CN103474993A - Quantitative analysis index of active bearing capacity of power network based on mapping elastic potential energy - Google Patents

Abstract

The active bearing capacity of a power network depends on such numerous factors as a power network structure, branch bearing capacity, size and distribution of power supply and load, and the like, and the quantitative analysis index of the active bearing capacity is still a difficult point in security analysis of the power network. The invention provides a quantitative analysis index of active bearing capacity of power network based on mapping elastic potential energy, comprising: mapping a branch state on the basis of a mapping elastic mechanics network model of the power network to obtain the mapping elastic potential energy of the power network branch; and adopting a potential energy superposition concept to obtain a calculation method of the mapping elastic potential energy of the power network. As shown in analysis and verified in examples, the mapping elastic potential energy can be used as the quantitative analysis index of the active bearing capacity of the power network; under a condition of constant total active load, the larger the value, the smaller the total active load margin of the power network is and the more unbalanced the active load of the branch is. The quantitative analysis index provided by the invention is used for enriching the theoretical basis of the security analysis of the power network and can be extensively applied to the aspects of planning, operation manner analysis, online scheduling of the power network, etc.

Description

Electric network active bearing capacity quantitative analysis index based on the mapping elastic potential energy

Technical field

Electric power system (electrical network) safety analysis.

Background technology

The most basic function of electrical network is active power (hereinafter to be referred as meritorious) transmission, therefore meritorious bearing capacity (or claiming meritorious transmittability), be the leading indicator that electric network security is analyzed, it depends on the factors such as the size of electric network composition, branch road bearing capacity, power supply and load and distribution.At present, the general qualitative analysis that adopts the verification of N-1 (even N-2) branch road limit for tonnage in real work, the quantitative analysis method of electric network active bearing capacity and index remain the difficult point in the electric network security analysis.

Statistics is found 15 years last century Mos, and U.S.'s accident of having a power failure on a large scale meets the self-organizing critical characteristic of complication system.Inspired, adopt the fail safe of the large electrical network of Complex Networks Theory analysis and evaluation to become current study hotspot.But complex network model is based on the graph theory model of wiring topology, the component parameters that does not comprise electrical network, more can not naturally embody grid nodes, branch road quantity of state and between physical relation, very difficult foundation comprises the composite target of electric network state amount and structural information simultaneously.

The structure of local indexes is relatively easy, but build thus the whole network index, is not easy, and desirable approach is to be formed by stacking by local indexes.What meet at present additivity has a potential energy index, and as node potential energy, Branch Potential Energy etc., but these indexs are all the concepts in the Power Network Transient Stability direct method, there is no clear and definite physical concept in static analysis; Also fail to prove after the element potential superposition principle the meritorious bearing capacity that can describe electrical network.Therefore it characterizes the theoretical foundation deficiency of electric network security.

Compare the definition in electrical network, " potential energy " has clear and definite, strict physical concept in mechanics, and the tool uniqueness.Similar to the meritorious bearing capacity of electrical network, the bearing capacity of elastic network(s) also depends on grid structure, branch road intensity, stressed size and distribution.The patent " electrical network-elastic mechanics network topology mapping method " (application publication number: CN 102227084 A) of applying for before this, electrical network is mapped to Elasticity network (hereinafter to be referred as the elastic network(s)) model of longitudinal stress, because branch road direction in the mapping elastic network(s) is identical, stressedly in the same way also meet additivity, therefore associated between total potential energy and total load.So, can, by the potential energy of mapping elastic network(s), analyze the meritorious bearing capacity of corresponding electrical network.

Summary of the invention

The present invention's " electric network active bearing capacity quantitative analysis index based on the mapping elastic potential energy ", mapping elastic network(s) model based on electrical network, state mapping by grid branch and elastic network(s) branch road, analyzed the mapping elastic potential energy of grid branch, adopt the potential superposition principle thinking, obtain the acquiring method of electrical network mapping elastic potential energy.Analyze and find and Example Verification, this mapping elastic potential energy can characterize the overall meritorious carrying nargin of electrical network and the harmony of the meritorious carrying of branch road: in certain total active load situation, its value is larger, and the overall meritorious carrying nargin of electrical network is less, and the meritorious carrying of branch road is more unbalanced; Its value is less, contrary.So can be used as the quantitative analysis index of electric network active bearing capacity.The present invention has enriched the theoretical foundation that electric network security is analyzed, and can be widely used in the aspects such as planning, operational mode analysis, on-line scheduling of electrical network.

The accompanying drawing explanation

Fig. 1 electrical network-elastic network(s) Topological Mapping, (1) electrical network, (2) mapping elastic network(s)

Fig. 2 equivalence mapping elasticity branch road

Fig. 3 is equivalence mapping elastic network(s) vertically

Fig. 4 New England 10 machine 39 node systems

The mapping elastic network(s) structure of Fig. 5 New England 10 machine 39 node systems

Mapping elastic network(s) structure after Fig. 6 New England 10 machine 39 node system line disconnection 21-22

Mapping elastic network(s) structure after Fig. 7 New England 10 machine 39 node system line disconnection 15-16

Figure 87 node system structure

Figure 94 plants the mapping elastic network(s) structure of sharing of load scheme, (1) outlet sharing of load scheme one, (2) outlet sharing of load scheme two, (3) outlet sharing of load scheme three, (4) outlet sharing of load scheme four

Embodiment

1. the state mapping of grid branch and elastic network(s) branch road

Negligible resistance, establishing AC network branch road L two end nodes is i, j, node voltage

phase difference be θ _ij, reactance is X _l.When electric network reactive-load is abundant, U _i, U _jchange littlely, can make

gaining merit of transmission is

P _L＝Csinθ _ij (1)

Make k _l=dP _l/ d θ _ij, being named as the mapping coefficient of elasticity of L, by formula (1), can be obtained

k _L＝Ccosθ _ij (2)

k _L＝P _L／tanθ _ij (3)

If F _l, x _lbe respectively active force and the elongation of elastic network(s) branch road l, coefficient of elasticity is k _l=dF _l/ dx _l.Set up the quantity of state mapping relations of L and l:

$\left\{\begin{array}{c}{P}_L=F_l\\ {\mathrm{\θ}}_{\mathrm{ij}}=x_l\\ k_L=k_l\end{array}\right.---\left(4\right)$

Corresponding with formula (1), (2), (3), the quantity of state of l closes and is

$\left\{\begin{array}{c}{F}_l=C\sin x_l\\ k_l=C\cos x_l\\ k_l=F_l/\tan x_l\end{array}\right.---\left(5\right)$

If θ _ijless, but the quantity of state relation approximately linear of L can be obtained by formula (1), (2), (3)

$\left\{\begin{array}{c}{P}_L=k_L\·{\mathrm{\θ}}_{\mathrm{ij}}\\ k_L=C\end{array}\right.---\left(6\right)$

According to formula (4), the quantity of state of corresponding linear l closes and is

$\left\{\begin{array}{c}{F}_l=k_l\·x_l\\ k_l=C\end{array}\right.---\left(7\right)$

2. the mapping elastic potential energy of grid branch

After l stretches, elastic potential energy is that external force is to its work,

E _l＝∫F _ldx _l (8)

According to formula (5), (8), obtain elastic potential energy and be

$E_l=F_l\tan \frac{x_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">l</figure-callout>}}}{2}=k_l\frac{{1-\cos x}_l}{{\cos x}_l}=\frac{{\cos x}_{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">l</figure-callout>}}}{1+{\cos x}_l}\&CenterDot;\frac{{F_l}^2}{k_l}---\left(9\right)$

According to formula (4) mapping relations, the mapping elastic potential energy that obtains L is

$E_L=P_L\tan \frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="ij"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">ij</figure-callout>}}}{2}=k_L\frac{1-{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}{{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}=\frac{{\cos \mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="ij"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">ij</figure-callout>}}}{1+{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}\&CenterDot;\frac{{P_L}^2}{k_L}---\left(10\right)$

If θ _ijless, the quantity of state of l, L all is approximately linear relationship.The elastic potential energy that is obtained l by formula (7), (8) is

$E_l=\frac{1}{2}{F}_l{x}_l=\frac{1}{2}{k}_l{x_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">l</figure-callout>}}}^2=\frac{{{\mathrm{<figure-callout\; id="2"\; label="F\; l"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">F</figure-callout>}}_l}^2}{2k_l}---\left(11\right)$

According to formula (4) mapping relations, the mapping elastic potential energy of circuit L is

$E_L=\frac{1}{2}{P}_L{\mathrm{\&theta;}}_{\mathrm{ij}}=\frac{1}{2}{k}_L{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="ij"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">ij</figure-callout>}}}^2=\frac{{{\mathrm{<figure-callout\; id="2"\; label="P\; L"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">P</figure-callout>}}_L}^2}{{2k}_L}---\left(12\right)$

Due to P _l, θ _ij, k _lwith F _l, x _l, k _lthe value correspondent equal, therefore E _lwith E _lalso meet mapping relations,

E _l＝E _L (13)

3. the mapping elastic potential energy of electrical network

Apply for a patent " electrical network-elastic mechanics network topology mapping method " (application publication number: CN 102227084A), electrical network is mapped to vertical stressed elastic network(s), and keeps the incidence relation of node, branch road constant, as shown in Figure 1 according to what announce.

If the mapping elastic network(s) consists of n bar branch road, no matter whether its branch road is the linear elasticity branch road, and its total potential energy all meets superimposed characteristics,

$E_{\mathrm{l\&Sigma;}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_{\mathrm{li}}---\left(14\right)$

E wherein _{the l ∑}and E _libe respectively elastic network(s) and the potential energy of i bar branch road wherein.Therefore the mapping elastic potential energy of electrical network is

$E_{\mathrm{L\&Sigma;}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_{\mathrm{Li}}---\left(15\right)$

E wherein _{the L ∑}and E _libe respectively electrical network and the mapping elastic potential energy of i bar branch road wherein.

Because branch road in elastic network(s) is vertical in the same way, branch road length is the difference in height of two end nodes, the phase place of the corresponding grid nodes voltage of height of node.If all branch roads are all the linear elasticity branch road, according to formula (11), (14), the potential energy that can obtain the linear elasticity net is

$E_{\mathrm{l\&Sigma;}}=\frac{1}{2}\mathrm{\&Sigma;}(F_{\mathrm{topi}}\&CenterDot;x_{\mathrm{topi}})-\frac{1}{2}\mathrm{\&Sigma;}(F_{\mathrm{botj}}\&CenterDot;x_{\mathrm{botj}})---\left(16\right)$

Wherein, F _topi, x _topifor stressed size and the height of elastic network(s) top node, F _botj, x _botjstressed size and height for load node.If ignore the active loss of electrical network, according to above formula, the mapping elastic potential energy of linear electrical network is

$E_{\mathrm{L\&Sigma;}}=\frac{1}{2}\mathrm{\&Sigma;}(P_{\mathrm{topi}}\&CenterDot;{\mathrm{\&theta;}}_{\mathrm{topi}})-\frac{1}{2}\mathrm{\&Sigma;}(P_{\mathrm{botj}}\&CenterDot;{\mathrm{\&theta;}}_{\mathrm{botj}})---\left(17\right)$

In above formula, P _topi, θ _topifor the injection of power source bus node in electrical network is meritorious and phase place, P _botj, θ _botjburden with power and phase place for load bus.

4. mapping elastic potential energy and electrical network are totally gained merit and are carried the relation of nargin

Because all branch roads in the mapping elastic network(s) are subject to force direction identical, therefore available 1 and this net potential energy E _{the l ∑}with total load F _{the l ∑}all equal elasticity branch road equivalences, the length of establishing equivalent branch road is x _leq, as shown in Figure 2.By formula (9), can be obtained

$E_{\mathrm{l\&Sigma;}}=F_{\mathrm{l\&Sigma;}}\tan \frac{x_{\mathrm{leq}}}{2}---\left(18\right)$

According to the quantity of state mapping relations, have

$E_{\mathrm{L\&Sigma;}}=P_{\mathrm{L\&Sigma;}}\tan \frac{{\mathrm{\&theta;}}_{\mathrm{Leq}}}{2}---\left(19\right)$

Wherein, E _{the l ∑}, P _{the L ∑}and θ _leqfor the mapping potential energy of corresponding electrical network, total active load and equivalent branch road phase difference.Above formula is visible: work as P _{the L ∑}during for a certain value, if E _{the L ∑}larger, θ _leqlarger; If E _{the L ∑}less, θ _leqless.

If equivalent branch road is linear characteristic, according to formula (11), (12), have

$\left\{\begin{array}{c}{E}_{\mathrm{l\&Sigma;}}=\frac{1}{2}{F}_{\mathrm{l\&Sigma;}}{x}_{\mathrm{leq}}\\ E_{\mathrm{L\&Sigma;}}=\frac{1}{2}{P}_{\mathrm{L\&Sigma;}}\&CenterDot;{\mathrm{\&theta;}}_{\mathrm{Leq}}\end{array}\right.---\left(20\right)$

Equally, work as P _{the L ∑}during for a certain value, if E _{the L ∑}larger, θ _leqlarger; If E _{the L ∑}less, θ _leqless.

In identical total active load situation, different electrical networks or same electrical network are under different running method, if E _{the L ∑}larger, θ _leqalso larger, show that on the whole the meritorious carrying nargin of electrical network is less, bearing capacity is poor, and the fail safe of merit angle is poor.

5. mapping elastic potential energy and grid branch are gained merit and are carried balanced relation

Because grid branch is meritorious unbalanced, even the overall bearing capacity of electrical network is stronger, some branch road also may approach overload.If branch road transships and excision automatically, may cause chain reaction, cause the local off-the-line of electrical network, even disintegrate.Therefore, require index angle internally, weigh the harmony of grid branch carrying.

The equilibrium of electric network active carrying, refer to the larger circuit of mapping coefficient of elasticity, should carry larger gaining merit.Owing to electrical network being mapped to the elastic network(s) of longitudinal stress, can by the associated nodes of mains side and load side and between path merged and the equivalence, be simplified to the structure shown in Fig. 3.

As shown in Figure 3, be provided with n bar branch road, the branch road mapping coefficient of elasticity that the i bar is corresponding, phase difference and the meritorious k that is respectively _li, θ _liand P _li, total burden with power is

there is following rule in discovery:

If P _{the L ∑}=const., meet following formula when branch road has the distribution of work

P _L1：P _l2：...：P _Ln=k _L1：k _L2：...：k _Ln (21)

Always shine upon elastic potential energy E _{the L ∑}minimum.

Proof: can obtain according to formula (10), (15)

$E_{\mathrm{L\&Sigma;}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(P_{\mathrm{Li}}\tan -\frac{{\mathrm{\&theta;}}_{\mathrm{Li}}}{2})---\left(22\right)$

In above formula, θ _liit is the phase difference at i bar branch road two ends.Adopt Lagrangian extremum method, build following Lagrange's equation

$E=E_{\mathrm{L\&Sigma;}}-\mathrm{\&lambda;}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}-P_{\mathrm{L\&Sigma;}})---\left(23\right)$

Wherein, λ is certain constant.E _{the L ∑}for the condition of extreme value is above formula, to the partial derivative of branch power, be zero,

$\frac{\&PartialD;E}{{\&PartialD;P}_{\mathrm{Li}}}=\frac{{\&PartialD;E}_{\mathrm{L\&Sigma;}}}{{\&PartialD;P}_{\mathrm{Li}}}-\mathrm{\&lambda;}\frac{\&PartialD;}{{\&PartialD;P}_{\mathrm{Li}}}(\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}-P_{\mathrm{L\&Sigma;}})=0---\left(24\right)$

Therefore have

$\frac{{\&PartialD;E}_{\mathrm{L\&Sigma;}}}{{\&PartialD;P}_{\mathrm{Li}}}-\mathrm{\&lambda;}(1-0)=0---\left(25\right)$

By formula (22), (25), can be obtained

$\tan \frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">L</figure-callout>}1}}{2}=\tan \frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HSA0000096009940000022.png,HSA0000096009940000051.png"\; state="\{\{state\}\}">L</figure-callout>}2}}{2}=...=\tan \frac{{\mathrm{\&theta;}}_{\mathrm{Ln}}}{2}---\left(26\right)$

Known according to formula (3), formula (26) is of equal value each other with formula (21).While meeting formula (21), E _{the L ∑}for extreme value.

If alternating current circuit is simplified and is mapped as the linear elasticity branch road, can obtain according to formula (12), formula (15)

$E_{\mathrm{L\&Sigma;}}=\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}{\mathrm{\&theta;}}_{\mathrm{Li}}---\left(27\right)$

Equally, adopt Lagrangian extremum method, obtain E _{the L ∑}extremum conditions be

θ _L1=θ _L2＝...＝θ _Ln (28)

Known according to formula (6), formula (28) is of equal value each other with (21).

So no matter the branch road characteristic is linear or non-linear, while meeting formula (21), when the meritorious carrying of grid branch is the most balanced, E _{the L ∑}for extreme value.

Because formula (21), (26), (28) are all of equal value, so E _{the L ∑}extreme point is unique.By the known minimum potential energy of problem itself, necessarily existed, therefore while meeting formula (21), E _{the L ∑}for minimum value.

Card is finished.

More than the analysis showed that, it is harmonious that the mapping elastic potential energy can characterize the meritorious carrying of grid branch.When total burden with power is constant, the mapping elastic potential energy is less, and the meritorious carrying of grid branch harmony is better.

6. sample calculation analysis

6.1 the computational accuracy analysis of electrical network mapping elastic potential energy

New England's 10 machine 39 node systems are as Fig. 4.Carry out trend calculating, its median generatrix 31 is balance node, and reference voltage is 345kV, and reference capacity is 100MVA, and mapping elastic network(s) structure is as Fig. 5.

Based on non-linear branch and linear branch mapping, the electrical network of using respectively formula (15) and (17) to obtain this system shines upon elastic potential energy perunit value (fiducial value is 100, disregards dimension), as shown in table 1.

The electrical network mapping elastic potential energy of table 1 New England 10 machine 39 node systems

In table 1, method 1 is theoretical strict acquiring method, and the error of method 2 only has 0.37%.Visible, when grid branch two ends phase difference, than hour (in this example, the phase difference maximum at all branch roads of electrical network two ends is no more than 10 °), adopt linear branch to shine upon and ignore the active loss of electrical network, the mapping elastic potential energy error of electrical network is very little.

Simulation result, verified the feasibility of the 3rd joint opinion method.

6.2 mapping elastic potential energy and electrical network be the relationship analysis of meritorious carrying nargin totally

New England's 10 machine 39 node systems of still take are example.Adopt table 1 method 2 to calculate, the mapping elastic potential energy of electrical network is 4.536327, and equivalent branch road phase difference is 0.147520.

In the situation that do not excise power supply and load and keep size, distribute constantly, grid branch is taken turns doing to N-1, according to potential variation, sort from big to small, get front 6 circuits, as shown in table 2.

Table 2 electrical network mapping elastic potential energy increment

Table 2 shows, after excising arbitrary grid branch, the equivalent branch road phase difference of electrical network all increases, show its totally meritorious carrying nargin diminish, bearing capacity dies down; In addition, the same order of growth of mapping elastic potential energy and equivalent branch road phase difference, show to shine upon elastic potential energy larger, and electrical network totally meritorious carrying nargin is less.In table 1, after excision circuit 21-22, mapping elastic potential energy increment maximum, electrical network is meritorious carrying nargin minimum totally.

For comparison directly perceived, excise respectively circuit 21-22 and 15-16, the mapping elastic network(s) structure of electrical network is as Fig. 6,7.Fig. 5 before the excision circuit, visible relatively, and Fig. 6 increases more obvious than the elongation of the overall elasticity of Fig. 7, and structure is more fragile, and meritorious bearing capacity descends more.

Simulation results show the 4th the joint theoretical analysis result.

6.3 the balanced relationship analysis of the meritorious carrying of mapping elastic potential energy and branch road

As shown in Table 3, 4, from left to right, Length Ratio is 600:400:300:240:200 to 7 node system parameters shown in Fig. 8 in 5 outlets, and the coefficient of elasticity ratio is approximately k ₁: k ₂: k ₃: k ₄: k ₅=1:1.5:2:2.5:3.

The outlet payload is as shown in table 5, and wherein the characteristics of burden with power are P ₁: P ₂: P ₃: P ₄: P ₅=1:1.5:2:2.5:3.Reference voltage is 500kV, and reference capacity is 100WM.Existing 4 kinds of sharing of load schemes, shine upon the elastic network(s) structure accordingly as Fig. 9.The corresponding grid nodes phase place of height of node in Fig. 9, branch road mapping coefficient of elasticity (perunit value) and meritorious trend (perunit value) are labeled in corresponding branch road side.

Employing formula (10), (15), calculate respectively the electrical network mapping elastic potential energy under 4 sharing of load schemes, and fiducial value is 100, and result is as shown in table 6.

Table 3 main transformer basic parameter

Table 4 essential parameter of circuit

Table 5 goes out specific electric load (perunit value)

Table 6 outlet sharing of load scheme and the relation of shining upon elastic potential energy

Table 6 is visible, and from scheme 1 to scheme 4, the mapping elastic potential energy of outlet and electrical network all increases progressively.In scheme 1, the burden with power of outlet than with the mapping coefficient of elasticity when identical, i.e. burden with power distributes when the most balanced, the mapping elastic potential energy minimum of electrical network; In scheme 4, the outlet burden with power than with the mapping coefficient of elasticity when contrary, i.e. burden with power distributes when least balanced, mapping elastic potential energy maximum.

Fig. 9 is visible, and in scheme 1, the elastic elongation of outlet all equates, stressed the most balanced, shows that the burden with power of outlet distributes the most balanced; In scheme 4, the elastic elongation of outlet is least balanced, and stressed least balanced, i.e. burden with power distributes least balanced.Scheme 2,3, the harmony that burden with power distributes is between the 1st, 4 kinds of situations.

Simulation results show the 5th the joint theoretical analysis result.

7. conclusion

Under idle abundant condition, the meritorious bearing capacity of electrical network depends on the factors such as the size of electric network composition, branch road bearing capacity, power supply and load and distribution, is difficult to quantitative analysis.The elastic network(s) bearing capacity depend on factor and electrical network similar, in mechanical system, but the elastic potential energy of Applied Physics definite conception, the bearer properties of analysing elastic net.After electrical network being mapped to the elastic network(s) of longitudinal stress, due to the quantity of state correspondent equal in electrical network and elastic network(s), the relationship consistency between quantity of state, therefore the bearer properties of elastic network(s) is exactly the meritorious bearer properties of electrical network.

Analyze and find, from overall angle, the mapping elastic potential energy can quantitatively be weighed the meritorious carrying nargin of electrical network; Angle, can weigh the meritorious harmony of carrying of grid branch internally; And, when the mapping elastic potential energy changes, totally carry nargin and inner to carry balanced variation tendency consistent.Therefore, the mapping elastic potential energy can be used as the quantitative analysis index of electric network active bearing capacity.Theory analysis and simulation analysis all show: in certain total active load situation, the mapping elastic potential energy is larger, and the electric network active bearing capacity is more weak.

The present invention has enriched the theoretical foundation that electric network security is analyzed, and can be widely used in the aspects such as planning, operational mode analysis, on-line scheduling of electrical network.

Claims (1)

1. One kind based on the mapping elastic potential energy electric network active bearing capacity quantitative analysis index, this index is characterised in that, comprises the steps:

   1) negligible resistance, establishing AC network branch road L two end nodes is i, j, node voltage

   

   

   phase difference be θ _ij, reactance is X _l, when electric network reactive-load is abundant, U _i, U _jchange littlely, can make transmission gains merit for P _l=Csin θ _ij, make k _l=dP _l/ d θ _ij, be named as the mapping coefficient of elasticity of L, can obtain k _l=Ccos θ _ij=P _l/ tan θ _ij;

   Active force and the elongation of 2) establishing elastic network(s) branch road l are respectively F _l, x _l, coefficient of elasticity is k _l=dF _l/ dx _l, set up the quantity of state mapping relations of L and l, i.e. P _l=F _l, θ _ij=x _l, k _l=k _l, according to step 1), it is F that the quantity of state of l closes _l=Csinx _l, k _l=Ccosx _l=F _l/ tanx _l;

   3) if θ _ijless, but the quantity of state relation approximately linear of L, according to step 1), can obtain P _l=k _lθ _ij, k _l=C, according to step 2), it is F that the quantity of state of corresponding linear l closes _l=k _lx _l, k _l=C;

   4) after l stretches, elastic potential energy is that external force is to its work, i.e. E _l=∫ F _ldx _l, according to step 2) in the quantity of state relation of l, obtain elastic potential energy

   

   according to step 2) in the quantity of state mapping relations of L and l, obtain the mapping elastic potential energy of L $E_L=P_L\tan \frac{{\mathrm{\&theta;}}_{\mathrm{ij}}}{2}=k_L\frac{1-{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}{{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}=\frac{{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}{{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}=\frac{{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}{1+{\cos \mathrm{\&theta;}}_{\mathrm{ij}}}\&CenterDot;\frac{{P_L}^2}{k_L},$ And E _l=E _l;

   5) if θ _ijless, the quantity of state of l, L all is approximately linear relationship, according to step 3), 4), obtain the elastic potential energy of l

   

   according to step 2) in the quantity of state mapping relations, obtain the mapping elastic potential energy of L $E_L=\frac{1}{2}{P}_L{\mathrm{\&theta;}}_{\mathrm{ij}}=\frac{1}{2}{k}_L{{\mathrm{\&theta;}}_{\mathrm{ij}}}^2=\frac{{P_L}^2}{{2k}_L},$ And E _l=E _l;

   6) electrical network is mapped to vertical stressed elastic network(s), and keeps the incidence relation of node, branch road constant, establish the mapping elastic network(s) and formed by n bar branch road, E _{the l ∑}and E _libe respectively elastic network(s) and the potential energy of i bar branch road wherein, no matter whether its branch road is the linear elasticity branch road, and its total potential energy all meets superimposed characteristics, therefore the mapping elastic potential energy of electrical network is e _{the L ∑}and E _libe respectively electrical network and the mapping elastic potential energy of i bar branch road wherein;

   7) if in the mapping elastic network(s), all branch roads are all the linear elasticity branch road, because branch road is vertical in the same way, branch road length is the difference in height of two end nodes, and the phase place of the corresponding grid nodes voltage of height of node, establish F _topi, x _topifor stressed size and the height of elastic network(s) top node, F _botj, x _botjfor the stressed size of load node and height, according to step 5), 6) in E _l, E _{the l ∑}formula, the potential energy that obtains the Linear Mapping elastic network(s) is

   

   therefore the mapping elastic potential energy of linear electrical network is

   

   p _topi, θ _topifor the injection of power source bus node in electrical network is meritorious and phase place, P _botj, θ _botjburden with power and phase place for load bus;

   8) because all branch roads in the mapping elastic network(s) are subject to force direction identical, therefore available 1 and this net potential energy E _{the l ∑}with total load F _{the l ∑}all equal elasticity branch road equivalences, the length of establishing equivalent branch road is x _leq, according to step 4), obtain

   

   if E _{the L ∑}, P _{l Σ}and θ _leqfor the mapping potential energy of corresponding electrical network, total active load and equivalent branch road phase difference, according to the quantity of state mapping relations, obtain $E_{\mathrm{L\&Sigma;}}=P_{\mathrm{L\&Sigma;}}\tan \frac{{\mathrm{\&theta;}}_{\mathrm{Leq}}}{2},$ If equivalent branch road is linear characteristic, according to step 5), obtain $E_{\mathrm{l\&Sigma;}}=\frac{1}{2}{F}_{\mathrm{l\&Sigma;}}{x}_{\mathrm{lep}},E_{\mathrm{L\&Sigma;}}=\frac{1}{2}{P}_{\mathrm{L\&Sigma;}}\&CenterDot;{\mathrm{\&theta;}}_{\mathrm{Leq}};$

   9) step 8) show, in identical total active load situation, different electrical networks or same electrical network are under different running method, if E _{the L ∑}larger, θ _leqalso larger, the overall meritorious carrying nargin of electrical network is less, and bearing capacity is poor, and the fail safe of merit angle is poor;

   10) by the associated nodes of mains side and load side and between path merged and equivalence, be simplified to vertical equivalence mapping elastic network(s), be provided with n bar branch road, the mapping coefficient of elasticity that i bar branch road is corresponding, phase difference and the meritorious k that is respectively _li, θ _liand P _li, total burden with power is

   

   find and prove rule, even P _{the L ∑}=const., meet P when branch road has the distribution of work _l1: P _l2: ...: P _ln=k _l1: k _l2: ..:k _lnthe time, always shine upon elastic potential energy E _{the L ∑}minimum;

   11) equilibrium of electric network active carrying, refer to the larger circuit of mapping coefficient of elasticity, should carry larger gaining merit, step 10) show, it is harmonious that the mapping elastic potential energy can characterize the meritorious carrying of grid branch, when total burden with power is constant, the mapping elastic potential energy is less, and the meritorious carrying of grid branch harmony is better;

   12) step 9), 11) from overall and interior angle, show respectively, the mapping elastic potential energy can quantitatively be weighed the meritorious carrying nargin of electrical network and the harmony of the meritorious carrying of grid branch, and when the mapping elastic potential energy changes, overall carrying nargin is consistent with the balanced variation tendency of inner carrying, therefore, the mapping elastic potential energy can be used as the quantitative analysis index of electric network active bearing capacity, in certain total active load situation, the mapping elastic potential energy is larger, and the electric network active bearing capacity is more weak.

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