CN105528530A - Method for calculating and analyzing three-phase power flow in distribution network - Google Patents

Abstract

The invention relates to a method for calculating and analyzing a three-phase power flow in a distribution network and solves the defect that distribution network three-phase power flow calculation has an error in contrast to the prior art. The method comprises following steps: carrying out a preprocessing process; carrying out forward-derivation process calculation; carrying out back substitution process calculation; according to obtained load branch current in each load node voltage correction forward-derivation process, iterating for forward derivation and back substitution calculation until each node voltage difference of adjacent two iterations is less than a convergence threshold. The method has more accurate calculation results and more complete consideration factors.

Description

Power distribution network three-phase power flow analytical approach

Technical field

The present invention relates to system for distribution network of power computing technique field, specifically power distribution network three-phase power flow analytical approach.

Background technology

The current power distribution automation SCADA system in China's urban and rural power grids enforcement is compared with dispatching automation SCADA system, the gauge point of system is the low-pressure side of substation transformer and the headend node of feeder line, and on main line and branched line not or have a small amount of gauge point (band remote measurement FTU).Therefore in order to provide the real-time running state of electrical network to operations staff, Real-time Power Flow calculates has become ingredient indispensable in power distribution automation SCADA system.From the angle of electric power netting safe running, what be concerned about is not the stable problem that unbalanced power causes, but the problem of circuit overload and voltage out-of-limit.Therefore, Real-time Power Flow computational problem gets back to electric current, the voltage's distribiuting problem of asking electrical network.And as can be seen from the data that the power distribution automation SCADA system dropped into is measured, there is serious asymmetrical three-phase in distribution load.Therefore, distribution Real-time Power Flow calculates except considering the features such as the radial pattern of electric network composition, R/X ratio are comparatively large, the numerous network size of node branch road is huge

Outward, the asymmetric feature of three-phase load should also be considered.The power distribution network Three Phase Power Flow how developing a kind of practicality has become the technical matters being badly in need of solving.

Summary of the invention

The object of the invention is to there is the defect of error to solve power distribution network three-phase power flow in prior art, providing a kind of power distribution network three-phase power flow analytical approach to solve the problems referred to above.

To achieve these goals, technical scheme of the present invention is as follows:

Power distribution network three-phase power flow analytical approach, comprises the following steps:

Preprocessing process, sorts to branch road each in real-time network, obtains the out branch sequence of calculation, tries to achieve the circuit branch road associated by each branch road end-node and load branch circuit;

Push away process computation before carrying out, according to the complex power calculated load branch current of each phase load of load bus, to the front of trend until source point calculates the distribution of current of each branch road according to KCL theorem from each load branch circuit, obtain the three-phase current of source point;

Carry out backward steps calculating, by the three-phase current of source point, the three-phase voltage from source point to each load bus according to all nodes of KVL computing system;

By the load branch circuit electric current pushed through before each load bus voltage correction of trying to achieve in journey, iteration pushes away before carrying out and calculates, until each node voltage difference of adjacent twice iteration is all less than convergence threshold with back substitution.

Push away process computation before described carrying out to comprise the following steps:

If each node voltage initial value is supply voltage, and using 10kV line voltage U AB as reference phasor;

Calculate the active loss △ P of the distribution transforming transformer of each phase of a, b, c _iwith reactive loss △ Q _i, its computing formula is as follows:

${\mathrm{\ΔP}}_i=I_i^2\×R_i+U_i^2\×G_i,$

${\mathrm{\ΔQ}}_i=I_i^2\×X_i+U_i^2\×B_i,$

Wherein, I _ifor current value, R _ifor resistance value, U _ifor magnitude of voltage, G _ifor conductivity unshakable in one's determination, X _ifor winding leakage reactance, B _ifor susceptance rate unshakable in one's determination;

Calculated load branch road three-phase current;

Calculated the three-phase current of each branch road to power supply point by the branch road sequence of calculation by end load branch circuit, its computing formula is as follows:

$\left[\begin{array}{c}{I}_{A,k}\\ I_{B,k}\\ I_{C,k}\end{array}\right]=\underset{j\∈KN}{\Σ}\left[\begin{array}{c}{I}_A,\stackrel{\→}{j}\\ I_B,\stackrel{\→}{j}\\ I_C,\stackrel{\→}{j}\end{array}\right],$

Wherein: I _a,kfor the A phase current of branch road K, I _b,kfor the B phase current of branch road K, I _c,kfor the C phase current of branch road K, KN is all branch road collection be connected in branch road K end-node, for the branch road collection associated by branch road K end-node.

Described backward steps calculating of carrying out comprises the following steps:

By the impedance of each part of path 3 × 3 rank matrix Z _lrepresent, then

$Z_l=\left(\begin{array}{ccc}{z}_{aa}& z_{ab}& z_{ac}\\ z_{ba}& z_{bb}& z_{bc}\\ z_{cz}& z_{cb}& z_{cc}\end{array}\right),$

Wherein: z _aa, z _bband z _ccbe self-impedance; z _ab, z _ac, z _ba, z _bc, z _czand z _cbbe transimpedance;

By power branch, by all node voltages of backward computational grid of the sequence of calculation, its computing formula is as follows:

$\left[\begin{array}{c}{U}_{A,m}\\ U_{B,m}\\ U_{C,m}\end{array}\right]=\left[\begin{array}{c}{U}_{A,s}\\ U_{B,s}\\ U_{C,s}\end{array}\right]-Z_{lk}\×\left[\begin{array}{c}{I}_{A,k}\\ I_{B,k}\\ I_{C,k}\end{array}\right]$

Wherein: m is the minor details period of branch road k, s is the first node number of branch road k, Z _lkfor the three-phase impedance matrix of circuit k, I _a,k, I _b,kand I _c,kbe respectively the three-phase current of branch road k, U _a,sfor the first node voltage of A phase branch road k, U _b,sfor the first node voltage of B phase branch road k, U _c,sfor the first node voltage of C phase branch road k, U _a,mfor the end-node voltage of A phase branch road k, U _b,mfor the end-node voltage of B phase branch road k, U _c,mfor the end-node voltage of C phase branch road k.

Described calculated load branch road three-phase current comprises the following steps:

Calculate AB phase rated capacity S _aB, BC phase rated capacity S _bCwith CA phase rated capacity S _cA, its computing formula is as follows:

S _AB＝P _a+△P _a+w(Q _a+△Q _a)，

S _BC＝P _b+△P _b+w(Q _b+△Q _b)，

S _CA＝P _c+△P _c+w(Q _c+△Q _c)，

Wherein: P _afor A phase active power, P _bfor B phase active power, P _cfor C phase active power, △ P _afor the active loss of A phase, △ P _bfor the active loss of B phase, △ P _cfor the active loss of C phase, Q _afor A phase reactive power, Q _bfor B phase reactive power, Q _cfor C phase reactive power, △ Q _afor A phase reactive loss, △ Q _bfor B phase reactive loss, △ Q _cfor C phase reactive loss, w is design factor;

Calculate distribution transforming transformation winding current, its computing formula is as follows:

$\left[\begin{array}{c}{I}_{AB}\\ I_{BC}\\ I_{CA}\end{array}\right]=\left[\begin{array}{c}{S}_{AB}/U_{AB}\\ S_{BC}/U_{BC}\\ S_{CA}/U_{CA}\end{array}\right],$

Wherein: I _aBfor the line current of AB phase, I _bCfor the line current of BC phase, I _cAfor the line current of CA phase, U _aBfor the line voltage of AB phase, U _bCfor the line voltage of BC phase, U _cAfor the line voltage of CA phase;

Calculate distribution transforming high-pressure side load current, its computing formula is as follows:

$\left[\begin{array}{c}{I}_A\\ I_B\\ I_C\end{array}\right]=\left[\begin{array}{c}{I}_{AB}-I_{CA}\\ I_{BC}-I_{AB}\\ I_{CA}-I_{BC}\end{array}\right],$

Wherein: I _afor the line current of A phase, I _bfor the line current of B phase, I _cfor the line current of C phase.

Described convergence threshold ε is 0.001.

Beneficial effect

Power distribution network three-phase power flow analytical approach of the present invention, compared with prior art result of calculation is more accurate, and Consideration is more comprehensive.The present invention carries out iterative processing by front pushing away with back substitution two processes, and each iteration is all revised load current, after iterating and revising, show that more real electric network swim calculates data.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention;

Fig. 2 is three-phase feeder line illustraton of model in prior art;

Fig. 3 is the substation transformer structural drawing of distribution transforming branch road to be distribution transforming branch road be " Δ/Yo " wiring in prior art.

Embodiment

For making to have a better understanding and awareness architectural feature of the present invention and effect of reaching, coordinating detailed description in order to preferred embodiment and accompanying drawing, being described as follows:

As shown in Figure 2, the elementary cell of distribution network is feeder line, and Turbo codes and Load flow calculation can in units of feeder lines.Distribution transforming branch road in Fig. 2 is the substation transformer of " Δ/Yo " wiring, as shown in Figure 3.The head end of 10kV distribution line is loose node (is the node that guarantee Jacobi matrix is nonsingular and choose in Load flow calculation, and only has this node), i.e. the root node of tree network.In actual electrical power distribution automatization system, the head end of distribution line is transformer station 10kV bus, as the voltage source node of three-phase symmetrical in three-phase power flow.The gauge point that substation transformer low pressure is surveyed is positioned at low pressure parallel capacitor and the low-voltage load sys node top along direction of tide, and thus Load flow calculation no longer considers the impact of shnt capacitor, and namely substation transformer low pressure surveys the PQ node for asymmetrical three-phase.

As shown in Figure 1, distribution three-phase Real-time Power Flow computational problem can be described as the effective value of known network topological sum component parameters, the active power of each phase of substation transformer low-pressure side and reactive power, substation bus bar voltage, asks the voltage of each node of network and flows through the electric current of each branch road.If substation bus bar is the power supply node of three-phase symmetrical, substation transformer low-pressure side is load bus, substation transformer branch road is load branch circuit.

Power distribution network three-phase power flow analytical approach of the present invention, comprises the following steps:

The first step, preprocessing process.Utilize the mode of prior art, sort, obtain the out branch sequence of calculation to branch road each in real-time network, try to achieve the circuit branch road associated by each branch road end-node and load branch circuit, this computation process only triggers when switch changed position and once calculates.

Second step, pushes away process computation before carrying out.According to the complex power calculated load branch current of each phase load of load bus, to the front of trend until source point calculates the distribution of current of each branch road according to KCL theorem from each load branch circuit, obtain the three-phase current of source point.It specifically comprises the following steps:

(1) set each node voltage initial value as supply voltage, and using 10kV line voltage U AB as reference phasor.In later stage iterative process, then carry out the correction computing of electric current with the three-phase voltage calculated.

(2) the active loss △ P of the distribution transforming transformer of each phase of a, b, c is calculated _iwith reactive loss △ Q _i, its computing formula is as follows:

${\mathrm{\ΔP}}_i=I_i^2\×R_i+U_i^2\×G_i,$

${\mathrm{\ΔQ}}_i=I_i^2\×X_i+U_i^2\×B_i,$

Wherein, I _ifor current value, R _ifor resistance value, U _ifor magnitude of voltage, G _ifor conductivity unshakable in one's determination, X _ifor winding leakage reactance, B _ifor susceptance rate unshakable in one's determination.

Calculate △ P thus _a, △ Q _a, △ P _b, △ Q _b, △ P _c, △ Q _c.

(3) calculated load branch road three-phase current, its concrete steps are as follows:

A, calculating AB phase rated capacity S _aB, BC phase rated capacity S _bCwith CA phase rated capacity S _cA, its computing formula is as follows:

S _AB＝P _a+△P _a+w(Q _a+△Q _a)，

S _BC＝P _b+△P _b+w(Q _b+△Q _b)，

S _CA＝P _c+△P _c+w(Q _c+△Q _c)，

Wherein: P _afor A phase active power, P _bfor B phase active power, P _cfor C phase active power, △ P _afor the active loss of A phase, △ P _bfor the active loss of B phase, △ P _cfor the active loss of C phase, Q _afor A phase reactive power, Q _bfor B phase reactive power, Q _cfor C phase reactive power, △ Q _afor A phase reactive loss, △ Q _bfor B phase reactive loss, △ Q _cfor C phase reactive loss, w is design factor, and its value carries out value according to actual needs.

B, calculating distribution transforming transformation winding current, its computing formula is as follows:

$\left[\begin{array}{c}{I}_{AB}\\ I_{BC}\\ I_{CA}\end{array}\right]=\left[\begin{array}{c}{S}_{AB}/U_{AB}\\ S_{BC}/U_{BC}\\ S_{CA}/U_{CA}\end{array}\right],$

Wherein: I _aBfor the line current of AB phase, I _bCfor the line current of BC phase, I _cAfor the line current of CA phase, U _aBfor the line voltage of AB phase, U _bCfor the line voltage of BC phase, U _cAfor the line voltage of CA phase.

At this, the complex power of each winding in high-pressure side equals a, b, c three-phase complex power of low-pressure side measurement respectively, thus low-pressure side bearing power can be converted into high-pressure side load current.

C, calculating distribution transforming high-pressure side load current, its computing formula is as follows:

$\left[\begin{array}{c}{I}_A\\ I_B\\ I_C\end{array}\right]=\left[\begin{array}{c}{I}_{AB}-I_{CA}\\ I_{BC}-I_{AB}\\ I_{CA}-I_{BC}\end{array}\right],$

Wherein: I _afor the line current of A phase, I _bfor the line current of B phase, I _cfor the line current of C phase.

(4) calculated the three-phase current of each branch road to power supply point by the branch road sequence of calculation by end load branch circuit, for branch road K, its computing formula is as follows:

$\left[\begin{array}{c}{I}_{A,k}\\ I_{B,k}\\ I_{C,k}\end{array}\right]=\underset{j\∈KN}{\Σ}\left[\begin{array}{c}{I}_A,\stackrel{\→}{j}\\ I_B,\stackrel{\→}{j}\\ I_C,\stackrel{\→}{j}\end{array}\right]$

Wherein: I _a,kfor the A phase current of branch road K, I _b,kfor the B phase current of branch road K, I _c,kfor the C phase current of branch road K, KN is all branch road collection be connected in branch road K end-node, for the branch road collection associated by branch road K end-node.

3rd step, carries out backward steps calculating.By the three-phase current of source point, the three-phase voltage from source point to each load bus according to all nodes of KVL computing system.Its concrete steps are as follows:

(1) by the impedance of each part of path 3 × 3 rank matrix Z _lrepresent, then

$Z_l=\left(\begin{array}{ccc}{z}_{aa}& z_{ab}& z_{ac}\\ z_{ba}& z_{bb}& z_{bc}\\ z_{cz}& z_{cb}& z_{cc}\end{array}\right),$

Wherein: z _aa, z _bband z _ccbe self-impedance; z _ab, z _ac, z _ba, z _bc, z _czand z _cbbe transimpedance.

(2) by power branch, by all node voltages of backward computational grid of the sequence of calculation, its computing formula is as follows:

$\left[\begin{array}{c}{U}_{A,m}\\ U_{B,m}\\ U_{C,m}\end{array}\right]=\left[\begin{array}{c}{U}_{A,s}\\ U_{B,s}\\ U_{C,s}\end{array}\right]-Z_{lk}\×\left[\begin{array}{c}{I}_{A,k}\\ I_{B,k}\\ I_{C,k}\end{array}\right]$

Wherein: m is the minor details period of branch road k, s is the first node number of branch road k, Z _lkfor the three-phase impedance matrix of circuit k, I _a,k, I _b,kand I _c,kbe respectively the three-phase current of branch road k, U _a,sfor the first node voltage of A phase branch road k, U _b,sfor the first node voltage of B phase branch road k, U _c,sfor the first node voltage of C phase branch road k, U _a,mfor the end-node voltage of A phase branch road k, U _b,mfor the end-node voltage of B phase branch road k, U _c,mfor the end-node voltage of C phase branch road k.

4th step, by the load branch circuit electric current pushed through before each load bus voltage correction of trying to achieve in journey, iteration pushes away before carrying out and calculates, until each node voltage difference of adjacent twice iteration is all less than convergence threshold with back substitution.Namely judge in the difference of adjacent node voltage effective value of trying to achieve for twice, whether its maximal value is less than given threshold criteria, convergence threshold ε can be 0.001.If so, then result of calculation is exported, if not, then push through the iterative computation of journey and backward steps before proceeding.Each iteration all by the loss of each load bus voltage correction substation transformer of trying to achieve, by revised transformer loss and given load power modified load branch current.Through iterating and revising, until each node voltage difference of twice iteration is all less than set-point, thus ensure that the accuracy of Load flow calculation.

More than show and describe ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; the just principle of the present invention described in above-described embodiment and instructions; the present invention also has various changes and modifications without departing from the spirit and scope of the present invention, and these changes and improvements all fall in claimed scope of the present invention.The protection domain of application claims is defined by appending claims and equivalent thereof.

Claims (5)

1. power distribution network three-phase power flow analytical approach, is characterized in that, comprises the following steps:

11) preprocessing process, sorts to branch road each in real-time network, obtains the out branch sequence of calculation, tries to achieve the circuit branch road associated by each branch road end-node and load branch circuit;

12) push away process computation before carrying out, according to the complex power calculated load branch current of each phase load of load bus, to the front of trend until source point calculates the distribution of current of each branch road according to KCL theorem from each load branch circuit, obtain the three-phase current of source point;

13) backward steps calculating is carried out, by the three-phase current of source point, the three-phase voltage from source point to each load bus according to all nodes of KVL computing system;

14) by the load branch circuit electric current pushed through before each load bus voltage correction of trying to achieve in journey, iteration pushes away before carrying out and calculates, until each node voltage difference of adjacent twice iteration is all less than convergence threshold with back substitution.

2. power distribution network three-phase power flow analytical approach according to claim 1, is characterized in that, push away process computation and comprise the following steps before described carrying out:

21) set each node voltage initial value as supply voltage, and using 10kV line voltage U AB as reference phasor;

22) the active loss △ P of the distribution transforming transformer of each phase of a, b, c is calculated _iwith reactive loss △ Q _i, its computing formula is as follows:

${\mathrm{\ΔP}}_i=I_i^2\×R_i+U_i^2\×G_i,$

${\mathrm{\ΔQ}}_i=I_i^2\×X_i+U_i^2\×B_i,$

Wherein, I _ifor current value, R _ifor resistance value, U _ifor magnitude of voltage, G _ifor conductivity unshakable in one's determination, X _ifor winding leakage reactance, B _ifor susceptance rate unshakable in one's determination;

23) calculated load branch road three-phase current;

24) calculated the three-phase current of each branch road to power supply point by the branch road sequence of calculation by end load branch circuit, its computing formula is as follows:

$\left[\begin{array}{c}{I}_{A,k}\\ I_{B,k}\\ I_{C,k}\end{array}\right]=\underset{j\∈KN}{\Σ}\left[\begin{array}{c}{I}_A,\stackrel{\→}{j}\\ I_B,\stackrel{\→}{j}\\ I_C,\stackrel{\→}{j}\end{array}\right],$

Wherein: I _a,kfor the A phase current of branch road K, I _b,kfor the B phase current of branch road K, I _c,kfor the C phase current of branch road K, KN is all branch road collection be connected in branch road K end-node, for the branch road collection associated by branch road K end-node.

3. power distribution network three-phase power flow analytical approach according to claim 1, is characterized in that, described backward steps calculating of carrying out comprises the following steps:

31) by the impedance of each part of path 3 × 3 rank matrix Z _lrepresent, then

$Z_l=\left(\begin{array}{ccc}{z}_{aa}& z_{ab}& z_{ac}\\ z_{ba}& z_{bb}& z_{bc}\\ z_{cz}& z_{cb}& z_{cc}\end{array}\right),$

Wherein: z _aa, z _bband z _ccbe self-impedance; z _ab, z _ac, z _ba, z _bc, z _czand z _cbbe transimpedance;

32) by power branch, by all node voltages of backward computational grid of the sequence of calculation, its computing formula is as follows:

$\left[\begin{array}{c}{U}_{A,m}\\ U_{B,m}\\ U_{C,m}\end{array}\right]=\left[\begin{array}{c}{U}_{A,s}\\ U_{B,s}\\ U_{C,s}\end{array}\right]-Z_{lk}\×\left[\begin{array}{c}{I}_{A,k}\\ I_{B,k}\\ I_{C,k}\end{array}\right]$

Wherein: m is the minor details period of branch road k, s is the first node number of branch road k, Z _lkfor the three-phase impedance matrix of circuit k, I _a,k, I _b,kand I _c,kbe respectively the three-phase current of branch road k, U _a,sfor the first node voltage of A phase branch road k, U _b,sfor the first node voltage of B phase branch road k, U _c,sfor the first node voltage of C phase branch road k, U _a,mfor the end-node voltage of A phase branch road k, U _b,mfor the end-node voltage of B phase branch road k, U _c,mfor the end-node voltage of C phase branch road k.

4. power distribution network three-phase power flow analytical approach according to claim 2, is characterized in that, described calculated load branch road three-phase current comprises the following steps:

41) AB phase rated capacity S is calculated _aB, BC phase rated capacity S _bCwith CA phase rated capacity S _cA, its computing formula is as follows:

S _AB＝P _a+△P _a+w(Q _a+△Q _a)，

S _BC＝P _b+△P _b+w(Q _b+△Q _b)，

S _CA＝P _c+△P _c+w(Q _c+△Q _c)，

Wherein: P _afor A phase active power, P _bfor B phase active power, P _cfor C phase active power, △ P _afor the active loss of A phase, △ P _bfor the active loss of B phase, △ P _cfor the active loss of C phase, Q _afor A phase reactive power, Q _bfor B phase reactive power, Q _cfor C phase reactive power, △ Q _afor A phase reactive loss, △ Q _bfor B phase reactive loss, △ Q _cfor C phase reactive loss, w is design factor;

42) calculate distribution transforming transformation winding current, its computing formula is as follows:

$\left[\begin{array}{c}{I}_{AB}\\ I_{BC}\\ I_{CA}\end{array}\right]=\left[\begin{array}{c}{S}_{AB}/U_{AB}\\ S_{BC}/U_{BC}\\ S_{CA}/U_{CA}\end{array}\right],$

Wherein: I _aBfor the line current of AB phase, I _bCfor the line current of BC phase, I _cAfor the line current of CA phase, U _aBfor the line voltage of AB phase, U _bCfor the line voltage of BC phase, U _cAfor the line voltage of CA phase;

43) calculate distribution transforming high-pressure side load current, its computing formula is as follows:

$\left[\begin{array}{c}{I}_A\\ I_B\\ I_C\end{array}\right]=\left[\begin{array}{c}{I}_{AB}-I_{CA}\\ I_{BC}-I_{AB}\\ I_{CA}-I_{BC}\end{array}\right],$

Wherein: I _afor the line current of A phase, I _bfor the line current of B phase, I _cfor the line current of C phase.

5. power distribution network three-phase power flow analytical approach according to claim 1, is characterized in that: described convergence threshold ε is 0.001.