CN113541156B - Reactive voltage adjustment method based on reactor compensation device - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
- H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
- H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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- Y02E40/30—Reactive power compensation
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Abstract
A reactive voltage adjustment method based on a reactor compensation device belongs to the field of power system operation. Firstly, acquiring topology parameters of a power distribution network, parameters of a transformer and a reactive compensation device, and prediction data of active and reactive loads; then, a reactive power optimization model of the power distribution network is established based on the parameters and the data; adopting second-order cone relaxation to convert the second-order cone relaxation into a second-order cone reactive power optimization problem and solving the second-order cone reactive power optimization problem; and obtaining the optimal switching gear of the compensating reactor or capacitor and the tap position of the transformer. On the premise of minimum network line loss, the reactive power optimization model of the power distribution network is efficiently solved, the switching strategy of the discrete adjustable reactive power compensation device and the selection of the transformer tap are obtained, the system voltage can be effectively controlled within the allowable range, and the safe and stable operation of the power system is ensured. The method can be widely applied to the field of operation management of power systems.
Description
Technical Field
The invention belongs to the field of power system operation, and particularly relates to a reactive voltage adjustment method based on a reactor compensation device.
Background
With the advancement of urban modern construction, the method has been widely developed to perform cable-down reconstruction on overhead transmission lines in order to further beautify cities, optimally allocate land resources, prevent overhead lines from being damaged by unreliability, cause accidents which harm personal and power grid safety, improve power supply reliability and ensure life and property safety of people.
The capacitance of the cable is larger than that of the overhead line, and for long-distance cable lines, the susceptance to ground and the charging capacity are gradually increased along with the increase of the length of the line; reactive losses in the series reactance of the line and reactive loads in the system are insufficient to maintain reactive power balance, which can lead to a large voltage in the distribution network with high cabling efficiency. Lighting loads, such as during night load valley periods, have a considerable weight, and they have a high power factor, which makes the problem of reactive redundancy and voltage bias of the system more pronounced.
For this reason, the conventional method of only configuring the capacitive reactive compensation device is no longer applicable, and the national grid company has already begun to try to adjust the voltage level by adding a reactor on the 10kV side of the power distribution network, and the related reactor switching strategy and its cooperation with the tap selection of the transformer are worth discussing.
The problem of realizing system voltage adjustment through the parallel compensation reactor can be simulated by establishing a reactive power optimization model of the power distribution network.
However, the existing research faces the following problems in modeling: sufficient consideration of the operation rule of the reactor, network line loss and influence of the distribution transformer on reactive voltage of the system is lacking.
With the continuous improvement of urban cable rate, the problem of power distribution network terminal voltage out-of-limit is increasingly severe, a new power distribution network reactive power optimization model needs to be established to obtain an operation method and a switching strategy of a reactive power compensation device, and reactive power voltage adjustment of the power distribution network is realized under the conditions of taking account of discrete adjustable characteristics of the reactive power compensation device, the influence of transformer tap selection on system reactive voltage and minimum network line loss, so that a powerful tool is provided for safe and stable operation of a power system.
Disclosure of Invention
The invention aims to provide a reactive voltage adjusting method based on a reactor compensation device. Under the condition or premise of minimum network line loss, the reactive power optimization model of the power distribution network is efficiently solved, the switching strategy of the discrete adjustable reactive power compensation device and the selection of the transformer tap are obtained, the system voltage can be effectively controlled within the allowable range, and the safe and stable operation of the power system is ensured.
The technical scheme of the invention is as follows: the reactive voltage adjusting method based on the reactor compensation device comprises the following steps of;
step one: and obtaining topology parameters of the power distribution network, parameters of a transformer and a reactive compensation device and prediction data of active and reactive loads. The parameters involved in this process are mainly: 1) The network structure of the distribution network, the resistance, reactance and the opposite susceptance of each branch, the length and the maximum current-carrying capacity of each cable line; 2) The voltage allowable deviation range of each node; 3) Rated capacity, voltage and tap position of the transformer; 4) Rated capacity of the reactive power compensation device and tap positions; 5) The size of active load and reactive load at the tail end of the distribution network.
Step two: and (3) establishing a reactive power optimization model of the power distribution network based on the parameters and the data obtained in the step one. The concrete model is as follows:
the minimum active loss of all branches of the network is taken as an objective function, namely:
wherein I is i,j 2 Can be obtained by the following formula:
the power balance constraint that accounts for each node in the network is derived from:
the operation constraint of the reactive power compensation device with adjustable switching capacity step by step is obtained by the following formula:
the voltage relationship between the head and the tail of each branch is obtained by the following formula:
wherein N is assumed due to the adjustable tap of the transformer T The gear is adjusted, U j 2 /t i,j 2 Further discretization may be expressed as follows:
the node voltage and branch current limit constraints are expressed as follows:
U j,min ≤U j ≤U j,max (8)
wherein V represents a set of distribution network nodes, (i, j) represents a branch consisting of nodes i and j, E represents a set of network branches, r i,j Representing the resistance of branch (I, j), I i,j 2 Is the square of the branch current amplitude, P i,j And Q i,j Respectively representing the active power and the reactive power passed by the branch (i, j), the positive direction of the flow of the branch (i, j) is from i to j, U i The voltage of node i is represented, pi (j) represents the head-end node set of the branch having j as the end node, delta (j) represents the end-node set of the branch having j as the head-end node, r i,j And x i,j Representing the resistance and reactance of the branches (i, j), b j To-earth susceptance, P, representing node j L,j And Q L,j Representing the active and reactive loads of node j, respectively, pairAt non-distribution network end nodes, P L,j ＝0,Q L,j ＝0，Q X,j And Q C,j Respectively represent the capacity of a reactor (capacitor) input by a node j, Q X,j,k (Q C,j,k ) Indicating the compensation capacity corresponding to the kth adjusting gear of the compensation device, I X,j,k (I C,j,k ) A 0-1 variable which indicates whether to select, T indicates a transformer branch set, T i,j I.e. the nonstandard transformation ratio, t, of branch (i, j) i,j,k Representing the regulating gear corresponding to tap k of the transformer branch (I, j), I i,j,k A 0-1 variable indicating whether tap k is selected, U j,min And U j,max Respectively representing the voltage limits of node j.
Considering that the length of a cable line of a power distribution network is often far smaller than the wavelength corresponding to the working frequency of the cable line, and the study object is the electric quantity relation of each node in the network, the cable line is based on a centralized parameter circuit theory and is carried out by adopting a pi-shaped equivalent circuit; the transformer adopts a gamma-type equivalent circuit.
In the third step, the specific implementation manner is as follows:
firstly, defining variables: 1) Node voltage amplitude square u j The method comprises the steps of carrying out a first treatment on the surface of the 2) Branch current amplitude square i i,j The following formula is shown:
further will i i,j ＝(P i,j 2 +Q i,j 2 )/U i 2 Adding to the constraint;
when the objective function is satisfied is i i,j Under the conditions of no upper limit of node load and the like, the strict increasing function of the node can be relaxed into the following formula:
further, since the above formula is equivalent to the following formula:
(2P i,j ) 2 +(2Q i,j ) 2 +(i i,j -u i ) 2 ≤(i i,j +u i ) 2 (12) The objective function can thus be expressed in the form of a normalized second order cone, namely:
further, the bilinear term (U j 2 /t i,j,k 2 )I i,j,k Namely (u) j /t i,j,k 2 )I i,j,k The large M method can be used to relax it into the following formula:
by using u as described above j And i i,j Replacing the relevant variables in the model, the objective function can be obtained as follows:
the flow equation can be modified accordingly to the following equation:
the voltage limit constraint may be changed to the following representation:
U j,min 2 ≤u j ≤U j,max 2 (17)
the cable current limit constraint may be changed to the following expression:
i i,j ≤I i,j,max 2 (18)
through the conversion, the original reactive power optimization problem is changed into the following model:
and the original problem is further expanded into a second-order cone reactive power optimization problem containing mixed integer variables, the existing Cplex or Gurobi algorithm software package can obtain the global optimal solution of the original problem through a cut plane method or a branch-and-bound method, and the optimal switching gear of the compensating reactor or capacitor and the tap position of the transformer are determined.
Compared with the prior art, the invention has the advantages that:
according to the power distribution network reactive power optimization model provided by the technical scheme of the invention, the influence of transformer tap selection on the reactive voltage of the system and the discrete adjustable characteristic of the reactor compensation device are fully considered, and the adopted planning method based on second order cone relaxation and bilinear term linearization based on a large M method can effectively realize efficient solution of the model. Compared with the existing research, the operation of the power distribution network can be simulated more accurately, and effective adjustment of voltage is realized. The mode can provide tools for reactive power optimization planning of the power system, ensures safe and stable operation of the power grid, and has a certain application prospect.
Drawings
Fig. 1 is an overall flow chart of the present invention.
Fig. 2 is a schematic diagram of an equivalent circuit of the distribution network taking into account the compensation means.
Fig. 3 is a topology of an example system power distribution network.
Detailed Description
The invention is further described below with reference to the drawings and examples.
Taking a certain actual power distribution network as an example for analysis and calculation. Referring to fig. 1, the implementation process of the present invention is as follows:
step one: and obtaining topology parameters of the power distribution network, parameters of a transformer and a reactive compensation device and prediction data of active and reactive loads.
The network topology of the example system is shown in fig. 3.
The line length and the impedance per unit length are indicated in FIG. 3, for a sodium-to-earth value of 5X 10 -4 S/km. Capacity of transformer50MVA, a transformation ratio of 110/10; tap gear is 110 (+ 8, -8) 1.25%/10kV; the short-circuit voltage percentage is 16.5%, the short-circuit loss is 206kW, susceptance B T The value was 0.0008S.
Assuming normal operation, the allowable deviation range of the 110kV bus voltage is-3% to +7% of the rated voltage of the system, the allowable deviation range of the 10kV bus voltage is 0% to +7% of the rated voltage of the system, and the adjustable reactors (capacitors) are additionally arranged at the nodes 4 and 5. The adjustable gear of the compensation reactance (capacitor) is shown in tables 1-2.
Assume that the night load is 30% of the full load capacity of the transformer and the load power factor is 0.95.
Table 1 Compensation reactor Adjustable gear
Table 2 compensating capacitor adjustable gear
Step two: and (3) establishing a reactive power optimization model of the power distribution network based on the parameters and the data obtained in the step one. The method is specifically as follows:
the minimum active loss of all branches of the network is taken as an objective function as shown in a formula (1), wherein I i,j 2 Can be obtained from formula (2). Taking into account the power balance constraint of each node in the network as shown in formula (3); the operation constraint of the reactive power compensation device with adjustable switching capacity step by step is shown as formulas (4) and (5); the voltage relationship between the head and the tail of each branch is shown as a formula (6), wherein N is assumed to be present because the tap of the transformer is adjustable T The gear is adjusted, U j 2 /t i,j 2 Can be further discretized as represented by formula (7); the node voltage and branch current limit constraints are as in equations (8) and (9). In addition, considering that the length of the cable line of the distribution network is often far smaller than the wavelength corresponding to the working frequency of the cable line, and the research object is the electric quantity relation of each node in the network, the cable line is based on the concentrated parameter circuit theoryAdopting a pi-shaped equivalent circuit for carrying out; the transformer adopts a gamma-type equivalent circuit; as shown in an equivalent circuit schematic diagram 2 of the power distribution network; in FIG. 2, the cabling resistance, reactance, and contrast susceptance correspond to R, respectively l 、X l And B l The transformer non-standard transformation ratio corresponds to k * The resistance, reactance and susceptance of the gamma equivalent circuit thereof respectively correspond to R T 、X T And B T The capacity of the compensation reactor and the capacitor respectively correspond to Q X And Q C The active load and the reactive load at the tail end of the distribution network respectively correspond to P L And Q L The active and reactive loads flowing through the line and the transformer respectively correspond to P l 、Q l 、P T And Q T 。
U j,min ≤U j ≤U j,max (8)
Where V represents a set of power distribution network nodes, (i, j) represents a branch consisting of nodes i and j, and E represents a set of network branches. r is (r) i,j Representing the resistance of branch (I, j), I i,j 2 Is the square of the branch current amplitude. P (P) i,j And Q i,j Respectively representing the active power and the reactive power passed by the branch (i, j), the positive direction of the flow of the branch (i, j) is from i to j, U i Representing the voltage at node i. Pi (j) represents the head end node set of the leg with j as the end node, and delta (j) represents the end node set of the leg with j as the head end node. r is (r) i,j And x i,j Representing the resistance and reactance of the branches (i, j), b j The pair susceptance of node j is represented. P (P) L,j And Q L,j Representing the active and reactive loads of node j, respectively, for non-distribution network end nodes, P L,j ＝0,Q L,j ＝0。Q X,j And Q C,j The capacity of the reactor (capacitor) to which the node j is put is shown. Q (Q) X,j,k (Q C,j,k ) Indicating the compensation capacity corresponding to the kth adjusting gear of the compensation device, I X,j,k (I C,j,k ) Indicating whether the 0-1 variable is selected. T represents a set of transformer branches, T i,j I.e. the non-standard transformation ratio of branch (i, j). t is t i,j,k Representing the regulating gear corresponding to tap k of the transformer branch (I, j), I i,j,k A 0-1 variable indicating whether tap k is selected. U (U) j,min And U j,max Respectively representing the voltage limits of node j.
Step three: and (3) based on the power distribution network reactive power optimization model obtained in the step two, converting the power distribution network reactive power optimization model into a second-order cone reactive power optimization problem by adopting second-order cone relaxation, and solving the second-order cone reactive power optimization problem. The method is specifically as follows:
firstly, defining variables: 1) Node voltage amplitude square u j The method comprises the steps of carrying out a first treatment on the surface of the 2) Branch current amplitude square i i,j As shown in formula (10).
Further will i i,j ＝(P i,j 2 +Q i,j 2 )/U i 2 Added to the constraint. When the objective function is satisfied is i i,j Under the conditions of no upper limit of node load, the function can be relaxed to the formula (11). It can be further found that the expression (11) and the expression (12) are equivalent, and thus the expression (11) can be expressed as a standard second order cone form, that is, the expression (13).
(2P i,j ) 2 +(2Q i,j ) 2 +(i i,j -u i ) 2 ≤(i i,j +u i ) 2 (12)
For bilinear term (U) in equation (7) j 2 /t i,j,k 2 )I i,j,k Namely (u) j /t i,j,k 2 )I i,j,k It can be relaxed to formula (14) using the large M method.
By using u as described above j And i i,j And replacing related variables in the model to obtain the change of the objective function from the formula (1) to the formula (15), correspondingly modifying the tide equation to the formula (16), changing the voltage limit constraint from the formula (8) to the formula (17), and changing the cable current limit constraint from the formula (9) to the formula (18).
U j,min 2 ≤u j ≤U j,max 2 (17)
i i,j ≤I i,j,max 2 (18)
Through the above conversion, the original reactive power optimization problem becomes a model (19). Therefore, the original problem is expanded to be a second-order cone reactive power optimization problem containing mixed integer variables, the existing Cplex, gurobi and other algorithm software packages can obtain the global optimal solution of the original problem through a cut plane method or a branch-and-bound method, and the optimal switching gear of the compensating reactance (capacitor) and the tap position of the transformer are determined.
The method comprises the following steps of: the switching plan of the reactive compensation device and the tap position of the transformer.
The calculation results are shown below:
firstly, the model is solved by considering the condition that the compensation reactor (capacitor) is not invested, and the result is that the solution is free, thereby explaining the necessity of the reactive power compensation device for voltage adjustment. And then put into the stepping adjustable compensation device, solve the reactive power optimization model proposed by the invention according to the above calculation example. The reactors (capacitors) added to the nodes 4 and 5 are named as reactors (capacitors) 1 and 2, respectively, and the transformers of the branches (2, 4) and the branches (3, 5) are named as transformers 1 and 2, respectively. The specific results are shown in tables 3 and 4.
TABLE 3 basic example calculation results
TABLE 4 node voltage results
From the calculation results, the node voltage can be controlled within the allowable range by additionally arranging the reactor at the load side, so that the problem of voltage out-of-limit is effectively solved. And in this example system, the optimal input capacity of the reactor is 5MVA, and the distribution transformer selects +5% and +6.25% taps, respectively.
The switching condition of the compensating reactor (capacitor) and the voltage of each point of the end load of the distribution network under the conditions of different scales and power factors are further studied, wherein the influence of different power factors in the load peak period of the daytime and the load valley period of the night is considered. The specific results are shown in Table 5.
TABLE 5 calculation results under different loads
As can be seen from table 5, as the load scale increases, the total network line loss increases significantly; and during the daytime load peak period (corresponding to the case of 0.7p.u. load), the bus voltage is regulated mainly by putting in the capacitor, and during the night load valley period (corresponding to the case of 0.3p.u. load), the bus voltage is regulated mainly by putting in the reactor. At the same load scale, the larger the load power factor is, the more resistance property tends to be presented, and the larger the network line loss is; the larger the capacity of the compensating reactor is due to the reduction of reactive load, otherwise, a capacitor is needed to be added to adjust the bus voltage; in addition, the greater the load power factor, the less the voltage drop along the branch, often requiring a higher gear transformer tap to avoid voltage violations.
Therefore, the reactive voltage adjustment method based on the reactor compensation device can effectively control the voltage of each node within the allowable range under different system loads, also consider the mutual coordination of the switching capacity of the compensation device and the tap selection of the transformer and provide reference for the operation strategy, and can provide powerful support for the safe and stable operation of the power system.
The invention can be widely applied to the field of operation management of power systems.
Claims (3)
1. The reactive voltage adjusting method based on the reactor compensation device is characterized by comprising the following steps of:
step one: obtaining topology parameters of a power distribution network, parameters of a transformer and a reactive compensation device and prediction data of active and reactive loads;
step two: establishing a reactive power optimization model of the power distribution network based on system parameters and load data;
step three: based on a reactive power optimization model of the power distribution network, adopting second-order cone relaxation to convert the second-order cone relaxation into a second-order cone reactive power optimization problem and solving the second-order cone reactive power optimization problem; the optimal switching gear of the reactive power compensation device and the tap position of the transformer which can effectively realize voltage adjustment are obtained;
the specific implementation manner of the second step is as follows:
the minimum active loss of all branches of the network is taken as an objective function, namely:
wherein I is i,j 2 Can be obtained by the following formula:
the power balance constraint that accounts for each node in the network is derived from:
the operation constraint of the reactive power compensation device with adjustable switching capacity step by step is obtained by the following formula:
the voltage relationship between the head and the tail of each branch is obtained by the following formula:
wherein N is assumed due to the adjustable tap of the transformer T The gear is adjusted, U j 2 /t i,j 2 Further discretization may be expressed as follows:
the node voltage and branch current limit constraints are expressed as follows:
U j,min ≤U j ≤U j,max (8)
wherein V represents a set of distribution network nodes, (i, j) represents a branch consisting of nodes i and j, E represents a set of network branches, r i,j Representing the resistance of branch (I, j), I i,j 2 Is the square of the branch current amplitude, P i,j And Q i,j Respectively representing the active power and the reactive power passed by the branch (i, j), the positive direction of the flow of the branch (i, j) is from i to j, U i The voltage at node i, pi (j) represents the terminal node jThe head end node set of the branch of the point, delta (j) represents the end node set of the branch taking j as the head end node, r i,j And x i,j Representing the resistance and reactance of the branches (i, j), b j To-earth susceptance, P, representing node j L,j And Q L,j Representing the active and reactive loads of node j, respectively, for non-distribution network end nodes, P L,j ＝0,Q L,j ＝0，Q X,j And Q C,j Respectively represent the capacity of the reactor/capacitor input by node j, Q X,j,k And Q C,j,k Indicating the compensation capacity corresponding to the kth adjusting gear of the compensation device, I X,j,k And I C,j,k A 0-1 variable which indicates whether to select, T indicates a transformer branch set, T i,j I.e. the nonstandard transformation ratio, t, of branch (i, j) i,j,k Representing the regulating gear corresponding to tap k of the transformer branch (I, j), I i,j,k A 0-1 variable indicating whether tap k is selected, U j,min And U j,max Respectively representing voltage limit values of the nodes j;
in the third step, the specific implementation manner is as follows:
firstly, defining variables: 1) Node voltage amplitude square u j The method comprises the steps of carrying out a first treatment on the surface of the 2) Branch current amplitude square i i,j The following formula is shown:
further will i i,j ＝(P i,j 2 +Q i,j 2 )/U i 2 Adding to the constraint;
when the objective function is satisfied is i i,j Under the conditions of no upper limit of node load and the like, the strict increasing function of the node can be relaxed into the following formula:
further, since the above formula is equivalent to the following formula:
(2P i,j ) 2 +(2Q i,j ) 2 +(i i,j -u i ) 2 ≤(i i,j +u i ) 2 (12)
the objective function can thus be expressed in the form of a normalized second order cone, namely:
bilinear term (U) j 2 /t i,j,k 2 )I i,j,k Namely (u) j /t i,j,k 2 )I i,j,k The large M method can be used to relax it into the following formula:
by using u as described above j And i i,j Replacing the relevant variables in the model, the objective function can be obtained as follows:
the flow equation can be modified accordingly to the following equation:
the voltage limit constraint may be changed to the following representation:
U j,min 2 ≤u j ≤U j,max 2 (17)
the cable current limit constraint may be changed to the following expression:
i i,j ≤I i,j,max 2 (18)
through the conversion, the original reactive power optimization problem is changed into the following model:
and the original problem is further expanded into a second-order cone reactive power optimization problem containing mixed integer variables, the existing Cplex or Gurobi algorithm software package can obtain the global optimal solution of the original problem through a cut plane method or a branch-and-bound method, and the optimal switching gear of the compensating reactor or capacitor and the tap position of the transformer are determined.
2. The reactive voltage adjustment method based on the reactor compensation device according to claim 1, wherein the method is characterized in that the length of a power distribution network cable line is often far smaller than the wavelength corresponding to the working frequency of the power distribution network cable line, and the research object is the electric quantity relation of each node in a network, and the power distribution network cable line is based on a centralized parameter circuit theory and is carried out by adopting a pi-shaped equivalent circuit; the transformer adopts a gamma-type equivalent circuit.
3. The reactive voltage adjustment method based on the reactor compensation device according to claim 1 is characterized in that the reactive voltage adjustment method fully considers the influence of transformer tap selection on the reactive voltage of the system and the discrete adjustable characteristic of the reactor compensation device, and the adopted planning method based on second order cone relaxation and bilinear term linearization based on a large M method can effectively realize efficient solution of a model, can more accurately simulate the operation of a power distribution network, realize effective adjustment of voltage, provide tools for reactive power optimization planning of a power system, and ensure safe and stable operation of the power grid.
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