CN105514999A - Prevention and control model for power grid static voltage stabilization and algorithm thereof - Google Patents

Abstract

The invention discloses a prevention and control model for power grid static voltage stabilization and an algorithm thereof. The prevention and control model for the power grid static voltage stabilization and the algorithm comprise a step (1) of establishment of the following objective functions; a step (2) of feasibility constrain analysis under a power grid operation state; a step (3) of grid system segmentation; and a step (4) of solving of a decomposition coordination interior point method of a model. The prevention and control model for the power grid static voltage stabilization based on section power based on the power constrain of a section between the regional power grids and the algorithm thereof are accurate and efficient. When the static voltage stabilization problem occurs when the interconnected power grids are in the normal operation state, after the interconnected power grids are prevented and controlled by the prevention and control model for the power grid static voltage stabilization and the algorithm, the system can meet the requirements for the static voltage stability margin and the requirements for section power constrain in the normal operation state, and the static voltage stability margin of the system is improved.

Description

A kind of electrical network static voltage stability Preventive Control Model and algorithm thereof

Technical field

The present invention relates to power domain, be specifically related to a kind of electrical network static voltage stability Preventive Control Model based on regional power grid discontinuity surface power constraint and algorithm thereof.

Background technology

Voltage stabilization is pith indispensable in the large stability analysis of electrical network three, and Static Analysis Method and dynamic analysing method can be adopted to analyze and research.Compare dynamic analysing method, Static Analysis Method because computational speed is fast, can fast scan analysis a large amount of electrical network N-1/N-2 fault, quantitatively can provide the advantages such as stability margin index, electric power system obtains applying more and more widely abroad, and started to enter the real-time online application stage, be the important means and the instrument that instruct bulk power grid safe and stable operation.

In recent years, in static voltage stability problem, propose both at home and abroad and manyly research and analyse method, comprise the feasible solution domain method of application power flow equation, multi-solutions method, Sensitivity Analysis Method, maximum power method, eigenvalue structure analysis, singular value decomposition method, minor interference analytic approach, time-domain-simulation analytic approach, catastrophe theory analytic approach and energy function analytic approach etc.Above-mentioned various method, has their own characteristics each in Mathematical Modeling, Mathematical Method etc., in practical, all have respective advantage and limitation.On the basis of summing up prior art achievement, this patent proposes a kind of electrical network static voltage stability Preventive Control Model based on regional power grid discontinuity surface power constraint and algorithm.

Summary of the invention

The object of the present invention is to provide a kind of electrical network static voltage stability Preventive Control Model based on regional power grid discontinuity surface power constraint and algorithm thereof.When interconnected network is when occurring static voltage stability problem under normal operating conditions, adopt this paper institute's static voltage stability Preventive Control Model of carrying and algorithm to after interconnected network enforcement prevention and control, system can be made to meet air extract requirement and section power constraint requirements under normal operating conditions, improve the air extract of system.Model and algorithm provided by the invention is correct, effective.

Above-mentioned purpose is achieved by the following technical solution:

A kind of electrical network static voltage stability Preventive Control Model and algorithm thereof, comprise the steps:

(1) following target function is set up,

$\min F=\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{(P_{Gi}^0-P_{Gi0})}^2{w}_{pi}+\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{(Q_{Gi}^0-Q_{Gi0})}^2{w}_{qi}+\underset{t=1}{\overset{N_T}{\mathrm{\Σ}}}{(k_t^0-k_{t0})}^2{w}_{kt}+\underset{i=1}{\overset{N_B}{\mathrm{\Σ}}}{C}_i{w}_i,$

Wherein, P _gi, Q _gi, k _tand C _irepresent that generating set meritorious to be exerted oneself, idlely to be exerted oneself respectively, on-load tap-changing transformer no-load voltage ratio and load bus cut burden with power amount, N _g, N _tand N _brepresent generator nodes, on-load tap-changing transformer number of units and system node number respectively, w _pi, w _qi, w _ktand w _irepresent the weight of each control measure respectively; Operation variable under normal operating condition before prevention and control represents with subscript 0, and the operation variable under the normal operating condition after prevention and control represents with subscript 0, with represent generating set to gain merit variable quantity and idle work variable quantity, represent load tap changer variable quantity, C _iw _irepresent reactor and inject idle regulation and control amount;

(2) the feasible constraints analysis under operation of power networks state:

$P_{Gi}^0-(P_{Di0}-C_i)-\underset{ij\∈S_{Li}}{\mathrm{\Σ}}{P}_{Lij}^0-\underset{ij\∈S_{Ti}}{\Σ}{P}_{Tij}^0=0,i=1,2,...,N_B,$

$\underset{ij\∈S_{link,n}}{\Σ}{P}_{ij,n}^0-P_{cut,n}^0=0,n=1,2,...,N_{cut},$

0≤C _i≤P _Di0i＝1,2,…,N _B，

Wherein, P _dithe each node burden with power of representative system, P _lijrepresent the active power on circuit branch road, P _tijrepresent the active power on on-load tap-changing transformer branch road, S _lirepresent the circuit set of fingers be connected with node i, S _tirepresent the on-load tap-changing transformer set of fingers be connected with node i, P _{ij, n}represent the active power that the interconnection between regional power grid in the n-th section transmits, P _{cut, n}represent the active power set point of the n-th section between regional power grid, S _{link, n}represent the set of the interconnection that the n-th section comprises between regional power grid, N _cutrepresent in electrical network the section number contacting each subnet;

(3) network system cutting, adopts the cutting method based on electrical distance between node, is divided into three steps:

Step one, eliminates and merges redundant node: utilize network static equivalence method to carry out preliminary abbreviation to original electrical network, eliminates the node that outlet number is few, comprises the node and intermediate node that are in radial networks end, reduces system scale;

Step 2, sub area division divides, and specifically comprises step S1 ~ S5:

S1, the electrical distance between computing node;

S2, choose any node x as initial point, the nearest node y of electrical distance is with it searched for as same district according to relative electrical distance, count region 1, the node z that search is nearest with node j electrical distance again, to make it with x, y, as same district, to repeat above step, until the node z of search repeats in zone 1;

S3, repeats S2, until all nodes have been divided in different regions all;

S4, calculate the average electrical distance in each region, wherein n represents the number of non-power generator node in subregion i, d _jkfor the relative average distance of node,

$\stackrel{\‾}{D_i}=\frac{1}{n}\underset{k,j\∈i}{\Σ}{d}_{jk},$

Definition E _jkbe used for searching for the node that electrical distance and other node in subregion are all far away,

$E_{jk}=\frac{\left|d_{jk}-\stackrel{\‾}{D_i}\right|}{\stackrel{\‾}{D_i}},(j,k\∈i);$

S5, calculates the relative electrical distance variance of each load bus, part is waved node and retains and each self-forming one district;

Step 3, node merges: after system partitioning is terminated, by node aggregation computing, all nodes in same region are formed a dummy node; Node aggregation carries out for subregion one by one, and the polymerization between regional is independent of each other;

(4) the composition decomposition interior point method of solving model.

Beneficial effect of the present invention:

Electrical network static voltage stability Preventive Control Model based on regional power grid discontinuity surface power constraint provided by the invention and algorithm accurate and effective thereof.When interconnected network is when occurring static voltage stability problem under normal operating conditions, adopt this paper institute's static voltage stability Preventive Control Model of carrying and algorithm to after interconnected network enforcement prevention and control, system can be made to meet air extract requirement and section power constraint requirements under normal operating conditions, improve the air extract of system.

Accompanying drawing explanation

Fig. 1: original electrical network carries out the schematic diagram of preliminary abbreviation;

Fig. 2: IEEE118 × 2 test macros.

Embodiment

Technical scheme of the present invention is described in detail below in conjunction with specific embodiment.The effect of embodiment is essentiality content of the present invention is described, but does not limit protection scope of the present invention with this.Those of ordinary skill in the art should be appreciated that and can modify to technical scheme of the present invention or equivalent replacement, and does not depart from essence and the protection range of technical solution of the present invention.

A kind of electrical network static voltage stability Preventive Control Model and algorithm thereof, comprise and set up feasible constraints condition under target function, setting operation of power networks state, set up system decomposition Coordination Model, and then ask for the increment of each subnet built-in variable in system, the optimization realizing system upgrades.

Specifically comprise the steps:

(1) following target function is set up,

$\min F=\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{(P_{Gi}^0-P_{Gi0})}^2{w}_{pi}+\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{(Q_{Gi}^0-Q_{Gi0})}^2{w}_{qi}+\underset{t=1}{\overset{N_T}{\mathrm{\Σ}}}{(k_t^0-k_{t0})}^2{w}_{kt}+\underset{i=1}{\overset{N_B}{\mathrm{\Σ}}}{C}_i{w}_i,$

Wherein, P _gi, Q _gi, k _tand C _irepresent that generating set meritorious to be exerted oneself, idlely to be exerted oneself respectively, on-load tap-changing transformer no-load voltage ratio and load bus cut burden with power amount, N _g, N _tand N _brepresent generator nodes, on-load tap-changing transformer number of units and system node number respectively, w _pi, w _qi, w _ktand w _irepresent the weight of each control measure respectively; Operation variable under normal operating condition before prevention and control represents with subscript 0, and the operation variable under the normal operating condition after prevention and control represents with subscript 0, with represent generating set to gain merit variable quantity and idle work variable quantity, represent load tap changer variable quantity, C _iw _irepresent reactor and inject idle regulation and control amount;

(2) the feasible constraints analysis under operation of power networks state:

$P_{Gi}^0-(P_{Di0}-C_i)-\underset{ij\∈S_{Li}}{\mathrm{\Σ}}{P}_{Lij}^0-\underset{ij\∈S_{Ti}}{\Σ}{P}_{Tij}^0=0,i=1,2,...,N_B,$

$\underset{ij\∈S_{link,n}}{\Σ}{P}_{ij,n}^0-P_{cut,n}^0=0,n=1,2,...,N_{cut},$

0≤C _i≤P _Di0i＝1,2,…,N _B，

Wherein, P _dithe each node burden with power of representative system, P _lijrepresent the active power on circuit branch road, P _tijrepresent the active power on on-load tap-changing transformer branch road, S _lirepresent the circuit set of fingers be connected with node i, S _tirepresent the on-load tap-changing transformer set of fingers be connected with node i, P _{ij, n}represent the active power that the interconnection between regional power grid in the n-th section transmits, P _{cut, n}represent the active power set point of the n-th section between regional power grid, S _{link, n}represent the set of the interconnection that the n-th section comprises between regional power grid, N _cutrepresent in electrical network the section number contacting each subnet;

(3) network system cutting, adopts the cutting method based on electrical distance between node, is divided into three steps:

Step one, eliminates and merges redundant node: utilize network static equivalence method to carry out preliminary abbreviation to original electrical network, eliminates the node that outlet number is few, comprises the node and intermediate node that are in radial networks end, reduces system scale;

As shown in Figure 1, by Nodes line number be 1 or 2 part of nodes cancellation.Wherein, node j can be expressed as n (n≤1) the individual node be connected on same bus.

This operation is mainly in order to carry out Static Equivalent to primitive network, and the node that a large amount of outlet number of cancellation is few, reduces system scale, promote the speed of subsequent calculations.

According to network static principle of equivalence:

$\left[\begin{array}{c}\·\\ I_j\\ I_i\\ I_k\\ \·\end{array}\right]=\left[\begin{array}{ccccc}\·& \·& \·& \·& \·\\ 0& y_{jj}& y_{ji}& y_{jk}& 0\\ \·& y_{ij}& y_{ii}& 0& \·\\ \·& y_{kj}& 0& y_{kk}& \·\\ \·& \·& \·& \·& \·\end{array}\right]\left[\begin{array}{c}\·\\ U_j\\ U_i\\ U_k\\ \·\end{array}\right]$

Wherein, I _j, I _i, I _kfor node Injection Current, y _jj, y _ji, y _jk, y _ij, y _ii, y _kj, y _kkfor node admittance, U _i, U _j, U _kfor busbar voltage.Cancellation node j, then have:

$\left[\begin{array}{cccc}\·& \·& \·& \·\\ \·& y_{ii}^{\′}& y_{ik}^{\′}& \·\\ \·& y_{ki}^{\′}& y_{kk}^{\′}& \·\\ \·& \·& \·& \·\end{array}\right]\left[\begin{array}{c}\·\\ U_i\\ U_k\\ \·\end{array}\right]=\left[\begin{array}{c}\·\\ I_i^{\′}\\ I_k^{\′}\\ \·\end{array}\right]$

$y_{ki}^{\′}=y_{ik}^{\′}=-\frac{1}{y_{jj}{y}_{ji}{y}_{jk}}$

$y_{ii}^{\′}=y_{ii}-\frac{1}{y_{jj}{y}_{ji}^2}$

$y_{kk}^{\′}=y_{kk}-\frac{1}{y_{jj}{y}_{jk}^2}$

$I_i^{\′}=I_i+\frac{y_{ji}}{\underset{p\∈i,k}{\Σ}{y}_{jp}}{I}_j$

$I_k^{\′}=I_k+\frac{y_{jk}}{\underset{p\∈i,k}{\Σ}{y}_{jp}}{I}_j$

Step 2, sub area division divides:

Suppose that eliminating the system after merging redundant node has n node, r generator node, n-r load bus, has according to DC flow model:

$\left[\begin{array}{c}{P}_G\\ P_L\end{array}\right]=\left[\begin{array}{cc}{B}_{G,G}& B_{G,L}\\ B_{L,G}& B_{L,L}\end{array}\right]\left[\begin{array}{c}{\mathrm{\θ}}_G\\ {\mathrm{\θ}}_L\end{array}\right]$

Wherein, P _grepresent generator node active power, P _lrepresent load bus active power, B _g,G, B _g,L, B _l,G, B _l,Lrepresent node admittance matrix, order:

S＝[B _L,L] ^-1

S _ijrepresent the electrical couplings degree of load bus i and j, then:

$d_{ij}=ln\left(\frac{1}{(s_{ij}+s_{ji})/2}\right),i\≠j$

Wherein: d _ij=0, i=ji, j=1,2 ... n-r

D _ijrepresent the relative electrical distance between node i and j, d _ijthe electrical connection of less expression between them is tightr.

Defined node i with the relative electrical distance mean value of other load bus is:

${\tilde{d}}_i=\frac{1}{n-r-1}\underset{j=1,j\≠i}{\overset{n-r}{\Σ}}{d}_{ij}$

By the relative electrical distance variances sigma (d of above formula definable node i with other node _i) be:

$\mathrm{\σ}\left(d_i\right)=\sqrt{\underset{j-1,j\≠i}{\overset{n-r}{\Σ}}{(d_{ij}-{\tilde{d}}_i)}^2}$

Specifically comprise step S1 ~ S5:

S1, the electrical distance between computing node;

S2, choose any node x as initial point, the nearest node y of electrical distance is with it searched for as same district according to relative electrical distance, count region 1, the node z that search is nearest with node j electrical distance again, to make it with x, y, as same district, to repeat above step, until the node z of search repeats in zone 1;

S3, repeats S2, until all nodes have been divided in different regions all;

S4, calculate the average electrical distance in each region, wherein n represents the number of non-power generator node in subregion i, d _jkfor the relative average distance of node,

$\stackrel{\‾}{D_i}=\frac{1}{n}\underset{k,j\∈i}{\Σ}{d}_{jk},$

Definition E _jkbe used for searching for the node that electrical distance and other node in subregion are all far away,

$E_{jk}=\frac{\left|d_{jk}-\stackrel{\‾}{D_i}\right|}{\stackrel{\‾}{D_i}},(j,k\∈i);$

S5, calculates the relative electrical distance variance of each load bus, part is waved node and retains and each self-forming one district;

Step 3, node merges: after system partitioning is terminated, by node aggregation computing, all nodes in same region are formed a dummy node; Node aggregation carries out for subregion one by one, and the polymerization between regional is independent of each other;

(4) the composition decomposition interior point method of solving model.

For the analysis of the analysis Coordination Model of system, can allow it under KT (Kuhn-Tucker) condition that there is certain error and Ku Entu, implements operation and computational analysis at authorization composition decomposition interior point method to iterations and intrasystem complementary gap, admissible error is here generally 10 ^-6.In concrete analysis process, we suppose that its iterations K value is 0, in this case, when the given optimized variable of electric power system is certain, its initial value just can be determined accurately, then can analyse the complementary gap of each subnet Optimized model algorithm of system scientifically, complementary gap here refers to the duality gap in prim al-dual interior point m ethod.Again according to the corresponding residue of above model formation analysis constraint, the value being worth K is generally K+1, if in the value of K and electric power system composition decomposition, point handles the analytical procedure of maximum iteration time in system-computed well in this case, can make to process the state do not restrained in system processing procedure, otherwise next step calculating will be entered; Then dual variable and the former variable of system in electric power system is upgraded according to the step will gone in system update then algorithm consummation; Then according to the coupled relation existed between the known variables analytical system region in each equation, then its relation function is determined, according to the system, coupled relation solving coupling variable calculating in electric power system, analyze, the increment of each subnet built-in variable in electric power system is obtained, so that the optimization that can realize system upgrades according to above-mentioned analytic process and coupling function equation.

For IEEE118 × 2 test macro, as shown in Figure 2,2 IEEE118 nodes and a section System's composition is had in system, in system, regional number is set to n, in network system, regional node i correspondence system node serial number is i+118 (n-1), in system, each regional power grid discontinuity surface specifies the interconnection of resistance to form by 3, specifies resistance to be respectively 0.0145,0.0164,0.0247 for three.And in the analytic process of system model may under heavy load condition and forecast failure state test macro fault, at this moment the load of node 161 and 43 must be increased, so that can reasonably verification process information, then we get 0.1 according to the stability margin desired value that electrical network Practical Project requirements set is model algorithm.

In simulation analysis, suppose that electric power system is transmitted section power designated value and is set as 5p.u., 4p.u., 3p.u. respectively under normal operating condition and forecast failure state, as can be seen from following table, under the crucial intended status of electric power system, the air extract value of system is all below 0.1, the requirement of air extract can not be met, in this case need to carry out prevention and control to system.

As can be seen from Table 1; coordination interior point method is adopted to solve; simulation analysis is carried out under serial computing pattern; for section power designated value: under each simulated conditions in 3p.u.; general only need the budget that 1 time iteration just can complete its algorithm, and then transmission section power that system meets air extract requirement under normal or forecast failure retrains also only to need 1 iterative analysis just can obtain.

Crucial forecast failure before table 1 electric power system prevention and control and relevant information thereof

The effect of above-described embodiment is essentiality content of the present invention is described, but does not limit protection scope of the present invention with this.Those of ordinary skill in the art should be appreciated that and can modify to technical scheme of the present invention or equivalent replacement, and does not depart from essence and the protection range of technical solution of the present invention.

Claims (1)

1. electrical network static voltage stability Preventive Control Model and an algorithm thereof, is characterized in that, comprises the steps:

(1) following target function is set up,

$\min F=\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{(P_{Gi}^0-P_{Gi0})}^2{w}_{pi}+\underset{i=1}{\overset{N_G}{\mathrm{\Σ}}}{(Q_{Gi}^0-Q_{Gi0})}^2{w}_{qi}+\underset{t=1}{\overset{N_T}{\mathrm{\Σ}}}{(k_t^0-k_{t0})}^2{w}_{kt}+\underset{i=1}{\overset{N_B}{\mathrm{\Σ}}}{C}_i{w}_i,$

Wherein, P _gi, Q _gi, k _tand C _irepresent that generating set meritorious to be exerted oneself, idlely to be exerted oneself respectively, on-load tap-changing transformer no-load voltage ratio and load bus cut burden with power amount, N _g, N _tand N _brepresent generator nodes, on-load tap-changing transformer number of units and system node number respectively, w _pi, w _qi, w _ktand w _irepresent the weight of each control measure respectively; Operation variable under normal operating condition before prevention and control represents with subscript 0, and the operation variable under the normal operating condition after prevention and control represents with subscript 0, with represent generating set to gain merit variable quantity and idle work variable quantity, represent load tap changer variable quantity, C _iw _irepresent reactor and inject idle regulation and control amount;

(2) the feasible constraints analysis under operation of power networks state:

$P_{Gi}^0-(P_{Di0}-C_i)-\underset{ij\∈S_{Li}}{\mathrm{\Σ}}{P}_{Lij}^0-\underset{ij\∈S_{Ti}}{\mathrm{\Σ}}{P}_{Tij}^0=0,i=1,2,...,N_B,$

$\underset{ij\∈S_{link,n}}{\mathrm{\Σ}}{P}_{ij,n}^0-P_{cut,n}^0=0,n=1,2,...,N_{cut},$

0≤C _i≤P _Di0i＝1,2,…,N _B，

Wherein, P _dithe each node burden with power of representative system, P _lijrepresent the active power on circuit branch road, P _tijrepresent the active power on on-load tap-changing transformer branch road, S _lirepresent the circuit set of fingers be connected with node i, S _tirepresent the on-load tap-changing transformer set of fingers be connected with node i, P _{ij, n}represent the active power that the interconnection between regional power grid in the n-th section transmits, P _{cut, n}represent the active power set point of the n-th section between regional power grid, S _{link, n}represent the set of the interconnection that the n-th section comprises between regional power grid, N _cutrepresent in electrical network the section number contacting each subnet;

(3) network system cutting, adopts the cutting method based on electrical distance between node, is divided into three steps:

Step one, eliminates and merges redundant node: utilize network static equivalence method to carry out preliminary abbreviation to original electrical network, eliminates the node that outlet number is few, comprises the node and intermediate node that are in radial networks end, reduces system scale;

Step 2, sub area division divides, and specifically comprises step S1 ~ S5:

S1, the electrical distance between computing node;

S2, choose any node x as initial point, the nearest node y of electrical distance is with it searched for as same district according to relative electrical distance, count region 1, the node z that search is nearest with node j electrical distance again, to make it with x, y, as same district, to repeat above step, until the node z of search repeats in zone 1;

S3, repeats S2, until all nodes have been divided in different regions all;

S4, calculate the average electrical distance in each region, wherein n represents the number of non-power generator node in subregion i, d _jkfor the relative average distance of node,

$\stackrel{\‾}{D_i}=\frac{1}{n}\underset{k,j\∈i}{\mathrm{\Σ}}{d}_{jk},$

Definition E _jkbe used for searching for the node that electrical distance and other node in subregion are all far away,

$E_{jk}=\frac{\left|d_{jk}-\stackrel{\‾}{D_i}\right|}{\stackrel{\‾}{D_i}},(j,k\∈i);$

S5, calculates the relative electrical distance variance of each load bus, part is waved node and retains and each self-forming one district;

Step 3, node merges: after system partitioning is terminated, by node aggregation computing, all nodes in same region are formed a dummy node; Node aggregation carries out for subregion one by one, and the polymerization between regional is independent of each other;

(4) the composition decomposition interior point method of solving model.