CN103701125B - The flexible power flow algorithm of a kind of power distribution network based on Sequential Quadratic Programming method - Google Patents

Abstract

The present invention relates to a distribution network flexible power flow algorithm, in particular to a distribution network flexible power flow algorithm based on the sequence quadratic programming method. The power flow equations are organically combined to form a distribution network power flow equation that takes into account the static characteristics of generators and loads and retains the second-order terms. In solving the above power flow equation, the present invention converts the problem of solving the power flow equation into a mathematical optimization problem with nonlinear constraints and uses the quadratic sequence programming method to solve it. Combining with engineering practice, the invention can not only obtain the node voltage phasor obtained by the conventional distribution network power flow algorithm, but also obtain the system frequency and the actual power of the generator and the load. Compared with the conventional power flow algorithm, the present invention does not need to set various node types, has good calculation convergence and higher calculation accuracy, and is more in line with the reality of the actual distribution network.

Description

A Flexible Power Flow Algorithm for Distribution Network Based on Sequential Quadratic Programming

technical field

The invention relates to a distribution network flexible power flow algorithm, in particular to a distribution network flexible power flow algorithm based on a sequence quadratic programming method.

Background technique

With the development of distributed generation technology, the trend of integrating distributed generation (DG) into the distribution network is becoming more and more obvious. After DG is connected to the grid, the structure and operation of the distribution network will undergo tremendous changes. Especially when operating in an isolated island, due to the support of distributed power sources, the isolated island can continue to operate to ensure the normal operation of part of the load, which can improve the power supply reliability of the distribution network. However, for distribution systems with distributed power sources, the conventional distribution network power flow algorithm and its derivative algorithms, due to the given conditions are too ideal, resulting in poor convergence and large calculation errors, and the calculation results are not consistent with the actual engineering. match.

In fact, both the load and the generator set have frequency and voltage regulation characteristics. Under steady-state conditions, the system frequency and voltage are not necessarily equal to the rated frequency and given voltage value. feature enables power distribution. Some scholars have proposed a new fast distribution network power flow algorithm, which converts the power flow equation into a second-order nonlinear matrix equation with independent variable correction through the strict Taylor series expansion of the quadratic power flow. It makes full use of the characteristics of the distribution network, and its Jacobian matrix remains unchanged during the solution process. The calculation process is relatively simple, and because it retains the second-order partial derivatives, it retains the Newton residual, and its calculation accuracy is higher than that of Newton algorithms Higher, but this algorithm does not consider the static characteristics of the generator and load.

The present invention integrates the concept and model of the flexible power flow of the power system, aiming at the power distribution network system, based on the power flow equation that retains the second-order item, and referring to the relevant literature, the distributed power supply is regarded as a controllable load and introduced into the second-order power flow equation, which is creative Combining the static characteristic equation of generator and load with the power flow equation of distribution network retaining the second order term, the power flow equation of distribution network considering the static characteristic of generator and load is formed. Then, the problem of solving the power flow equation is transformed into an optimization problem and an appropriate optimization goal is set, which is solved by quadratic sequence programming, and a flexible power flow of distribution network based on sequence quadratic programming is proposed. Combining with engineering practice, the invention can not only obtain the node voltage phasor obtained by the conventional distribution network power flow algorithm, but also obtain the system frequency and the actual power of the generator and the load. It is no longer necessary to set various node types, and the convergence is good, the calculation accuracy is higher, and it is more in line with the actual distribution network.

Contents of the invention

A flexible power flow algorithm for distribution network based on sequence quadratic programming, characterized in that:

The invention creatively combines the static characteristic equation of the generator and the load with the power flow equation of the distribution network retaining the second-order item, and forms the power flow equation of the distribution network considering the static characteristic of the generator and the load. Then, the problem of solving the power flow equation is transformed into an optimization problem and an appropriate optimization goal is set, which is solved by quadratic sequence programming, and a flexible power flow of distribution network based on sequence quadratic programming is proposed.

Combining with engineering practice, the invention can not only obtain the node voltage phasor obtained by the conventional distribution network power flow algorithm, but also obtain the system frequency and the actual power of the generator and the load. Compared with the conventional power flow algorithm, the present invention does not need to set various node types, has good calculation convergence and higher calculation accuracy, and is more in line with the reality of the actual distribution network.

Technical scheme of the present invention is as follows:

A distribution network flexible power flow method based on the sequence quadratic programming method, characterized in that: based on the following power flow equation:

Δx ^T a _i Δx+b _i ^T Δx-p _Li =0,i∈(1,n)

Δx ^T d _i Δx+g _i ^T Δx-q _Li =0,i∈(1,n)

in,

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\\ {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]$

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]$

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}\end{array}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; ;</span>$

G _i =[G _i1 G _i2 ... G _in ];

$\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}\end{array}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]<span\; class="notranslate">\; ;</span>$

B _i =[B _i1 B _i2 ... B _in ];

G _in represents the magnitude of branch admittance between nodes i and n, p _Li is the integrated actual load active power of node i, q _Li is the integrated actual load reactive power of node i;

The specific processing includes the following steps:

Step 1. Randomly select one of the above 2n equations, specifically: Δx ^T a _k Δx+b _k ^T Δx-p _Lk =0 or Δx ^T d _k Δx+g _k ^T Δx-q _Lk = 0, take the minimum value of abs(Δx ^T a _k Δx+b _k ^T Δx-p _Lk ) or abs(Δx ^T d _k Δx+g _k ^T Δx-q _Lk ) as the optimization target, and the remaining 2n-1 If the equation is used as an equality constraint, the solution of the power flow equation is transformed into a mathematical optimization with multiple nonlinear constraints;

Step 2. Based on Step 1, the solution of the power flow equation is converted into a mathematical optimization with multiple nonlinear constraints. The optimization is solved by sequential quadratic programming; specifically, the minimum value of the objective function is set to 0, and its search The process of optimizing to the minimum value is essentially the process of solving the power flow equation.

In the above-mentioned distribution network flexible power flow method based on the sequential quadratic programming method, the power flow equation of the power grid is based on the following formula:

The active power-frequency static characteristic relation equation and the reactive power-voltage static characteristic relation equation of the generator static characteristic, namely

P _Gi =K _fi (f _i0 -f)

Q _Gi =K _Ui (U _i0 -U _i )

In the formula, f _i0 is the no-load frequency of unit i; K _fi is the active power-frequency adjustment coefficient of unit i; U _i0 is the no-load voltage of unit i; K _Ui is the reactive power-voltage adjustment coefficient of unit i; f is the system frequency, U _i is the node voltage amplitude of node i;

The static characteristics of the load can be determined by the relationship equation of the static characteristics of the load, that is,

P _Li =P _Li0 [1+K _PUi (U _i -1)][1+K _Pfi (f-1)]

Q _Li =Q _Li0 [1+K _QUi (U _i -1)][1+K _Qfi (f-1)]

In the formula, P _Li0 and Q _Li0 are the active and reactive power of load i under the rated voltage and rated frequency, called the load base point frequency; K _PUi , K _Pfi and K _QUi , K _Qfi are the active power and reactive power of the load respectively Voltage adjustment coefficient and frequency adjustment coefficient of power;

Then combined with the generator and load static characteristic formula, for each node of the power grid, if there is only load on node i, then S _Li =P _Li +jQ _Li ; if there is only generator on node i, since the generator generates power, Contrary to the load characteristics, it is written as S _Li =-(P _Gi +jQ _Gi ); by analogy, when there are both loads and generators on a certain node, the comprehensive consideration is S _Li =P _Li +jQ _Li -( P _Gi +jQ _Gi ); for convenience, the above three cases are uniformly defined as

S _Li =p _Li +jq _Li ,i∈(1,n)

p=(p _Li ) ^T ∈ R ^n×1 ,q=(q _Li ) ^T ∈ R ^n×1

In the formula, p _Li is the integrated actual load active power of node i, q _Li is the integrated actual load reactive power of node i, and R ^n×1 represents a real number matrix with n rows and one column.

In the above-mentioned flexible power flow method for distribution network based on sequential quadratic programming method, in the step 1,

In the Cartesian coordinate system, the node voltage vector of the distribution network is defined as

$\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; e</span>}\\ \mathrm{<span\; class="notranslate">\; f</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

and define $\mathrm{\&Delta;x}=\left[\begin{array}{c}\mathrm{\&Delta;e}\\ \mathrm{\&Delta;f}\end{array}\right]=\left[\begin{array}{c}e-e_0\\ f-f_0\end{array}\right],$ Among them, under the common initial condition of flat start, e ₀ =(1) ^T ∈ R ^n×1 , f ₀ =(0) ^T ∈ R ^n×1

Under the condition of flat start, strict Taylor series expansion is carried out on the quadratic power flow equation, and the distribution network power flow equation with quadratic term considering the static characteristics of the generator and the load and retaining the Newton residual can be expressed as

$\mathrm{<span\; class="notranslate">\; J\&Delta;x</span>}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}\mathrm{<span\; class="notranslate">\; J\&Delta;x</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}$

Compared with the conventional power flow algorithm, S _L in the formula considers the static characteristics of the generator and the load, rather than the general constant load model. in

$\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}& \mathrm{<span\; class="notranslate">\; B</span>}\\ \mathrm{<span\; class="notranslate">\; B</span>}& \mathrm{<span\; class="notranslate">\; G</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; p</span>}\\ \mathrm{<span\; class="notranslate">\; q</span>}\end{array}\right]$

In the formula, B is the imaginary part of the network node admittance matrix, G is the real part of the network node admittance matrix, where

$\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;e</span>}}& <span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}\\ \stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;f</span>}}& \stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;e</span>}}\end{array}\right]<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; diag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;f</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; diag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

It can be clearly seen that the power flow equation derived above, which takes into account the static characteristics of the generator and the load and retains the second-order term, is a quadratic nonlinear matrix equation about Δx, which is difficult to solve directly. If the above power flow equation is slightly processed, it can be converted into an optimization problem for solving nonlinear constraints. The above power flow equation contains a total of 2n equations, which can be expanded and written as

Δx ^T a _i Δx+b _i ^T Δx-p _Li =0,i∈(1,n)

Δx ^T d _i Δx+g _i ^T Δx-q _Li =0,i∈(1,n)

Randomly select one of the equations Δx ^T a _k Δx+b _k ^T Δx-p _Lk =0 or Δx ^T d _k Δx+g _k ^T Δx-q _Lk =0, and no longer use this equation as an equality constraint, Instead, the minimum value of abs(Δx ^T a _k Δx+b _k ^T Δx-p _Lk ) or abs(Δx ^T d _k Δx+g _k ^T Δx-q _Lk ) is used as the optimization goal, while the rest of the equations are still regarded as equations Constraints exist. From a mathematical analysis, the minimum value of the objective function should be 0, and its optimization to the minimum value essentially completes the solution of the power flow equation. Therefore, it is feasible to transform the solution of the power flow equation into an optimization problem. Since the Sequential Quadratic Programming method (Sequential Quadratic Programming) has global convergence and maintains local superlinear convergence, it is currently one of the most effective methods for solving nonlinear constrained optimization problems. Therefore, Sequential Quadratic Programming is used to solve the above The problem of solving the power flow equations is transformed into a mathematical optimization problem with nonlinear constraints.

Therefore, the present invention has the following advantages: combined with engineering practice, it can not only obtain the node voltage phasor obtained by the conventional distribution network power flow algorithm, but also obtain the system frequency and the actual power of the generator and load. It is no longer necessary to set various node types, the calculation convergence is good and the calculation accuracy is higher, and it is more in line with the actual distribution network

detailed description

The technical solution of the present invention will be further specifically described below through examples and in conjunction with data analysis.

Example:

The method proposed in this patent has been verified under multiple calculation example models. Due to space limitations, this embodiment takes the improved IEEE33 calculation example as an example, based on simulation data and MATLAB calculation data, to verify the feasibility and effectiveness of the method proposed in this paper. analysis and verification. Details are as follows:

Based on the IEEE33 standard calculation example, it is properly improved. Since the balance node is no longer needed in the flexible power flow algorithm, the balance node in the IEEE33 node system is transformed into a generator node for calculation. The standard IEEE33 system contains 37 branch circuits and 5 ring networks. It is a standard power distribution system with ring networks. The reference value is set to S _B =600kVA, V _B =10kV.

Table 1 shows the power flow calculation results of the benchmark 50HZ example. The calculation data column in the table is the result calculated by the algorithm in this paper, and the simulation data column is based on the improved IEEE33 example data and the static characteristics of the generator and load in the relevant The data obtained by modeling and simulation in the software. It can be seen that the error between the calculation results of the voltage amplitudes of each node and the simulation results is very small, which shows the effectiveness of the algorithm.

Table 1 Comparison of power flow calculation results of benchmark examples

node simulation data calculate data node simulation data calculate data 1 1.0000 1.0000 18 0.9288 0.9291 2 0.9955 0.9955 19 0.9928 0.9928 3 0.9787 0.9787 20 0.9701 0.9702 4 0.9730 0.9730 twenty one 0.9638 0.9639 5 0.9676 0.9677 twenty two 0.9581 0.9581 6 0.9552 0.9553 twenty three 0.9702 0.9703 7 0.9537 0.9538 twenty four 0.9536 0.9637 8 0.9519 0.9520 25 0.9423 0.9424 9 0.9469 0.9470 26 0.9536 0.9537 10 0.9462 0.9463 27 0.9517 0.9518 11 0.9462 0.9463 28 0.9438 0.9439 12 0.9464 0.9465 29 0.9384 0.9385 13 0.9412 0.9413 30 0.9335 0.9336 14 0.9393 0.9394 31 0.9287 0.9288 15 0.9390 0.9389 32 0.9278 0.9280 16 0.9360 0.9361 33 0.9281 0.9283 17 0.9305 0.9307

Regarding the corresponding situation of the angle, the situation of several representative nodes is selected below for illustration, and the specific data are shown in Table 2.

Table 2 Comparison of angle calculation results of benchmark examples

node simulation data calculate data 9 -0.3072 -0.3067 18 -0.28499 -0.2867 25 -0.0417 -0.0416 30 0.0725 0.0723 33 -0.242 -0.240

It can be seen from Table 2 that the error between the calculation results of the angles of each node and the simulation results is very small, which shows the correctness of the calculation.

In order to reflect the advantages of considering the static characteristics of the generator and the load, the benchmark calculation example is slightly modified, and the load on the node 30 with a relatively large base power is selected, and its base power is increased by 3 times. Then, due to the increase of active and reactive power of the load, the output of the generator must be adjusted accordingly. As a result, the frequency of the generator decreases to increase active power processing, and the terminal voltage decreases to increase reactive output to achieve a new balance.

After calculation, the steady-state frequency of the modified system drops to 49.77HZ, and the machine terminal voltage drops to 0.9770p.u. The change trend is in line with the static characteristics of the generator, which reflects the system's active power balance and frequency adjustment, reactive power balance and In the relationship of voltage adjustment, when the load of the system has changed, a new power balance is achieved under the joint action of the adjustment effect of the static characteristics of the generator and the load. The comparison between the specific algorithm calculation data and the simulation data is shown in Table 3.

Table 3 Comparison of power flow calculation results of the modified example

Under non-50HZ conditions, for the angle correspondence, similarly, select several representative nodes here to analyze whether they correspond or not, see Table 4 below for details.

Table 4 Comparison of angle calculation results of the modified example

node simulation data calculate data 9 0.1897 0.1886 18 0.6305 0.6294 25 0.7510 0.7503 30 1.2421 1.2411 33 0.7335 0.7329

Similar to the results in the case of 50HZ, the angle error of the power flow calculation results of the improved calculation example is also very small. In summary, it can be seen that comparing the calculation results of the present invention for the above calculation examples with the simulation results, the error is very small, which shows the correctness of the algorithm.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention belongs can make various modifications or supplements to the described specific embodiments or adopt similar methods to replace them, but they will not deviate from the spirit of the present invention or go beyond the definition of the appended claims range.

Claims (3)

1. A power distribution network flexible power flow method based on a sequence quadratic programming method is characterized in that: based on the following power flow equation:

Δx^Ta_iΔx+b_i ^TΔx-p_Li＝0,i∈(1,n)

Δx^Td_iΔx+g_i ^TΔx-q_Li＝0,i∈(1,n)

wherein,

$a_i=\left[\begin{array}{cc}-G\left(i\right)& B\left(i\right)\\ -B\left(i\right)& -G\left(i\right)\end{array}\right],b_i=\left[\begin{array}{c}-G_i^T\\ B_i^T\end{array}\right]$

$d_i=\left[\begin{array}{cc}B\left(i\right)& G\left(i\right)\\ -G\left(i\right)& B\left(i\right)\end{array}\right],g_i=\left[\begin{array}{c}{B}_i^T\\ G_i^T\end{array}\right]$

G_i＝[G_i1G_i2...G_in]；

B_i＝[B_i1B_i2...B_in]；

G_inrepresenting nodesAmplitude of branch admittance between i and n, p_LiIs the integrated real load active power of node i, q_LiIs the comprehensive actual load reactive power of the node i;

the specific treatment comprises the following steps:

step 1, arbitrarily selecting one of the 2n equations, specifically: Δ x^Ta_kΔx+b_k ^TΔx-p_Lk0 or Δ x^Td_kΔx+g_k ^TΔx-q_Lk0, abs (Δ x)^Ta_kΔx+b_k ^TΔx-p_Lk) Or abs (Δ x)^Td_kΔx+g_k ^TΔx-q_Lk) The minimum value of (3) is used as an optimization target, and the rest 2n-1 equations are used as equality constraints, so that the solution of the power flow equation is converted into mathematical optimization containing a plurality of nonlinear constraints;

step 2, based on the step 1, converting the solution of the power flow equation into a mathematical optimization containing a plurality of nonlinear constraints, wherein the optimization is solved by adopting a sequential quadratic programming method; specifically, the minimum value of the objective function is set to 0, and the process of optimizing the minimum value is substantially the process of solving the power flow equation.

2. The power distribution network flexible power flow method based on the sequential quadratic programming method according to claim 1, characterized in that: the power flow equation of the power grid is based on the following formula:

active power-frequency static characteristic relation equation and reactive power-voltage static characteristic relation equation of static characteristic of generator, i.e.

P_Gi＝K_fi(f_i0-f)

Q_Gi＝K_Ui(U_i0-U_i)

In the formula (f)_i0The no-load frequency of the unit i is set; k_fiThe active power-frequency regulation coefficient of the unit i is obtained; u shape_i0The no-load voltage of the unit i is obtained; k_UiThe reactive power-voltage regulation coefficient of the unit i is obtained; f is the system frequency, U_iThe node voltage amplitude of node i;

the load-static characteristic can be derived from the load-static characteristic relation equation, i.e.

P_Li＝P_Li0[1+K_PUi(U_i-1)][1+K_Pfi(f-1)]

Q_Li＝Q_Li0[1+K_QUi(U_i-1)][1+K_Qfi(f-1)]

In the formula, P_Li0And Q_Li0The active power and the reactive power of the load i under the rated voltage and the rated frequency are called as the base point power of the load; k_PUi、K_PfiAnd K_QUi、K_QfiVoltage regulating coefficients and frequency regulating coefficients of load active power and reactive power respectively;

then combining a generator and a load static characteristic formula to obtain the comprehensive actual load power S of the node i_LiFor the node i, there are three cases that only load exists on the grid node i, only generator exists on the node i, and both load and generator exist on the node i, and under the three cases, the comprehensive actual load power S of the node i is defined_LiExpressed as:

S_Li＝p_Li+jq_Li,i∈(1,n)

p＝(p_Li)^T∈R^n×1,q＝(q_Li)^T∈R^n×1

in the formula, p_LiIs the integrated real load active power of node i, q_LiFor the combined real load reactive power of node i, R^n×1A matrix of real numbers representing n rows and 1 column.

3. The power distribution network flexible power flow method based on the sequential quadratic programming method according to claim 1, characterized in that: in the step 1, the step of processing the raw material,

under a rectangular coordinate system, defining a node voltage vector of the power distribution network as

$v=\left[\begin{array}{c}e\\ f\end{array}\right],e={\left(e_i\right)}^T\&Element;R^{n\&times;1},f={\left(f_i\right)}^T\&Element;R^{n\&times;1}$

And define $\mathrm{\&Delta;}x=\left[\begin{array}{c}\mathrm{\&Delta;}e\\ \mathrm{\&Delta;}f\end{array}\right]=\left[\begin{array}{c}e-e_0\\ f-f_0\end{array}\right],$ Wherein, under the condition of the common flat start initial value, e₀＝(1)^T∈R^n×1,f₀＝(0)^T∈R^n×1

Under the condition of flat start, strict Taylor series expansion is carried out on a quadratic power flow equation, and a power grid power flow equation with a quadratic term and retained Newton residual errors considering the static characteristics of a generator and a load can be expressed as

$J\mathrm{\&Delta;}x+\mathrm{\&Delta;}\tilde{x}J\mathrm{\&Delta;}x=S_L$

S in the formula is compared with the conventional power flow algorithm_LIs a constant load model which comprehensively considers the static characteristics of the generator and the load, and is not a general constant load model, wherein

$J=\left[\begin{array}{cc}-G& B\\ B& G\end{array}\right],S_L=\left[\begin{array}{c}p\\ q\end{array}\right]$

Wherein B is the imaginary part of the admittance matrix of the network node and G is the real part of the admittance matrix of the network node, wherein

$\mathrm{\&Delta;}\tilde{x}=\left[\begin{array}{cc}\widetilde{\mathrm{\&Delta;}e}& -\widetilde{\mathrm{\&Delta;}f}\\ \widetilde{\mathrm{\&Delta;}f}& \widetilde{\mathrm{\&Delta;}e}\end{array}\right],\widetilde{\mathrm{\&Delta;}e}=diag\left({\mathrm{\&Delta;e}}_i\right),\widetilde{\mathrm{\&Delta;}f}=diag\left({\mathrm{\&Delta;f}}_i\right).$