WO2015035577A1

WO2015035577A1 - Quantitative analysis method for active power load capability of power grid based on mapping elastic potential energy

Info

Publication number: WO2015035577A1
Application number: PCT/CN2013/083331
Authority: WO
Inventors: 竺炜
Original assignee: Zhu Wei
Priority date: 2013-09-11
Filing date: 2013-09-11
Publication date: 2015-03-19

Abstract

Provided is a quantitative analysis method for the active power load capability of a power grid based on mapping elastic potential energy. Based on a mapped elastic mechanical network model of the power grid, the mapped elastic potential energy of a power grid branch is obtained by means of branch state mapping. The mapped elastic potential energy of the power grid is obtained by using potential energy superposition. Analysis discovers and simulations verify that the mapped elastic potential energy can be used as a quantitative analysis index of the active power load capability of the power grid. The method enriches the theoretical basis of power grid safety analysis, and can be widely applied to power grid planning, operation mode analysis, online dispatching, and the like.

Description

Quantitative analysis method for active power carrying capacity of power grid based on mapping elastic potential energy

Technical field

Power system (grid) safety analysis. Background technique

The most basic function of the power grid is active power (hereinafter referred to as active power) transmission. Therefore, active load capacity (or active power transmission capability) is the main indicator of grid safety analysis, which depends on grid structure, branch load capacity, power supply and load. The size and distribution of many other factors. At present, the qualitative analysis of the N-l (or even N-2) branch load limiting check is generally used in practical work. The quantitative analysis method and index of the active load carrying capacity of the power grid are still the difficulties in the safety analysis of the power grid.

Statistics show that in the last fifteen years of the last century, large blackouts in the United States met the self-organized criticality of complex systems. Inspired by the use of complex network theory to analyze the safety of large power grids has become a hot research topic. However, the complex network model is based on the graph theory model of the wiring topology. It does not include the component parameters of the grid, and it does not naturally reflect the physical relationship between the grid nodes and the branch state and the physical relationship between them. It is difficult to establish the state quantity and structure information of the grid. Comprehensive indicators.

The construction of local indicators is relatively easy, but it is not easy to construct a network-wide indicator. The ideal way is to add local indicators. At present, there are potential energy indicators that satisfy the superposition, such as node potential energy and branch potential energy. However, these indicators are concepts in the direct method of grid transient stability. There is no clear physical concept in static analysis. It is also impossible to prove the potential energy of components. The active carrying capacity of the grid can be described later. Therefore, its theoretical basis for characterizing grid security is insufficient.

Compared with the definition in the power grid, "potential energy" has a clear and strict physical concept in mechanics and is unique. Similar to the active carrying capacity of the grid, the carrying capacity of the elastic network also depends on the grid structure, branch strength, force size and distribution. The previously applied patent "Grid-elasticity network topology mapping method" (application publication number: CN 102227084 A), the grid is mapped into a longitudinally-loaded elastic mechanical network (hereinafter referred to as elastic network) model, due to the mapping of the elastic network The direction is the same, the same direction force also satisfies the superposition, so the total potential energy is related to the total load. Therefore, the active carrying capacity of the corresponding power grid can be analyzed by mapping the potential energy of the elastic network. Summary of the invention

According to the present invention, the quantitative analysis index of the active load capacity of the power grid based on the mapped elastic potential energy, based on the grid elastic network model, analyzes the mapping elastic potential energy of the power grid branch through the state map of the power grid branch and the elastic network branch, and uses the potential energy The idea of superposition is obtained, and the method for obtaining the elastic potential energy of the grid mapping is obtained. The analysis finds that the elastic potential energy of the map can characterize the overall active load margin of the grid and the balance of the active load of the branch: Under a certain total active load, the larger the value, the overall active load of the grid The smaller the degree, the more uneven the active load of the branch; the smaller the value, the opposite. Therefore, it can be used as a quantitative analysis indicator of the active carrying capacity of the power grid. The invention enriches the theoretical basis of grid security analysis and can be widely applied to grid planning, operation mode analysis, online scheduling and the like. DRAWINGS

Figure 1 Grid-elastic network topology mapping, (1) grid, (2) mapping elastic network Specification Figure 2 Equivalent Mapping Elastic Branch Figure 3 Vertical Equivalent Mapping Elastic Network Figure 4 New England 10-machine 39-node system Figure 5 New England 10-machine 39-node system mapping elastic network structure Figure 6 New England 10-machine 39-node system cut-off Mapping elastic network structure after line 21-22Fig.7 Mapping elastic network structure after the New England 10-machine 39-node system cuts off the line 15-16 Figure 8 7-node system structure Figure 9 Mapping elastic network structure of four load distribution schemes, ( 1) Outgoing load distribution plan one, (2) Outgoing load distribution plan II, (3) Out line load distribution plan III, (4) Out line load distribution plan four specific implementation

1. State map of the grid branch and the elastic network branch

Ignore the resistance, set the AC grid branch node to /, _ /, the node voltage ί /,., the phase difference is ., the reactance is ^. When the grid is not fully reactive, the U C / / change is small, so that c = ^. The active power of the transmission is

P _L = C (1) Let = άΡ Ιάθ , the mapping elastic coefficient named, obtained by equation (1)

k _L = C^e _tJ (2) k^ P t^ (3) Set, respectively, the force and elongation of the elastic mesh branch/, and the spring constant is _{= £} ^/ . Establish a state quantity mapping relationship between £ and /: = _Xl (4)

A = ^k i

Corresponding to equations (1), (2), and (3), the state quantity relationship of / is

If it is small, the state quantity relationship of Z can be approximately linearized, and can be obtained by equations (1), (2), and (3).

According to equation (4), the corresponding linear / state j ΐ relationship is

/ =

(7)

2. Mapping of the potential energy of the grid branch

/ After stretching, the elastic potential energy is the work done by the external force, ie

_{_{Ei = JF t dx t (8}} ) according to formula (5), (8), the elastic potential energy is obtained

1 -

(9) cos x _{ 1 + cos x _l

According to the mapping relationship of equation (4), the obtained mapping elastic potential energy is

θ,. 1 - cos θ,. COS θ,. ²

E _L = P _L ti two k _L ^l L two ^l - L (10)

2 cos 9 _tJ 1 + cos 9 _t k _L

If it is small, the state quantity of /, is. The elastic potential energy obtained by equations (7) and (8) is

According to the mapping relationship of equation (4), the mapping elastic potential energy of the line is

E _L = »(12) _Since, θ ϋ, and F _t, _Xl, corresponding to the values equal, and it also satisfies _£ mapping relationship, i.e.,

E, = E _L (13)

3. Grid mapping elastic potential energy

According to the published patent application "Grid-elasticity network topology mapping method" (application publication number: CN 102227084

A), the grid is mapped to a vertically stressed elastic network, and the relationship between nodes and branches is kept unchanged, as shown in Figure 1.

Let the mapping elastic network be composed of strips, regardless of whether its branch is a linear elastic branch, its total potential energy satisfies the superposition characteristics, ie

E _a = ^E u (14) where _∑ and are respectively the potential energy of the elastic network and the first branch thereof. Therefore, the mapping elastic potential energy of the power grid is

E _L∑ =∑E _Ll (15) where E _L∑ and E _Li are the mapped elastic potentials of the grid and the z- _th branch, respectively.

Since the branches in the elastic network are perpendicular to the same direction, the length of the branch is the height difference between the nodes at both ends, and the height of the node corresponds to the phase of the voltage of the grid node. If all the branches are linear elastic branches, according to equations (11) and (14), the potential energy of the linear elastic mesh is obtained. Description

El∑ ⁼ ~ ^ ( top/ · p ) - Σ ( b.t. · b.t ) (16) where p,., is the force level and height of the top node of the elastic net, J . , x _b . The force level and height of the load node. If the active loss of the grid is neglected, according to the above formula, the elastic potential energy is

In the above formula, . , ρ, is the injected active and phase of the power bus node in the grid. .6 _; is the active load and phase of the load node.

4. The relationship between the mapping elastic potential energy and the overall active load margin of the power grid

Since all the branches in the mapped elastic network have the same force direction, one elastic branch equivalent to the potential energy and the total load of the network can be used, and the equivalent branch length is 3⁄4 _3⁄4 , as shown in Fig. 2. Available from formula (9)

3⁄4=^tan^ (18) According to the state quantity mapping relationship, there is

_3⁄4 _∑ = _i∑ tan^ (19) where E _L _∑ , /1 _∑ and 6^ are the mapped potential energy, total active load and equivalent branch phase difference of the corresponding grid. The above formula can be seen: When £ _∑ is a certain value, if _i _∑ is larger, _q is larger; if _{∑ is} smaller, the smaller is.

If the equivalent branch is linear, according to 11), (12), then

Similarly, when P _{£ ∑} is a certain value, if _i _∑ is larger, _q is larger; if _{∑ is} smaller, the smaller is.

At the same total active load, different or the same power grid at different operation modes, when _Ε ίΣ larger, the larger, in general show a smaller margin active carrier grid, poor carrying capacity, The power angle is less secure.

5. The relationship between the mapping elastic potential energy and the balance of active load of the power grid branch

Due to the unbalanced power distribution of the power grid, even if the overall load capacity of the power grid is strong, some branches may be close to overload. If the branch is overloaded and automatically removed, it may cause a chain reaction, causing the grid to partially dissociate or even collapse. Therefore, the metric can be used to measure the balance of the power grid branch from an internal perspective.

The equalization of the active load of the power grid refers to the line with a large mapping elasticity coefficient, which should carry a large active power. Since the grid is mapped into a longitudinally-loaded elastic network, the associated nodes on the power supply side and the load side and the paths between them can be combined and equivalent, and simplified into the structure shown in FIG.

As shown in Fig. 3, there is a strip branch road, and the corresponding branch map corresponding to the elastic coefficient, phase difference and active power are , and / L., and the total active load is Ρ _∑ = . Found that the following rules exist:

ι=1

If P _Li = const., when the branch active distribution satisfies the following formula Description

(21) The total mapping elastic potential energy _{i is the} smallest.

Proof: According to formulas (10) and (15)

i(3⁄4tan (22)

L

In the above formula, it is the phase difference between the ends of the first branch. Construct the following Lagrangian equation using the Lagrangian extremum method

E = E _L∑ -A( _∑P _Ll -P _L∑ ) (23) where A is a constant. _I∑ is the extreme value

So there is

Available from equations (22) and (25)

Tan— = tan— = ··· = tan— (26)

2 2 2

According to the formula (3), the formula (26) and the formula (21) are equivalent to each other. I.e. satisfies the formula (21), _E extremum.

If the AC line is simplified to be mapped to a linear elastic branch, it can be obtained according to equations (12) and (15).

E∑∑ ⁼ ∑3⁄4^J (27) Similarly, using the Lagrangian extremum method, the extreme condition of the _∑ is

e _Ll =9 _L1 =--- = e _Ln (28) According to the formula (6), the equations (28) and (21) are equivalent to each other.

Therefore, no matter whether the branch characteristic is linear or non-linear, when the equation (21) is satisfied, that is, when the active load of the power grid branch is the most balanced, ∑ is the extreme value.

Since the formula (21), (26), (28) are equivalent, so _Σ extremal point is unique. It is known from the problem itself that the minimum potential energy must exist, so when the equation (21) is satisfied, _∑ is the minimum value.

The certificate is completed.

The above analysis shows that the mapping elastic potential energy can characterize the balance of active load of the power grid branch. When the total active load is constant, the smaller the mapping elastic potential energy, the better the balance of the active load of the power grid branch.

6. Example analysis

6.1 Analysis of calculation accuracy of elastic potential energy of power grid mapping

The New England 10-machine 39-node system is shown in Figure 4. The power flow calculation is performed, wherein the bus bar 31 is a balanced node, the reference voltage is 345 kV, the reference capacity is 100 MVA, and the mapping elastic network structure is as shown in FIG. 5.

Based on the nonlinear branch and the linear branch map, the grid-embedded elastic potential energy values of the system are obtained by equations (15) and (17), respectively (the reference value is 100, not the gauge:), as shown in Table 1. Instruction manual

Table 1 New England 10-machine 39-node system grid mapping elastic potential energy

Method Grid mapping elastic potential energy (standard value)

1. Adoption formula (10), (15) 4.553242

2, using the formula (12), (17) 4.536327 Table 1, the method 1 is a strict theoretical method, the error of the method 2 is only 0.37%. It can be seen that when the phase difference between the two ends of the grid branch is small (in this example, the phase difference between the ends of all the branches of the grid does not exceed 10° at the maximum), the linear branch map is used and the active loss of the grid is ignored, and the mapped elastic potential energy of the grid The error is small.

The simulation results verify the feasibility of the theoretical method in Section 3.

6.2 Analysis of the relationship between the mapping elastic potential energy and the overall active load margin of the power grid

The New England 10-machine 39-node system is still used as an example. Calculated by Method 2 of Table 1, the mapped elastic potential energy of the power grid is 4.536327, and the equivalent branch phase difference is 0.147520.

Under the condition that the power supply and load are not cut off and the size and distribution are kept unchanged, N-l is sequentially made to the grid branch, and the first six lines are taken according to the change of potential energy from large to small, as shown in Table 2.

Table 2 Grid mapping elastic potential energy increment

Mapping elastic potential energy increment Δ3⁄4 _Σ equivalent branch phase difference ^ ^

Serial number

(standard value) (radian)

1 21-22 1.476665 0.195541

2 28-29 0.758188 0.172177

3 2-3 0.518366 0.164378

4 23-24 0.483779 0.163253

5 16-21 0.430813 0.161530

6 15-16 0.375668 0.159737

Table 2 shows that after cutting off any grid branch, the phase difference of the equivalent branch of the grid increases, indicating that the overall active load margin becomes smaller and the bearing capacity becomes weaker. In addition, the mapping elastic potential energy and equivalent branch phase are mapped. The difference between the growth and the order of the difference indicates that the greater the potential elasticity of the mapping, the smaller the overall active load margin of the grid. In Table 1, after the line 21-22 is cut off, the mapping elastic potential energy increases the most, and the overall active load margin of the power grid is the smallest.

For visual comparison, the lines 21-22 and 15-16 are respectively cut off, and the mapped elastic network structure of the grid is shown in Figures 6 and 7. Compared with Figure 5 before the cut-off line, it can be seen that Figure 6 is more obvious than the overall elastic elongation of Figure 7, the structure is more fragile, and the active load capacity is more reduced.

The simulation results verify the theoretical analysis results in Section 4.

6.3 Analysis of the relationship between the mapping elastic potential energy and the balanced load of branch active power

The parameters of the 7-node system shown in Figure 8 are shown in Tables 3 and 4. The five outlets are from left to right, the length ratio is 600:400:300:240:200, and the elastic coefficient ratio is approximately m.k ₅ =1:1.5. :2:2.5:3.

The output load is shown in Table 5. The active load is characterized by: ₂ : P _{3 :} P _{4 : J} P ₅ =1: 1.5: 2: 2.5: 3. The reference voltage is 500kV and the reference capacity is 100WM. There are four kinds of load distribution schemes, and the corresponding mapping elastic network structure is shown in Fig. 9. The node height in Figure 9 corresponds to the grid node phase, and the branch map elasticity coefficient (standard value) and active power flow (marked value) are marked next to the corresponding branch. Instruction manual

Using the formula (10 (15), calculate the grid mapping elastic potential energy under the 4-load distribution scheme, the benchmark value is 100, 3⁄4 as shown in Table 6.

Table 3 Basic parameters of main transformer

Capacity ratio resistance (standard value) reactance (standard value)

600WM 500/13.8kV 0.000 37 0.023 32

Table 4 Basic parameters of the line

Branch 2-3 2-4 2-5 2-6 2-7 Length (km) 600 400 300 240 200 Resistance (standard value) 0.006 3 0.004 2 0.003 2 0.002 5 0.002 1 Reactance (standard value) 0.074 4 0.049 6 0.037 2 0.029 8 0.024 8

Table 5 Outlet load (standard value)

8 ₁ S ₂ =P ₂ +jQ ₂ S ₃ =P ₃ jQ ₃ S ₄ =P ₄ +jQ ₄ S ₅ =P ₅ +jQ ₅

0.5+j0.02 0.75+0.03j l+0.04j 1.25+0.05 1.5+0.06J

Table 6 Relationship between outgoing load distribution scheme and mapped elastic potential energy

Active load ratio main transformer + outlet line grid mapping elastic potential energy

What is the distribution of the case ^^ϋ ^ , ,

Mapping elastic coefficient ratio mapping elastic potential energy (standard value) (standard value)

1

0.300 420+0.097 207 0.397 627

2 2.5:1.5:1:2:3

1:1.5:2:2.5:3 0.301 159+0.126 477 0.427 636

3:2:1:1.5:2.5

3 1:1.5:2:2.5:3 0.302 281+0.150 115 0.452 396

4 3:2.5:2:1.5:1

1:1.5:2:2.5:3 0.302 461+0.163 151 0.465 612 Table 6 shows that from Scheme 1 to Scheme 4, the mapping elastic potentials of the outgoing line and the grid are increasing. In scheme 1, when the active load ratio of the outgoing line is the same as the mapping elastic coefficient ratio, that is, when the active load distribution is the most balanced, the mapping elastic potential energy of the power grid is the smallest; in the scheme 4, when the active power load ratio of the outgoing line is opposite to the mapping elastic coefficient ratio, the active power is When the load distribution is the most uneven, the mapping elasticity potential is the largest.

As can be seen from Fig. 9, in the scheme 1, the elastic elongation of the outlets are equal, and the force is the most balanced, indicating that the active load distribution of the outlet is the most balanced; in the scheme 4, the elastic elongation of the outlet is the most uneven, and the force is the most uneven, that is, The active load distribution is the most uneven. Scheme 2, 3, the balance of active load distribution is between the first and fourth cases.

The simulation results verify the theoretical analysis results in Section 5.

7. Conclusion

Under the condition of insufficient power, the active carrying capacity of the power grid depends on many factors such as the power grid structure, the bearing capacity of the branch, the size and distribution of the power supply and the load, etc. It is difficult to quantitatively analyze. The factors that determine the carrying capacity of the elastic network are similar to those of the power grid. In the force system, the elastic potential energy with clear physical concept can be applied to analyze the bearing characteristics of the elastic network. After the grid is mapped into a longitudinally-loaded elastic network, the relationship between the state quantities is consistent because the state quantities in the grid and the elastic network are equal, so the load-bearing characteristics of the elastic network are the active load-bearing characteristics of the grid.

The analysis finds that from the overall perspective, the mapped elastic potential energy can quantitatively measure the active load margin of the power grid; from the internal perspective, the balance of the active load of the power grid branch can be measured; and when the mapped elastic potential energy changes, the overall load margin and internal bearer are both Description

The trend of change is consistent. Therefore, the mapping elastic potential energy can be used as a quantitative analysis index of the active carrying capacity of the grid. Theoretical analysis and simulation analysis show that under certain total active load, the greater the mapping elastic potential energy, the weaker the active carrying capacity of the power grid.

The invention enriches the theoretical basis of grid security analysis and can be widely applied to grid planning, operation mode analysis, online scheduling and the like.

Claims

1. A quantitative analysis index of active power carrying capacity of a power grid based on mapping elastic potential energy, the indicator is characterized by the following steps:

1) Ignore the resistance, set the phase difference between the two nodes of the AC grid branch, the node voltage, and the reactance is ^. When the grid is not fully reactive, the UC// change is small, so C = ^, then the transmission The merit is /l=C _S m ., let k, =

The force and elongation of the elastic mesh branch I are respectively, X, and the elastic coefficient is k = dF dx, and the state quantity mapping relationship between £ and / is established, that is, the corpse _i= , k _L =k 〖, according to the steps 1), the state quantity relationship of / is = C _S m , k ₍ =C cos x _l = F _l /tan x _l ;

3) If it is small, the state quantity relationship can be approximately linearized. According to step 1), k _L = C can be obtained. According to step 2), the corresponding linear / state quantity relationship is k _{l =} C;

4) After stretching, the elastic potential energy is the work done by the external force, S卩, = fF x, according to the state quantity relationship in step 2), the elastic potential energy _tai = i^3⁄4 = ^^^ is obtained, according to the step 2) Neutralization / state quantity mapping off

2 cosx, 1 + cos x _l k _t , the resulting mapped elastic potential energy 3⁄4= _£ta i yt _£ i^3⁄4=^^.^l, and

2 cos θ _{] 1 + cos θ _{] k _L

5) If it is small, the state quantities of 1. are approximately linear. According to steps 3) and 4), the elastic potential energy of ^ is obtained = ^ -3⁄4 = - = - ' according to the state quantity mapping relationship in step 2) Get the mapped elastic potential energy of L

2 2 2

E _L =

6) Mapping the power grid into a vertically-stressed elastic network, and keeping the relationship between nodes and branches unchanged. The mapping elastic network consists of “strips, 3⁄4 _∑ and . respectively elastic network and 第支The potential energy of the road, whether its branch is a linear elastic branch, its total potential energy satisfies the superposition characteristic, ie 3⁄4 _∑ =3⁄4 3⁄4, so the mapped elastic potential energy of the grid is _∑ = , ., ^ and E _Li are respectively the grid and The mapped elastic potential energy of the i-th branch;

7) If all the branches in the mapped elastic network are linear elastic branches, since the branches are perpendicular to the same direction, the length of the branches is the height difference between the nodes at both ends, and the node height corresponds to the phase of the voltage of the grid node, and F _t is set. _p; , x _top ,. is the force level and height of the top node of the elastic net, x _b . _t . For the force magnitude and height of the load node, according to the 3⁄4 and _ffi formulas in steps 5) and 6), the potential energy of the linearly mapped elastic network is E =^∑{F . _top; ) -^∑(F _otj _3⁄40 ,), so the linear elastic potential energy of the linear grid is = ∑(Κ.)_ ∑(H _; ), which is the injected active and phase of the power bus node in the grid, _b . _t , 6> _b . _t is the active load and phase of the load node;

8) Since all the branches in the mapped elastic network have the same force direction, one can be equal to the potential energy and the total load _{该 of} the network. The elastic branch of the claim is equivalent, and the length of the equivalent branch is _q . According to step 4), _{= J} F _ffitan ^ is obtained, and P _{L ∑} and _q are the mapped potential energy, total active load and corresponding power grid. Equivalent branch phase difference, according to the state quantity mapping relationship, obtain E _i∑ = P _L∑ tan^l, if the equivalent branch is linear, according to step 5), get E _K =^F _l∑ x _kq , E _L∑ =^P _L∑ · 0 _Leq ;

9) Step 8) shows that under the same total active load, different grids or the same grid under different operating modes, if i _{∑ is} larger, _q is also larger, and the overall active load margin of the grid is smaller, bearing Poor ability, poor safety of power angle;

10) Combine and equilibrate the associated nodes on the power supply side and the load side and the equivalent between them, simplifying into a longitudinal equivalent mapping elastic network, and providing the mapping elastic coefficient and phase difference corresponding to the strip branch and the branch branch. The active _powers are ., . and ., the total active load is, and the law is found and proved, that is, if p _i∑ = _cons t, when the branch active distribution is satisfied

P _Ll :P _l2 : ... :P _Ln =k _Ll :k _L1 : ...: k _Ln , the total mapped elastic potential energy E _{Li is} minimum;

11) The equalization of the active load of the power grid refers to the line with a large mapping elasticity coefficient, which should carry a large active power. Step 10) shows that the mapped elastic potential energy can characterize the equalization of the active load of the power grid branch, that is, when the total active load is constant The smaller the mapping elastic potential energy, the better the balance of the active load of the power grid branch;

12) Steps 9) and 11) indicate from the overall and internal perspectives that the mapping elastic potential energy can quantitatively measure the active load margin of the grid and the balance of the active load of the grid branch, and when the mapping elastic potential energy changes, the overall bearing margin and The trend of internal load balancing is consistent. Therefore, the mapping elastic potential energy can be used as a quantitative analysis index of the active load capacity of the power grid. Under certain total active load conditions, the greater the mapping elastic potential energy, the weaker the active carrying capacity of the power grid.