Weak link identification and planning method for power grid transmission section feasible region improvement

Abstract

The application discloses a weak link identification and planning method for power grid transmission section feasible region improvement, and mainly comprises the following steps: 1) establishing an optimal power flow model; 2) solving the optimal power flow model by using a multi-parameter planning theory; 3) establishing a power system weak link identification model based on a transmission section power transmission feasible region R T and a feasible region vertex coordinate matrix V T at t time; 4) solving the power system weak link identification model to obtain a to-be-upgraded planning line set Ω l and a generator set Ω g ; 5) establishing a power system planning model; 6) inputting the to-be-upgraded planning line set Ω l and the generator set Ω g into the power system planning model to complete the upgrading planning of the power system weak link. The application can effectively improve the transmission section power transmission capacity by depicting the transmission section power transmission feasible region, identifying the lines and generators limiting the transmission section power transmission capacity and determining a reasonable planning scheme for upgrading and reconstruction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system optimization planning, in particular to a weak link identification and planning method for power grid transmission section feasible region improvement. BACKGROUND

[0002] In recent years, with the rapid growth of new energy and load, the uncertainty of power system operation is enhanced, the operation safety domain is reduced, and the power of key transmission sections of power grid is blocked, which brings risks to the safe operation of power grid. In order to ensure that the key transmission sections of power grid have enough transmission capacity to support the safe and stable operation of power grid, it is urgent to upgrade and transform the existing elements through reasonable planning scheme to expand the power transmission feasible region of transmission section and improve the power transmission capacity of transmission section. However, the planning problem of large-scale system has many integer variables, which makes it difficult for traditional methods to solve it. SUMMARY

[0003] The purpose of the present application is to solve the problems in the prior art.

[0004] The technical scheme adopted to achieve the purpose of the present application is as follows: a weak link identification and planning method for power grid transmission section feasible region improvement mainly includes the following steps:

[0005] 1) Obtain power system data and establish an optimal power flow model.

[0006] Further, the obtained power system data includes load power data of each node of the power system, a unit-node connection matrix I g and a power transmission transfer distribution factor matrix A PTDF .

[0007] Further, the objective function of the optimal power flow model is as follows:

[0008] min c T P g,t (1)

[0009] In the formula, P g,t is the unit output vector at time t, and c is the power generation cost vector of the generator.

[0010] The constraint conditions of the optimal power flow model include line transmission power equality constraint, upper and lower limit constraints of power system variables and power balance constraint.

[0011] The line transmission power equality constraint is as follows:

[0012] P l,t =A PTDF (I g P g,t -P d,t ) (2)

[0013] P l,t = [P l1 P l2 … P ln …] T (n = 1, 2, …, N l ) (3)

[0014] P g,t = [P g1 P g2 … P gi … P rg1 P rg2 … P rgj …] T

[0015] (i = 1, 2, …, N g j = 1, 2, …, N rg ) (4)

[0016] where P l,t is the line flow vector at time t. P ln is the transmission power on the nth line. N l is the number of lines in the power grid. P g,t is the unit output vector at time t. P d,t = [P1 P2 … P m …] T is the node load power vector at time t. m = 1, 2, …, N b . P m is the load power at node m. N b is the number of nodes in the power grid. P gi and P r g j are the outputs of the ith thermal power unit and the jth wind power unit, respectively. N g and N r g are the number of thermal power units and wind power units in the power grid, respectively.

[0017] The upper and lower limits of the power system variables are as follows:

[0018]

[0019]

[0020] where the superscript and subscript (*) represent the upper and lower limits of the variable (*), respectively.

[0021] The power balance constraint is as follows:

[0022] ∑Pg,t =∑P d,t (7)

[0023] Where, P g,t is the unit output vector at time t, P d,t is the node load power vector at time t.

[0024] 2) Using multi-parameter planning theory to solve the optimal power flow model, the feasible region R of power transmission section at time t is obtained. T And the feasible region vertex coordinate matrix V T =[P f1 P f2 ... P fk ...]. k=1,2,...,N k .P fk is the coordinate corresponding to the kth feasible region vertex, N k is the number of vertices in the feasible region.

[0025] Furthermore, the method of solving the optimal power flow model using multi-parameter planning theory is as follows: the power of the key transmission section of the power grid P f,t The optimal power flow model is solved by taking the variables other than the planning parameters in the optimal power flow model as the optimization variables.

[0026] 3) Based on the feasible region R of power transmission section at time t T And the feasible region vertex coordinate matrix V T ,To establish a weak link identification model for the power system, the main steps are as follows:

[0027] 3.1) Take the key transmission section power P f,t is the feasible region vertex coordinate matrix V T The coordinate values ​​of each vertex in are:

[0028] P f,t =P fk (k=1,2,...,N k ) (8)

[0029] Where, P f,t P is the power vector of the key transmission section of the power grid at time t. f k is the coordinate corresponding to the kth vertex, N k is the number of vertices.

[0030] 3.2) Substitute formula (8) into the optimal power flow model, solve the optimal power flow model, and obtain the line that satisfies formula (9) and formula (10) and generators The line and generators The weak link of the power system at time t.

[0031]

[0032]

[0033] wherein, is the line flow vector. is the generator output vector. is the line capacity upper limit matrix. is the generator output lower limit matrix.

[0034] 3.3) Return to step 3.1 until all times in the power system dispatch period T are traversed, establishing the line set Ω l and the generator set Ω g to be upgraded.

[0035] 4) Solve the power system weak link identification model to obtain the line set Ω l and the generator set Ω g to be upgraded.

[0036] 5) Establish the power system planning model, the main steps are as follows:

[0037] 5.1) Establish the line upgrade and reconstruction model, namely:

[0038]

[0039]

[0040] wherein, is the transmission capacity upper limit of the nth line. k l is the line capacity expansion proportionality coefficient. x ln is the impedance parameter of the nth line. x l is the line impedance parameter matrix. k x is the impedance reduction proportionality coefficient. u ln is the 0-1 variable corresponding to the nth line. Ω l is the set of lines to be upgraded.

[0041] 5.2) Establish the generator upgrade and reconstruction model, namely:

[0042]

[0043] wherein, P gi is the transmission capacity lower limit of the ith thermal power unit, k g is the unit flexibility reconstruction proportionality coefficient, u gi is the 0-1 variable corresponding to the ith thermal power unit, Ωg is the set of generators to be upgraded.

[0044] 5.3) Based on the line upgrading model and the generator upgrading model, the objective function of the power system planning model is established, i.e.:

[0045]

[0046] wherein, P f,t is the transmission power of the transmission section at time t. T is the total scheduling period.

[0047] 5.4) The constraint conditions of the power system planning model are established, including the investment cost constraint, the planning element quantity constraint, the node power balance constraint, the line power flow balance constraint, the node phase angle upper and lower limit constraint, the unit output upper and lower limit constraint, the line power flow upper and lower limit constraint and the thermal power unit ramping constraint.

[0048] The investment cost constraint is shown as follows:

[0049]

[0050] wherein, c ln is the nth line upgrading cost. c gi is the flexibility upgrading cost of the ith thermal power unit. C budget is the total available cost. is the output upper limit of the ith thermal power unit. is the capacity upper limit of the nth line. Ω g is the set of generators to be upgraded. Ω l is the set of lines to be upgraded.

[0051] wherein, the nth line upgrading cost c ln is shown as follows:

[0052]

[0053]

[0054] x i ∈{0,1} (18)

[0055] wherein, c ln is the nth line upgrading cost. c l,i is the corresponding cost under the ith upgrading scheme. x i is the 0-1 variable corresponding to the ith upgrading scheme. N is the number of upgrading schemes.

[0056] The flexibility upgrading cost of the ith thermal power unit c gi is shown as follows:

[0057] c gi=w g (1-k g ) P gi (19)

[0058] Where c gi is the flexibility transformation cost of the i-th thermal power unit, w g is the unit capacity transformation cost, k g It is the unit flexibility modification ratio coefficient. P gi is the lower limit of the transmission capacity of the i-th thermal power unit.

[0059] The planning component quantity constraints are as follows:

[0060]

[0061] Where u gi is the 0-1 variable corresponding to the i-th thermal power unit, u ln is the 0-1 variable corresponding to the nth line, u max is the maximum number of planned components, Ω g is the set of generators to be upgraded, Ω l A collection of lines to be upgraded.

[0062] The node power balance constraints are as follows:

[0063]

[0064] Where, is the output of the i-th thermal power unit connected to node m at time t, is the output of the j-th wind turbine connected to node m at time t, P d,t is the load power at node m at time t, is the outflow power of the bth line connected to node m at time t, is the set of thermal power units connected to node m, is the set of wind turbines connected to node m, is the set of lines connected to node m, N b is the number of grid nodes, and T is the total scheduling period.

[0065] The line power flow balance constraints are as follows:

[0066]

[0067] Where, P l,t is the line power flow matrix at time t, θ ij,t is the node phase difference matrix at time t, x lis the line impedance parameter matrix, and T is the total scheduling period.

[0068] The upper and lower limits of the node phase angle are shown as follows:

[0069] -π≤θ t ≤π (t = 1, 2,..., T) (23)

[0070] In the formula, θ t is the node phase angle matrix at time t.

[0071] The upper and lower limits of the unit output are shown as follows:

[0072]

[0073]

[0074] In the formula, P w,t is the wind turbine output matrix at time t, and P g,t is the thermal power unit output matrix at time t.

[0075] The upper and lower limits of the line power flow are shown as follows:

[0076]

[0077] In the formula, P l,t is the line power flow matrix at time t.

[0078] The ramping constraints of the thermal power unit are shown as follows:

[0079] R down ≤P g,t -P g,t-1 ≤R up (t = 2, 3,..., T) (27)

[0080] In the formula, P g,t and P g,t-1 are the thermal power unit output matrices at time t and time t-1, respectively, R down is the unit ramping-down capability matrix, R up is the unit ramping-up capability matrix, and T is the total scheduling period.

[0081] 6) Input the to-be-upgraded planning line set Ω l and the generator set Ω g into the power system planning model to complete the upgrade planning of the weak links of the power system.

[0082] It is worth noting that the application depicts the power transmission feasible region of the transmission section by establishing an optimal power flow model and solving based on multi-parameter programming theory; then, a weak link identification model is established, and the weak links (including lines, generators, etc.) of the power system are identified according to the constraints in action on the boundary of the feasible region, and are taken as the elements to be upgraded to reduce the integer variables; finally, an upgrading planning model is constructed for the weak links, and a reasonable upgrading planning scheme is obtained by solving, so as to effectively improve the power transmission capacity of the transmission section. In summary, the application depicts the power transmission feasible region of the transmission section, identifies the lines and generators that limit the power transmission capacity of the transmission section, and determines a reasonable planning scheme for upgrading and reconstruction, which can effectively improve the power transmission capacity of the transmission section.

[0083] The technical effect of the application is self-evident. The application proposes a weak link identification and planning method for power grid transmission section feasible region improvement, which pre-identifies the weak links such as lines and generators that limit the power transmission capacity of the transmission section, reduces the integer variables of the planning model, and thus efficiently solves the model and gives a reasonable upgrading planning scheme. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 An IEEE30 node test system schematic diagram used for the embodiment;

[0085] Figure 2 A transmission section transmission power feasible region at the moment of maximum load (t=19);

[0086] Figure 3 M0, M1 and M2 transmission section transmission power feasible region at the moment of maximum load (t=19). DETAILED DESCRIPTION

[0087] The application will be further described below in conjunction with the embodiments, but should not be understood as limiting the above-mentioned subject matter of the application to the following embodiments. Various substitutions and modifications can be made according to ordinary technical knowledge and conventional means in the art without departing from the above-mentioned technical idea of the application, and all should be included in the protection scope of the application.

[0088] Embodiment 1:

[0089] The weak link identification and planning method for power grid transmission section feasible region improvement mainly includes the following steps:

[0090] 1) Obtain power system data and establish an optimal power flow model.

[0091] The power system data includes the load power data of each node of the power system, the unit-node connection matrix I gand a power transfer distribution factor (PTDF) matrix A PTDF wherein the load data at time t is denoted as P d,t = [P1 P2 …P m …] T (m = 1, 2, …, N b ).

[0092] The objective function of the optimal power flow model is as follows:

[0093] min c T P g,t (1)

[0094] wherein P g,t is the unit output vector at time t, and c is the power generation cost vector of the generator.

[0095] The constraint conditions of the optimal power flow model include line transmission power equality constraint, upper and lower limit constraints of power system variables, and power balance constraint.

[0096] The line transmission power equality constraint is as follows:

[0097] P l,t = A PTDF (I g P g,t -P d,t ) (2)

[0098] P l,t = [P l1 P l2 … P ln …] T (n = 1, 2, …, N l ) (3)

[0099] P g,t = [P g1 P g2 … P gi … P rg1 P rg2 … P rgj …] T

[0100] (i = 1, 2, …, N g j = 1, 2, …, N rg ) (4)

[0101] wherein P l,t is the line power flow vector at time t. P ln is the transmission power on the nth line. N l is the number of grid lines. P g,tis the unit output vector at time t. d,t = [P1 P2... P m ...] T is the node load power vector at time t. m = 1, 2,..., N b . P m is the load power at node m. N b is the number of nodes in the power grid. gi and P r g j are the output of the i-th thermal power unit and the j-th wind power unit, respectively. g , N r g are the number of thermal power units and the number of wind power units in the power grid, respectively.

[0102] The upper and lower limits of the power system variables are as follows:

[0103]

[0104]

[0105] In the formula, the superscript and the subscript (*) represent the upper limit and the lower limit of the variable (*) respectively.

[0106] The power balance constraint is as follows:

[0107] ∑P g,t = ∑P d,t (7)

[0108] In the formula, P g,t is the unit output vector at time t, and P d,t is the node load power vector at time t.

[0109] 2) Use the multi-parameter programming theory to solve the optimal power flow model to obtain the power transmission feasible region R T and the feasible region vertex coordinate matrix V T = [P f1 P f2 ... P fk ...]. k = 1, 2,..., N k . P fk is the coordinate corresponding to the k-th feasible region vertex, and N k is the number of feasible region vertices.

[0110] The method for solving the optimal power flow model using the multi-parameter programming theory is as follows: taking the key power transmission section power P f,t of the power grid as the programming parameter, taking the variables other than the programming parameter in the optimal power flow model as the optimization variables, and using CPLEX or other software to solve the optimal power flow model.

[0111] 3) Power transmission feasible region R based on power transmission of transmission section at t moment T and feasible region vertex coordinate matrix V T , the main steps are as follows:

[0112] 3.1) Take the key power P of transmission section f,t is the coordinate value of each vertex in the feasible region vertex coordinate matrix V T , that is:

[0113] P f,t = P fk (k = 1, 2,..., N k ) (8)

[0114] In the formula, P f,t is the power vector of the key transmission section of the power grid at t moment. P f k is the coordinate corresponding to the kth vertex, N k is the number of vertices.

[0115] 3.2) Substitute formula (8) into the optimal power flow model, solve the optimal power flow model, and obtain the line and generator satisfying formula (9) and formula (10). and generator The line and generator

[0116] are the weak links of the power system at t moment.

[0117]

[0118] In the formula, is the line flow vector. is the generator output vector. is the upper limit matrix of line capacity. is the lower limit matrix of generator output.

[0119] 3.3) Return to step 3.1 until all moments in the dispatching period T of the power system are traversed, and establish the line set Ω l and the generator set Ω g to be upgraded.

[0120] 4) Use CPLEX and other software to solve the weak link identification model of the power system, and obtain the line set Ω l and the generator set Ω g to be upgraded.

[0121] 5) Establish the power system planning model, and the main steps are as follows:

[0122] 5.1) Obtain the line impedance parameter matrix x l Considering that the capacity upper limit and impedance parameters of the line will change after the line is reconstructed by selecting one of the N reconstruction schemes, a line reconstruction model is established, that is:

[0123]

[0124]

[0125] wherein, is the transmission capacity upper limit of the nth line. k l is the line capacity expansion proportionality coefficient. x ln is the impedance parameter of the nth line. x l is the line impedance parameter matrix. k x is the impedance reduction proportionality coefficient. u ln is the 0-1 variable corresponding to the nth line. Ω l is the set of lines to be upgraded.

[0126] 5.2) Establish a generator upgrade and reconstruction model, that is:

[0127]

[0128] wherein, P gi is the transmission capacity lower limit of the ith thermal power generator, k g is the unit flexibility reconstruction proportionality coefficient, u gi is the 0-1 variable corresponding to the ith thermal power generator, Ω g is the set of generators to be upgraded.

[0129] 5.3) Based on the line upgrade and reconstruction model and the generator upgrade and reconstruction model, establish the objective function of the power system planning model, that is:

[0130]

[0131] wherein, P f,t is the transmission power of the transmission section at time t. T is the total scheduling period.

[0132] 5.4) Establish the constraint conditions of the power system planning model, including investment cost constraints, planning element quantity constraints, node power balance constraints, line power flow balance constraints, node phase angle upper and lower limit constraints, unit output upper and lower limit constraints, line power flow upper and lower limit constraints, and thermal power generator climbing constraints.

[0133] The investment cost constraint is as follows:

[0134]

[0135] wherein, cln The retrofit cost of the nth line. c gi The flexibility retrofit cost of the ith thermal power unit. c budget The total available cost. The output upper limit of the ith thermal power unit. The capacity upper limit of the nth line. Ω g The set of power generators to be upgraded. Ω l The set of lines to be upgraded.

[0136] wherein the nth line retrofit cost c ln is as follows:

[0137]

[0138]

[0139] x i ∈{0,1} (18)

[0140] wherein the nth line retrofit cost c ln is as follows: l,i The corresponding cost under the ith retrofit scheme. x i The 0-1 variable corresponding to the ith retrofit scheme, and N is the number of retrofit schemes.

[0141] The flexibility retrofit cost of the ith thermal power unit c gi is as follows:

[0142] c gi = w g (1-k g ) P gi (19)

[0143] wherein the nth line retrofit cost c gi is as follows: g The unit capacity retrofit cost, k g The unit capacity retrofit cost, k P gi The transmission capacity lower limit of the ith thermal power unit.

[0144] The planning element quantity constraint is as follows:

[0145]

[0146] wherein the nth line retrofit cost c gi is as follows: ln The 0-1 variable corresponding to the ith thermal power unit, u max The 0-1 variable corresponding to the nth line, u gΩ is the set of generators to be upgraded l Ω is the set of lines to be upgraded.

[0147] The node power balance constraints are shown as follows:

[0148]

[0149] where, Pit is the output of the ith thermal generator connected to node m at time t, Pjt is the output of the jth wind generator connected to node m at time t, d,t Pmt is the load power at node m at time t, Pbt is the outgoing power of the bth line connected to node m at time t, ΩT is the set of thermal generators connected to node m, ΩW is the set of wind generators connected to node m, ΩL is the set of lines connected to node m, b N is the number of grid nodes, and T is the total scheduling period.

[0150] The line power flow balance constraints are shown as follows:

[0151]

[0152] where, l,t Pt is the line power flow matrix at time t, ij,t Xt is the node phase angle difference matrix at time t, l Z is the line impedance parameter matrix, and T is the total scheduling period.

[0153] The upper and lower limits of the node phase angle are shown as follows:

[0154] -π≤θ t ≤π (t = 1, 2,..., T) (23)

[0155] where, t Xt is the node phase angle matrix at time t.

[0156] The upper and lower limits of the generator output are shown as follows:

[0157]

[0158]

[0159] where, w,t Pwt is the wind generator output matrix at time t, g,t Ptt is the thermal generator output matrix at time t.

[0160] The upper and lower limits of the line power flow are shown as follows:

[0161]

[0162] Where, P l,t is the line power flow matrix at time t.

[0163] The ramp constraints of thermal power units are as follows:

[0164] R down ≤P g,t -P g,t-1 ≤R up (t=2,3,...,T) (27)

[0165] Where, P g,t and P g,t-1 are the output matrices of thermal power units at time t and time t-1, R down is the unit's ramp capability matrix, R up is the ramping capability matrix of the unit, and T is the total scheduling period.

[0166] 6) Collect the planned lines to be upgraded into Ω l and the generator set Ω g Input it into the power system planning model, use CPLEX and other software to solve the power system planning model, and complete the upgrade plan of the weak links in the power system.

[0167] Example 2:

[0168] The experiments on applying the weak link identification and planning method for improving the feasible region of power transmission sections are as follows:

[0169] 1) Establish a test system: as shown in the attached Figure 1 As shown in Figure 1, the IEEE 30-node test system includes 6 generators. The generators at nodes 1, 2, and 5 are wind turbines, the generators at nodes 11, 13, and 15 are thermal power units, and lines (4, 12) and (6, 10) are key transmission sections.

[0170] 2) Establishing the optimal power flow model

[0171] 2.1) Input load power

[0172] Input the load data at time t. Here, we take the load data at the maximum load time (t=19) as an example to form formula (1):

[0173] P d,19 =[0, 13.23, ..., 10.84, ..., 14.02] T (1)

[0174] Where, P d,19 is the node load power vector at time t=19.

[0175] 2.2) Establishing the line transmission power equation constraint

[0176] Obtaining the unit-node connection matrix I g , the power transfer distribution factor (PTDF) matrix A PTDF . As follows:

[0177]

[0178] Establishing the constraint using the input data in equation (1) as follows:

[0179] P l,19 = A PTDF (I g P g,19 -P d,19 ) (2)

[0180] P l,19 = [P l1 P l2 … P ln …] T (n = 1, 2, …, 41) (3)

[0181] P g,19 = [P g1 P g2 P g3 P rg1 P rg2 P rg3 ] T (4)

[0182] In the formula: P l,19 is the line flow vector at t = 19, P ln is the transmission power on the nth line. P g,19 is the unit output vector at t = 19, P d,19 is the node load power vector at t = 19, I g is the power grid unit-node connection matrix, A PTDF is the power transfer distribution factor matrix of the power grid. P gi and P r g j are the outputs of the ith thermal power unit and the jth wind power unit, respectively.

[0183] 2.3) Establishing the upper and lower limit constraints of system variables

[0184] Obtaining the upper and lower limit matrices of line transmission capacity and the upper and lower limit matrices of generator output, as follows:

[0185] Table 1 System variable data

[0186]

[0187] The upper and lower bound constraints of system variables are established as follows:

[0188]

[0189]

[0190] where P l,19 is the line flow vector at t = 19, P g,19 is the unit output vector at t = 19. The superscript and subscript (*) represent the upper and lower bounds of the variable (*) respectively.

[0191] 2.4) Establishing power balance constraints

[0192] The system power balance constraint equation is established as follows:

[0193] ∑P g,19 = ∑P d,19 (7)

[0194] where P g,19 is the unit output vector at t = 19, P d,19 is the node load power vector at t = 19.

[0195] 2.5) Establishing objective function

[0196] The power generation cost vector c of the generator is obtained as follows:

[0197] c = [500, 550, 600, 0, 0, 0] T

[0198] The objective function is established with the lowest total power generation cost as follows:

[0199] min c T P g,19 (8)

[0200] where P g,19 is the unit output vector at t = 19, c is the power generation cost vector of the generator.

[0201] 2.6) Setting planning parameters

[0202] The transmission sections of the test system are line (4, 12) and line (6, 10), which correspond to the 15th and 11th lines respectively. The critical transmission sections of the power grid are set as the planning parameters X as follows:

[0203] X = P f,19 P f,19 = [Pl11 ,P l15 ] T (9)

[0204] Where, P f,19 is the power vector of the key transmission section of the power grid at time t=19.

[0205] So far, equations (1)-(8) are the optimal power flow model established by the present invention. Then, the key transmission section power P of the power grid at time t=19 is f,19 As planning parameters, as shown in formula (39), all remaining variables are used as optimization variables, and the model is solved using multi-parameter planning to obtain the feasible region R of power transmission section at time t = 19. T And the feasible region vertex coordinate matrix V T (See attached Figure 1 ).

[0206] 3) Identify weak links

[0207] First, obtain the feasible region vertex coordinate matrix V T :

[0208]

[0209] Where, P fk is the coordinate corresponding to the kth vertex.

[0210] Then take the key transmission section power P f,19 V T The coordinate values ​​of each vertex in:

[0211] P f,19 =P fk (k=1,2,...,9) (11)

[0212] Where, P f,19 is the power vector of the key transmission section of the power grid at time t=19, P fk is the coordinate corresponding to the k-th vertex,

[0213] Bring equation (11) back to the optimal power flow model (1)-(8), solve it using CPLEX, and count the lines P that meet conditions (12)-(13). *l and generator P *g :

[0214]

[0215]

[0216] Where, is the line power flow vector at time t=19, is the generator output vector at t=19, is the line capacity upper limit matrix, is the generator output lower limit matrix.

[0217] At this point, equations (40)-(43) are the weak link identification model established by the present application, wherein the line and the generator are the weak links identified at t=19, and the results are as follows:

[0218]

[0219] The line and the generator are taken as the elements to be upgraded. After traversing all the weak links at all times, according to the total statistical results, the line set Ω l and the generator set Ω g to be upgraded are formed, and the results are as follows:

[0220] Ω l = [P l6 , P l30 , P l35 ] Ω g = [P g1 , P g2 , P g3 ]

[0221] 4) Constructing a planning model

[0222] 4.1) Establishing a line upgrading and reconstruction model

[0223] Obtain the line impedance parameter x l matrix, as follows:

[0224] x l = [0.06, 0.19, 0.17, …, 0.06]

[0225] Consider selecting one of the three reconstruction schemes to reconstruct the line, and the capacity upper limit and impedance parameter of the line will change accordingly. Accordingly, the line reconstruction model is established as follows:

[0226]

[0227]

[0228] In the equation, is the transmission capacity upper limit of the nth line, k l is the line capacity increasing proportion coefficient (the values of the three reconstruction schemes are 1.3, 1.6 and 2, respectively), x ln is the impedance parameter of the nth line, and k xis the impedance reduction coefficient (the values ​​of the three transformation schemes are: 0.78, 0.63 and 0.5 respectively), u ln is the 0-1 variable corresponding to the nth line, Ω l A collection of lines to be upgraded.

[0229] Establish the line modification cost as follows:

[0230]

[0231]

[0232] x i ∈{0,1} (18)

[0233] Where c ln is the cost of reconstructing the nth line, c l,i is the cost corresponding to the i-th transformation plan (the values ​​of the three transformation plans are: 1×10 7 , 1.5×10 7 and 2.4×10 7 ), x i is the 0-1 variable corresponding to the i-th transformation plan.

[0234] 4.2) Establishing a generator upgrade model

[0235] The generator transformation model is established as follows:

[0236]

[0237] Where, P gi is the lower limit of the transmission capacity of the i-th thermal power unit, k g is the unit flexibility transformation ratio coefficient, u gi is the 0-1 variable corresponding to the i-th thermal power unit, Ω g is the set of generators to be upgraded, N l is the number of power grid lines.

[0238] Establish the generator modification cost as follows:

[0239] c gi =w g (1-k g ) P gi (20)

[0240] Where c gi is the flexibility transformation cost of the i-th thermal power unit, w g is the unit capacity transformation cost, which is 8×10 5 , k gThe unit flexibility modification proportion coefficient k is 0.5≤k≤1. g P gi The lower limit of the transmission capacity of the i-th thermal power unit.

[0241] 4.3) Establishing the planning model objective function

[0242] The objective function is established by taking the maximum transmission power of the transmission section in the dispatching period T=24 as the objective, as follows:

[0243]

[0244] In the formula, P f,t is the transmission power of the transmission section at time t.

[0245] 4.4) Obtaining the capacity reference value baseMVA and establishing the investment cost constraint

[0246] BaseMVA=100

[0247]

[0248] In the formula, c ln is the modification cost of the n-th line, c gi is the flexibility modification cost of the i-th thermal power unit, C budget is the total available cost, and the value is 6×10 7 , The upper limit of the i-th thermal power unit output is The capacity upper limit of the n-th line is g The set of generators to be upgraded is l The set of lines to be upgraded is

[0249] 4.5) Establishing the planning element quantity constraint

[0250]

[0251] In the formula, u gi is the 0-1 variable corresponding to the i-th thermal power unit, u ln is the 0-1 variable corresponding to the n-th line, u max is the maximum value of the planning element quantity, and the value is 4, the set of generators to be upgraded is g The set of lines to be upgraded is l

[0252] 4.6) Establishing the node power balance constraint

[0253]

[0254] In the formula, ​​Pit is the ith thermal power unit output connected to node m at time t, Pjt is the jth wind power unit output connected to node m at time t, d,t Pmt is the load power at node m at time t, Pmt is the jth wind power unit output connected to node m at time t, Pmt is the jth wind power unit output connected to node m at time t, Pmt is the jth wind power unit output connected to node m at time t, Pmt is the jth wind power unit output connected to node m at time t,

[0255] 4.7) Establish line power flow balance constraints

[0256]

[0257] Pmt is the jth wind power unit output connected to node m at time t, l,t Pmt is the jth wind power unit output connected to node m at time t, ij,t Pmt is the jth wind power unit output connected to node m at time t, l Pmt is the jth wind power unit output connected to node m at time t,

[0258] 4.8) Establish upper and lower limits of node phase angle

[0259] -π≤θ t ≤π (t=1,2,...,24) (26)

[0260] Pmt is the jth wind power unit output connected to node m at time t, t Pmt is the jth wind power unit output connected to node m at time t,

[0261] 4.9) Obtain wind power unit predicted output values and establish upper and lower limits of unit output

[0262] Table 2 Wind power unit predicted output

[0263]

[0264]

[0265]

[0266] Pmt is the jth wind power unit output connected to node m at time t, w,t Pmt is the jth wind power unit output connected to node m at time t, g,t Pmt is the jth wind power unit output connected to node m at time t, Pmt is the jth wind power unit output connected to node m at time t, (*) Pmt is the jth wind power unit output connected to node m at time t,

[0267] 4.10) Establish upper and lower limits of line power flow

[0268]

[0269] Pmt is the jth wind power unit output connected to node m at time t,l,t is the line flow matrix at time t, and the superscript represents the upper limit of the variable (*).

[0270] 4.11) Establishing the climbing constraint of thermal power units

[0271] R down ≤ P g,t -P g,t-1 ≤ R up (t = 2, 3,..., T) (30)

[0272] In the formula, P g,t and P g,t-1 are the output matrices of thermal power units at time t and time t-1 respectively, R down is the climbing ability matrix of the unit, and the value is R up is the climbing ability matrix of the unit, and the value is

[0273] Up to now, the formula (14)-(30) is the weak link upgrading planning model established by the present application, which can be solved by using a commercial solver such as CPLEX, and finally the upgrading planning scheme of line capacity expansion and generator flexibility transformation is obtained.

[0274] Example 3:

[0275] The experiment for verifying the weak link identification and planning method for power grid transmission section feasible region improvement mainly includes the following:

[0276] 1) Establish an IEEE30 node system.

[0277] 2) Select the method for comparative analysis:

[0278] M0: No upgrading and transformation of lines and generators;

[0279] M1: Upgrading and transformation of non-weak link lines or generators;

[0280] M2: Upgrading and transformation of weak link lines or generators.

[0281] 3) Comparative results:

[0282] Table 3 Comparative experimental results

[0283]

[0284] According to the data in the above table, firstly, comparing M0 and M1 can know that the daily maximum transmission power and the daily maximum transmission power of the power transmission section in M1 are slightly increased compared with M0, but the effect is not obvious, which shows that after the transformation of the non-weak link line or generator, the power transmission capacity of the power transmission section has not been effectively improved; under the same investment cost, the daily maximum transmission power and the daily maximum transmission power of the power transmission section in M2 reach 1933.4 MWh and 128.7 MW, respectively, which are increased by 39.7%, 23.8%, 38.1% and 24% compared with M0 and M1, respectively, which shows that after the upgrading and transformation of the weak link line and generator by using the method proposed in the application, the power transmission capacity of the power transmission section can be effectively improved. In addition, the transmission power feasible region of the power transmission section of M0, M1 and M2 at the moment of maximum load (t=19) can be obtained by using the method proposed in the application, as shown in the attached Figure 3 Compared with M0, the transmission power feasible region of the power transmission section in M1 has almost no change, and the transmission power feasible region of the power transmission section in M2 has a significant expansion, which also shows that the method proposed in the application can effectively improve the power transmission feasible region of the power transmission section.

Claims

1. A method for identifying and planning weak links for power grid transmission section feasible region improvement, characterized in that, The method comprises the following steps: 1) obtaining power system data and establishing an optimal power flow model; 2) Using multi-parameter programming theory to solve the optimal power flow model, get the transmission section power transmission feasible region R at time t T and the feasible region vertex coordinate matrix V T = [P f1 P f2 ...P fk ]; k = 1, 2,..., N k ; P fk is the coordinate corresponding to the kth feasible region vertex, N k is the number of feasible region vertices; 3) the power transmission feasible region R of the power transmission section at time t T and the feasible region vertex coordinate matrix V T , and establish the weak link identification model of the power system. 4) The weak link identification model of the power system is solved, and the set of planning lines to be upgraded Ω is obtained l and the set of generators Ω g ; 5) establishing a power system planning model; 6) the set of lines to be upgraded Ω l and the set of generators Ω g into the power system planning model, and complete the upgrade planning of the weak links of the power system; The steps of establishing the weak link identification model of the power system are as follows: 3.1) Take the power P of the critical transmission section f,t For each vertex coordinate value in the feasible region vertex coordinate matrix V T i.e.: P f,t = P fk (k = 1, 2,..., N k ) (8) In the formula, P f,t is the power vector of the key transmission section of the power grid at time t; P fk is the coordinate corresponding to the kth vertex, N k is the number of vertices; 3.2) Bring formula (8) into the optimal power flow model, solve the optimal power flow model, and get the line and generators The line and generators is the weak link of the power system at time t. wherein is the line flow vector; is the generator output vector; is the line capacity upper bound matrix; is the generator output lower bound matrix; 3.3) return to step 3.1) until all time instants within the power system dispatch period T are traversed, establishing the set of lines Ω to be upgraded l and the set of generators Ω g ; The steps of establishing the power system planning model are as follows: 5.1) establishing a line upgrading and reconstruction model; 5.2) establishing a generator upgrading and reconstruction model; 5.3) based on the line upgrading and reconstruction model and the generator upgrading and reconstruction model, establishing a power system planning model objective function; 5.4) establishing power system planning model constraints, including investment cost constraints, planning element quantity constraints, node power balance constraints, line power flow balance constraints, node phase angle upper and lower limit constraints, unit output upper and lower limit constraints, line power flow upper and lower limit constraints, and thermal power unit ramping constraints.

2. The method of identifying and planning for weak links for grid transmission section feasibility space improvement according to claim 1, wherein: The power system data includes load power data of each node of the power system, a unit-node connection matrix I g and a power transmission transfer distribution factor matrix A PTDF .

3. The method for identifying and planning the weak link of power grid transmission section feasible region improvement according to claim 1 or 2, characterized in that, The objective function of the optimal power flow model is as follows: min c T P g,t (1) In the formula, P g,t is the unit output vector at time t, and c is the power generation cost vector of the generator. The constraints of the optimal power flow model include line transmission power equality constraints, power system variable upper and lower limit constraints, and power balance constraints; The line transmission power equality constraints are as follows: P l,t = A PTDF (I g P g,t -P d,t ) (2) P l,t = [P l1 P l2 … P ln …] T (n = 1, 2,..., N l ) (3) P g,t = [P g1 P g2 … P gi … P rg1 P rg2 … P rgj …] T (i = 1, 2,..., N g j = 1, 2,..., N rg ) (4) where P l,t is the line flow vector at time t; P ln is the transmission power on the nth line; N l is the number of grid lines; P g,t is the unit output vector at time t; P d,t = [P1 P2… P m …] T is the node load power vector at time t; m = 1, 2, …, N b ; P m is the load power at node m; N b is the number of grid nodes; P gi and P rgj are the output of the ith thermal power unit and the jth wind power unit, respectively; N g , N rg are the number of thermal power units and the number of wind power units in the grid, respectively. The power system variable upper and lower limit constraints are as follows: wherein the superscript and the subscript (*) denote the upper and lower limits of the variable (*), respectively; The power balance constraints are as follows: ∑P g,t =∑P d,t (7) In the formula, P g,t is the unit output vector at time t, P d,t is the node load power vector at time t.

4. The method of identifying and planning for weak links for grid transmission section feasibility space improvement according to claim 1, wherein, The method for solving the optimal power flow model by using the multi-parameter programming theory is as follows: taking the power P f,t of the key transmission section of the power grid as the programming parameter, and taking the variables in the optimal power flow model except the programming parameter as the optimization variables to solve the optimal power flow model.

5. The method of identifying and planning for weak links for grid transmission section feasibility space improvement according to claim 1, wherein, The steps of establishing the power system planning model are as follows: 1) establishing a line upgrading and reconstruction model, that is: In the formula, is the upper limit of transmission capacity of the nth line; k l is the line capacity expansion proportionality coefficient; x ln is the impedance parameter of the nth line; x l is the line impedance parameter matrix; k x is the impedance reduction proportionality coefficient; u ln is the 0-1 variable corresponding to the nth line; Ω l is the set of lines to be upgraded; 2) establishing a generator upgrading and reconstruction model, that is: In the formula, P gi is the lower limit of the transmission capacity of the i th thermal power unit, k g is the unit flexibility renovation proportion coefficient, u gi is the 0-1 variable corresponding to the i th thermal power unit, Ω g is the set of power generators to be upgraded, N l is the number of grid lines; 3) based on the line upgrading and reconstruction model and the generator upgrading and reconstruction model, establishing a power system planning model objective function, that is: In the formula, P f,t is the transmission power of the transmission section at time t; T is the total dispatch period; 4) establishing power system planning model constraints, including investment cost constraints, planning element quantity constraints, node power balance constraints, line power flow balance constraints, node phase angle upper and lower limit constraints, unit output upper and lower limit constraints, line power flow upper and lower limit constraints, and thermal power unit ramping constraints; The investment cost constraints are as follows: where c ln is the cost of retrofitting the nth line; c gi is the cost of retrofitting the ith thermal power unit flexibility; C budget is the total available cost; is the upper limit of the ith thermal power unit output; is the upper limit of the capacity of the nth line; Ω g is the set of power generators to be upgraded; Ω l is the set of lines to be upgraded; baseMVA is the capacity base value; wherein the cost c of converting the nth line ln As shown below: x i ∈{0,1} (18) wherein c ln is the cost of the n-th line; c l,i is the corresponding cost under the i-th modification scheme; x i is the 0-1 variable corresponding to the i-th modification scheme, and N is the number of modification schemes. The cost c of flexibility improvement of the i th thermal power unit gi As shown below: c gi = w g (1-k g ) P gi (19) In the formula, c gi is the cost of flexibility retrofit of the i th thermal power unit, w g is the unit capacity retrofit cost, k g is the unit flexibility retrofit proportionality coefficient; P gi is the lower limit of transmission capacity of the i th thermal power unit; The planning element quantity constraints are as follows: In the formula, u gi is the 0-1 variable corresponding to the ith thermal power generating unit, u ln is the 0-1 variable corresponding to the nth line, u max is the maximum value of the planning element quantity, Ω g is the set of generating units to be upgraded, Ω l is the set of lines to be upgraded; The node power balance constraints are as follows: wherein, is the output of the ith thermal power unit connected to the mth node at time t, is the output of the jth wind power unit connected to the mth node at time t, P d,t is the load power at the mth node at time t, is the outflow power of the bth line connected to the mth node at time t, is the set of thermal power units connected to the mth node, is the set of wind power units connected to the mth node, is the set of lines connected to the mth node, N b is the number of grid nodes, and T is the total scheduling period. The line power flow balance constraints are as follows: In the formula, P l,t is the line flow matrix at time t, θ ij,t is the node phase angle difference matrix at time t, x l is the line impedance parameter matrix, and T is the total dispatch period. The node phase angle upper and lower limit constraints are as follows: -π < θ t ≤ π (t = 1, 2,..., T) (23) In the formula, θ t is the phase angle matrix of the node at time t; The unit output upper and lower limit constraints are as follows: In the formula, P w,t is the output matrix of the wind turbine at time t, P g,t is the output matrix of the thermal power unit at time t; The line power flow upper and lower limit constraints are as follows: In the formula, P l,t is the line flow matrix at time t; The thermal power unit ramping constraints are as follows: R down ≤P g,t -P g,t-1 ≤R up (t = 2, 3,..., T) (27) In the formula, P g,t and P g,t-1 are the power output matrices of thermal power units at time t and t-1, respectively, R down is the down ramping capability matrix of the units, R up is the up ramping capability matrix of the units, and T is the total scheduling period.

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