ratio M_kAll will have an influence on the internal voltage e of the VSC_i,f_iAnd a voltage modulation ratio M_kThe fluctuation occurs, and then the node voltage and the node injection current of the node connected with the VSC in the alternating current distribution network fluctuate.

The above-mentioned VSC internal voltage e_i,f_iAnd a voltage modulation ratio M_kThe voltage fluctuation is in inverse proportion to the modulation ratio under the premise of not considering the power fluctuation, so that the voltage modulation ratio M is higher when the voltage fluctuation is higher_kThe fluctuations decrease. VSC internal voltage e_i,f_iDependent on e in direct or inverse proportion to the amount of voltage fluctuation_i,f_iAnd thus its fluctuation size is uncertain. The voltage fluctuation quantity has indirect influence on the node voltage of the alternating-current power distribution network and the fluctuation of node injection current, and an absolute direct ratio or inverse ratio relation does not exist.

In actual operation, the amount of power fluctuation acts simultaneously with the amount of voltage fluctuation, and therefore, the VSC internal voltage e_i,f_iAnd a voltage modulation ratio M_kThe node voltage of the alternating current distribution network and the fluctuation of node injection current are the result of the combined action of a plurality of fluctuation variables.

In this embodiment, the step S3 specifically includes the following steps:

step S31: establishing a power equation, a node voltage equation and a VSC voltage relational expression in the interval tide of the alternating-current and direct-current hybrid power distribution network, carrying out interval Taylor expansion, and establishing three deterministic equations under the uncertain tide;

in an uncertain power flow equation considering the volatility of a distributed power supply such as wind power, photoelectricity and the like and the load volatility, the power fluctuation of a node i in an alternating-current power distribution network is expressed as an interval value:

[P_i]＝P_ic+[-ΔP_i,ΔP_i](9)

[Q_i]＝Q_ic+[-ΔQ_i,ΔQ_i](10)

P_ic,Q_icrespectively the central value of the active power interval and the reactive power interval, delta P_i,ΔQ_iRespectively the active power fluctuation quantity and the reactive power fluctuation quantity;

in an uncertain power flow equation considering the fluctuation of a photovoltaic equal-distribution type power supply and the load fluctuation, the power fluctuation of a node i in a direct-current power distribution network is represented as an interval value;

is the active power interval central value of the direct current distribution network,

is the active power fluctuation amount;

in an uncertain power flow equation considering node voltage fluctuation in the direct-current power distribution network, the voltage fluctuation of a node j connected with a kth VSC in the direct-current power distribution network is represented as an interval value;

in addition, the active power transmission quantity between the direct current distribution network and the VSC is also fluctuated under the influence of voltage fluctuation, and influences are generated on the load flow and the modulation ratio in the VSC and the alternating current distribution network; therefore, fluctuation variables in the uncertainty trend of the alternating current-direct current hybrid power distribution network comprise active power, reactive power and fluctuating load of injection nodes of the distributed power supply, and node voltage fluctuation quantity and active power transmission fluctuation quantity connected with VSC in the direct current power distribution network

In the above formula, the first and second carbon atoms are,_Pi＝[-ΔP_i,ΔP_i]the active power fluctuation quantity of the node is obtained by adding the active power injected by the node and the active power load of the node in intervals,_Qi＝[-ΔQ_i,ΔQ_i]the node reactive power fluctuation quantity is obtained by adding the reactive power injected into the node and the node reactive power load in intervals,

representing the node voltage fluctuation quantity of nodes connected with VSC in the direct current distribution network,

representing the active power transmission fluctuation amount between the direct current distribution network and the VSC;

the expression of the interval between the node voltage equation and the node power equation in the 2 … L AC distribution network is as follows:

ΔP_i＝(P_ic+_Pi)-e_i()a_i()-f_i()b_i()＝0 (15)

ΔQ_i＝(Q_ic+_Qi)-f_i()a_i()+e_i()b_i()＝0 (16)

1,2, …, n, and the PV node adopts formula (17) instead of formula (16); the expression of the interval between the node voltage equation and the node power equation in the direct-current power distribution network is as follows:

i is 1,2, …, r; the constant voltage node adopts an equation (20) instead of an equation (19); in the droop control mode, an interval expression of a node j connected with the kth VSC in the direct-current distribution network is as follows:

the kth VSC voltage relational interval expression is as follows:

combining equations (14) - (22), the uncertain power flow equation of the alternating current-direct current hybrid power distribution network is expressed as a matrix equation:

the uncertain power flow matrix equation Δ I (W (), (0) includes equations (14) and (18), Δ P (W (), (0) includes equations (15), (19) and (21), Δ Q (W (), (0) includes equation (16), and Δ U (W (), (0) includes equations (17), (20) and (22). Wherein W is represented as:

W＝[e₁(),f₁(),a₁(),b₁(),e₂(),f₂(),a₂(),b₂()…M₁(),M₂()…V₁ ^d(),I₁ ^d(),V₂ ^d(),I₂ ^d()…]

(24)

the direct-current power distribution network contains 2r state quantities, and the alternating-current power distribution network and the VSC contain 4n + L state quantities;

the system operates under the ground state value before power fluctuation, and the fluctuation variable is equal to_cAnd therefore, performing interval taylor expansion on the power uncertain power flow equation at the system ground state operation value by adopting an interval taylor expansion method, wherein after the power equation only contains node voltage, a second term of a state quantity such as node injection current and the like and a first term of a fluctuation variable, the higher order of the equation is infinitesimal 0 after the equation is expanded to the second order, the node voltage equation only contains the first term of the state quantity, the second derivative of the node voltage equation is 0, and the taylor expansion formula of the function F (W (),) 0 is as follows:

where Δ [ - Δ, Δ ], the above equation is always 0, as long as:

F(W(_c),_c)＝0 (26)

the first derivative formula (27) and the second derivative formula (28) of the function are developed as follows

Therefore, the following three deterministic equations are obtained

F(W(_c),_c)＝0 (31)

In the direct-current power distribution network, x is 2r, and y represents the number of active power fluctuation variables; in an alternating current distribution network and VSC, x is 4n + L, and y represents the number of active, reactive and voltage fluctuation variables;

step S32: expanding the three deterministic equations, and calculating the derivative of the power function to the power fluctuation variable and the derivative of the voltage relational expression in the VSC to the voltage fluctuation quantity in the DC distribution network; formula (31) is a fluctuating variable ═_cPerforming load flow calculation by adopting a cow pulling method when the ground state load flow is 0;

the expansion of equation (32) is as follows:

in the above formula, z is the number of matrix equations F (W (),) ═ 0, in the dc distribution network, z ═ x ═ 2r, and in the matrix equations F₁-F_rAs an equation of node voltage, F_r+1-F_2rIs an active power equation; in an alternating current distribution network and VSC, z is equal to x is equal to 4n + L, and F is in a matrix equation₁-F_2nAs an equation of node voltage, F_2n+1-F_4nIs an active and reactive power equation, F_4n+1-F_4n+LIs a VSC voltage relational equation;

derivative of matrix equation to fluctuation amount

The derivative is 0 when no power fluctuation occurs in the node, and the derivative is 1 when power fluctuation occurs. When the voltage of a node connected with the kth VSC in the direct-current distribution network fluctuates, the derivative of the VSC voltage relational equation (22) to the voltage fluctuation quantity

The values of (a) are as follows:

k is 1,2 … L, the kth VSC voltage relational expression is the 4n + k equation of matrix equation F (W (),) < 0 of the AC distribution network, M_kcThe voltage modulation ratio basic state operation value of the kth VSC is obtained;

the expression of formula (33) is as follows:

due to the requirement of satisfying the voltage relation (22), compared with a pure alternating current distribution network, the second derivative of the alternating current distribution network matrix equation connected with the direct current distribution network to the fluctuation amount increases the matrix

When in use_iIs the i voltage fluctuation quantity and W of a node in a direct current power distribution network_aWhen the modulation ratio of the VSC connected with the node i is the same, the 4n + k equations in the alternating-current power distribution network, namely the second derivative of the voltage relational expression of the kth VSC to the fluctuation quantity

As non-zero elements, the following is specifically calculated:

wherein the modulation ratio M_kIs the 4n + k th element in the state quantity W. The other elements of the matrix are all 0, so the matrix is highly sparse. The first derivative of the state variable to the fluctuation variable is obtained by calculating equations (34), (36)

Second derivative of

The method is substituted into the following formula, and a state quantity interval value is solved;

W_cthe specific values of the state quantities in the ground state are as follows:

step S33: calculating a Jacobian matrix and a Hessian matrix under the augmented rectangular coordinate power flow model, and analyzing the sparsity of the Jacobian matrix and the Hessian matrix adopting the augmented rectangular coordinate power flow model;

jacobian matrix in equation (34) for extended rectangular coordinates

The specific calculation is as follows:

in the alternating-current distribution network:

the elements of the matrix in equation (40) are as follows:

is a 2 n-order matrix;

in formulae (41) to (43), a_n,b_nInjecting the real part and the imaginary part, e, of the current into the node n of the AC distribution network_n,f_nIs node n voltageReal and imaginary parts of, G_nn,B_nnFor the real and imaginary parts of the node n admittance, G_1n＝G_n1The real part of the transadmittance of node 1 and node n, which are equal, B_1n＝B_n1Node 1 and node n have equal imaginary parts of transadmittance.

In the formula (44), the reaction mixture is,

the voltage of the internal node of the 1 st VSC is respectively a real part and an imaginary part, subscript i is the node number of the node in the alternating current network, and superscript (1,2i-1) represents element e_iThe position in the matrix.

Respectively a real part and an imaginary part of the voltage of an internal node of the L-th VSC, subscript j is a node label of the node in the AC network, and superscripts also represent positions;

M₁，M_Lvoltage modulation ratios of 1 st, L VSCs,

node voltage values connected with 1 st VSC and L VSC in the direct-current power distribution network respectively;

in the direct current distribution network:

the direct-current power distribution network comprises r nodes;

the above matrix A_I，A_V，D_I，D_VThe non-diagonal elements in the I are all 0, so the sparsity in the Jacobian matrix is very high; rectangular coordinates for augmentation in equation (36)The hessian matrix h (f) below is specifically calculated as follows:

in the alternating-current distribution network:

the highest order of the node voltage equation is 1 st order, Hessian matrix H (F)₁)-H(F_2n) 0 matrices of 4n + L levels;

hessian matrix H (F) of the nodal power equation_2n+1)-H(F_4n) For sparse matrix, the active power equation for node i Heisen matrix H (F)_2n+2i-1) Is a 4n + L-order matrix, wherein the matrix comprises

The value is 1, other elements are 0, the sparsity of the Hessian matrix of the reactive power equation is the same, and the highest value of i is n;

hessian matrix H (F) of VSC voltage relational equation_4n+1)-H(F_4n+L) Are all 4n + L-order matrices, in which

Three non-zero elements in the matrix, all others being 0; m_jFor the modulation ratio of the jth converter station, e_cj,f_cjCompacting an imaginary part for the alternating current side of the jth converter station, wherein the highest value of j is L;

in the direct current distribution network:

node voltage equation hessian matrix H (F)₁)-H(F_r) Is a 0 matrix of 2r order;

node power equation hessian matrix H (F)_r+1)-H(F_2r) All are 2r order matrixes, wherein the active power equation of the node i is in Hessian matrix

The value is 1, the others are all 0, and the highest value of i is r;

in this embodiment, the specific content of step S4 is:

interval variables in an uncertain power flow equation considering wind power, photoelectric and other distributed generation volatility in the alternating-current power distribution network are power values, wherein the interval value of power injection power of a node i power supply is

The interval variable in the uncertain power flow equation considering the load power fluctuation is a power value, wherein the load power interval value of the node i is

And (3) carrying out interval operation on active and reactive power of the node:

in the formulae (47) to (56),

power injection for node iThe central value of the active power interval is,

is the central value, delta P, of the active power interval of the node i load_i ^SInjecting active power interval fluctuation quantity delta P for node i power supply_i ^LThe fluctuation amount of the load active power interval of the node i,

is the central value of the load reactive power interval of the node i,

injecting the reactive power interval central value for the power supply of the node i,

the fluctuation amount of the reactive power interval of the load of the node i,

injecting a reactive power interval fluctuation quantity into a power supply of a node i;

in the direct-current power distribution network, interval variables in an uncertain power flow equation considering distributed power generation volatility such as photoelectricity are power values, wherein the interval value of power injection power of a node i power supply is

The interval variable in the uncertain power flow equation considering the load power fluctuation is a power value, wherein the load power interval value of the node i is

Performing interval operation on active power of node

Formulas (57) - (61)

The direct current distribution network node i power source injects the central value of the active power interval,

the central value of the load active power interval of the node i,

injecting the fluctuation quantity of the active power interval into the power supply of the node i,

loading the fluctuation quantity of the active power interval for a node i;

substituting the calculated active power and reactive power fluctuation variables in the AC/DC distribution network into a formula (13), injecting active power into a node, wherein the reactive power fluctuation range is +/-20%, and the power base value is

P_ic，Q_icOn the basis of the node, the active power and the reactive power fluctuation quantity of the node are obtained, and the fluctuation variable is subjected to calculation

_PiAnd_Qiand (4) assigning to obtain a fluctuation variable matrix, and further performing interval load flow calculation on the alternating current and direct current hybrid power distribution network, wherein the specific calculation process is described in detail in step S5 and step S6.

In this embodiment, the specific content of step S5 is:

selecting active power source fluctuation node and load fluctuation node in direct-current power distribution networkCalculating the active power fluctuation amplitude of the node, wherein the node injection power fluctuation amplitude is +/-20 percent at the power basic value

Calculating the power fluctuation amount on the basis of the power fluctuation amount; the basic value of the node injection active power is an active power operation value before the node injection active power fluctuates; after obtaining the fluctuation amount of the active power, the fluctuation variable is adjusted

Assigning a value to obtain a fluctuation variable matrix, wherein the fluctuation variable matrix only comprises active power fluctuation variables in the direct current power distribution network and has the order of 1 multiplied by r; the interval power flow calculation of the direct current distribution network is carried out, the Jacobian matrix of the direct current distribution network is firstly calculated through the formula (46), and then the state quantity V is obtained according to the formula (34)_i ^d,

For wave change

The hessian matrix of the direct current distribution network is calculated by the formula (30), and the state quantity is obtained according to the formula (36)

For fluctuating variables

The second derivative of (2) is obtained by the equation (38) for the voltage of the node of the direct-current distribution network, and the interval value of the current injected into the node is obtained.

In this embodiment, the specific content of step S6 is:

step S5, acquiring a node injection power interval value of the direct-current power distribution network, and acquiring an interval value of node voltage and node injection current in the direct-current power distribution network through interval load flow calculation of the direct-current power distribution network; therefore, the active power transmission interval value between the direct current distribution network and the VSC is obtained through the formula (3), and the active power transmission fluctuation quantity is calculated according to the formula (9)

Through formulas (7) and (8) for acquiring node voltage fluctuation quantity connected with VSC in direct-current power distribution network

Therefore, considering the influence of the fluctuation of the active power value of the direct-current power distribution network input to the alternating-current power distribution network and the voltage fluctuation condition of the direct-current power distribution network on the alternating-current power distribution network, selecting power fluctuation nodes of the alternating-current power distribution network, wherein the active and reactive injection power fluctuation amplitudes of the nodes are +/-20%, and the power fluctuation nodes are set at a power basic value P_ic，Q_icBased on the calculated active power fluctuation amount_PiAmount of fluctuation of reactive power_Qi(ii) a Therefore, the fluctuation amount of active power transmission between the DC distribution network and the VSC

Node voltage fluctuation amount of direct current power distribution network

Active power fluctuation quantity injected into AC distribution network node_PiAnd node injected reactive power fluctuation amount_QiForming a fluctuation variable matrix of the alternating-current power distribution network, wherein the fluctuation variable matrix is a 1 x (2n +2L) order matrix; firstly, calculating a Jacobian matrix of the alternating current distribution network by using a formula (40), and then solving the node voltage, the node injection current and the voltage modulation ratio fluctuation variable of the alternating current distribution network according to a formula (34)

And_Qithe first derivative of (a); firstly, the Hessian matrix is calculated through the formula (30), and then the node voltage, the node injection current and the voltage modulation ratio fluctuation variable of the alternating current distribution network are solved according to the formula (36)

_PiAnd_Qiand finally, solving the interval values of the node voltage, the node injection current and the voltage modulation ratio of the alternating-current distribution network by the equation (38). It is preferable thatIn the present embodiment, a specific example is as follows: in the embodiment, interval power flow calculation is performed on an IEEE33 node expanded alternating current and direct current hybrid power distribution network, and Matlab2014a is adopted for programming under a processor Intel (R) core (TM) i5-3230 CPU. System reference capacity S_B100MVA, and the reference voltage on the AC side and the DC side is U _B10 kV. Wind power generation is connected into the alternating current power distribution network, photovoltaic power generation is connected into the direct current power distribution network, and the specific connection position is shown in figure 1. The power fluctuation amplitude is set to be +/-20%, the uncertain power comprises active power and reactive power generated by a wind driven generator, active power generated by photovoltaic power generation and load power fluctuation, wherein nodes 2, 3, 4, 5, 9, 10, 11, 16, 17, 19, 22, 27, 29 and 31 are selected for load power fluctuation in the alternating current power distribution network, and the load power of the direct current power distribution network does not fluctuate. The method provided by the embodiment is compared with a Monte Carlo method, wherein the Monte Carlo method is defaulted to be uniformly distributed in an interval, and the calculation times are 10000 times.

The main parameter in the voltage source converter comprises an impedance value Z_cAnd susceptance value B_fSpecific values thereof are given in table 1. And meanwhile, a control mode adopted by the voltage source converter when the alternating current-direct current hybrid power distribution network adopts a master-slave control strategy and an equivalent control strategy is given.

TABLE 1 parameters and control modes of voltage source converters

1 Master slave control

1) Analysis of calculation results of interval load flow of direct-current power distribution network

The direct-current power distribution network of the IEEE33 node expanded alternating-current and direct-current power distribution network comprises 6 nodes, wherein a node 2 and a node 4 are connected with a voltage source converter, a node 5 and a node 6 are connected with photovoltaic power generation, and the fluctuation ranges are +/-20%. The voltage source converter 1 is fixed

In the control mode, the voltage source converter 2 is constant P_cControl modes, divided into a master-slave control mode scenarioAnd respectively adopting an interval Taylor expansion method and a Monte Carlo method to carry out interval load flow calculation of the direct-current power distribution network.

It can be seen from fig. 2 that the node voltage amplitude calculation result obtained by the interval taylor expansion method has complete wrapping property on the calculation result of the monte carlo method, and the effectiveness of the method can be proved. Meanwhile, interval load flow calculation is carried out on node injection current, the calculation result is shown in fig. 3, fig. 4 shows a fluctuation value of direct current distribution network node injection power obtained according to an interval value of node voltage and node injection current, active power input to a node 2 by a voltage source converter 1 fluctuates within the range of [0.0071 and 0.0111], and when the fluctuation amplitude in the direct current distribution network is large, the power transmission direction can be changed. The node 4 is in a constant active power control mode, the voltage of the node 4 fluctuates within the range of [0.9917,0.9947], the node injection power obtained by multiplying the current value is within the range of [0.000037,0.000058], and the difference value of the upper limit power and the lower limit power is extremely small and is lower than the convergence precision of 0.0001.

2) Analysis of alternating current distribution network interval load flow calculation result

A wind driven generator is connected to a node 26 in an alternating current distribution network, active power and reactive power loads of 12 nodes are selected, the fluctuation ranges are +/-20%, the direct current sides of two voltage source converters are affected by the fluctuation amount of the direct current distribution network, therefore, the alternating current distribution network comprises 28 fluctuation variables, and interval power flow calculation is carried out by adopting an interval Taylor expansion method and a Monte Carlo method respectively.

As can be seen from fig. 5 and 6, the node voltage amplitude calculation result of the interval taylor expansion method has complete wrapping property on the calculation result of the monte carlo method, and the effectiveness of the method can be proved. The node 1 is a balance node, in the scene of a master-slave control mode, the node 14 is connected with the voltage source converter 2, and the control mode is a fixed U_sTherefore, the voltage amplitudes of the node 1 and the node 14 are always unchanged, the voltage amplitude fluctuation range of the nodes near the node 1 and the node 14 is small, the PV node can effectively restrain the voltage fluctuation amount, and the voltage amplitude fluctuation of the node far away from the PV node is severe.

Modulation ratio M of voltage source converter₁，M₂The per-unit values of the modulation ratios are all 1,in interval power flow calculation, along with the fluctuation of a voltage value, the modulation ratio is in accordance with the fluctuation of the voltage relation of an alternating current-direct current power distribution network, and the calculation result is as follows

TABLE 2 Voltage modulation ratio distribution

2 peer to peer control

Droop control parameter k in peer-to-peer control mode scenario_droopAnd (5) when the fluctuation variables in the direct current distribution network and the alternating current distribution network are unchanged, performing interval power flow calculation by respectively adopting an interval Taylor expansion method and a Monte Carlo method.

1) Interval power flow calculation of direct-current power distribution network

The fluctuation variable in the direct-current power distribution network is still photovoltaic power generation power, the fluctuation amplitude is +/-20%, the node 2 and the node 4 adopt a droop control mode, and the voltage standard value

As can be seen from fig. 7, the calculation result of the interval taylor expansion method has complete wrapping property for the calculation result of the monte carlo method, and the voltage fluctuation amplitude of the node 4 in the peer-to-peer control mode is effectively reduced compared with the master-slave control mode when the fluctuation amounts are the same.

The node injection power and the node voltage difference value are in a linear relation, and when the voltage value is lower than the voltage standard value, the node power injection amount of the power distribution network is increased according to a droop control mode, so that the voltage value is raised.

Fig. 8 shows the fluctuation of the node injection power, and it can be seen from the nodes 2 and 4 that when the voltage reaches the upper bound, the lower bound of the node injection power is corresponded, so that the result obtained by using the interval taylor expansion method is completely reasonable.

2) Interval power flow calculation of alternating-current power distribution network

When an equivalent control mode is adopted, the voltage values and the injection powers of the nodes 2 and 4 in the direct-current power distribution network are fluctuation quantities and are input into the alternating-current power distribution network and the voltage source converter, so that 2 fluctuation variables are added to 30 fluctuation variables on the original basis when interval power flow calculation of the alternating-current power distribution network is carried out.

Compared with the master-slave control mode, referring to the voltage fluctuation diagrams of fig. 3 and 8 and the power fluctuation diagrams of fig. 5 and 9, it can be seen that the fluctuation ranges of the node 4 voltage and the node 2 injection power are both reduced in the peer-to-peer control mode, and meanwhile, because the node voltage and the node injection power are both fluctuated in the peer-to-peer control mode, the node 7 and the node 34 of the voltage source converter 1 are connected in the alternating-current power distribution network, the node voltage amplitude fluctuation range is reduced, and the voltage source converter 2 is controlled by using the constant alternating-current voltage, so that the voltage amplitude fluctuation is not influenced.

As shown in fig. 10, compared to the constant power control method in the master-slave control, the power fluctuation range of the voltage source converter 2 in the peer-to-peer control method is increased, and thus the power fluctuation range of the node 35 is increased.

TABLE 3 Voltage modulation ratio distribution

Compared with a constant voltage control mode of the direct current distribution network node 2 in master-slave control, the voltage fluctuation range of the node 2 in an equivalent control mode is increased, and compared with a constant power control mode of the direct current distribution network node 4 in master-slave control, the voltage fluctuation range of the node 4 in an equivalent control mode is reduced.

The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (7)

1. An alternating current-direct current hybrid power distribution network interval power flow calculation method based on an interval Taylor expansion method is characterized by comprising the following steps:

step S1: respectively determining a control mode corresponding to each VSC according to a master-slave control strategy and an equivalent control strategy of the alternating-current and direct-current hybrid power distribution network, combining multiple control modes of the VSCs with an interval power flow algorithm, analyzing node voltages of the direct-current power distribution network under different control modes in the interval power flow, and analyzing node injection currents and active power transmission fluctuation conditions between the direct-current power distribution network and the VSCs;

step S2: providing a voltage relation formula which is required to be met by a VSC modulation ratio in the interval tide, VSC internal node voltage and direct-current distribution network node voltage, determining a voltage fluctuation variable in the direct-current distribution network, and analyzing the influence of the voltage fluctuation variable on the VSC internal node voltage, the alternating-current distribution network node voltage and the modulation ratio;

step S3: writing a Jacobian matrix and a Hessian matrix under an augmented rectangular coordinate according to a node voltage equation, a power equation and a voltage relational column in the alternating-current and direct-current hybrid power distribution network;

step S4: selecting a load power fluctuation node and a photovoltaic power generation and wind power generation access node, determining a node power fluctuation amount and an interval central value by adopting an interval algorithm, and establishing a fluctuation variable matrix;

step S5: the method comprises the steps that an alternating current-direct current decoupling load flow algorithm is adopted, interval load flow calculation of a direct current power distribution network is firstly carried out, node voltage of the direct current power distribution network is obtained, a first derivative and a second derivative of a node injection current interval variable to a fluctuation variable are obtained, and interval values of the node voltage, the node current and node injection power of the direct current power distribution network are calculated;

step S6: the method comprises the steps of obtaining node voltage and node injection power interval values of the direct-current power distribution network, considering influences of power value fluctuation of the direct-current power distribution network input to the alternating-current power distribution network and voltage fluctuation conditions of the direct-current power distribution network on the alternating-current power distribution network, selecting load power fluctuation nodes of the alternating-current power distribution network, and carrying out interval load flow calculation on the alternating-current power distribution network.

2. The method for calculating the interval power flow of the alternating-current/direct-current hybrid power distribution network based on the interval taylor expansion method according to claim 1, wherein the specific content of the step S1 is as follows:

the control strategy of the alternating current-direct current hybrid power distribution network mainly comprises a master-slave control strategy and an equivalent control strategy, wherein under the master-slave control strategy, one VSC is used as a master station and adopts a constant direct current voltage control mode to stabilize a direct current voltage value, and other VSCs adopt constant power control modes to control an active power transmission value; under an equivalent control strategy, all converter stations adopt a droop control mode, and the node voltage of the direct-current power distribution network and the node injection current active power value are adjusted simultaneously;

for a single VSC, the control modes comprise a constant direct-current voltage, a constant alternating-current voltage, a constant active or reactive power control mode and a droop control mode;

and (3) a constant direct-current voltage control mode:

controlling the voltage value of the node to be a fixed value, wherein the power fluctuation in interval load flow calculation causes the fluctuation of the injection current of the node, so that the injection power of the node is an interval value;

in the above formula

Injecting power into the direct current distribution network node,

is the voltage of the node, and is,

a current is injected for the node and,

the amount of power fluctuation is injected for the node,

injecting a current fluctuation amount into the node; when no other power is injected, the power of the direct current distribution network injected with VSC is

During power fluctuation, when the fluctuation amount isWhen the amplitude is higher, the power transmission direction can be changed, and the conversion of rectification and inversion states can be realized; fluctuation of voltage amplitude and phase angle of nodes in the VSC is caused by fluctuation of injection power of nodes of the direct-current power distribution network, and fluctuation of each state quantity in the alternating-current power distribution network is further caused;

constant power control mode:

in a constant power control mode, when the power injection values of other nodes fluctuate, the node voltage and the node injection current slightly fluctuate, and the power fluctuation value calculated by multiplying the node voltage and the node injection current is lower than the convergence precision, so that the node injection power is considered to be a constant value within an allowable error range; because an alternating current-direct current decoupling power flow algorithm is adopted, the fixed active power transmission value is changed into the fixed P_c，P_cThe active power transmission value between the VSC and the direct current power distribution network; value of reactive power transmission Q_sMaintaining a constant value, and setting the fluctuation amount to 0;

the droop control mode is as follows:

when voltage of a node connected with the VSC in the direct-current power distribution network rises or falls, the VSC determines a power value of an injection node according to a voltage deviation value;

in the above formula K_droopAnd

in order to control the parameters of the device,

and

meanwhile, when the power injection values of other nodes fluctuate, the fluctuation of the node voltage and the node injection current can be caused at the same time, and therefore, the node injection power can also fluctuate correspondingly

According to the interval algorithm, the node injection power is as follows:

when no other power is injected, the active power of VSC injected into the direct current power distribution network is

Constant alternating voltage control mode:

under the augmented rectangular coordinate, the constant alternating voltage control mode maintains the voltage amplitude of the node i to be 1 constantly, and the following control mode is adopted:

e_i＝1 f_i＝0

(5)

in the above formula e_iIs the real part of the node voltage, f_iIs the node voltage imaginary part; there is no power fluctuation variable in the fixed AC voltage equation, and only the relation e in the Jacobian matrix_iTherefore, the node voltage amplitude can be kept constant at 1 in the interval power flow calculation, namely the voltage amplitude U_i＝1。

3. The method for calculating the interval power flow of the alternating-current/direct-current hybrid power distribution network based on the interval taylor expansion method according to claim 1, wherein the specific content of the step S2 is as follows:

combining an interval Taylor expansion method and a control mode of the AC/DC hybrid power distribution network to obtain a power flow model adopting the interval Taylor expansion method in the AC/DC hybrid power distribution network, wherein voltage relation equations required to be satisfied on two sides of the VSC are as follows

In the above formula, M_kAdopting per unit value and reference value for the voltage modulation ratio of the kth VSC

Wherein the content of the first and second substances,

e_i,f_ithe real part and the imaginary part of the voltage of the internal node of the kth VSC are provided, each VSC comprises an internal node,

the node voltage value is connected with the kth VSC in the direct-current power distribution network; when the control mode is constant DC voltage control, the node voltage

Is a constant value; when the control mode is droop control and constant active power control, the node voltage

The node voltage is near to a per unit value of 1 when the direct current distribution network runs under the ground state, so that the node voltage is an interval value

Is interval voltage

The square of the central value, after the square operation of the node voltage interval,

deviation of section center value of

In the ground state tide before power fluctuation, the power distribution network operates

Thus, the formula (7) is defined as

Is unfolded by

The interval represented is no longer a symmetric interval, and therefore

As follows

In the above formula

Voltage fluctuation amount [ delta V ] of node connected with VSC in direct-current power distribution network_lowj,ΔV_hj]For the VSC internal voltage e_i,f_iAnd a voltage modulation ratio M_kAll will have an influence on the internal voltage e of the VSC_i,f_iAnd a voltage modulation ratio M_kThe fluctuation occurs, and then the node voltage and the node injection current of the node connected with the VSC in the alternating current distribution network fluctuate.

4. The method for calculating the interval power flow of the alternating-current/direct-current hybrid power distribution network based on the interval taylor expansion method according to claim 1, wherein the step S3 specifically includes the following steps:

step S31: establishing a power equation, a node voltage equation and a VSC voltage relational expression in the interval tide of the alternating-current and direct-current hybrid power distribution network, carrying out interval Taylor expansion, and establishing three deterministic equations under the uncertain tide;

in an uncertain power flow equation considering the volatility of a distributed power supply such as wind power, photoelectricity and the like and the load volatility, the power fluctuation of a node i in an alternating-current power distribution network is expressed as an interval value:

[P_i]＝P_ic+[-ΔP_i,ΔP_i]

(9)

[Q_i]＝Q_ic+[-ΔQ_i,ΔQ_i]

(10)

P_ic,Q_icrespectively the central value of the active power interval and the reactive power interval, delta P_i,ΔQ_iRespectively the active power fluctuation quantity and the reactive power fluctuation quantity;

in an uncertain power flow equation considering the fluctuation of a photovoltaic equal-distribution type power supply and the load fluctuation, the power fluctuation of a node i in a direct-current power distribution network is represented as an interval value;

is the active power interval central value of the direct current distribution network,

is the active power fluctuation amount;

in an uncertain power flow equation considering node voltage fluctuation in the direct-current power distribution network, the voltage fluctuation of a node j connected with a kth VSC in the direct-current power distribution network is represented as an interval value;

in addition, the active power transmission quantity between the direct current distribution network and the VSC is also fluctuated under the influence of voltage fluctuation, and influences are generated on the load flow and the modulation ratio in the VSC and the alternating current distribution network; therefore, fluctuation variables in the uncertainty trend of the alternating current-direct current hybrid power distribution network comprise active power, reactive power and fluctuating load of injection nodes of the distributed power supply, and node voltage fluctuation quantity and active power transmission fluctuation quantity connected with VSC in the direct current power distribution network

In the above formula, the first and second carbon atoms are,_Pi＝[-ΔP_i,ΔP_i]the active power fluctuation quantity of the node is obtained by adding the active power injected by the node and the active power load of the node in intervals,_Qi＝[-ΔQ_i,ΔQ_i]the node reactive power fluctuation quantity is obtained by adding reactive power injected by the node and the node reactive power load in intervals, wherein i is 1,2, … and n;

representing the node voltage fluctuation quantity of nodes connected with VSC in the direct current distribution network,

the active power transmission fluctuation amount between the direct current distribution network and the VSC is represented, and k is 1 and 2 … L; the expression of the interval between the node voltage equation and the node power equation in the alternating-current power distribution network is as follows:

ΔP_i＝(P_ic+_Pi)-e_i()a_i()-f_i()b_i()＝0

(15)

ΔQ_i＝(Q_ic+_Qi)-f_i()a_i()+e_i()b_i()＝0

(16)

1,2, …, n, and the PV node adopts formula (17) instead of formula (16); the expression of the interval between the node voltage equation and the node power equation in the direct-current power distribution network is as follows:

i is 1,2, …, r; the constant voltage node adopts an equation (20) instead of an equation (19); in the droop control mode, an interval expression of a node j connected with the kth VSC in the direct-current distribution network is as follows:

the kth VSC voltage relational interval expression is as follows:

combining equations (14) - (22), the uncertain power flow equation of the alternating current-direct current hybrid power distribution network is expressed as a matrix equation:

the uncertain power flow matrix equation Δ I (W (), (0) includes equations (14) and (18), Δ P (W (), (0) includes equations (15), (19) and (21), Δ Q (W (), (0) includes equation (16), and Δ U (W (), (0) includes equations (17), (20) and (22); wherein W is represented as:

W＝[e₁(),f₁(),a₁(),b₁(),e₂(),f₂(),a₂(),b₂()…M₁(),M₂()…V₁ ^d(),I₁ ^d(),V₂ ^d(),I₂ ^d()…]

(24)

the direct-current power distribution network contains 2r state quantities, and the alternating-current power distribution network and the VSC contain 4n + L state quantities;

the system operates under the ground state value before power fluctuation, and the fluctuation variable is equal to_cAnd therefore, performing interval taylor expansion on the power uncertain power flow equation at the system ground state operation value by adopting an interval taylor expansion method, wherein after the power equation only contains node voltage, a second term of a state quantity such as node injection current and the like and a first term of a fluctuation variable, the higher order of the equation is infinitesimal 0 after the equation is expanded to the second order, the node voltage equation only contains the first term of the state quantity, the second derivative of the node voltage equation is 0, and the taylor expansion formula of the function F (W (),) 0 is as follows:

where Δ [ - Δ, Δ ], the above equation is always 0, as long as:

F(W(_c),_c)＝0 (26)

the first derivative formula (27) and the second derivative formula (28) of the function are developed as follows

Therefore, the following three deterministic equations are obtained

F(W(_c),_c)＝0 (31)

In the direct-current power distribution network, x is 2r, and y represents the number of active power fluctuation variables; in an alternating current distribution network and VSC, x is 4n + L, and y represents the number of active, reactive and voltage fluctuation variables;

step S32: expanding the three deterministic equations, and calculating the derivative of the power function to the power fluctuation variable and the derivative of the voltage relational expression in the VSC to the voltage fluctuation quantity in the DC distribution network; formula (31) is a fluctuating variable ═_cPerforming load flow calculation by adopting a cow pulling method when the ground state load flow is 0;

the expansion of equation (32) is as follows:

in the above formula, z is the number of matrix equations F (W (),) ═ 0, in the dc distribution network, z ═ x ═ 2r, and in the matrix equations F₁-F_rAs an equation of node voltage, F_r+1-F_2rIs an active power equation; in an alternating current distribution network and VSC, z is equal to x is equal to 4n + L, and F is in a matrix equation₁-F_2nAs an equation of node voltage, F_2n+1-F_4nIs an active and reactive power equation, F_4n+1-F_4n+LIs a VSC voltage relational equation;

derivative of matrix equation to fluctuation amount

When the node does not generate power fluctuation, the derivative is 0, and when the node generates power fluctuation, the derivative is a fluctuation quantity coefficient 1; when the voltage of a node connected with the kth VSC in the direct-current distribution network fluctuates, the derivative of the VSC voltage relational equation (22) to the voltage fluctuation quantity

The values of (a) are as follows:

k is 1,2 … L, the kth VSC voltage relational expression is the 4n + k equation of matrix equation F (W (),) < 0 of the AC distribution network, M_kcThe voltage modulation ratio basic state operation value of the kth VSC is obtained;

the expression of formula (33) is as follows:

due to the requirement of satisfying the voltage relation (22), compared with a pure alternating current distribution network, the second derivative of the alternating current distribution network matrix equation connected with the direct current distribution network to the fluctuation amount increases the matrix

When in use_iIs the i voltage fluctuation quantity and W of a node in a direct current power distribution network_aWhen the modulation ratio of the VSC connected with the node i is the same, the 4n + k equations in the alternating-current power distribution network, namely the second derivative of the voltage relational expression of the kth VSC to the fluctuation quantity

As non-zero elements, the following is specifically calculated:

wherein the modulation ratio M_kIs the 4n + k th element in the state quantity W. The other elements of the matrix are all 0, so the matrix is highly sparse. The first derivative of the state variable to the fluctuation variable is obtained by calculating equations (34), (36)

Second derivative of

The method is substituted into the following formula, and a state quantity interval value is solved;

W_cthe specific values of the state quantities in the ground state are as follows:

step S33: calculating a Jacobian matrix and a Hessian matrix under the augmented rectangular coordinate power flow model, and analyzing the sparsity of the Jacobian matrix and the Hessian matrix adopting the augmented rectangular coordinate power flow model;

jacobian matrix in equation (34) for extended rectangular coordinates

The specific calculation is as follows:

in the alternating-current distribution network:

the elements of the matrix in equation (40) are as follows:

is a 2 n-order matrix;

in formulae (41) to (43), a_n,b_nInjecting the real part and the imaginary part, e, of the current into the node n of the AC distribution network_n,f_nFor the real and imaginary part of the voltage at node n, G_nn,B_nnFor the real and imaginary parts of the node n admittance, G_1n＝G_n1The real part of the transadmittance of node 1 and node n, which are equal, B_1n＝B_n1Node 1 and node n have equal imaginary parts of transadmittance.

In the formula (44), the reaction mixture is,

f_i ^(1,2i)the real part and the imaginary part of the voltage of the internal node of the 1 st VSC are respectively shown, subscript i is the node number of the node in the alternating current network, and superscript (1,2i-1) represents element e_iThe position in the matrix.

Respectively a real part and an imaginary part of the voltage of an internal node of the L-th VSC, subscript j is a node label of the node in the AC network, and superscripts also represent positions;

M₁，M_Lvoltage modulation ratio, V, of 1 st, L VSC, respectively_i ^d,

Node voltage values connected with 1 st VSC and L VSC in the direct-current power distribution network respectively;

in the direct current distribution network:

the direct-current power distribution network comprises r nodes;

the above matrix A_I，A_V，D_I，D_VThe non-diagonal elements in the I are all 0, so the sparsity in the Jacobian matrix is very high; the hessian matrix h (f) in the formula (36) in the augmented rectangular coordinate is specifically calculated as follows:

in the alternating-current distribution network:

the highest order of the node voltage equation is 1 st order, Hessian matrix H (F)₁)-H(F_2n) 0 matrices of 4n + L levels;

hessian matrix H (F) of the nodal power equation_2n+1)-H(F_4n) For sparse matrix, the active power equation for node i Heisen matrix H (F)_2n+2i-1) Is a 4n + L-order matrix, wherein the matrix comprises

The value is 1, other elements are 0, the sparsity of the Hessian matrix of the reactive power equation is the same, and the highest value of i is n;

hessian matrix H (F) of VSC voltage relational equation_4n+1)-H(F_4n+L) Are all 4n + L-order matrices, in which

Three non-zero elements in the matrix, all others being 0; m_jFor the modulation ratio of the jth converter station, e_cj,f_cjCompacting an imaginary part for the alternating current side of the jth converter station, wherein the highest value of j is L;

in the direct current distribution network:

node voltage equation hessian matrix H (F)₁)-H(F_r) Is a 0 matrix of 2r order;

node power equation hessian matrix H (F)_r+1)-H(F_2r) All are 2r order matrixes, wherein the active power equation of the node i is in Hessian matrix

The value is 1, all others are 0, and the highest value of i is r.

5. The alternating current-direct current hybrid distribution network improved interval power flow algorithm based on the interval taylor expansion method as claimed in claim 1, wherein the specific content of the step S4 is as follows:

interval variables in an uncertain power flow equation considering wind power, photoelectric and other distributed generation volatility in the alternating-current power distribution network are power values, wherein the interval value of power injection power of a node i power supply is

The interval variable in the uncertain power flow equation considering the load power fluctuation is a power value, wherein the load power interval value of the node i is

And (3) carrying out interval operation on active and reactive power of the node:

ΔP_i＝ΔP_i ^L+ΔP_i ^S

(53)

in the formulae (47) to (56),

injecting the central value of the active power interval for the power supply of the node i,

is the central value, delta P, of the active power interval of the node i load_i ^SInjecting active power interval fluctuation quantity delta P for node i power supply_i ^LThe fluctuation amount of the load active power interval of the node i,

is the central value of the load reactive power interval of the node i,

injecting the reactive power interval central value for the power supply of the node i,

the fluctuation amount of the reactive power interval of the load of the node i,

injecting a reactive power interval fluctuation quantity into a power supply of a node i;

in the direct-current power distribution network, interval variables in an uncertain power flow equation considering distributed power generation volatility such as photoelectricity are power values, wherein the interval value of power injection power of a node i power supply is

The interval variable in the uncertain power flow equation considering the load power fluctuation is a power value, wherein the load power interval value of the node i is

Performing interval operation on active power of node

ΔP_i ^d＝ΔP_i ^dL+ΔP_i ^dS

(61)

Formulas (57) - (61)

Injecting active power interval central value for a direct current distribution network node i power supply,

is the central value, delta P, of the active power interval of the node i load_i ^dSInjecting active power interval fluctuation quantity delta P for node i power supply_i ^dLLoading the fluctuation quantity of the active power interval for a node i;

substituting the calculated active power and reactive power fluctuation variables in the AC/DC distribution network into a formula (13), injecting active power into a node, wherein the reactive power fluctuation range is +/-20%, and the power base value is

P_ic，Q_icOn the basis of the node, the active power and the reactive power fluctuation quantity of the node are obtained, and the fluctuation variable is subjected to calculation

_PiAnd_Qiand (5) assigning to obtain a fluctuation variable matrix, and further performing interval load flow calculation on the alternating current and direct current hybrid power distribution network.

6. The method for calculating the interval power flow of the alternating-current/direct-current hybrid power distribution network based on the interval taylor expansion method according to claim 1, wherein the specific content of the step S5 is as follows:

active power supply fluctuation nodes and load fluctuation nodes in the direct-current power distribution network are selected, node active power fluctuation amplitude is calculated, node injection power fluctuation amplitude is +/-20%, and the node active power fluctuation amplitude is calculated at a power basic value

Calculating the power fluctuation amount on the basis of the power fluctuation amount; the basic value of the node injection active power is an active power operation value before the node injection active power fluctuates; after obtaining the fluctuation amount of the active power, the fluctuation variable is adjusted

Assigning a value to obtain a fluctuation variable matrix, wherein the fluctuation variable matrix only comprises active power fluctuation variables in the direct current power distribution network and has the order of 1 multiplied by r; the interval power flow calculation of the direct current distribution network is carried out, the Jacobian matrix of the direct current distribution network is firstly calculated through the formula (46), and then the state quantity V is obtained according to the formula (34)_i ^d,

For fluctuating variables

The hessian matrix of the direct current distribution network is calculated by the formula (30), and the state quantity V is obtained according to the formula (36)_i ^d,

For fluctuating variables

The second derivative of (2) is obtained by the equation (38) to obtain the interval value of the node voltage and the node injection current of the direct current distribution network.

7. The method for calculating the interval power flow of the alternating-current/direct-current hybrid power distribution network based on the interval taylor expansion method according to claim 1, wherein the specific content of the step S6 is as follows:

step S5, acquiring a node injection power interval value of the direct-current power distribution network, and acquiring an interval value of node voltage and node injection current in the direct-current power distribution network through interval load flow calculation of the direct-current power distribution network; therefore, the active power transmission interval value between the direct current distribution network and the VSC is obtained through the formula (3), and the active power transmission fluctuation quantity is calculated according to the formula (9)

Through formulas (7) and (8) for acquiring node voltage fluctuation quantity connected with VSC in direct-current power distribution network

Therefore, considering the influence of the fluctuation of the active power value of the direct-current power distribution network input to the alternating-current power distribution network and the voltage fluctuation condition of the direct-current power distribution network on the alternating-current power distribution network, selecting power fluctuation nodes of the alternating-current power distribution network, wherein the active and reactive injection power fluctuation amplitudes of the nodes are +/-20%, and the power fluctuation nodes are set at a power basic value P_ic，Q_icBased on the calculated active power fluctuation amount_PiAmount of fluctuation of reactive power_Qi(ii) a Therefore, the fluctuation amount of active power transmission between the DC distribution network and the VSC

Node voltage fluctuation amount of direct current power distribution network

Active power fluctuation quantity injected into AC distribution network node_PiAnd node injected reactive power fluctuation amount_QiForming a fluctuation variable matrix of the alternating-current power distribution network, wherein the fluctuation variable matrix is a 1 x (2n +2L) order matrix; firstly, calculating a Jacobian matrix of the alternating current distribution network by using a formula (40), and then solving the node voltage, the node injection current and the voltage modulation ratio fluctuation variable of the alternating current distribution network according to a formula (34)

And_Qithe first derivative of (a); firstly, the Hessian matrix is calculated through the formula (30), and then the node voltage, the node injection current and the voltage modulation ratio fluctuation variable of the alternating current distribution network are solved according to the formula (36)

_PiAnd_Qiand finally, solving the interval values of the node voltage, the node injection current and the voltage modulation ratio of the alternating-current distribution network by the equation (38).

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