CN105119269B - A kind of probabilistic loadflow computational methods for considering Multi-terminal Unified Power Flow Controller - Google Patents

Abstract

The present invention relates to a kind of probabilistic loadflow computational methods for considering Multi-terminal Unified Power Flow Controller, power flow algorithm is set up to the power network containing Multi-terminal Unified Power Flow Controller first, equivalent multiterminal injecting power model is set up according to UPFC actual installation situation, Load flow calculation is carried out using Newton-Laphson method and the steady-state operation point of power network is determined, linearization calculation is carried out to the electric network swim equation comprising the equivalent multiterminal injecting power models of UPFC in steady-state operation point, Jacobian matrix is obtained；Secondly, random chance density function is set up to various enchancement factors in power network, calculate after each rank cumulant for obtaining each stochastic variable, the corresponding cumulant for obtaining grid nodes voltage, line power is calculated on the basis of Jacobian matrix using Cumulants method, the probability density function of node voltage and line power is finally given.The probabilistic loadflow that the present invention realizes the power networks of UPFC containing multiterminal is calculated, and the influence for analysis power network randomness to operation of power networks creates condition.

Description

Random power flow calculation method considering multi-end unified power flow controller

Technical Field

The invention relates to a calculation method of an electric power system, in particular to a random power flow calculation method comprising a multi-terminal Unified Power Flow Controller (UPFC), and belongs to the field of dispatching operation of the electric power system.

Background

With the rapid development of high-power electronic devices and control technologies thereof, flexible alternating current transmission technology (FACTS) plays an increasingly important role in power grids. As an ultra-fast dynamic element, different from a traditional electric control mechanical device, the FACTS device can adjust the state of a system in real time, quickly and smoothly, meet the requirement of flexibly controlling the system tide, greatly improve the controllability of the system tide and the voltage under the condition of not changing the topological structure of a network and the scheduling plan of a generator set, ensure that a power transmission line runs under the condition of approaching the thermal stability limit of the power transmission line, increase the running safety domain of the existing power system, reduce the power transmission loss, greatly reduce the standby capacity of an interconnected system, and better exert the economy of networked running.

The Unified Power Flow Controller (UPFC) is a third generation FACTS element, also is the most powerful and comprehensive thyristor control device, and is a novel power flow control device formed by combining a parallel compensation static synchronous compensator (STATCOM) and a series compensation Static Synchronous Series Compensator (SSSC).

Because the UPFC has a strong line power flow control capability and will bring a large influence on the operating state of the power system after being put into use, a detailed modeling analysis is performed on the power system containing the UPFC to know the influence degree of the UPFC on the power system, which provides a challenge to the traditional power flow algorithm. The traditional power flow algorithm does not take the influence of the UPFC into account, so the traditional power flow algorithm is an analysis method based on node boundary conditions, and the power flow algorithm containing the UPFC has control constraint conditions besides the node boundary conditions, so the traditional power flow algorithm has the characteristics different from the traditional power flow algorithm in specific application. Considering that the power grid uncertainty random power flow calculation result directly depends on the calculation result of the deterministic power flow, for the random power flow calculation containing the UPFC, the aspects of element model selection, how to take the influence of the UPFC into consideration, specific power flow algorithm implementation and the like are carefully discussed to obtain the optimal random power flow calculation effect. The UPFC is the most powerful FACTS device, not only is rich in control function, but also is typical in model structure, and sufficient discussion of the UPFC has certain universal significance in analyzing random trend algorithm containing various FACTS devices.

Disclosure of Invention

The invention aims to provide a random power flow calculation method considering a multi-terminal unified power flow controller, which is characterized in that an equivalent multi-terminal injection power model is established according to the actual installation condition of a UPFC (unified power flow controller), power flow calculation is carried out on a power grid, and a steady-state operation point is obtained; secondly, establishing a random probability density function for various random factors (such as node load, wind power plant and photovoltaic power generation) in the power grid, calculating the probability density function of node voltage and line power by using a semi-invariant method, and finally realizing the random power flow calculation with the multi-end UPFC.

Therefore, the invention adopts the following technical scheme:

a random power flow calculation method considering a multi-terminal unified power flow controller comprises the following steps:

(1) establishing a steady-state model of the multi-terminal UPFC according to the actual installation position of the multi-terminal UPFC;

(2) establishing a power grid load flow calculation data model according to power grid data and an established multi-terminal UPFC steady-state model, performing load flow calculation by adopting a Newton-Raphson method, and determining a steady-state operating point of a power grid;

(3) calculating a power grid load flow equation containing the multi-end UPFC according to the steady-state operating point of the power grid to perform linear calculation, and obtaining a Jacobian matrix;

(4) establishing probability density functions of random variables of loads, wind power and active power of a photovoltaic power station in a power grid, and calculating to obtain semi-invariants of each order of the random variables;

(5) according to a semi-invariant method, each order semi-invariant of node voltage and line active power and a probability density function thereof are calculated by utilizing each order semi-invariant and a Jacobian matrix of the existing random variables, and finally calculation of the random power flow of the power grid with the multi-end UPFC is achieved.

The multi-terminal UPFC has two or more series transformers installed on different lines at the same time and shares one parallel transformer.

And a multi-terminal UPFC steady-state model is modeled by adopting an equivalent injection power method.

When the multi-end UPFC comprises two series transformers and a parallel transformer which are arranged on different lines, the control effect of the UPFC on the power flow is transferred to nodes on two sides of the line according to an equivalent power injection method, and the equivalence is as follows: the serial sides of the UPFC are respectively arranged on lines i-j and i-k, and respectively use a controllable voltage sourceAndshowing that the parallel side is arranged on the i side of the bus and a controllable current source is usedTo represent

Andthe equivalent injected apparent power of the UPFC at the i, j and k sides of the buses respectively has the following specific calculation formula:

in the formula,voltages of nodes i and j, respectively; g_ij+jb_ij、g_ik+jb_ikAdmittance between nodes i and j, i and k, respectively; b is_c1、B_c2Ground admittance for nodes i and j, i and k, respectively; denotes taking the conjugate value.

When the load flow containing the multi-end UPFC is calculated, for the nodes which do not contain the UPFC in the outgoing line, the power balance equation is shown as the following formula (8) and (9):

ΔP_m＝P_G,m-P_L,m-∑_n∈mU_mU_n(G_mncosθ_mn+B_mnsinθ_mn) (8)

ΔQ_m＝Q_G,m-Q_L,m-∑_n∈mU_mU_n(G_mnsinθ_mn-B_mncosθ_mn) (9)

in the formula,. DELTA.P_m、ΔQ_mRespectively the active and reactive power deviations of node m; p_G,m、Q_G,mThe active power and the reactive power of the generator at the node m are respectively; p_L,m、Q_L,mRespectively the active and reactive loads of node m; g_mn、B_mnRespectively corresponding nodes m and n to the real part and the imaginary part of the admittance matrix; u shape_m、U_nThe voltage amplitudes of nodes m and n, respectively; theta_mnIs the phase angle difference between nodes m and n.

For the nodes with UPFC installed in the outgoing line, at least comprising the nodes i, j, k, the power balance equation is shown in the formulas (10) to (15):

where Re denotes a real part, Im denotes an imaginary part, Δ P_i、ΔQ_i、ΔP_j、ΔQ_j、ΔP_k、ΔQ_kThe active and reactive power deviations of the nodes i, j, k, respectively; p_G,i、Q_G,i、P_G,j、Q_G,j、P_G,k、Q_G,kThe active power and the reactive power of the generators at the nodes i, j and k are respectively; p_L,i、Q_L,i、P_L,j、Q_L,j、P_L,k、Q_L,kRespectively the active and reactive loads of nodes i, j, k; g_in、B_in、G_jn、B_jn、G_kn、B_knNodes i and n, j and n, and k and n correspond to the real part and the imaginary part of the admittance matrix respectively; u shape_i、U_j、U_kVoltage amplitudes of nodes i, j and k are respectively; theta_in、θ_jn、θ_knIs the phase angle difference between nodes i and n, j and n, k and n.

The method for calculating the random power flow of the multi-terminal unified power flow controller realizes the random power flow calculation of the power grid under the condition of considering the randomness of the load, the generator and the line, can effectively analyze the control effect of the multi-terminal unified power flow controller on the power grid power flow, and plans the actual power grid. The construction and the operation have important practical significance.

The random load flow calculation method of the multi-terminal unified load flow controller (UPFC) is used for performing random load flow calculation on the basis of considering various uncertain factors of a power grid, realizes random load flow calculation of the power grid comprising the multi-terminal UPFC, and creates conditions for analyzing the influence of the randomness of the power grid on the operation of the power grid.

Drawings

FIG. 1 is a flow chart of a method for calculating a random power flow of a power grid with a multi-terminal UPFC according to the invention;

FIG. 2 is a power model of a UPFC;

fig. 3 is an equivalent injection power model of the UPFC.

Detailed Description

In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.

The invention relates to a random power flow calculation method for a multi-terminal Unified Power Flow Controller (UPFC), which is used for performing random power flow calculation on the basis of considering various uncertain factors of a power grid. As shown in fig. 1, the method comprises the following steps:

(1) establishing a steady-state model of the multi-terminal UPFC according to the actual installation position of the multi-terminal UPFC;

(2) establishing a power grid load flow calculation data model according to power grid data and an established multi-terminal UPFC steady-state model, performing load flow calculation by adopting a Newton-Raphson method, and determining a steady-state operating point of a power grid;

(3) according to the steady-state operating point of the power grid, carrying out linear calculation on a power grid load flow equation containing the multi-terminal UPFC, and obtaining a Jacobian matrix;

(4) establishing probability density functions of random variables of loads, wind power and active power of a photovoltaic power station in a power grid, and calculating to obtain semi-invariants of each order of the random variables;

(5) according to a semi-invariant method, each order semi-invariant of node voltage and line active power and a probability density function thereof are calculated by utilizing each order semi-invariant and a Jacobian matrix of the existing random variables, and finally calculation of the random power flow of the power grid with the multi-end UPFC is achieved.

In the step (1), a multi-terminal UPFC steady-state model is modeled by adopting an equivalent injection power method, and an equivalent circuit model is shown in FIG. 2 by taking two series transformers and one parallel transformer as an example.

Wherein the serial sides of the UPFCs are respectively installed on the lines i-j and i-k,with separately controllable voltage sourcesAndshowing that the parallel side is arranged on the i side of the bus and a controllable current source is usedAnd (4) showing. The regulation effect of the UPFC on the power flow of the power transmission line is mainly realized by regulating a series voltage source, and the amplitude phase of the series voltage source is adjustable, so that the passing active power and the passing reactive power on the power transmission line are controlled; the parallel current source ensures that the total active exchange quantity of the UPFC device and the system is zero.

According to the equivalent power injection method, the control effect of the UPFC on the power flow can be transferred to nodes on two sides of the circuit where the UPFC is located, which is equivalent to network transformation, and an equivalent model is shown in FIG. 3.

In the figure, the position of the upper end of the main shaft,andthe equivalent injected apparent power of the UPFC at the i, j and k sides of the buses respectively has the following specific calculation formula:

the active power of the UPFC device itself should satisfy: the active power injected into the system by the series voltage source is equal to the active power absorbed from the system by the parallel current source, and the equation is expressed as follows:

wherein,voltages of nodes i and j, respectively; g_ij+jb_ij、g_ik+jb_ikAdmittance between nodes i and j, i and k, respectively; b is_c1、B_c2Ground admittance for nodes i and j, i and k, respectively;the conjugate value of equivalent current at the parallel side of the UPFC;is the conjugate value of the current between lines i and j;is the conjugate value of the current between lines i and k.

The formula (20) and the formula (21) are respectively substituted into the formula (19) to obtain,

in the formula: u shape_i、U_jIs the voltage amplitude of node i, j; theta_i、θ_jIs the voltage phase angle of the node i, j;is the current between nodes i, j;is the current between nodes i, k; u shape_se1、U_se2The voltage amplitude of the equivalent power supply at the series side; theta_se1、θ_se2The phase angle of the voltage of the equivalent power supply on the series side; g_ij、b_ijThe real and imaginary parts of the admittance between nodes i and j; g_ik、b_ikThe real and imaginary parts of the admittance between nodes i and k; b is_c1、B_c2Ground admittance for nodes i and j, i and k, respectively; i is_sh、θ_shRespectively injecting current to the parallel sidesAmplitude and phase angle of.

In the step (2), when the load flow containing the multi-end UPFC is calculated, for the node which does not contain the UPFC in the outgoing line, the power balance equation is shown as the following formula (23) and (24):

ΔP_m＝P_G,m-P_L,m-∑_n∈mU_mU_n(G_mncosθ_mn+B_mnsinθ_mn) (23)

ΔQ_m＝Q_G,m-Q_L,m-∑_n∈mU_mU_n(G_mnsinθ_mn-B_mncosθ_mn) (24)

in the formula,. DELTA.P_m、ΔQ_mRespectively the active and reactive power deviations of node m; p_G,m、Q_G,mThe active power and the reactive power of the generator at the node m are respectively; p_L,m、Q_L,mRespectively the active and reactive loads of node m; g_mn、B_mnRespectively node m and n correspond to the leaderThe real and imaginary parts of the nano-matrix; u shape_m、U_nThe voltage amplitudes of nodes m and n, respectively; theta_mnIs the phase angle difference between nodes m and n;

for the node with the UPFC installed in the outgoing line, taking the node i, j, k as an example, the power balance equation is shown in the formulas (25) to (30):

where Re denotes a real part, Im denotes an imaginary part, Δ P_i、ΔQ_i、ΔP_j、ΔQ_j、ΔP_k、ΔQ_kThe active and reactive power deviations of the nodes i, j, k, respectively; p_G,i、Q_G,i、P_G,j、Q_G,j、P_G,k、Q_G,kThe active power and the reactive power of the generators at the nodes i, j and k are respectively; p_L,i、Q_L,i、P_L,j、Q_L,j、P_L,k、Q_L,kActive and inactive respectively for nodes i, j, kWork load; g_in、B_in、G_jn、B_jn、G_kn、B_knNodes i and n, j and n, and k and n correspond to the real part and the imaginary part of the admittance matrix respectively; u shape_i、U_j、U_kVoltage amplitudes of nodes i, j and k are respectively; theta_in、θ_jn、θ_knIs the phase angle difference between nodes i and n, j and n, k and n.

Therefore, the equations (16) - (19), (22) - (30) constitute all the equations of the grid power flow calculation with the multi-terminal UPFC.

In the step (3), after the Newton-Raphson method is adopted to carry out load flow calculation on the power grid to obtain a system operation steady state point, the load flow equation is linearized to obtain a Jacobian matrix of the steady state operation point. After the semi-invariants of the load, the wind power or the photovoltaic random variable are calculated, the semi-invariants of the node voltage and the line active power are calculated based on a semi-invariants method, and finally a probability density function is obtained to realize the calculation of the random load flow.

The basic steps and computational methods of the present invention and the advantages of the present invention have been shown and described. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. A random power flow calculation method considering a multi-terminal unified power flow controller is characterized by comprising the following steps:

(1) establishing a steady-state model of the multi-terminal UPFC according to the actual installation position of the multi-terminal UPFC;

(2) establishing a power grid load flow calculation data model according to power grid data and an established multi-terminal UPFC steady-state model, performing load flow calculation by adopting a Newton-Raphson method, and determining a steady-state operating point of a power grid;

(3) according to the steady-state operating point of the power grid, carrying out linear calculation on a power grid load flow equation containing the multi-terminal UPFC, and obtaining a Jacobian matrix;

(4) establishing probability density functions of random variables of loads, wind power and active power of a photovoltaic power station in a power grid, and calculating to obtain semi-invariants of each order of the random variables;

(5) according to a semi-invariant method, each order semi-invariant of node voltage and line active power and a probability density function thereof are calculated by utilizing each order semi-invariant and a Jacobian matrix of the existing random variables, and finally calculation of the random power flow of the power grid with the multi-end UPFC is achieved.

2. The random power flow calculation method considering the multi-terminal unified power flow controller of claim 1, wherein the multi-terminal UPFC has two or more series transformers simultaneously installed on different lines and shares one parallel transformer.

3. The method of claim 2, wherein the multi-port UPFC steady-state model is modeled by an equivalent injection power method.

4. The random power flow calculation method considering the multi-terminal unified power flow controller according to claim 2 or 3, wherein when the multi-terminal UPFC includes two series transformers and one parallel transformer installed on different lines, the control effect of the UPFC on the power flow is transferred to the nodes on both sides of the line according to the equivalent power injection method, and the equivalence is as follows: the serial sides of the UPFC are respectively arranged on lines i-j and i-k, and respectively use a controllable voltage sourceAndshowing that the parallel side is arranged on the i side of the bus and a controllable current source is usedRepresents;

andthe equivalent injected apparent power of the UPFC at the i, j and k sides of the buses respectively has the following specific calculation formula:

$S_i^F={\stackrel{\·}{U}}_i{\stackrel{\·}{I}}_{sh}^{*}-{\stackrel{\·}{U}}_i{\[{\stackrel{\·}{U}}_{se1}(g_{ij}+{\mathrm{jb}}_{ij}+\frac{{\mathrm{jB}}_{c1}}{2})\]}^{*}-{\stackrel{\·}{U}}_i{\[{\stackrel{\·}{U}}_{se2}(g_{ik}+{\mathrm{jb}}_{ik}+\frac{{\mathrm{jB}}_{c2}}{2})\]}^{*}---\left(1\right)$

$S_j^F={\stackrel{\·}{U}}_j{\[{\stackrel{\·}{U}}_{se1}(g_{ij}+{\mathrm{jb}}_{ij})\]}^{*}---\left(2\right)$

$S_k^F={\stackrel{\·}{U}}_j{\[{\stackrel{\·}{U}}_{se2}(g_{ik}+{\mathrm{jb}}_{ik})\]}^{*}---\left(3\right)$

in the formula,voltages of nodes i and j, respectively; g_ij+jb_ij、g_ik+jb_ikAdmittance between nodes i and j, i and k, respectively; b is_c1、B_c2Ground admittance for nodes i and j, i and k, respectively; denotes taking the conjugate value.

5. The method for calculating the random power flow considering the multi-terminal unified power flow controller according to claim 4, wherein when the power flow including the multi-terminal UPFC is calculated, for the node not including the UPFC in the outgoing line, the power balance equation is shown in the following formulas (8) and (9):

ΔP_m＝P_G,m-P_L,m-∑_n∈mU_mU_n(G_mncosθ_mn+B_mnsinθ_mn) (8)

ΔQ_m＝Q_G,m-Q_L,m-∑_n∈mU_mU_n(G_mnsinθ_mn-B_mncosθ_mn) (9)

in the formula,. DELTA.P_m、ΔQ_mRespectively the active and reactive power deviations of node m; p_G,m、Q_G,mThe active power and the reactive power of the generator at the node m are respectively; p_L,m、Q_L,mRespectively the active and reactive loads of node m; g_mn、B_mnRespectively corresponding nodes m and n to the real part and the imaginary part of the admittance matrix; u shape_m、U_nThe voltage amplitudes of nodes m and n, respectively; theta_mnIs the phase angle difference between nodes m and n.

6. The random power flow calculation method considering the multi-terminal unified power flow controller according to claim 5, wherein the nodes for installing the UPFC in the outgoing line at least comprise nodes i, j, k, and the power balance equation of the nodes is shown in formulas (10) to (15):

${\mathrm{\ΔP}}_i=P_{G,i}-P_{L,i}-{\mathrm{\Σ}}_{n\∈i}{U}_i{U}_n(G_{in}{\mathrm{cos\θ}}_{in}+B_{in}{\mathrm{sin\θ}}_{in})+\mathrm{Re}\left(S_i^F\right)---\left(10\right)$

${\mathrm{\ΔQ}}_i=Q_{G,i}-Q_{L,i}-{\mathrm{\Σ}}_{n\∈i}{U}_i{U}_n(G_{in}{\mathrm{sin\θ}}_{in}-B_{in}{\mathrm{cos\θ}}_{in})-Im\left(S_i^F\right)---\left(11\right)$

${\mathrm{\ΔP}}_j=P_{G,j}-P_{L,j}-{\mathrm{\Σ}}_{n\∈j}{U}_j{U}_n(G_{jn}{\mathrm{cos\θ}}_{jn}+B_{jn}{\mathrm{sin\θ}}_{jn})+\mathrm{Re}\left(S_j^F\right)---\left(12\right)$

${\mathrm{\ΔQ}}_j=Q_{G,j}-Q_{L,j}-{\mathrm{\Σ}}_{n\∈j}{U}_j{U}_n(G_{jn}{\mathrm{sin\θ}}_{jn}-B_{jn}{\mathrm{cos\θ}}_{jn})-Im\left(S_j^F\right)---\left(13\right)$

${\mathrm{\ΔP}}_k=P_{G,k}-P_{L,k}-{\mathrm{\Σ}}_{n\∈k}{U}_k{U}_n(G_{kn}{\mathrm{cos\θ}}_{kn}+B_{kn}{\mathrm{sin\θ}}_{kn})+\mathrm{Re}\left(S_k^F\right)---\left(14\right)$

${\mathrm{\ΔQ}}_k=Q_{G,k}-Q_{L,k}-{\mathrm{\Σ}}_{n\∈k}{U}_k{U}_n(G_{kn}{\mathrm{sin\θ}}_{kn}-B_{kn}{\mathrm{cos\θ}}_{kn})-Im\left(S_k^F\right)---\left(15\right)$

where Re denotes a real part, Im denotes an imaginary part, Δ P_i、ΔQ_i、ΔP_j、ΔQ_j、ΔP_k、ΔQ_kThe active and reactive power deviations of the nodes i, j, k, respectively; p_G,i、Q_G,i、P_G,j、Q_G,j、P_G,k、Q_G,kThe active power and the reactive power of the generators at the nodes i, j and k are respectively; p_L,i、Q_L,i、P_L,j、Q_L,j、P_L,k、Q_L,kRespectively the active and reactive loads of nodes i, j, k; g_in、B_in、G_jn、B_jn、G_kn、B_knNodes i and n, j and n, and k and n correspond to the real part and the imaginary part of the admittance matrix respectively; u shape_i、U_j、U_kVoltage amplitudes of nodes i, j and k are respectively; theta_in、θ_jn、θ_knAre nodes i and n,Phase angle differences of j and n, and k and n.