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 the flexible power flow algorithm of a kind of power distribution network, particularly relate to the flexible power flow algorithm of a kind of power distribution network based on Sequential Quadratic Programming method, the distribution power flow equation of generator and Static Characteristics of Loads and reservation second order term creatively organically combines by the present invention, defines the distribution power flow equation of the reservation second order term taking into account generator and Static Characteristics of Loads.Solving above power flow equation, the Solve problems of this power flow equation is converted into a mathematical optimization problem containing nonlinear restriction and also solves with secondary sequence law of planning by the present invention's employing.Incorporation engineering of the present invention is actual, can obtain the available node voltage phasor of regular distribution net power flow algorithm, 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 type, and computational convergence is good and computational accuracy is higher, and more realistic power distribution network is actual.

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, particularly relate 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 huge change will occur.Particularly when islet operation, due to the support of distributed power source, isolated island can continue to run with the normal work of guarantee section 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 comparatively large, result of calculation conforms to not to the utmost with engineering reality.

In fact, that load or generating set all have frequency and voltage regulating characteristics, under steady state operating conditions, system frequency and voltage need not be equal to rated frequency and given magnitude of voltage, and load and generating set are all realize power division according to respective static characteristic.Scholar is had to propose a kind of quick Power Flow Calculation Methods For Distribution Network newly, by carrying out strict Taylor series expansion to Secondary trend, power flow equation is changed the second nonlinear matrix equation changed into containing independent variable correction to solve, it takes full advantage of power distribution network feature, in solution procedure, its Jacobian matrix remains constant, calculation process is comparatively simple, and namely remain newton's residual error because it retains second order local derviation item, its computational accuracy is higher relative to Newton-like methods, but this algorithm does not consider 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, based on the power flow equation retaining second order term, and distributed power source is regarded as with reference to related documents the power flow equation that controlled load introduces second order term, creatively generator is combined with the distribution power flow equation retaining second order term with Static Characteristics of Loads equation, defines the distribution power flow equation taking into account generator and Static Characteristics of Loads.Then the problem solving power flow equation be converted into an optimization problem and set suitable Optimization goal, utilizing secondary sequence to plan and solve, proposing 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 regular distribution net power flow algorithm, also can try to achieve the actual power of system frequency and generator, load.No longer need to arrange all kinds of node type, 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:

Generator and Static Characteristics of Loads equation creatively organically combine with the distribution power flow equation retaining second order term by the present invention, define the distribution power flow equation taking into account generator and Static Characteristics of Loads.Then the problem solving power flow equation be converted into an optimization problem and set suitable Optimization goal, utilizing secondary sequence to plan and solve, proposing 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 regular distribution net power flow algorithm, 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 type, 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 _i1G _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 _i1B _i2...B _in];

G _inrepresent the amplitude of the branch admittance between node i and n, p _lifor the comprehensive actual load active power of node i, q _lifor the comprehensive actual load reactive power of node i;

Concrete process 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, then solving of power flow equation is converted into a mathematical optimization containing multiple nonlinear restriction;

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

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 the relation equation of generator static characteristic and reactive power-Voltage Static characteristic relation equation, namely

P _Gi=K _fi(f _i0-f)

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

In formula, f _i0for the idling frequency of unit i; K _fifor the active power-Frequency regulation factor of unit i; U _i0for the floating voltage of unit i; K _uifor the reactive power-voltage regulation coefficient of unit i; F is system frequency, U _ifor the node voltage amplitude of node i;

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

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 of the load i under rated voltage and rated frequency and reactive power, 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 node i only has load, so S _li=P _li+ jQ _li; If node i only has generator, because generator sends power, contrary with part throttle characteristics, be so written as S _li=-(P _gi+ jQ _gi); Analogize, when load existing on certain node has again generator time, consider, 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}represent the real number matrix of capable 1 row of n.

In the flexible trend method of above-mentioned a kind 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 define $\mathrm{\Δx}=\left[\begin{array}{c}\mathrm{\Δe}\\ \mathrm{\Δf}\end{array}\right]=\left[\begin{array}{c}e-e_0\\ f-f_0\end{array}\right],$ 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, carry out strict Taylor series expansion to quadratic form power flow equation, the distribution power flow equation considering the band 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 _lconsider 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

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

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

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.Mathematically analyze, target function mark minimum value should be 0, and its optimizing in fact just completes solving for power flow equation to minimum value.Therefore it is feasible for the Solve problems of power flow equation being converted into that an optimization problem processes.Because Sequential Quadratic Programming method (SequentialQuadraticProgramming) has global convergence, keep local power flow simultaneously, be one of way the most effectively solving Solution of Nonlinear Optimal Problem optimum effect at present, therefore select and adopt SQP to solve the above-mentioned Solve problems being converted into the power flow equation of the mathematical optimization problem of nonlinear restriction.

Therefore, the present invention has the following advantages: incorporation engineering is actual, can obtain the available node voltage phasor of regular distribution net power flow algorithm, also can try to achieve the actual power of system frequency and generator, load.No longer need to arrange all kinds of node type, 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 multiple example model, as space is limited, the present embodiment, for for the IEEE33 example improved, based on emulated data and MATLAB calculated data, is analyzed the feasibility of this paper institute extracting method and validity and verifies.Concrete condition is as follows:

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

The calculation of tidal current of what table 1 provided is benchmark 50HZ example, in table, calculated data row are herein results of calculating of algorithm, and emulated data row are then the data calculated according to the IEEE33 example data after improving and generator and Static Characteristics of Loads modeling and simulating in associated software.Can see, the result of calculation of the voltage magnitude of each node and the error of simulation result very little, describe the validity of this algorithm.

Table 1 benchmark example calculation of tidal current contrasts

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 below selecting several representative node is described, and concrete data refer to table 2.

Table 2 benchmark example angle calculation Comparative 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

Can see from table 2, result of calculation and the simulation result error of the angle of each node are very little, indicate the correctness of calculating.

Considering generator and Static Characteristics of Loads advantage to embody, benchmark example slightly being made an amendment, chooses the load on the larger node of reference power 30, its reference power is increased 3 times.So because the active reactive of load increases, exerting oneself of generator must adjust accordingly, and consequently the frequency decrease of generator is to increase meritorious process, and set end voltage declines and reaches new balance to increase idle exerting oneself.

Through calculating, the steady frequency of amended system drops to 49.77HZ, set end voltage have decreased to 0.9770p.u., its variation tendency meets generator static characteristic feature, embody the relation of the active power balance of system and frequency adjustment, reactive power equilibrium and Voltage Cortrol, when the load of system there occurs changed, be issued to new power-balance in the mediating effect+6 acting in conjunction of generator and Static Characteristics of Loads.Concrete algorithm calculated data and the contrast situation of emulated data, refer to table 3.

The contrast of rear example calculation of tidal current revised by table 3

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

Table 4 amended example angle calculation Comparative 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 improving the calculation of tidal current of later example is also very little.To sum up can see the result of calculation by the present invention is directed to above-mentioned example, with the Comparative result of emulation, error is very little, describes the correctness of algorithm.

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 amendment or supplement or adopt similar mode to substitute to described specific embodiment, but can't depart from spirit of the present invention or surmount the scope that appended claims defines.

Claims (3)

1., based on the flexible trend method of power distribution network of Sequential Quadratic Programming method, it 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 _i＝[G _i1G _i2...G _in]；

B _i＝[B _i1B _i2...B _in]；

G _inrepresent the amplitude of the branch admittance between node i and n, p _lifor the comprehensive actual load active power of node i, q _lifor the comprehensive actual load reactive power of node i;

Concrete process 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, then solving of power flow equation is converted into a mathematical optimization containing multiple nonlinear restriction;

Step 2, based on step 1, solving of power flow equation is converted into a mathematical optimization containing multiple nonlinear restriction, and this optimization adopts Sequential Quadratic Programming method to solve; Be specifically 0 by target function minimum value value, and its optimizing to the process nature of minimum value be exactly the process solved for power flow equation.

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 the relation equation of generator static characteristic and reactive power-Voltage Static characteristic relation equation, namely

P _Gi＝K _fi(f _i0-f)

Q _Gi＝K _Ui(U _i0-U _i)

In formula, f _i0for the idling frequency of unit i; K _fifor the active power-Frequency regulation factor of unit i; U _i0for the floating voltage of unit i; K _uifor the reactive power-voltage regulation coefficient of unit i; F is system frequency, U _ifor the node voltage amplitude of node i;

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

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 of the load i under rated voltage and rated frequency and reactive power, be called load basic point power; 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, having respectively grid nodes i only has in load, node i only has existing load in generator and node i to have again three kinds of situations of generator, then in three kinds of situations, and defined node i comprehensive 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}represent the real number matrix of 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 define $\mathrm{\Δ}x=\left[\begin{array}{c}\mathrm{\Δ}e\\ \mathrm{\Δ}f\end{array}\right]=\left[\begin{array}{c}e-e_0\\ f-f_0\end{array}\right],$ 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, carry out strict Taylor series expansion to quadratic form power flow equation, the electric network swim equation considering the band quadratic term of the reservation newton residual error of generator and Static Characteristics of Loads can be expressed as

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

Compared to conventional Load Flow algorithm, the S in formula _lthe permanent load model having considered 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

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