CN103701125A - Flexible power flow algorithm for power distribution network based on sequential quadratic programming method - Google Patents

Abstract

The invention relates to a flexible power flow algorithm for a power distribution network, particularly relates to the flexible power flow algorithm for the power distribution network based on a sequential quadratic programming method, creatively and organically combines a power generator and load static characteristics with a power flow equation for the power distribution network, which retains a second-order term and combines with the power generator and the load static characteristics, to form the power flow equation for the power distribution network, which retains the second-order term. On resolution of the power flow equation, the resolution issue of the power flow equation is converted to a mathematical optimization issue containing non-linear constraints, and the sequential quadratic programming method is used for resolution. The flexible power flow algorithm provided by the invention is combined with engineering practice, voltage phasors of the nodes, which can be obtained by the conventional power flow algorithm for the power distribution network, can be figured out, and the frequency of a system and the actual power of the power generator and a load can also be figured out. Compared with the conventional power flow algorithm, the flexible power flow algorithm provided by the invention does not need to set the types of the various nodes, the computational convergence is good, the computational precision is higher, and the flexible power flow algorithm is more in line with the practice of the actual power distribution network.

Description

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

Technical field

The present invention relates to the flexible power flow algorithm of a kind of power distribution network, relate in particular to the flexible power flow algorithm of a kind of power distribution network based on Sequential Quadratic Programming method.

Background technology

Along with the development of distributed generation technology, the trend that distributed power source (DG) is incorporated to power distribution network is more and more obvious, and after DG is grid-connected, the structure of power distribution network and operation all will huge variation occur.Particularly, when islet operation, due to the support of distributed power source, isolated island can continue operation to guarantee the normal work of sub-load, can improve the power supply reliability of power distribution network.But for containing the distribution system of distributed power source, conventional Power Flow Calculation Methods For Distribution Network and derivative algorithm thereof, because given condition is too idealized, cause that its convergence is poor, the error of calculation is larger, and result of calculation conforms to not to the utmost with engineering reality.

In fact, be load or generating set all has frequency and voltage-regulation characteristic, under steady state condition, system frequency and voltage need not be equal to rated frequency and given magnitude of voltage, and load and generating set are all to realize power division according to static characteristic separately.There is scholar to propose a kind of new quick Power Flow Calculation Methods For Distribution Network, by secondary trend being carried out to strict Taylor series expansion, power flow equation is changed to the second nonlinear matrix equation changing into containing independent variable correction to be solved, it takes full advantage of power distribution network feature, in solution procedure, its Jacobian matrix remains constant, calculation process is comparatively simple, and because retaining second order local derviation item, it has retained newton's residual error, its computational accuracy is higher with respect to Newton-like methods, but this algorithm is not considered generator and Static Characteristics of Loads.

The flexible trend concept of integrated power system of the present invention, model, be directed to distribution network system, power flow equation based on retaining second order term, and regard distributed power source as power flow equation that controlled load is introduced second order term with reference to related documents, creatively generator is combined with the distribution power flow equation that retains second order term with Static Characteristics of Loads equation, has formed the distribution power flow equation of taking into account generator and Static Characteristics of Loads.Then the problem that solves power flow equation be converted into an optimization problem and set suitable Optimization goal, utilizing secondary sequence to plan to solve, having proposed the flexible trend of power distribution network based on Sequential Quadratic Programming method.Incorporation engineering of the present invention is actual, can obtain the available node voltage phasor of conventional Power Flow Calculation Methods For Distribution Network, also can try to achieve the actual power of system frequency and generator, load.No longer need all kinds of node types are set, and the good computational accuracy of convergence is higher, more realistic power distribution network is actual.

Summary of the invention

The flexible power flow algorithm of power distribution network based on Sequential Quadratic Programming method, is characterized in that:

The present invention creatively organically combines generator and Static Characteristics of Loads equation with the distribution power flow equation that retains second order term, formed the distribution power flow equation of taking into account generator and Static Characteristics of Loads.Then the problem that solves power flow equation be converted into an optimization problem and set suitable Optimization goal, utilizing secondary sequence to plan to solve, having proposed the flexible trend of power distribution network based on Sequential Quadratic Programming method.

Incorporation engineering of the present invention is actual, can obtain the available node voltage phasor of conventional Power Flow Calculation Methods For Distribution Network, also can try to achieve the actual power of system frequency and generator, load.Compared to conventional Load Flow algorithm, the present invention no longer needs to arrange all kinds of node types, and computational convergence is good and computational accuracy is higher, and more realistic power distribution network is actual.

Technical scheme of the present invention is as follows:

The flexible trend method of power distribution network based on Sequential Quadratic Programming method, is characterized in that: based on following electric network swim 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,

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

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

$G\left(i\right)=\left[\begin{array}{c}0\\ \begin{array}{cccc}{G}_{i1}& G_{i2}& ...& G_{\mathrm{in}}\end{array}\\ 0\end{array}\right];$

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

$B\left(i\right)=\left[\begin{array}{c}0\\ \begin{array}{cccc}{B}_{i1}& B_{i2}& ...& B_{\mathrm{in}}\end{array}\\ 0\end{array}\right];$

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

G _inthe amplitude that represents the branch road admittance between node i and n, p _lifor the comprehensive actual load active power of node i, q _licomprehensive actual load reactive power for node i;

Concrete processing comprises the following steps:

Step 1, chooses arbitrarily one of them in an above-mentioned 2n equation, specifically: Δ x ^ta _kΔ x+b _k ^tΔ x-p _lk=0 or Δ x ^td _kΔ x+g _k ^tΔ x-q _lk=0, with abs (Δ x ^ta _kΔ x+b _k ^tΔ x-p _lk) or abs (Δ x ^td _kΔ x+g _k ^tΔ x-q _lk) value minimum as optimization aim, and remaining 2n-1 equation is as equality constraint, solving of power flow equation is converted into one containing the mathematical optimization of a plurality of nonlinear restrictions;

Step 2, based on step 1, is converted into one containing the mathematical optimization of a plurality of nonlinear restrictions by solving of power flow equation, and this optimization adopts SQP to solve; By target function mark minimum value value, be specifically 0, and its optimizing is exactly the process solving for power flow equation to the process nature of minimum value.

In the flexible trend method of above-mentioned a kind of power distribution network based on Sequential Quadratic Programming method, described electric network swim equation is based on following formula:

Active power-frequency static characteristic relation equation of generator static characteristic and reactive power-Voltage Static characteristic relation equation,

P _Gi=K _fi(f _i0-f)

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

In formula, f _i0idling frequency for unit i; K _fiactive power-Frequency regulation factor for unit i; U _i0floating voltage for unit i; K _uireactive power-voltage regulation coefficient for unit i; F is system frequency, U _inode voltage amplitude for node i;

Static Characteristics of Loads can be by Static Characteristics of Loads relation equation,

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 formula, P _li0and Q _li0for the meritorious and reactive power of the load i under rated voltage and rated frequency, be called load basic point frequency; K _pUi, K _pfiand K _qUi, K _qfibe respectively voltage regulation coefficient and the Frequency regulation factor of load active power and reactive power;

Then in conjunction with generator and Static Characteristics of Loads formula, for each node of electrical network, if only have load, so S in node i _li=P _li+ jQ _li; If only there is generator in node i, because generator is to send power, contrary with part throttle characteristics, be written as so S _li=-(P _gi+ jQ _gi); Analogize, when existing load has generator again on certain node, consider and have S _li=P _li+ jQ _li-(P _gi+ jQ _gi); For simplicity, by above-mentioned three kinds of situation unified definitions, be

S _Li=p _Li+jq _Li,i∈(1,n)

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

In formula, p _lifor the comprehensive actual load active power of node i, q _lifor the comprehensive actual load reactive power of node i, R ^{n * 1}the real number matrix that represents capable 1 row of n.

In the above-mentioned a kind of flexible trend method of power distribution network based on Sequential Quadratic Programming method, in described step 1,

Under rectangular coordinate system, the node voltage vector of definition power distribution network is

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

And definition $\mathrm{\Δx}=\left[\begin{array}{c}\mathrm{\Δe}\\ \mathrm{\Δf}\end{array}\right]=\left[\begin{array}{c}e-e_0\\ f-f_0\end{array}\right],$ Wherein, under conventional flat startup initial condition, e ₀=(1) ^t∈ R ^{n * 1}, f ₀=(0) ^t∈ R ^{n * 1}

Under flat entry condition, quadratic form power flow equation is carried out to strict Taylor series expansion, considered that the distribution power flow equation with quadratic term of the reservation newton residual error of generator and Static Characteristics of Loads can be expressed as

$\mathrm{J\Δx}+\widetilde{\mathrm{\Δx}}\mathrm{J\Δx}=S_L$

Compared to conventional Load Flow algorithm, the S in formula _lconsidered generator and Static Characteristics of Loads, but not general permanent load model.Wherein

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

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

$\widetilde{\mathrm{\Δx}}=\left[\begin{array}{cc}\widetilde{\mathrm{\Δe}}& -\widetilde{\mathrm{\Δ}}f\\ \widetilde{\mathrm{\Δf}}& \widetilde{\mathrm{\Δe}}\end{array}\right],\widetilde{\mathrm{\Δe}}=\mathrm{diag}\left(\mathrm{\Δ}{e}_i\right),\widetilde{\mathrm{\Δf}}=\mathrm{diag}\left(\mathrm{\Δ}{f}_i\right)$

The power flow equation that can see significantly the reservation second order term of taking into account generator and Static Characteristics of Loads that above derivation obtains be one about the quadratic nonlinearity matrix equation of Δ x, be difficult to its direct solution.If above-mentioned power flow equation is slightly dealt with, can be converted into an optimization problem that solves nonlinear restriction.Above-mentioned power flow equation containing 2n equation, launches to be write as to it altogether

Δx ^Ta _iΔx+b _i ^TΔx-p _Li=0,i∈(1,n)

Δx ^Td _iΔx+g _i ^TΔx-q _Li=0,i∈(1,n)

Choose arbitrarily one of them equation DELTA x ^ta _kΔ x+b _k ^tΔ x-p _lk=0 or Δ x ^td _kΔ x+g _k ^tΔ x-q _lk=0, no longer using this equation as equality constraint, but with abs (Δ x ^ta _kΔ x+b _k ^tΔ x-p _lk) or abs (Δ x ^td _kΔ x+g _k ^tΔ x-q _lk) value is minimum as optimization aim, and all the other equations still exist as equality constraint.From mathematics, analyze, target function mark minimum value should be 0, and its optimizing has in fact just completed solving for power flow equation to minimum value.Therefore it is feasible the Solve problems of power flow equation being converted into an optimization problem processes.Because Sequential Quadratic Programming method (Sequential Quadratic Programming) has global convergence, keep local superlinear convergence simultaneously, be one of way the most effectively solving at present the optimum effect of Solution of Nonlinear Optimal Problem, therefore select the Solve problems that adopts SQP to solve the power flow equation of the above-mentioned mathematical optimization problem that is converted into nonlinear restriction.

Therefore, the present invention has the following advantages: incorporation engineering is actual, can obtain the available node voltage phasor of conventional Power Flow Calculation Methods For Distribution Network, also can try to achieve the actual power of system frequency and generator, load.No longer need to arrange all kinds of node types, computational convergence is good and computational accuracy is higher, and more realistic power distribution network is actual

Embodiment

Below by embodiment, and in conjunction with data analysis, technical scheme of the present invention is described in further detail.

Embodiment:

This patent institute extracting method is verified under a plurality of example models, as space is limited, the present embodiment is example for take improved IEEE33 example, based on emulated data and MATLAB calculated data, feasibility and the validity of this paper institute extracting method is analyzed and is verified.Concrete condition is as follows:

Take IEEE33 standard example as basis, it is improved appropriately.Owing to no longer needing balance node in flexible power flow algorithm, for the balance node in IEEE33 node system, transform generator node as and calculate.Standard IEEE 33 systems contain 37 branch roads, and 5 looped networks are the distribution system containing looped network of standard, and fiducial value is set to S _b=600kVA, V _b=10kV.

What table 1 provided is the calculation of tidal current of benchmark 50HZ example, in table, calculated data row are results that algorithm calculates herein, and emulated data row are according to IEEE33 example data and generator and the Static Characteristics of Loads data that modeling and simulating calculates in relevant software after improving.Can see, the result of calculation of the voltage magnitude of each node and the error of simulation result are very little, and the validity of this algorithm has been described.

The contrast of table 1 benchmark example calculation of tidal current

Node	Emulated data	Calculated data	Node	Emulated data	Calculated 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	21	0.9638	0.9639
						5	0.9676	0.9677	22	0.9581	0.9581
6	0.9552	0.9553	23	0.9702	0.9703
						7	0.9537	0.9538	24	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	?	?	?

About the corresponding situation of angle, the situation of below selecting several representative nodes describes, and concrete data refer to table 2.

The contrast of table 2 benchmark example angle calculation result

Node	Emulated data	Calculated 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

From table 2, can see, result of calculation and the simulation result error of the angle of each node are very little, have shown the correctness of calculating.

In order embodying, to consider generator and Static Characteristics of Loads advantage, benchmark example slightly to be made an amendment, choose the load on the node 30 that reference power is larger, its reference power is increased to 3 times.Due to the meritorious idle increase of load, exerting oneself of generator must be adjusted accordingly so, and consequently the frequency of generator declines to increase meritorious processing, and set end voltage declines to increase the idle balance that reaches new of exerting oneself.

Through calculating, the steady frequency of amended system drops to 49.77HZ, set end voltage has dropped to 0.9770p.u., its variation tendency meets generator static characteristic feature, the active power balance of system and the relation that frequency adjustment, reactive power equilibrium and voltage are adjusted have been embodied, in the situation that the load of system occurred to have changed, in the adjusting effect acting in conjunction of generator and Static Characteristics of Loads, be issued to new power-balance.Concrete algorithm calculated data and the contrast situation of emulated data, refer to table 3.

Table 3 is revised rear example calculation of tidal current contrast

Under non-50HZ condition, for the corresponding situation of angle, similarly, at this, also select several representative nodes and whether analyze its correspondence, refer to following table 4.

The contrast of the amended example angle calculation of table 4 result

Node	Emulated data	Calculated 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 with the result in 50HZ situation, the angular error of calculation of tidal current of improving later example is also very little.To sum up can see and will the present invention is directed to the result of calculation of above-mentioned example, with the result contrast of emulation, error is very little, and the correctness of algorithm has been described.

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various modifications or supplement or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Claims (3)

1. the flexible trend method of the power distribution network based on Sequential Quadratic Programming method, is characterized in that: based on following electric network swim 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,

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

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

$G\left(i\right)=\left[\begin{array}{c}0\\ \begin{array}{cccc}{G}_{i1}& G_{i2}& ...& G_{\mathrm{in}}\end{array}\\ 0\end{array}\right];$

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

$B\left(i\right)=\left[\begin{array}{c}0\\ \begin{array}{cccc}{B}_{i1}& B_{i2}& ...& B_{\mathrm{in}}\end{array}\\ 0\end{array}\right];$

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

G _inthe amplitude that represents the branch road admittance between node i and n, p _lifor the comprehensive actual load active power of node i, q _licomprehensive actual load reactive power for node i;

Concrete processing comprises the following steps:

Step 1, chooses arbitrarily one of them in an above-mentioned 2n equation, specifically: Δ x ^ta _kΔ x+b _k ^tΔ x-p _lk=0 or Δ x ^td _kΔ x+g _k ^tΔ x-q _lk=0, with abs (Δ x ^ta _kΔ x+b _k ^tΔ x-p _lk) or abs (Δ x ^td _kΔ x+g _k ^tΔ x-q _lk) value minimum as optimization aim, and remaining 2n-1 equation is as equality constraint, solving of power flow equation is converted into one containing the mathematical optimization of a plurality of nonlinear restrictions;

Step 2, based on step 1, is converted into one containing the mathematical optimization of a plurality of nonlinear restrictions by solving of power flow equation, and this optimization adopts SQP to solve; By target function mark minimum value value, be specifically 0, and its optimizing is exactly the process solving for power flow equation to the process nature of minimum value.

2. the flexible trend method of a kind of power distribution network based on Sequential Quadratic Programming method according to claim 1, is characterized in that: described electric network swim equation is based on following formula:

Active power-frequency static characteristic relation equation of generator static characteristic and reactive power-Voltage Static characteristic relation equation,

P _Gi=K _fi(f _i0-f)

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

In formula, f _i0idling frequency for unit i; K _fiactive power-Frequency regulation factor for unit i; U _i0floating voltage for unit i; K _uireactive power-voltage regulation coefficient for unit i; F is system frequency, U _inode voltage amplitude for node i;

Static Characteristics of Loads can be by Static Characteristics of Loads relation equation,

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 formula, P _li0and Q _li0for the meritorious and reactive power of the load i under rated voltage and rated frequency, be called load basic point frequency; K _pUi, K _pfiand K _qUi, K _qfibe respectively voltage regulation coefficient and the Frequency regulation factor of load active power and reactive power;

Then in conjunction with generator and Static Characteristics of Loads formula, for the comprehensive actual load power S of node i _li, for node i, have respectively and on grid nodes i, only have three kinds of situations that only have existing load in generator and node i have again generator in load, node i, in three kinds of situations, defined node i actual load power S _libe expressed 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 formula, p _lifor the comprehensive actual load active power of node i, q _lifor the comprehensive actual load reactive power of node i, R ^{n * 1}the real number matrix that represents capable 1 row of n.

3. the flexible trend method of a kind of power distribution network based on Sequential Quadratic Programming method according to claim 1, is characterized in that: in described step 1,

Under rectangular coordinate system, the node voltage vector of definition power distribution network is

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

And definition $\mathrm{\Δx}=\left[\begin{array}{c}\mathrm{\Δe}\\ \mathrm{\Δf}\end{array}\right]=\left[\begin{array}{c}e-e_0\\ f-f_0\end{array}\right],$ Wherein, under conventional flat startup initial condition, e ₀=(1) ^t∈ R ^{n * 1}, f ₀=(0) ^t∈ R ^{n * 1}

Under flat entry condition, quadratic form power flow equation is carried out to strict Taylor series expansion, considered that the electric network swim equation with quadratic term of the reservation newton residual error of generator and Static Characteristics of Loads is expressed as

$\mathrm{J\Δx}+\mathrm{\Δ}\tilde{x}\mathrm{J\Δx}=S_L$

Compared to conventional Load Flow algorithm, the S in formula _lconsidered generator and Static Characteristics of Loads, but not general permanent load model, wherein

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

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

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