CN102611106B - Maximum load supply capability evaluation method of medium-voltage power distribution network for loop power supply - Google Patents

Abstract

The invention provides a maximum load supply capability evaluation method of a medium-voltage power distribution network for loop power supply. The method comprises determining the regression model of a multivariable nonlinear regression curve representing the quantitative relationship between the output power flow of a substation and a leading switching station based on a power flow tracing theory; establishing a maximum load supply capability target function of the medium-voltage power distribution network; and resolving of the target function by sequential quadratic programming method while considering the requirement of N-1 criterion of power supply security for urban power grid and selecting the network power balance, the circuit thermal stability limit, the bus voltage, and the power of a power output node and a load node as the constraint conditions to obtain the optimum solution, i.e. the maximum load supply capability of the medium-voltage power distribution network for loop power supply.

Description

A kind of net capability appraisal procedure of ring type supply medium voltage distribution network

Technical field

The invention belongs to distribution system net capability and calculate field, particularly a kind of net capability appraisal procedure of ring type supply medium voltage distribution network.

Background technology

Urban distribution network is the main composition part of electric power system, is undertaking the effect that guarantees the reliable continued power of user and provide the good quality of power supply, is the important infrastructure of urban construction and economic development and necessary energy supply system.Past power construction " retransmit, gently confession, don't work " phenomenon causes reasonably planning and the fund input of power distribution network long-term lacking, poor infrastructure.Along with developing rapidly and the quick increase of power load of urban economy, the contradiction that power distribution network has presented electricity " can't get into, can not fall any more, do not use ".For distribution construction and major network development are adapted, meet the demand of city load development, for regional economic development provides reliable guarantee, guaranteeing that, under the prerequisite of urban distribution network safety, reliability service, the power supply capacity that improves distribution system becomes a problem demanding prompt solution in current urban power network planning work.

Power distribution network net capability MLSC (Maximum Load Supply Capability) refers at the equal nonoverload of the equipment such as distribution line and transformer and each node voltage all under not out-of-limit condition, the peak load that system can be supplied.The abundance of power distribution network power supply capacity be whether determine power distribution network can effectively dissolve major network power, meet the key of customer charge demand, be one of key factor determining regional economic development; The assessment of power distribution network power supply capacity, for optimizing grid structure, is instructed planning and the operation of urban distribution network, has huge economic benefit and social benefit.

The common method of calculating at present power distribution network net capability has linear programming technique, interior point method, capacity-load ratio method and peak load method of multiplicity etc.Document [1-3] adopts respectively peak load method of multiplicity, Network Maximal-flow method and capacity-load ratio method to ask for power distribution network net capability, these methods only with feeder line load estimation network shift power supply capacity, ignored the impact of network practical structures on power supply capacity.Document [4-5] has proposed to adopt the linear programming model based on DC power flow, and the peak load that can supply take network is as target function.But this variation of busbar voltage amplitude and the resistance of circuit ignored, and only solve the active power part of Line Flow, although can greatly reduce amount of calculation, improve computational speed, but for power distribution network particularly for 10kV grid structure, because the resistance of circuit is not often much smaller than reactance, therefore adopt DC power flow algorithm to calculate, resultant error can be larger.Document [6] proposes a kind of based on Trust Region urban network max power supply capability method, the method is carried out solving of power flow equation based on AC power flow,, transformer capacity thermally-stabilised take generate output, circuit, busbar voltage are as basic constraints, take network net capability as target function, but the method need to take Parameter Perturbation Method to carry out second order equivalence to target function at each search point, the precision of Equivalent Model is larger on the impact of result, and the complexity of calculating increases greatly.In document [7-9] regulation urban power network planning, should consider when arbitrary line outage or main transformer of transformer station are out of service still can guarantee to the planning principles of user's continued power, document [10-11] proposes to take into account the power distribution network power supply capacity computational methods of " N-1 " criterion, although the method can directly be calculated power distribution network power supply capacity, without iteration, have advantages of that computational speed is fast, but adopting direct method to have gained solution is not the optimal solution problem under existing constraints, error is larger in some cases, when the basic reason of its generation is to calculate each main transformer load factor in power supply capacity solution procedure, think that all main transformer load factor is identical in same interconnection unit, this does not meet actual.

Existing power distribution network power supply capacity computation model and method be generally for the distribution network of open loop operation, for the model of the net capability of ring type supply power distribution network, rarely has report.

List of references

[1] Qiu Wenqian. by minimax load multiple assessment mains supply ability [J]. east china electric power, 1994, (10); 29-30

[2] Hou Youhua, Zhang Qiang, Yu Hai etc. the analysis and research [J] of power grid of West Inner Mongolia power supply capacity. Inner Mongol power technology, 200119 (2): 1-4

[3 old gold and jade, inscription on ancient bronze objects dragon. city network planning draw in about the problems of value [J] of transformer capacity-load ratio. for electricity consumption, 2004,21 (5): 18-20.

[4] Zhang Liping, model tomorrow. urban network max power supply capability evaluation algorithms [J]. electric power network technique, 2008,32 (9): 68-71.

[5] Shu Hongchun, Hu Zejiang, Liu Zongbing.On-line evaluating method of urban network max power supply capability and application thereof [J]. electric power network technique, 2006,30 (9): 46-50.

[6] Li Hongjun, Li Jingru, Yang Weihong.Urban distribution network power supply capacity adequacy evaluation [J] based on Trust Region. electric power network technique, 2010,34 (8): 92-96.

[7] State Grid Corporation of China. urban power network planning and designing guide rule [S]. Beijing: State Grid Corporation of China, 2006.

[8]K.hator Suresh K，Leung Lawrence C.Power distribution planning：a review of model sand issues[J].IEEE Transactions on Power Systems，1997，12(3)：115121159.

[9] Shanghai Electric Power Co. the regulation [S] of the some engineering philosophies of Shanghai Power Network. Shanghai: Shanghai Electric Power Co, 2004.

[10] Xiao Jun, Gu Wenzhuo, Guo Xiaodan,, etc. distribution system power supply capacity model [J] Automation of Electric Systems, 2011 (35): 47-52.

[11] Wang Chengshan, Luo Fengzhang, Xiao Jun, etc. the distribution system power supply capacity computational methods [J] based on main transformer interconnecting relation. Proceedings of the CSEE, 2009,29 (13): 86-91.

Summary of the invention

For the restriction of deficiency and the scope of application of existing power distribution network net capability, the present invention proposes a kind of net capability appraisal procedure of the ring type supply middle voltage distribution networks based on multivariate nonlinear regression analysis model, to meet the actual needs of ring type supply power distribution network net capability computation model, i.e. " N-1 " criterion requirement of urban distribution network power supply safety.

Technical scheme of the present invention is a kind of net capability appraisal procedure of ring type supply medium voltage distribution network, and described ring type supply medium voltage distribution network comprises the ring network that transformer station and multiple switching station connect and compose, and comprises the following steps:

Step 1, the basic data of input ring type supply medium voltage distribution network;

Step 2, according to basic data described in step 1, carries out the trend of ring type supply medium voltage distribution network and calculates;

Step 3, in step 2, trend is calculated on the basis of acquired results, carries out trend tracking, determines distribution condition and switching station the draw situation to transformer station 10 kV outgoing line power of each transformer station 10 kV outgoing line power in switching station in ring type supply medium voltage distribution network;

Step 4, take trend calculating acquired results and step 3 gained trend tracking results in step 2 as initial point, within the scope of switching station load capacity, adopt monte carlo method to determine that in ring network, many groups of loads of switching station distribute, the load distribution situation of each group switching station is carried out respectively to trend calculating and trend tracking, obtain many group trend tracking results, and the leading switching station of definite transformer station 10 kV outgoing line power;

Step 5, in step 4, gained is organized on the basis of trend tracking results more, sets up the multivariate nonlinear regression analysis model between transformer station 10 kV outgoing line power and leading switching station;

Step 6, based on step 5 gained multivariate nonlinear regression analysis model, sets up the net capability model of ring type supply medium voltage distribution network;

Step 7, solves the globally optimal solution of net capability model, obtains the net capability model of ring type supply medium voltage distribution network, obtains the net capability of ring type supply medium voltage distribution network according to net capability model.

And in step 2, the trend that adopts Newton-Raphson method to carry out ring type supply medium voltage distribution network is calculated, concrete mode is as follows,

First iterative computation node voltage value, establishing current is the k time iteration, k=0, carries out following steps,

1) the node voltage value e calculating by the k-1 time iteration ^(k)and f ^(k), calculate the amount of unbalance of current each node

with wherein

be the amount of unbalance of i node active power,

be the amount of unbalance of i node reactive power,

it is the amount of unbalance of i node voltage square; When k=0, the node voltage value e that the k-1 time iteration calculates ^(k)and f ^(k)directly adopt the initial value e of the node voltage value of input ⁽⁰⁾and f ⁽⁰⁾;

2) press condition verification convergence below,

$\max \left\{\right|{\mathrm{\&Delta;P}}_i^{\left(k\right)},{\mathrm{\&Delta;Q}}_i^{\left(k\right)},{\mathrm{\&Delta;V}}_i^{2\left(k\right)}\left|\right\}<\mathrm{\&epsiv;}$

If satisfied condition, iteration leaves it at that, and does not meet and continues to calculate, and ε is predetermined threshold value;

3) each element of calculating Jacobian matrix;

4) according to Jacobean matrix array, write update equation, ask the correction of node voltage value

with

5) revise each node voltage value, wherein the voltage correction formula of i node is as follows

$e_i^{(k+1)}=e_i^{\left(k\right)}+{\mathrm{\&Delta;e}}_i^{\left(k\right)},f_i^{(k+1)}=f_i^{\left(k\right)}+{\mathrm{\&Delta;f}}_i^{\left(k\right)}$

6) iterations k=k+1, returns to 1) continuation iterative process;

After iteration finishes, the power in power and the network of calculated equilibrium node distributes, and establishes use represent that i node is to circuit electric current I between j node _ijgrip altogether, the computing formula of transmission line power is as follows:

$S_{\mathrm{ij}}=P_{\mathrm{ij}}+{\mathrm{jQ}}_{\mathrm{ij}}={\stackrel{\&CenterDot;}{V}}_i{\hat{I}}_{\mathrm{ij}}=V_i^2{\hat{y}}_{i0}+{\stackrel{\&CenterDot;}{V}}_i({\stackrel{\&CenterDot;}{V}}_i-{\stackrel{\&CenterDot;}{V}}_j){\hat{y}}_{\mathrm{ij}}$

Wherein, S _ijbe the apparent power of i node to circuit between j node, P _ijbe the active power of i node to circuit between j node, Q _ijbe the reactive power of i node to circuit between j node,

be the voltage phasor of i node,

be the admittance over the ground of i node,

be the voltage phasor of j node,

be the admittance of i node to circuit between j node; The value of i is 1,2 ..., n, the value of j is 1,2 ..., n, i ≠ j, n is node sum.

And in step 3, the concrete mode of carrying out trend tracking is as follows,

1) according to step 2, calculate the trend result of gained normal condition system, form lossless network;

2) based on lossless network, form downstream distribution matrix A, node active power matrix P _lLwith the total power matrix P that gains merit that injects of node _tT;

Downstream distribution matrix A=(a _ij) _{n × n}, wherein matrix element a _ijcomputing formula as follows,

Wherein, P _ijfor the active power that circuit i-j is transmitted to j node by i node-flow, P _tjbe total injection active power of j node;

P _LL＝diag(P _L1，P _L2，…P _Ln)

Wherein, P _l1, P _l2... P _lnrespectively the 1st, 2 ..., the active power of n node;

P _TT＝diag(P _T1，P _T2，…P _Tn)

Wherein, P _t1, P _t2... P _tnrespectively the 1st, 2 ..., total injection active power of n node;

3) calculate the inverse matrix of downstream distribution matrix A, and calculate the load of switching station to the power draw coefficient matrix K of branch road _l=P _lL(P _tTa ^t) ^-1;

4) establishing certain switching station is i node, between s node and t node, connects and composes branch road s-t, the draw P of the load of i node of calculating to line power _li-st=k _litp _st;

Wherein, P _li-stthe load that refers to i node draws the active power of branch road s-t, K _l=(k _lit) _{n × n}element k _litrefer to that the load of i node is to the distribution coefficient matrix of branch road s-t, P _strefer to the active power of branch road s-t.

And in step 5, the concrete mode of setting up the multivariate nonlinear regression analysis model between transformer station 10 kV outgoing line power and leading switching station is as follows,

(5.1) establishing certain switching station is i node, is designated as switching station i, and the load of switching station i is followed the tracks of nonlinear curve model to the trend of drawing power of circuit l and is

$P_{l-\mathrm{Li}}=a_0+a_1{P}_{\mathrm{Li}}+a_2{P}_{\mathrm{Li}}^2+...+a_t{P}_{\mathrm{Li}}^t$

Wherein, P _l-Lifor the power that switching station i draws from circuit l, P _lifor the load of switching station i, a ₀, a ₁... a _tfor regression coefficient, t is the number of times of trend aircraft pursuit course, and the value of l is 1,2 ... L, L is circuit sum;

(5.2) load of setting up switching station i is followed the tracks of nonlinear curve model to the polynary trend of drawing power of circuit l

$P_{l-\mathrm{Li}}=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(a_{\mathrm{ik}1}{P}_{\mathrm{Lk}1}+a_{\mathrm{ik}2}{P}_{\mathrm{Li}2}+...+a_{\mathrm{ikt}}{P}_{\mathrm{Lit}})+a_0$

Wherein, m is switching station sum, for the t power of the load of switching station k, the value of k is 1,2 ... m; a _ikj, j={1,2 ..., t} represents the model P of the power that switching station i draws from circuit l _lktthe regression coefficient of item, a ₀for constant term coefficient;

(5.3) multivariate nonlinear regression analysis model of setting up line power and leading institute switching station is:

From trend, follow the tracks of theory, the power of circuit l is all distributed to leading switching station simultaneously, and the power of circuit l is

$P_{\mathrm{Pl}}=\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{P}_{l-\mathrm{Lf}}=\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}(\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(a_{\mathrm{fk}1}{P}_{\mathrm{Lk}1}+a_{\mathrm{fk}2}{P}_{\mathrm{Lf}2}+...+a_{\mathrm{fkt}}{P}_{\mathrm{Lft}})+a_0)$

$=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(P_{\mathrm{Lk}1}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fk}1}+P_{\mathrm{Lf}2}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fk}2}+...+...P_{\mathrm{Lft}}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fkt}})+{\hat{a}}_0$

$=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{\hat{a}}_{k1}{P}_{\mathrm{Lk}1}+{\hat{a}}_{k2}{P}_{\mathrm{Lk}2}+...+{\hat{a}}_{\mathrm{kt}}{P}_{\mathrm{Lkt}}+{\hat{a}}_0$

Wherein, P _l-Lfbe f the power that leading switching station i draws from circuit l, n _ztake the quantity of switching station as the leading factor, for the estimator of constant term coefficient,

j={1,2 ..., the estimator that t} is regression coefficient.

And in step 6, the net capability model of setting up ring type supply medium voltage distribution network is as follows,

$\max \mathrm{MLSC}=\underset{i}{\mathrm{\&Sigma;}}{P}_{\mathrm{Li}}=\underset{l}{\mathrm{\&Sigma;}}{P}_{\mathrm{Pl}}$

$s.t.\left\{\begin{array}{c}{P}_i=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_{k1}{P}_{\mathrm{Lk}1}+a_{k2}{P}_{\mathrm{Lk}2}+...+a_{\mathrm{kt}}{P}_{\mathrm{Lkt}}\\ I=\mathrm{YV}\\ P_{\mathrm{Li}\min }\&le;P_{\mathrm{Li}}\&le;P_{\mathrm{Li}\max }\\ P_{i\min }\&le;P_i\&le;P_{i\max }\\ U_{i\min }\&le;U_i\&le;U_{i\max }\end{array}\right.$

Wherein, P _libe the active power of i node, the value of i is 1,2 ..., n; P _plfor the power of circuit l, the value of l is 1,2 ... L, L is circuit sum;

When i node is transformer station, meet P _imin≤ P _i≤ P _imax, P _i, P _imin, P _imaxbe the actual active power of 10kV outlet and the bound thereof of i node, this node is transformer station, regression coefficient a _kjadopt step 5 gained estimator

j={1,2 ..., t}; U _i, U _imin, U _imaxbe busbar voltage and the bound thereof of i node; When i node is switching station, meet P _limin≤ P _li≤ P _limax, P _li, P _limin, P _limaxfor actual institute's on-load and the bound thereof of i node; Node current I and node voltage V meet I=YV, and Y is node admittance matrix.

And, in step 7, based on sequential quadratic programming method, solve the globally optimal solution of net capability model.

The invention provides a kind of computation model and method for solving of net capability of ring type supply medium voltage distribution network.By trend, follow the tracks of the theoretical Multiple Non Linear Regression curve model between leading switching station in transformer station 10 kV outgoing line power and the important power distribution network of ring type supply of setting up, on this basis, the net capability of ring type supply power distribution network is converted into and solves the peaked target function model of all transformer station 10 kV outgoing line power, considering transforming plant main transformer simultaneously, under the requirement of circuit " N-1 " and the thermally-stabilised limit of circuit, determine power-balance, branch power, the constraints of node busbar voltage.By the optimal solution of sequential quadratic programming method solving model, i.e. the net capability of ring type supply power distribution network.The present invention breaks through conventional method and is only suitable for the defect of moving high voltage distribution network with open loop, can in global scope, solve the optimal solution of target function simultaneously, and computational speed quick and precisely, can be medium voltage distribution network new quantification, theory and assessment tool is provided.

Accompanying drawing explanation

Fig. 1 is the flow chart of the embodiment of the present invention;

The ring-like medium voltage distribution network structure chart of 2 station 6 switching station that Fig. 2 provides for the embodiment of the present invention.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is removed, intactly described.

The present invention proposes a kind of net capability model of the ring type supply medium voltage distribution network based on Multiple Non Linear Regression curve model, the flow chart of embodiment is as shown in Figure 1, now as an example of the example network shown in Fig. 2 example, describes:

Step 1, the basic data of input ring type supply medium voltage distribution network:

Generally, in ring type supply medium voltage distribution network, comprise transformer station, power plant, switching station etc., basic data comprises the load of system line and unit, switching station, the component parameters information such as transformer.While processing actual electric network, in model, except medium voltage distribution network, circuit, unit in high voltage distribution network also should be inputted.

In embodiment, research object as shown in Figure 2, be one and comprise 2 110kV transformer stations, the ring type supply 10kV intermediate distribution system of 6 switching stations, is designated as respectively transformer station 1, transformer station 2, switching station 1, switching station 2, switching station 3, switching station 4, switching station 5, switching station 6.Switching station 1, switching station 2, switching station 3, switching station 4, switching station 5 and switching station 6 annulars are connected, and transformer station 1 connects switching station 1, switching station 2, switching station 3, and transformer station 2 connects switching station 4, switching station 5, switching station 6.Foundation comprises line parameter circuit value, the main transformer parameter of transformer station, the load (the system loading parameter of embodiment) of switching station and the isoparametric basic database of normal operating mode of system.The normal operating mode of system refers to the state of waiting the system rack actual motion of asking maximum load capacity, and for example one has the power distribution network of ring network shelf structure, and the normal operating mode of system is open loop operation or operation with closed ring.The basic data that embodiment relates to is as shown in table 1-3:

Table 1 line parameter circuit value

Table 2 switching station load parameter

Note: reactive power is 0.95 to choose according to power factor (PF)

Table 3 transformer station parameter

Step 2, according to basic data described in step 1, carries out the trend of ring type supply medium voltage distribution network and calculates.The adoptable tidal current computing method of the present invention has Newton-Raphson method, PQ decomposition method etc. and embodiment carries out ring type supply medium voltage distribution network by Newton-Raphson method and carries out trend calculating, and Newton-Raphson method is prior art.Adopt Newton-Raphson method to carry out the calculating of example power flow equation, the active power result of each branch road is as shown in table 4

Table 4 branch road active power

For the sake of ease of implementation, what the trend that provides employing Newton-Raphson method to carry out ring type supply medium voltage distribution network was calculated is described as follows,

(1) trend fundamental equation

Formula (2.1) has provided the math equation of power flow equation,

$\frac{P_i-{\mathrm{jQ}}_i}{\stackrel{\stackrel{\&CenterDot;}{^}}{V}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{Y}_{\mathrm{ij}}{\stackrel{\&CenterDot;}{V}}_j(i,j=\mathrm{1,2,3},...,n)---\left(2.1\right)$

V _imin≤V _i≤V _imax (2.2)

P _Gimin≤P _Gi≤P _Gimax (2.3)

Q _Gimin≤Q _Gi≤Q _Gimax (2.4)

|δ _i-δ _j|＜|δ _i-δ _j| _max (2.5)

The fundamental equation that wherein (2.1) formula trend is calculated, the constraint of (2.2) formula node voltage.Formula (2.3) and (2.4) are the active power of power supply node and the constraints of reactive power in network, and formula (2.5) is the merit angle constraint between node; P _i, Q _irefer to active power and the reactive power of i node,

refer to the voltage vector of j node,

refer to

conjugation, Y _ijrefer to the transadmittance of i node and j node.V _i, V _iminand V _imaxbe respectively i node voltage and bound vector thereof; P _gi, P _giminand P _gimaxbe respectively i node active power and bound vector thereof; Q _gi, Q _giminand Q _gimaxbe respectively i node reactive power and bound vector thereof; | δ _i-δ _j| and | δ _i-δ _j| _maxbe merit angular difference and the merit angular difference upper limit between i node and j node.The alleged node of the present invention is the power supply node that has generator, in this area also referred to as bus.

(2) basic principle of the inferior method of newton-pressgang

To solve nonlinear equation F (x)=0, the basic principle of Newton method is described as example.While solving this equation, first near true value, get initial value x ⁽⁰⁾, establish x=x ⁽⁰⁾+ Δ x ⁽⁰⁾, Δ x ⁽⁰⁾for x ⁽⁰⁾correction.By f (x ⁽⁰⁾+ Δ x ⁽⁰⁾)=0 is at x ⁽⁰⁾near Taylor expansion:

$f(x^{\left(0\right)}+{\mathrm{\&Delta;x}}^{\left(0\right)})=f\left(x^{\left(0\right)}\right)+f^{\&prime;}\left(x^{\left(0\right)}\right)*{\mathrm{\&Delta;x}}^{\left(0\right)}+f^{\&prime;\&prime;}\left(x^{\left(0\right)}\right)*\frac{{\left({\mathrm{\&Delta;x}}^{\left(0\right)}\right)}^2}{2!}+...+f^n\left(x^{\left(0\right)}\right)*\frac{{\left({\mathrm{\&Delta;x}}^{\left(0\right)}\right)}^n}{n!}+...\left(2.6\right)$

As Δ x ⁽⁰⁾when value is very little, in (2.6) formula, Derivative Terms and higher derivative item are negligible, and formula (2.6) is converted into:

f(x ⁽⁰⁾+Δx ⁽⁰⁾)＝f(x ⁽⁰⁾)+f′(x ⁽⁰⁾)*Δx ⁽⁰⁾＝0

That is:

f(x ⁽⁰⁾)＝-f′(x ⁽⁰⁾)*Δx ⁽⁰⁾ (2.7)

Obtain about Δ x ⁽⁰⁾update equation, separate this equation and both can obtain Δ x ⁽⁰⁾.Use formula x=x ⁽⁰⁾+ Δ x ⁽⁰⁾revise initial value x ⁽⁰⁾can obtain new initial value x ⁽¹⁾, then obtain new correction amount x ⁽¹⁾, so iterate down, until meet convergence criterion, obtain the numerical solution of full scale equation.

(3) calculation procedure of Newton-Raphson method

When trend is calculated, first to input the initial data of network and the set-point of each node and form node admittance matrix.Based on voltage vector

in iterative process, the real part of k minor node magnitude of voltage is designated as e ^(k), the imaginary part of k minor node magnitude of voltage is designated as f ^(k), the initial value e of input node voltage value ⁽⁰⁾and f ⁽⁰⁾(what indexing did not represent is the vector of the magnitude of voltage composition of all nodes), puts iteration count k=0.Then start to carry out iteration, iterative process is as follows:

1) the node voltage value e calculating by last (the k-1 time) iteration ^(k)and f ^(k)(when k=0, be given initial value e ⁽⁰⁾and f ⁽⁰⁾), calculate current (the k time) each node amount of unbalance of (comprising substation bus bar and switching station bus)

with

wherein

be the amount of unbalance of i node active power,

be the amount of unbalance of i node reactive power,

it is the amount of unbalance of i node voltage square.

2) press condition verification convergence below,

$\max \left\{\right|{\mathrm{\&Delta;P}}_i^{\left(k\right)},{\mathrm{\&Delta;Q}}_i^{\left(k\right)},{\mathrm{\&Delta;V}}_i^{2\left(k\right)}\left|\right\}<\mathrm{\&epsiv;}---\left(2.8\right)$

If convergence, iteration leaves it at that, and proceeds to the power that calculates each Line Flow and balance node, and prints out result of calculation.Do not restrain and continue to calculate.ε is predetermined threshold value, and enough little amount is set while specifically implementing.

3) each element of calculating Jacobian matrix, writes update equation for row, and concrete calculating belongs to prior art.

4) according to Jacobean matrix array, write update equation, ask the correction of node voltage value

with specific implementation belongs to prior art.

5) revise the voltage of each node, wherein the voltage correction formula of i node is as follows

$e_i^{(k+1)}=e_i^{\left(k\right)}+{\mathrm{\&Delta;e}}_i^{\left(k\right)},f_i^{(k+1)}=f_i^{\left(k\right)}+{\mathrm{\&Delta;f}}_i^{\left(k\right)}---\left(2.9\right)$

6) iterative computation adds 1, returns to 1) continuation iterative process.

After iteration finishes, the power that also will calculate in power and the network of balance node distributes (as table 4).Balance node voltage in iterative process remains unchanged, and is the node that a voltage remains unchanged.

As used

represent that i node is to circuit electric current I between j node _ijgrip altogether, the computing formula of transmission line power is as follows:

$S_{\mathrm{ij}}=P_{\mathrm{ij}}+j{Q}_{\mathrm{ij}}={\stackrel{\&CenterDot;}{V}}_i{\hat{I}}_{\mathrm{ij}}=V_i^2{\hat{y}}_{i0}+{\stackrel{\&CenterDot;}{V}}_i({\stackrel{\&CenterDot;}{V}}_i-{\stackrel{\&CenterDot;}{V}}_j){\hat{y}}_{\mathrm{ij}}---\left(2.10\right)$

S _ij: i node is to the apparent power of circuit between j node

P _ij: i node is to the active power of circuit between j node

Q _ij: i node is to the reactive power of circuit between j node

the voltage phasor of i node

the admittance over the ground of i node

the voltage phasor of j node

i node is to the admittance of circuit between j node

The value of i is 1,2 ..., n, the value of j is 1,2 ..., n, i ≠ j, n is node sum.

Step 3, in step 2, trend is calculated on the basis of acquired results, carries out trend tracking, determines distribution condition and switching station the draw situation to transformer station 10 kV outgoing line power of each transformer station 10 kV outgoing line power in switching station in ring type supply medium voltage distribution network.

The calculation of tidal current of embodiment based on step 2, by the power loss equivalence of circuit, in the load at circuit two ends, ring network is treated to lossless network, and trend tracking results is as shown in table 5.

The power division (MW) of table 5 transformer station 10 kV outgoing line to load

The power draw situation of switching station and the power division situation of transformer station as known from Table 5.As switching station 2 draws 5.4747MW active power and 2.1253MW active power from circuit 2 and transformer station 2 respectively, the total power that has drawing is 7.6MW, equal switching station with total active power; The power division of circuit e is 0.0362MW to the active power of switching station 1, and the active power of switching station 5 is 7.0648MW, and the active power of switching station 6 is 0.8979MW, and the off line power of transformer station is all distributed to switching station load; Other switching stations draw power and transformer station distributes power to be shown in Table 5.

The present invention further provides trend and followed the tracks of implementation method, comprised following sub-step:

1) according to step 2, calculate the trend result of gained normal condition system, form lossless network;

2) based on lossless network, form downstream distribution matrix A, node active power matrix P _lLwith the total power matrix P that gains merit that injects of node _tT;

3) calculate the inverse matrix of downstream distribution matrix A, and calculate the load of switching station to the power draw coefficient matrix K of branch road _l=P _lL(P _tTa ^t) ^-1;

4) establishing certain switching station is i node, between s node and t node, connects and composes branch road s-t, the draw P of the load of i node of calculating to line power _li-st=k _litP _st;

Wherein, P _li-stthe load that refers to i node draws the active power of branch road s-t, K _l=(k _lit) _{n × n}element k _litrefer to that the load of i node is to the distribution coefficient matrix of branch road s-t, P _strefer to the active power of branch road s-t.

For the sake of ease of implementation, provide and carry out the relevant of trend tracking and be described as follows,

(3.1) the concrete mode of setting up downstream distribution matrix is:

By research object equivalence, be lossless network, based on calculation of tidal current, set up internodal downstream distribution matrix A=(a _ij) _{n × n}

I node can be designated as circuit i-j to circuit between j node.

In formula, remember P _ij(>=0) is the active power to j node transmission by i node-flow, P _tjbe total injection active power of j node.

The information such as the size that between node, downstream distribution matrix has comprised internodal connecting relation, the branch road active power flow direction and node injecting power.

(3.2) setting up the load of switching station and the trend of circuit follows the tracks of the concrete mode of analytic modell analytical model and is:

Switching station load closes drawing of transformer station 10 kV outgoing line power

P _Li-st＝K _LP _st (3.2)

If i node is load bus, in network, has between s node and t node and connect and compose branch road s-t.

Wherein P _li-stthe load that refers to i node draws the active power of branch road s-t, K _l=(k _lit) _{n × n}element k _litthe distribution coefficient of the load that refers to i node to branch road s-t, P _strefer to the active power of branch road s-t.In embodiment, having the node of load is switching station.

Switching station load draws coefficient matrix K to line power _l=(k _lit) _{n × n}for

K _L＝P _LL(P _TTA ^T) ^-1 (3.3)

P _LL＝diag(P _L1，P _L2，…P _Ln) (3.4)

P _TT＝diag(P _T1，P _T2，…P _Tn) (3.5)

Wherein P _lithe active power of i node, P _lLthe node active power matrix of n × n dimension, wherein P _l1, P _l2... P _lnrespectively the 1st, 2 ..., the active power of n node; P _titotal injection active power of i node, P _tTtotal gain merit power matrix, the wherein P of injecting of node of n × n dimension _t1, P _t2... P _tnrespectively the 1st, 2 ..., total injection active power of n node, n is node sum; Formula (3.2) reflects the qualitative relationships between switching station load and line power, i.e. the draw situation of switching station load power demand to each line power and each line power distribution condition in each switching station.Switching station i to the active power of branch road s-t draw into

P _Li-st＝k _LitP _st (3.6)

Step 4, take trend calculating acquired results and step 3 gained trend tracking results in step 2 as initial point, within the scope of switching station load capacity, adopt monte carlo method to determine that in ring network, many groups of loads of switching station distribute, the load distribution situation of each group switching station is carried out respectively to trend calculating and trend tracking, obtain many group trend tracking results, and the leading switching station of definite transformer station 10 kV outgoing line power.

Leading switching station is on a certain some larger switching stations of circuit active power impact.Can be based on tidal current analysis result, utilize trend to follow the tracks of theoretical, determine the situation of drawing that the distribution condition of ring-like each transformer station 10 kV outgoing line power in switching station load and switching station are loaded to transformer station 10 kV outgoing line.As initial point, adopt the switching station load parameter perturbation method of Monte Carlo to determine the leading switching station of transformer station 10 kV outgoing line power.Monte carlo method is prior art, and it will not go into details in the present invention.

The leading switching station of embodiment gained transformer station 10 kV outgoing line power is as shown in table 6.

The leading switching station of table 6 transformer station outlet

Bus	Bus	Numbering	Leading switching station
				Transformer station 1	Switching station 1	a	1236
Transformer station 1	Switching station 2	b	123
				Transformer station 1	Switching station 3	c	1234
Transformer station 2	Switching station 4	d	23456
				Transformer station 2	Switching station 5	e	456
Transformer station 2	Switching station 6	f	12456

Step 5, in step 4, gained is organized on the basis of trend tracking results more, sets up the multivariate nonlinear regression analysis model between transformer station 10 kV outgoing line power and leading switching station.Embodiment, based on trend tracking results, obtains the multivariate nonlinear regression analysis model between each transformer station 10 kV outgoing line and leading switching station by least-squares estimation matching, because the precision of quadratic polynomial is enough high, therefore adopts quadratic polynomial.

(5.1) establishing certain switching station is i node, is designated as switching station i, and switching station i load is followed the tracks of nonlinear curve model to the trend of drawing power of circuit l and is

$P_{l-\mathrm{Li}}=a_0+a_1{P}_{\mathrm{Li}}+a_2{P}_{\mathrm{Li}}^2+...+a_t{P}_{\mathrm{Li}}^t---\left(5.1\right)$

P in formula _l-Lithe power drawing from circuit l for switching station i; P _lifor the load of switching station i; a ₀, a ₁... a _tfor regression coefficient; T is the number of times of trend aircraft pursuit course.The value of L can be 1,2 ... L, L is circuit sum, the present embodiment, for ease of difference node, is a by the value of the label l of circuit, b, c, d, e, f.

(5.2) load of switching station i is followed the tracks of nonlinear curve model to the polynary trend of drawing power of circuit l

The load of switching station i is not only relevant with place load own to the power draw of circuit l, to other switching stations with load also relevant, switching station i loads relevant to all switching stations to the power draw of circuit l and has a non-linear relation:

$P_{l-\mathrm{Li}}=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(a_{\mathrm{ik}1}{P}_{\mathrm{Lk}1}+a_{\mathrm{ik}2}{P}_{\mathrm{Li}2}+...+a_{\mathrm{ikt}}{P}_{\mathrm{Lit}})+a_0---\left(5.2\right)$

In formula, m is switching station quantity,

for k is with the t power of loading with lotus, a _ikj, j={1,2 ..., t} represents that switching station i load is to P in the polynary trend tracking nonlinear curve model that draws power of circuit l _litthe coefficient of item, a ₀for constant term coefficient, k represents k load of ring-like electrical network, and in embodiment, load is all that switching station provides, and therefore the value of k is 1,2 ... m.

(5.3) multivariate nonlinear regression analysis model of line power and leading switching station

From trend, follow the tracks of theory, the power of circuit l is all distributed to leading switching station simultaneously, and the power of circuit l is

$P_{\mathrm{Pl}}=\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{P}_{l-\mathrm{Lf}}=\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}(\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(a_{\mathrm{fk}1}{P}_{\mathrm{Lk}1}+a_{\mathrm{fk}2}{P}_{\mathrm{Lf}2}+...+a_{\mathrm{fkt}}{P}_{\mathrm{Lft}})+a_0)$

$=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(P_{\mathrm{Lk}1}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fk}1}+P_{\mathrm{Lf}2}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fk}2}+...+...P_{\mathrm{Lft}}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fkt}})+{\hat{a}}_0---\left(5.3\right)$

$=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{\hat{a}}_{k1}{P}_{\mathrm{Lk}1}+{\hat{a}}_{k2}{P}_{\mathrm{Lk}2}+...+{\hat{a}}_{\mathrm{kt}}{P}_{\mathrm{Lkt}}+{\hat{a}}_0$

Wherein, P _l-Lfbe f the power that leading switching station draws from circuit l, n _ztake the quantity of switching station as the leading factor,

for the estimator of constant term coefficient,

j={1,2 ..., the estimator that t} is regression coefficient.A _ikj, j={1,2 ..., t}, P _lktimplication is with 5.2 formulas.

The specific implementation of embodiment is as follows:

The target function of tradition net capability is switching station load sum maximum in network, is shown below,

$\mathrm{MLSC}=\underset{i}{\mathrm{\&Sigma;}}{P}_{\mathrm{Li}}$

For the ring type supply power distribution network shown in example, non-transformer in system, (if contain power supply, node processing is to send the load of power), the power sum of the off line power of transformer station and transformer station 10 kV outgoing line equals switching station load sum, is shown below.

P _a+P _b+P _c+P _d+P _e+P _f＝P _L2+P _L3+P _L4+P _L5+P _L6+P _L7

The ring-like system shown in example is not in the situation that considering via net loss, its net capability can be equivalent to the net capability of transformer station 10 kV outgoing line, the net capability that is ring-like power distribution network is converted into the target function take transformer station 10 kV outgoing line as variable, is shown below.

$\mathrm{MLSC}=\underset{i}{\mathrm{\&Sigma;}}{P}_{\mathrm{Li}}=\underset{l}{\mathrm{\&Sigma;}}{P}_{\mathrm{Pl}}(l=a,b,c,d,e,f)$

In step 5, obtained the multivariate regression models of each transformer station 10 kV outgoing line and leading switching station:

$P_{\mathrm{Pl}}=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{\hat{a}}_{k1}{P}_{\mathrm{Lk}1}+{\hat{a}}_{k2}{P}_{\mathrm{Lk}2}+...+{\hat{a}}_{\mathrm{kt}}{P}_{\mathrm{Lkt}}+{\hat{a}}_0(l=a,b,c,d,e,f)$

The multivariate regression models coefficient of transformer station 10 kV outgoing line and leading switching station is as shown in table 7:

The multivariate regression models parameter of table 7 circuit a and leading switching station

The multivariate regression models that is circuit a and leading switching station is shown below

$P_{\mathrm{Pa}}={0.4227P}_{L1}+{0.0044P}_{L1}^2+{0.2164P}_{L2}-{0.0112P}_{L2}^2+{0.0847P}_{L3}+$

${0.0186P}_{L3}^2+{0.1656P}_{L6}+{0.0082P}_{L6}^2$

In like manner, can obtain other 5 10kV transformer stations outlets and the corresponding multivariate regression models of dominating switching station

The multivariate regression models parameter of table 8 circuit b and leading switching station

The multivariate regression models that is circuit b and leading switching station is shown below

$P_{\mathrm{Pb}}={0.1609P}_{L1}-{0.0051P}_{L1}^2+{0.3270P}_{L2}+{0.0060P}_{L2}^2+{0.1252P}_{L3}-$

${0.0106P}_{L3}^2$

The multivariate regression models parameter of table 9 circuit c and leading switching station

The multivariate regression models that is circuit c and leading switching station is shown below

$P_{\mathrm{Pc}}={0.1170P}_{L1}+{0.0040P}_{L1}^2+{0.2286P}_{L2}-{0.0123P}_{L2}^2+{0.5034P}_{L3}+$

${0.0064P}_{L3}^2+{0.1734P}_{L3}-{0.0072P}_{L4}^2$

The multivariate regression models parameter of table 10 circuit d and leading switching station

The multivariate regression models that is circuit d and leading switching station is shown below

$P_{\mathrm{Pd}}={0.0809P}_{L2}-{0.0080P}_{L2}^2+{0.1545P}_{L3}+{0.0068P}_{L3}^2+{0.4517P}_{L4}+$

${0.0025P}_{L4}^2+0.2107P_{L5}+0.0021P_{L5}^2+0.0844P_{L6}-{0.0844}_{L6}^2$

The multivariate regression models parameter of table 11 circuit e and leading switching station

The multivariate regression models that is circuit e and leading switching station is shown below

$P_{\mathrm{Pe}}=0.2134P_{L4}-0.2145P_{L4}^2+0.4662P_{L5}-{0.0023P}_{L5}^2+0.1651P_{L6}+$

${0.0074P}_{L6}^2$

The multivariate regression models parameter of table 12 circuit f and leading switching station

The multivariate regression models that is circuit f and leading switching station is shown below

$P_{\mathrm{Pf}}=0.1721P_{L1}-0.0316P_{L1}^2+0.0915P_{L2}+0.0052P_{L2}^2+0.0701P_{L4}-$

$0.0066P_{L4}^2+0.1384P_{L5}-0.0025P_{L5}^2+0.4515P_{L6}-0.0065P_{L6}^2$

Step 6, based on step 5 gained multivariate nonlinear regression analysis model, set up the net capability model of ring type supply medium voltage distribution network:

Ring-like power distribution network also needs to meet trend balance, describes by the relation between node current I and node voltage V, that is:

I＝YV

Wherein, Y is node admittance matrix.Herein, node current I and node voltage V are current matrix and the voltage matrix of all n node.

Consider the thermally-stabilised requirement of " N-1 " power reguirements and the circuit of electrical network, the power upper limit of branch road is thought of as the half of the thermally-stabilised power-carrying of circuit simultaneously, is multiplied by a correction factor re simultaneously; Lower limit is considered the Economic load rate of circuit.Be shown below

$\left\{\begin{array}{c}{P}_{i\min }\&le;P_i\&le;P_{i\max }\\ P_{i\min }=P_E\\ P_{i\max }=\mathrm{re}\frac{1}{2}{P}_H\end{array}\right.$

Wherein P _ethe power that circuit Economic load rate is corresponding, P _hit is the thermally-stabilised limit of circuit.

For the switching station in actual power distribution network, due to the difference of specification capacity and region that each switching station supplies load, switching station with load satisfy condition and be shown below:

P _Limin≤P _Li≤P _Limax

Wherein P _lirefer to the burden with power of i node, P _liminand P _limaxrefer to the upper and lower bound of the burden with power of i node.The voltage of i node meets the bound constraint of node voltage,

U _imin≤U _i≤U _imax

Therefore by the above various model that has formed ring-like power distribution network net capability suc as formula shown in (6.1):

$\max \mathrm{MLSC}=\underset{i}{\mathrm{\&Sigma;}}{P}_{\mathrm{Li}}=\underset{l}{\mathrm{\&Sigma;}}{P}_{\mathrm{Pl}}$

$s.t.\left\{\begin{array}{c}{P}_i=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_{k1}{P}_{\mathrm{Lk}1}+a_{k2}{P}_{\mathrm{Lk}2}+...+a_{\mathrm{kt}}{P}_{\mathrm{Lkt}}\\ I=\mathrm{YV}\\ P_{\mathrm{Li}\min }\&le;P_{\mathrm{Li}}\&le;P_{\mathrm{Li}\max }\\ P_{i\min }\&le;P_i\&le;P_{i\max }\\ U_{i\min }\&le;U_i\&le;U_{i\max }\end{array}\right.---\left(6.1\right)$

In formula: when i node is transformer station, meet P _imin≤ P _i≤ P _imax, P _imin, P _imaxbe actual active power and the bound thereof of i node (transformer station) 10kV outlet, establish the total A bar of relevant transformer station outlet;

U _i, U _imin, U _imaxbe busbar voltage and the bound thereof of i node, establish B altogether of busbar voltage to be investigated;

When i node is switching station, meet P _liminn≤ P _li≤ P _limax, P _li, P _limin, P _limaxfor i node (switching station) actual institute on-load and bound thereof, establish total C of the upper switching station of ring.

Step 7, solves the globally optimal solution of net capability model, obtains the net capability model of ring type supply medium voltage distribution network, obtains the net capability of ring type supply medium voltage distribution network according to net capability model.

Shown in formula (6.1), Solution of Nonlinear Optimal Problem can be done following simplification, and equality constraint has been embodied in multivariate nonlinear regression analysis model, and inequality constraints in formula (6.1) is converted into simple inequality g _i(P _l)>=0, i ∈ I={1,2 ..., A+B+C},, wherein P _lfor node load vector, maximum public have can have following statement:

$\left\{\begin{array}{cc}\min & f\left(P_L\right)=-1*f_{\mathrm{MLSC}}\left(P_L\right)=-1*\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}{P}_L,\\ s.t.& g_i\left(P_L\right)\&GreaterEqual;0,i\&Element;I=\{\mathrm{1,2},...,A+B+C\},\end{array}\right.$

Can adopt newton--Lagrange, SQP, trusted zones, the methods such as intelligent algorithm solve the globally optimal solution of net capability model.Embodiment adopts based on Sequential Quadratic Programming method and asks the maximum of the corresponding ring type supply medium voltage distribution network of formula (6.1) for the optimal solution of electric model, can Fast Convergent.Based on sequential quadratic programming method, solve this model below.

At set point (P _{l (k)}, μ _k) (μ represents Lagrange multiplier, and k represents iteration, P the k time _{l (k)}represent the P of the k time iteration _l, μ _krepresent the Lagrange multiplier of the k time iteration) afterwards, by constraint function linearisation, and it is approximate that Lagrangian is carried out to quadratic polynomial, obtains the quadratic programming subproblem of following form:

$\min \frac{1}{2}{d}^T{B}_{k}d+\&dtri;f{\left(P_{L\left(k\right)}\right)}^{T}d=\frac{1}{2}{d}^T{B}_{k}d+I^T*d$

s.t.g(P _L(k))+A _kd≥0

Wherein, I=-1*[1,1 ..., 1] ^t,

b _klagrangianL (P _{l (k)}, μ _k) extra large gloomy matrix approximate, d is cost function φ (P _l, μ, σ) descent direction, σ is penalty factor.

Adopt augmentation Lagrange cost function φ (x, v, r) to improve superlinear convergence step acceptance, overcome Maratos effect, expression formula is as follows:

$\mathrm{\&phi;}(P_L,v,r)=f\left(P_L\right)-\underset{j\&Element;J(P_L,\mathrm{\&mu;})}{\mathrm{\&Sigma;}}({\mathrm{\&mu;}}_j{g}_j\left(P_L\right)-\frac{1}{2}{\mathrm{\&sigma;}}_j{g}_j^2\left(P_L\right))$

Wherein:

J(P _L，μ)＝{j∈I|g _j(P _L)≤μ _j/σ _j}。

As long as guarantee $\mathrm{\&sigma;}\&GreaterEqual;\left[\frac{-{\left(d_k^y\right)}^T{A}_k{W}_k{Z}_k{d}_k^z-h{\left(P_{L\left(k\right)}\right)}^T\&dtri;\mathrm{\&mu;}{\left(P_{L\left(k\right)}\right)}^T{d}_k}{{\left|\right|g\left(P_{L\left(k\right)}\right)\left|\right|}^2}\right]+\stackrel{\&OverBar;}{\mathrm{\&delta;}},$ D _kbe cost function φ (P _li, μ, σ) descent direction.

Wherein, Z _kcolumn vector be kernel N (A _k) one group of base,

for g (P _{l (k)}) to P _{l (k)}jacobian matrix, d _ky to component

w _kfor LagrangianL (P _{l (k)}, μ _k) extra large gloomy matrix.

In sum, summary algorithm steps is as follows:

Step 0: given initial point (x ₀, μ ₀) ∈ R ⁿ× R ^n+m+l, symmetric positive definite matrix B ₀∈ R ^{n × n}.Calculate

$A_0=\&dtri;g{\left(P_{L\left(0\right)}\right)}^T$

Select parameter η ∈ (0,0.5), ρ ∈ (0,1), admissible error 0≤ε ₁, ε ₂≤ 1, make k:=0.

Step 1: solve subproblem

$\min \frac{1}{2}{d}^T{B}_{k}d+\&dtri;f{\left(P_{L\left(k\right)}\right)}^{T}d$

s.t.g(P _L(k))+A _kd≥0

Obtain optimal solution d _k.

Step 2: if || d _k|| ₁≤ ε ₁, and || (g _k)-|| ₁≤ ε ₂, stop calculating, obtain an approximate KT point (P of former problem _lk, μ _k).

Step 3: for cost function φ (P _{l (k)}, σ), select penalty function σ _k, make d _kthat this function is at x _kthe descent direction at place.

Step 4: adopt existing Armijio searching method, way of search is, makes m _kthe minimum nonnegative integer m that following inequality is set up:

φ(P _L(k)+ρ ^md _k，σ _k)-φ(P _L(k)，σ _k)≤ηρ ^mφ′(x _k，σ；d _k)

Make step factor

p _{l (k+1)}:=P _{l (k)}+ α _kd _k.

Step 5: calculate the Jacobian matrix after the k+1 time iteration:

$A_{k+1}=\&dtri;f{\left(x_{k+1}\right)}^T$

And least square multiplier ${\mathrm{\&mu;}}_{k+1}={\left[A_{k+1}{A}_{k+1}^T\right]}^{-1}{A}_{k+1}\&dtri;f_{k+1}$

Step 6: correction matrix B _kfor B _k+1, order

s _k＝P _L(k+1)-P _L(k)＝α _kd _k， $y_k={\&dtri;}_{x}L(P_{L(k+1)},{\mathrm{\&mu;}}_{k+1},{\mathrm{\&lambda;}}_{k+1})-{\&dtri;}_{x}L(P_{L\left(k\right)},{\mathrm{\&mu;}}_{k+1},{\mathrm{\&lambda;}}_{k+1}),$

$B_{k+1}=B_k-\frac{B_k{s}_k{s}_k^T{B}_k}{s_k^T{B}_k{s}_k}+\frac{z_k{z}_k^T}{s_k^T{z}_k}$

Wherein, s _kbe the step-size in search of k step, y _kfor Jacobian matrix increment, z _k=θ _ky _k+ (1-θ _k) B _ks _kfor B _kthe modifying factor of matrix.

Parameter θ _kbe defined as

Step 7: make k:=k+1, turn step 1.

Embodiment writes SQP method calculation procedure according to above step, and its result is as shown in (7.1):

MLSC＝44.37MW (7.1)

Now each switching station with load and the power of transformer station 10 kV outgoing line respectively if table (13) is with as shown in table (14).

During the maximum power supply of table 13 switching station with load

Switching station	Active power (MW)	Switching station	Active power (MW)
				Switching station 1	10	Switching station 3	6.77
Switching station 2	4.22	Switching station 3	7.62

Switching station 2

6.77

Switching station 3

8.99

The power of transformer station's outlet during the maximum power supply of table 14

Circuit	Active power (MW)	Circuit	Active power (MW)
				Circuit a	8.00	Circuit d	7.38
Circuit b	5.05	Circuit e	8.00
				Circuit c	0.0800	Circuit f	0.0800

To sum up, the example system providing take Fig. 2 is example, describes the computational process of the net capability of the ring type supply medium voltage distribution network based on multivariate nonlinear regression analysis model in detail.From numerical results, the present invention can solve the net capability model of ring type supply power distribution network, and theory of algorithm is solid, can draw the globally optimal solution of target function.Can cross simultaneously and draw at network and in net capability state be, corresponding switching station load and the power situation of transformer station 10 kV outgoing line, can provide effective suggestion for the optimization of urban distribution network and planning.

Applied specific case herein principle of the present invention and way of example are set forth, the explanation of above embodiment is just for helping to understand method of the present invention and core concept thereof; , for one of ordinary skill in the art, according to thought of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention meanwhile.

Claims (6)

1. a net capability appraisal procedure for ring type supply medium voltage distribution network, described ring type supply medium voltage distribution network comprises the ring network that transformer station and multiple switching station connect and compose, and it is characterized in that, comprises the following steps:

Step 1, the basic data of input ring type supply medium voltage distribution network;

Step 2, according to basic data described in step 1, carries out the trend of ring type supply medium voltage distribution network and calculates;

Step 3, in step 2, trend is calculated on the basis of acquired results, carries out trend tracking, determines distribution condition and switching station the draw situation to transformer station 10 kV outgoing line power of each transformer station 10 kV outgoing line power in switching station in ring type supply medium voltage distribution network;

Step 4, take trend calculating acquired results and step 3 gained trend tracking results in step 2 as initial point, within the scope of switching station load capacity, adopt monte carlo method to determine that in ring network, many groups of loads of switching station distribute, the load distribution situation of each group switching station is carried out respectively to trend calculating and trend tracking, obtain many group trend tracking results, and the leading switching station of definite transformer station 10 kV outgoing line power;

Step 5, in step 4, gained is organized on the basis of trend tracking results more, sets up the multivariate nonlinear regression analysis model between transformer station 10 kV outgoing line power and leading switching station;

Step 6, based on step 5 gained multivariate nonlinear regression analysis model, sets up the net capability model of ring type supply medium voltage distribution network;

Step 7, solves the globally optimal solution of net capability model, obtains the net capability model of ring type supply medium voltage distribution network, obtains the net capability of ring type supply medium voltage distribution network according to net capability model.

2. the net capability appraisal procedure of ring type supply medium voltage distribution network according to claim 1, is characterized in that: in step 2, the trend that adopts Newton-Raphson method to carry out ring type supply medium voltage distribution network is calculated, and concrete mode is as follows,

First iterative computation node voltage value, establishing current is the k time iteration, k=0, carries out following steps,

1) the node voltage value e calculating by the k-1 time iteration ^(k)and f ^(k), calculate the amount of unbalance Δ P of current each node _i ^(k), Δ Q _i ^(k)with Δ V _i ^{2 (k)}, wherein Δ P _i ^(k)be the amount of unbalance of i node active power, Δ Q _i ^(k)be the amount of unbalance of i node reactive power, Δ V _i ^{2 (k)}it is the amount of unbalance of i node voltage square; When k=0, the node voltage value e that the k-1 time iteration calculates ^(k)and f ^(k)directly adopt the initial value e of the node voltage value of input ⁽⁰⁾and f ⁽⁰⁾;

2) press condition verification convergence below,

max{|ΔP _i ^(k),ΔQ _i ^(k),ΔV _i ^2(k)|}＜ε

If satisfied condition, iteration leaves it at that, and does not meet and continues to calculate, and ε is predetermined threshold value;

3) each element of calculating Jacobian matrix;

4) according to Jacobean matrix array, write update equation, ask the correction amount e of node voltage value _i ^(k)with Δ f _i ^(k);

5) revise each node voltage value, wherein the voltage correction formula of i node is as follows

e _i ^(k+1)＝e _i ^(k)+Δe _i ^(k),f _i ^(k+1)＝f _i ^(k)+Δf _i ^(k)

6) iterations k=k+1, returns to 1) continuation iterative process;

After iteration finishes, the power in power and the network of calculated equilibrium node distributes, and establishes use represent that i node is to circuit electric current I between j node _ijgrip altogether, the computing formula of transmission line power is as follows:

$S_{\mathrm{ij}}=P_{\mathrm{ij}}+{\mathrm{jQ}}_{\mathrm{ij}}={\stackrel{\&CenterDot;}{V}}_i{\hat{I}}_{\mathrm{ij}}={V_i}^2\widehat{y_{i0}}+{\stackrel{\&CenterDot;}{V}}_i({\stackrel{\&CenterDot;}{V}}_i-{\stackrel{\&CenterDot;}{V}}_j){\hat{y}}_{\mathrm{ij}}$

Wherein, S _ijbe the apparent power of i node to circuit between j node, P _ijbe the active power of i node to circuit between j node, Q _ijbe the reactive power of i node to circuit between j node, be the voltage phasor of i node,

be the admittance over the ground of i node,

be the voltage phasor of j node,

be the admittance of i node to circuit between j node; The value of i is 1,2 ..., n, the value of j is 1,2 ..., n, i ≠ j, n is node sum.

3. the net capability appraisal procedure of ring type supply medium voltage distribution network according to claim 2, is characterized in that: in step 3, the concrete mode of carrying out trend tracking is as follows,

1) according to step 2, calculate the trend result of gained normal condition system, form lossless network;

2) based on lossless network, form downstream distribution matrix A, node active power matrix P _lLwith the total power matrix P that gains merit that injects of node _tT;

Downstream distribution matrix A=(a _ij) _{n × n}, wherein matrix element a _ijcomputing formula as follows,

Wherein, P _ijfor the active power that circuit i-j is transmitted to j node by i node-flow, P _tjbe total injection active power of j node;

P _LL＝diag(P _L1,P _L2,…P _Ln)

Wherein, P _l1, P _l2... P _lnrespectively the 1st, 2 ..., the active power of n node;

P _TT＝diag(P _T1,P _T2,…P _Tn)

Wherein, P _t1, P _t2... P _tnrespectively the 1st, 2 ..., total injection active power of n node;

3) calculate the inverse matrix of downstream distribution matrix A, and calculate the load of switching station to the power draw coefficient matrix K of branch road _l=P _lL(P _tTa ^t) ^-1;

4) establishing certain switching station is i node, between s node and t node, connects and composes branch road s-t, the draw P of the load of i node of calculating to line power _li-st=k _litp _st;

Wherein, P _li-stthe load that refers to i node draws the active power of branch road s-t, K _l=(k _lit) _{n × n}element k _litrefer to that the load of i node is to the distribution coefficient matrix of branch road s-t, P _strefer to the active power of branch road s-t.

4. the net capability appraisal procedure of ring type supply medium voltage distribution network according to claim 3, is characterized in that: in step 5, the concrete mode of setting up the multivariate nonlinear regression analysis model between transformer station 10 kV outgoing line power and leading switching station is as follows,

(5.1) establishing certain switching station is i node, is designated as switching station i, and switching station i load is followed the tracks of nonlinear curve model to the trend of drawing power of circuit l and is

$P_{l-\mathrm{Li}}=a_0+a_1{P}_{\mathrm{Li}}+a_2{P}_{\mathrm{Li}}^2+...+a_t{P}_{\mathrm{Li}}^t$

Wherein, P _l-Lifor the power that switching station i draws from circuit l, P _lifor the load of switching station i, a ₀, a ₁... a _tfor regression coefficient, t is the number of times of trend aircraft pursuit course, and the value of l is 1,2 ... L, L is circuit sum;

(5.2) load of setting up switching station i is followed the tracks of nonlinear curve model to the polynary trend of drawing power of circuit l

$P_{l-\mathrm{Li}}=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(a_{\mathrm{ik}1}{P}_{\mathrm{Lk}1}+a_{\mathrm{ik}2}{P}_{\mathrm{Lk}2}+...+a_{\mathrm{ikt}}{P}_{\mathrm{Lkt}})+a_0$

Wherein, m is switching station sum, for the j power of the load of switching station k, the value of k is 1,2 ... m; a _ikj, j={1,2 ..., t} represents the model P of the power that switching station i draws from circuit l _lktthe regression coefficient of item, a ₀for constant term coefficient;

(5.3) multivariate nonlinear regression analysis model of setting up line power and leading switching station is:

From trend, follow the tracks of theory, the power of circuit l is all distributed to leading switching station simultaneously, and the power of circuit l is

$\begin{array}{c}{P}_{\mathrm{Pl}}=\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{P}_{l-\mathrm{Lf}}=\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}(\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(a_{\mathrm{fk}1}{P}_{\mathrm{Lk}1}+a_{\mathrm{fk}2}{P}_{\mathrm{Lf}2}+...+a_{\mathrm{fkt}}{P}_{\mathrm{Lft}})+a_0)\\ =\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}(P_{\mathrm{Lk}1}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fk}1}+P_{\mathrm{Lf}2}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fk}2}+...+...P_{\mathrm{Lft}}\underset{f=1}{\overset{n_z}{\mathrm{\&Sigma;}}}{a}_{\mathrm{fkt}})+{\hat{a}}_0\\ =\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{\hat{a}}_{k1}{P}_{\mathrm{Lk}1}+{\hat{a}}_{k2}{P}_{\mathrm{Lk}2}+...+{\hat{a}}_{\mathrm{kt}}{P}_{\mathrm{Lkt}}+{\hat{a}}_0\end{array}$

Wherein, P _l-Lfbe f the power that leading switching station draws from circuit l, n _ztake the quantity of switching station as the leading factor,

for the estimator of constant term coefficient,

for the estimator of regression coefficient.

5. the net capability appraisal procedure of ring type supply medium voltage distribution network according to claim 4, is characterized in that: in step 6, the net capability model of setting up ring type supply medium voltage distribution network is as follows,

$\begin{array}{cc}\max & \mathrm{MLSC}=\underset{i}{\mathrm{\&Sigma;}}{P}_{\mathrm{Li}}=\underset{l}{\mathrm{\&Sigma;}}{P}_{\mathrm{Pl}}\end{array}$

$s.t.\left\{\begin{array}{c}{P}_i=\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_{k1}{P}_{\mathrm{Lk}1}+a_{k2}{P}_{\mathrm{Lk}2}+...+a_{\mathrm{kt}}{P}_{\mathrm{Lkt}}\\ I=\mathrm{YV}\\ P_{\mathrm{Li}\min }\&le;P_{\mathrm{Li}}\&le;P_{\mathrm{Li}\max }\\ P_{i\min }\&le;P_i\&le;P_{i\max }\\ U_{i\min }\&le;U_i\&le;U_{i\max }\end{array}\right.$

Wherein, P _libe the active power of i node, the value of i is 1,2 ..., n; P _plfor the power of circuit l, the value of l is 1,2 ... L, L is circuit sum;

When i node is transformer station, meet P _imin≤ P _i≤ P _imax, P _i, P _imax, P _iminbe the actual active power of 10kV outlet and the bound thereof of i node, this node is transformer station, regression coefficient a _kjadopt step 5 gained estimator

u _i, U _imax, U _iminbe busbar voltage and the bound thereof of i node; When i node is switching station, meet P _limin≤ P _li≤ P _limax, P _li, P _limax, P _liminfor actual institute's on-load and the bound thereof of i node; Node current I and node voltage V meet I=YV, and Y is node admittance matrix.

6. the net capability appraisal procedure of ring type supply medium voltage distribution network according to claim 5, is characterized in that: in step 7, solve the globally optimal solution of net capability model based on sequential quadratic programming method.