A Digital Modeling Method for DC Systems Based on Gradient Descent Machine Algorithm

Abstract

This invention relates to the field of power transmission and transformation engineering technology, and discloses a digital modeling method for DC systems based on gradient descent machine algorithm, including the following steps: S1: Machine algorithm analysis; By predicting and analyzing data, especially analyzing unknown new data, accurate statistical prediction and solutions for the data are achieved; S1.1: Gradient descent algorithm is applied to the existing data; First, the coefficient vector is initialized, and then the coefficient vector value is iteratively updated step by step to minimize the objective function until convergence; Gradient descent is an iterative algorithm. An appropriate initial value x(0) is selected, and the value of x is continuously updated to minimize the objective function until convergence. Since the negative gradient direction is the direction that makes the function value decrease the fastest, the value of x is updated in the negative gradient direction at each step of the iteration, thereby achieving the purpose of reducing the function value.

Description

Technical Field

[0001] This invention relates to the field of power transmission and transformation engineering technology, specifically to a digital modeling method for DC systems based on gradient descent machine algorithms. Background Technology

[0002] With the State Grid advocating the construction of a new power system based on new energy sources, ensuring the safe and stable operation of the power system through digital and intelligent means is essential. Currently, digital simulation and modeling technologies for DC systems still lack sufficient research depth. Furthermore, there is a lack of research on digital modeling techniques for DC miniature circuit breaker level differences and cable calculations; research mainly focuses on equipment selection, system simulation, and battery modeling. With the continuous promotion and development of digital technology and computer machine learning algorithms in engineering construction, the traditional simple calculations and applications of DC system feeder level differences are no longer sufficient to meet current requirements. Moreover, the complex circuit nonlinearities resulting from the integration of high proportions of new energy sources will have a significant impact on DC systems, necessitating an urgent shift towards intelligent and digital development. To address this, this paper proposes a digital modeling method for DC systems based on gradient descent machine learning algorithms, fully utilizing digital technology and machine learning algorithms to improve the precision, practicality, and integration of DC system calculations in engineering projects. Summary of the Invention

[0003] (a) Technical problems to be solved

[0004] To address the shortcomings of existing technologies, this invention provides a digital modeling method for DC systems based on the gradient descent machine algorithm.

[0005] (II) Technical Solution

[0006] To achieve the above objectives, the present invention provides the following technical solution: a digital modeling method for DC systems based on gradient descent machine learning algorithm, comprising the following steps:

[0007] S1: Machine algorithm analysis;

[0008] By predicting and analyzing data, especially unknown new data, we can achieve accurate statistical predictions and solutions for data.

[0009] S1.1: Perform gradient descent algorithm on the existing data;

[0010] First, the coefficient vector is initialized, and then the coefficient vector values ​​are iteratively updated step by step to minimize the objective function until convergence.

[0011] Gradient descent is an iterative algorithm that selects an appropriate initial value x(0), iterates continuously, updates the value of x, and minimizes the objective function until convergence. Since the negative gradient direction is the direction that makes the function value decrease the fastest, the value of x is updated in the negative gradient direction at each step of the iteration, thereby achieving the purpose of reducing the function value.

[0012] The gradient descent algorithm mainly consists of:

[0013] enter:

[0014] Output: The minimum point x of f(x) * ;

[0015] K1 takes the initial value X (0) ∈R n Set k=0

[0016] K2 calculates f(X) (k) )

[0017] K3 calculates the gradient g k =g(X) (k) When ||g k When || < ε, stop the iteration and let X * =X (k) Otherwise, let p k =-g(X) (k) Find λ. k ,make

[0018]

[0019] K4 X (k+1) =X (k) +λ k p k Calculate f(X) (k+1) )

[0020] When ||f(X) (k+1) )-f(X (k) || < ε or || X (k+1) -X (k) When || < ε, stop the iteration and let X * =X (k+1)

[0021] K5 Otherwise, set k = k + 1 and go to K3;

[0022] S1.2: Simulate DC circuit breaker step differences and cable calculations using the gradient descent algorithm;

[0023] Under normal circumstances, the short-circuit current of a DC system can be expressed by the mathematical relationship between the cable cross-section and the resistance of the DC circuit breaker. The rated tripping current value of the DC miniature circuit breaker should ensure that the trip unit can reliably not operate when the next-level circuit breaker outlet is short-circuited and that the trip unit can reliably operate when the current-level circuit breaker outlet is short-circuited. Considering the closest intermediate value as the optimal value, the function set in this way is a differentiable function.

[0024] When calculating the short-circuit current of a DC system, a value needs to be assumed for the rated current of the DC circuit breaker, from which the resistance value of the DC circuit breaker can be derived; an initial value X is set for the rated tripping current of each stage of the DC circuit breaker. (0) This allows us to derive the coefficients of the mathematical relationship; we define a cost function J(θ), expressed in the common root mean square error form as follows:

[0025]

[0026] In equation (1), h θ (X (i) It can be expressed as a differentiable function as:

[0027] h θ (X (i) )=C0θ0 -1 +C1θ1 -1 +C2θ2 -1 +C3X (i) C0, C1, and C2 are the median values ​​of the parameters for the three cable cross-sections; C3 is the parameter value for converting the rated current of the DC miniature circuit breaker into a resistance value.

[0028] In the cost function J(θ), there are three variables, namely θ0, θ1, and θ2, which represent three different levels of cable cross-sections: from the battery circuit to the DC main cabinet, from the DC main cabinet to the DC distribution cabinet, and from the DC distribution cabinet to the end.

[0029] S2: Digital modeling for calculating the differential calculation of DC system feeder circuit breakers;

[0030] S2.1: Digital modeling of DC feeder load;

[0031] Digital modeling mainly involves assigning load factors, normal current, fault discharge time and other attribute information to the loads with the above characteristics, and then modeling the scale of equipment involved in the DC system.

[0032] S2.2: Modeling of differential coordination of DC circuit breakers;

[0033] Digital modeling of DC circuit breaker differential coordination mainly targets the configuration of three-level DC circuit breakers and the configuration of four-level DC circuit breakers.

[0034] S2.2.1: Configuration of three-level DC circuit breakers;

[0035] The configuration of three-level DC circuit breakers mainly involves the differential coordination between the second and third level DC circuit breakers and the selection of circuit breakers, which is the protection coordination of the DC circuit breaker outlet from the DC feeder cabinet to any protection cabinet in the main control room.

[0036] Q1 Third-level DC circuit breaker calculation:

[0037] Calculation of short-circuit current in DC system:

[0038] I SC =U n / ∑R i

[0039] ∑R i =r+R L1 +R S2 +R L2 +R S3

[0040] Q2 Second-stage DC circuit breaker calculation:

[0041] For calculating the short-circuit current of a DC system, refer to formula I. SC =U n / ∑R i ,∑R i =r+R L1 +R S2 +R L2 +R S3 R is removed from the sum of the loop resistances. s3 (Internal resistance of DC circuit breaker in main transformer protection cabinet), the calculated short-circuit current is Id3 at the end of DC feeder cabinet S2 circuit breaker.

[0042] According to the 5044 DC specification, the second-stage DC circuit breaker can be configured as a type C DC circuit breaker. This section compares three types of DC circuit breakers to ensure proper coordination:

[0043] The instantaneous tripping range of the CH type DC circuit breaker is: 14In×(1-20%)----14In×(1+20%);

[0044] The instantaneous tripping range of the type C DC circuit breaker is: 10In×(1-20%)----10In×(1+20%);

[0045] Three-stage DC circuit breaker short-circuit short-delay setting value: 10In×(1-20%)----10In×(1+20%), time constant 5ms, short-circuit instantaneous trip current value 1680A;

[0046] If CH is selected, the upper limit of the instantaneous tripping value is 14In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value is 14In×(1 - 20%) > Id4;

[0047] If a C-type miniature circuit breaker is selected, the upper limit of the instantaneous tripping value is 10In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value is 10In×(1 - 20%) > Id4;

[0048] If neither the CH type nor the C type meets the grading coordination requirements, a three-stage circuit breaker can be selected, that is, the upper limit of the short-time delay tripping value meets 10In×(1 + 20%) < Id3;

[0049] S2.2.2: Configuration of four-pole DC circuit breakers;

[0050] In the configuration of four-pole DC circuit breakers, the main ones are the second and third levels, referring to the grading coordination and circuit breaker configuration types between the DC circuit breaker of the DC feeder panel in the main control room and the DC circuit breaker of the DC distribution panel in the equipment area, as well as the grading coordination between the third and fourth levels, that is, the coordination between the DC circuit breaker of the DC distribution panel and the DC circuit breaker of the terminal intelligent control panel or the power distribution area DC; most of the equipment in the intelligent substation is in the power distribution area, so most of the DC loads of the whole station are concentrated in the DC distribution panel; and because the distance between the DC distribution panel and the DC feeder panel in the main control room is closer than the layout of the conventional intelligent substation, when a short circuit occurs at the outlet of the DC distribution panel, the short-circuit current may be within the instantaneous action area of the upper-level DC circuit breaker, causing越级tripping;

[0051] Here, two types of DC circuit breakers will be compared to meet the grading coordination:

[0052] For the molded case DC circuit breaker, the instantaneous tripping range is: 10In, the ultimate short-time withstand current is 20 - 30 kA, and the time is 15 ms;

[0053] For the molded case selective DC circuit breaker, the instantaneous tripping value is 18In×(1 - 20%) ---- 18In×(1 + 20%), the short-circuit short-time delay current setting value is 10In×(1 - 20%) ---- 10In×(1 + 20%), and the short-circuit short-time delay setting value is 30 - 60 ms;

[0054] If a molded case DC circuit breaker is selected, then Id4 < 10In < Id3, and the rated current of the selected DC circuit breaker can be obtained;

[0055] If a molded case selective DC circuit breaker is selected, the upper limit of the instantaneous tripping value is 18In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value is 18In×(1 - 20%) > Id4; if the instantaneous tripping does not meet the selectivity requirements, the upper limit of the short-time delay tripping value is 10In×(1 + 20%) < Id3;

[0056] S3: Digital modeling of DC system cables;

[0057] Digital modeling of DC systems requires accurate calculation and modeling of cable cross-sections. The cable cross-section should be selected based on two conditions: the cable's long-term allowable current carrying capacity and the circuit's allowable voltage drop, as shown in the following formula:

[0058] I pc ≥I ca1

[0059]

[0060] I ca =max(I ca1 ,I ca2 )

[0061] In the formula: I pc For the cable's allowable current carrying capacity, A; I ca1 Calculate the current (A; S) for long-term operation of the circuit. cac For the calculated cross-section of the cable, mm 2 l represents the resistivity, taken as 0.0184 Ω·mm for copper conductors. 2 / m; L is the cable length, in meters; I ca To calculate the allowable voltage drop, the current (A) is calculated; ΔU p The allowable voltage drop of the circuit is V; I ca1 Calculate the current (A) for long-term operation of the circuit; I ca2 Calculate the current A for short-time operation of the circuit.

[0062] S3.1: Calculation and modeling of battery circuit cables;

[0063] In the formula: I ca1 The battery discharge rate current during the power outage period, in A; I ca2 The initial impulse discharge current (1 minute) of the accident is expressed in A.

[0064] I ca1 =I d1h =K c ×C 10

[0065]

[0066] S3.2: Calculation and modeling of the cable from the DC feeder to the DC distribution panel;

[0067]

[0068] S3.3: According to the regulations, the load current of the DC cabinet to the terminal circuit in a centralized radial power supply shall be calculated according to I... d calculate;

[0069]

[0070] S3.4: Calculation and modeling of DC power distribution cables to other protective shields;

[0071] According to the regulations, the load current from the DC cabinet to the terminal circuit in a layered radial power supply system is I. d calculate;

[0072] Condition one:

[0073] Condition two:

[0074] The value is either condition one or condition two, or the relation value.

[0075] S4: Digital modeling results;

[0076] S4.1 DC load statistical calculation modeling results;

[0077] DC load statistical calculation modeling and analysis mainly involves classifying and calculating all loads. Based on the fault discharge time of each equipment load, the statistical device automatically outputs the calculated capacity, load current and normal current. Finally, the discharge current is obtained for each 30-minute period in the total fault discharge time from the initial 1 minute to 240 minutes.

[0078] S4.2 Results of cable cross-section and DC micro-fracture modeling using gradient descent algorithm;

[0079] By leveraging machine algorithms and digital modeling techniques, the complex calculations of various levels of cables and the coordination of different levels of DC micro-interrupts in DC systems can be simplified and digitally represented.

[0080] Input the cross-sectional parameters of the three-level cables from the battery to the DC main panel, from the DC main panel to the DC sub-panel, and from the DC sub-panel to the end load into the configuration diagram; input the rated current parameters of the four-level DC miniature circuit breakers for the battery outlet circuit breaker, the DC main panel outlet circuit breaker, the DC sub-panel outlet circuit breaker, and the end load outlet circuit breaker into the configuration diagram; through machine algorithms, iterate using the gradient descent algorithm, and finally select the optimal calculation result that meets the requirements;

[0081] By verifying the data of rated current and tripping current of each level of DC micro-interrupt calculated from the digital results, as well as the calculated cross-section of the cable, the sensitivity and level coordination are verified, thereby validating the effectiveness and accuracy of this digital modeling.

[0082] Preferably, in S1.2, m is the number of data points in the dataset, that is, the number of samples, and X... (i) Y represents the data point for the rated current of each stage of the DC miniature circuit breaker in the DC system. (i)These are experimental data from the manufacturer for different models of DC miniature circuit breakers, h θ (X (i) ) is the intermediate optimized value of the short-circuit current at the outlet of the next-level circuit breaker and the short-circuit current at the outlet of the current-level circuit breaker after iterative calculation, where θ is the different cable cross-section values.

[0083] Preferably, in the formula of S2.2.1: I sc Main transformer protection cabinet output short-circuit current, A; U n The nominal voltage of the DC power supply system is taken as 220V; ∑R i R is the sum of the circuit resistances, in Ω; r is the internal resistance of the valve-regulated lead-acid battery, in mΩ; L1 The internal resistance of the cable connecting the battery and the rectifier panel is given in Ω; R s2 R is the internal resistance of the DC circuit breaker in the DC feeder panel, in Ω; L2 The internal resistance of the cable connecting the DC feeder panel and the main transformer protection cabinet is given in Ω; R s3 To protect the internal resistance of the DC circuit breaker inside the cabinet, Ω.

[0084] Preferably, in step S2.2.1, according to the 5044 DC specification, the third-level DC circuit breaker should be a type B DC circuit breaker, that is, a type B DC circuit breaker should be installed on the protection cabinet in the main control room. This satisfies the differential coordination requirement.

[0085] 7×I n <I d4 (where I) n This refers to the rated current of the third-level (Type B) circuit breaker in a three-level circuit breaker configuration, typically configured with 3A or 4A, and a maximum of 6A; I d4 This refers to the short-circuit current at the final outlet, which is the short-circuit current at the outlet of the protection cabinet.

[0086] Preferably, in S2.2.2, the fourth-level DC circuit breaker is selected as follows:

[0087] Refer to the selection of the third-level DC circuit breaker in the configuration of a three-level DC circuit breaker. It is also a type B DC circuit breaker. The short-circuit current in the calculation is Id5, which is the short-circuit current at the end of the fourth-level DC circuit breaker.

[0088] Preferably, in S2.2.2, the third-stage DC circuit breaker is selected as follows:

[0089] The calculation method for the second-level DC circuit breaker in the configuration of a three-level DC circuit breaker can be referenced. That is, compare three types of DC circuit breakers: CH type DC circuit breaker, C type DC circuit breaker and three-section DC circuit breaker to meet the level coordination. The upper limit of the instantaneous tripping value short circuit current is Id5 (the short circuit current at the output end of the DC circuit breaker in the local intelligent control cabinet or prefabricated cabin panel cabinet), and the lower limit of the instantaneous tripping value short circuit current is Id4 (the short circuit current at the output of the DC circuit breaker in the prefabricated cabin DC distribution cabinet).

[0090] Preferably, in S2.2.2, the second-stage DC circuit breaker is selected as follows:

[0091] According to the regulations, the second-stage DC circuit breaker should be a molded case DC circuit breaker. The calculation of the short-circuit current in the DC system can refer to Formula I. SC =U n / ∑R i ,∑R i =r+R L1 +R S2 +R L2 +R S3 Calculations are performed; the short-circuit current at the DC circuit breaker outlet from the DC feeder cabinet to the DC distribution cabinet in the main control room is Id3, and the short-circuit current at the DC circuit breaker outlet in the DC distribution cabinet is Id4.

[0092] Preferably, in S2.2, the DC circuit breaker configuration of the substation mainly includes load-side circuit breakers, distribution-side circuit breakers, feeder-side circuit breakers, and battery-side circuit breakers.

[0093] (III) Beneficial Effects

[0094] Compared with existing technologies, this invention provides a digital modeling method for DC systems based on gradient descent machine learning algorithms, which has the following advantages:

[0095] This paper presents a digital modeling method for DC systems based on a gradient descent machine learning algorithm. By leveraging machine learning and digital modeling techniques, it simplifies and digitally represents the complex calculations of various levels of cables and the differential coordination of different levels of DC micro-circuit breakers in DC systems. The method inputs the cross-sectional parameters of the three-level cables (battery to DC main panel, DC main panel to DC sub-panel, and DC sub-panel to end load) into the configuration diagram. Similarly, it inputs the rated current parameters of the four-level DC micro-circuit breakers (battery outlet circuit breaker, DC main panel outlet circuit breaker, DC sub-panel outlet circuit breaker, and end load outlet circuit breaker) into the configuration diagram. Through machine learning and iterative gradient descent, the optimal calculation result that meets the requirements is ultimately selected. Attached Figure Description

[0096] Figure 1 This is a flowchart illustrating the calculation process for the DC system circuit breaker and cable cross-section of the present invention.

[0097] Figure 2 This is a schematic diagram of the three-stage DC circuit breaker for the DC system feeder of the present invention;

[0098] Figure 3 This is a table showing the corresponding locations of the three-stage DC circuit breakers of this invention;

[0099] Figure 4 This is a schematic diagram of the four-stage DC circuit breaker for the DC system feeder of the present invention;

[0100] Figure 5 This is a table showing the corresponding locations of the four-stage DC circuit breakers of this invention;

[0101] Figure 6 This is a table showing the selection requirements for battery circuit cables for this invention.

[0102] Figure 7 This is a table showing the cable selection requirements from the DC feeder circuit to the DC distribution panel in this invention;

[0103] Figure 8 This is a table showing the selection requirements for DC feeder cables to other protective screens in this invention;

[0104] Figure 9 This is a table showing the selection requirements for DC power distribution cables to other protective screens in this invention. Detailed Implementation

[0105] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0106] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0107] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0108] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0109] like Figure 1-9 As shown, the present invention provides a technical solution: a digital modeling method for DC systems based on gradient descent machine learning algorithm, comprising the following steps:

[0110] S1: Machine algorithm analysis;

[0111] By predicting and analyzing data, especially unknown new data, we can achieve accurate statistical predictions and solutions for data.

[0112] S1.1: Perform gradient descent algorithm on the existing data;

[0113] First, the coefficient vector is initialized, and then the coefficient vector values ​​are iteratively updated step by step to minimize the objective function until convergence.

[0114] Gradient descent is an iterative algorithm that selects an appropriate initial value x(0), iterates continuously, updates the value of x, and minimizes the objective function until convergence. Since the negative gradient direction is the direction that makes the function value decrease the fastest, the value of x is updated in the negative gradient direction at each step of the iteration, thereby achieving the purpose of reducing the function value.

[0115] The gradient descent algorithm mainly consists of:

[0116] enter:

[0117] Output: The minimum point x of f(x) * ;

[0118] K1 takes the initial value X (0) ∈R n Set k=0

[0119] K2 calculates f(X) (k) )

[0120] K3 calculates the gradient g k =g(X) (k) When ||g k When || < ε, stop the iteration and let X * =X (k) Otherwise, let p k=-g(X) (k) Find λ. k ,make

[0121]

[0122] K4 X (k+1) =X (k) +λ k p k Calculate f(X) (k+1) )

[0123] When ||f(X) (k+1) )-f(X (k) || < ε or || X (k+1) -X (k) When || < ε, stop the iteration and let X * =X (k+1)

[0124] K5 Otherwise, set k = k + 1 and go to K3;

[0125] S1.2: Simulate DC circuit breaker step differences and cable calculations using the gradient descent algorithm;

[0126] Under normal circumstances, the short-circuit current of a DC system can be expressed by the mathematical relationship between the cable cross-section and the resistance of the DC circuit breaker. The rated tripping current value of the DC miniature circuit breaker should ensure that the trip unit can reliably not operate when the next-level circuit breaker outlet is short-circuited and that the trip unit can reliably operate when the current-level circuit breaker outlet is short-circuited. Considering the closest intermediate value as the optimal value, the function set in this way is a differentiable function.

[0127] When calculating the short-circuit current of a DC system, a value needs to be assumed for the rated current of the DC circuit breaker, from which the resistance value of the DC circuit breaker can be derived; an initial value X is set for the rated tripping current of each stage of the DC circuit breaker. (0) This allows us to derive the coefficients of the mathematical relationship; we define a cost function J(θ), expressed in the common root mean square error form as follows:

[0128]

[0129] In equation (1), h θ (X (i) It can be expressed as a differentiable function as:

[0130] h θ (X (i) )=C0θ0 -1 +C1θ1 -1 +C2θ2 -1 +C3X (i)C0, C1, and C2 are the median values ​​of the parameters for the three cable cross-sections; C3 is the parameter value for converting the rated current of the DC miniature circuit breaker into a resistance value.

[0131] In the cost function J(θ), there are three variables, namely θ0, θ1, and θ2, which represent three different levels of cable cross-sections: from the battery circuit to the DC main cabinet, from the DC main cabinet to the DC distribution cabinet, and from the DC distribution cabinet to the end.

[0132] S2: Digital modeling for calculating the differential calculation of DC system feeder circuit breakers;

[0133] S2.1: Digital modeling of DC feeder load;

[0134] Digital modeling mainly involves assigning load factors, normal current, fault discharge time and other attribute information to the loads with the above characteristics, and then modeling the scale of equipment involved in the DC system.

[0135] S2.2: Modeling of differential coordination of DC circuit breakers;

[0136] Digital modeling of DC circuit breaker differential coordination mainly targets the configuration of three-level DC circuit breakers and the configuration of four-level DC circuit breakers.

[0137] S2.2.1: Configuration of three-level DC circuit breakers;

[0138] The configuration of three-level DC circuit breakers mainly involves the differential coordination between the second and third level DC circuit breakers and the selection of circuit breakers, which is the protection coordination of the DC circuit breaker outlet from the DC feeder cabinet to any protection cabinet in the main control room.

[0139] Q1 Third-level DC circuit breaker calculation:

[0140] Calculation of short-circuit current in DC system:

[0141] I SC =U n / ∑R i

[0142] ∑R i =r+R L1 +R S2 +R L2 +R S3

[0143] Q2 Second-stage DC circuit breaker calculation:

[0144] For calculating the short-circuit current of a DC system, refer to formula I. SC =U n / ∑R i ,∑R i =r+R L1 +RS2 +R L2 +R S3 R is removed from the sum of the loop resistances. s3 (Internal resistance of DC circuit breaker in main transformer protection cabinet), the calculated short-circuit current is Id3 at the end of DC feeder cabinet S2 circuit breaker.

[0145] According to the 5044 DC specification, the second-stage DC circuit breaker can be configured as a type C DC circuit breaker. This section compares three types of DC circuit breakers to ensure proper coordination:

[0146] The instantaneous tripping range of the CH type DC circuit breaker is: 14In×(1-20%)----14In×(1+20%);

[0147] The instantaneous tripping range of the type C DC circuit breaker is: 10In×(1-20%)----10In×(1+20%);

[0148] Three-stage DC circuit breaker short-circuit short-delay setting value: 10In×(1-20%)----10In×(1+20%), time constant 5ms, short-circuit instantaneous trip current value 1680A;

[0149] If CH is selected, the upper limit of the instantaneous trip value is 14In×(1+20%)<Id3, and the lower limit of the instantaneous trip value is 14In×(1-20%)>Id4;

[0150] If a C-type micro-circuit is selected, the upper limit of the instantaneous trip value is 10In×(1+20%)<Id3, and the lower limit of the instantaneous trip value is 10In×(1-20%)>Id4;

[0151] If neither CH type nor C type meets the differential coordination requirement, a three-stage circuit breaker can be selected, that is, the upper limit of short-delay trip value 10In×(1+20%)<Id3 is met;

[0152] S2.2.2: Configuration of four-level DC circuit breakers;

[0153] The configuration of four-level DC circuit breakers mainly involves the second and third levels, referring to the differential coordination and circuit breaker configuration between the DC circuit breakers in the DC feeder panel of the main control room and the DC circuit breakers in the DC distribution panel of the equipment area, as well as the differential coordination between the third and fourth levels, i.e., the coordination between the DC circuit breakers in the DC distribution panel and the DC circuit breakers in the terminal intelligent control panel or distribution area. In intelligent substations, most of the equipment is located in the distribution area, so most of the DC load of the entire station is concentrated in the DC distribution panel. Moreover, since the distance between the DC distribution panel and the DC feeder panel in the main control room is closer than that in conventional intelligent substations, when a short circuit occurs at the output of the DC distribution panel, the short circuit current may be within the instantaneous operating range of the DC circuit breaker at the next higher level, causing cascading tripping.

[0154] Here, two types of DC circuit breakers will be compared to meet the grading coordination:

[0155] The molded case DC circuit breaker has an instantaneous tripping range of 10In, a rated short-time withstand current of 20 - 30kA, and a time of 15ms;

[0156] The molded case selective DC circuit breaker has an instantaneous tripping value of 18In×(1 - 20%) ---- 18In×(1 + 20%), a short-circuit short-time delay current setting value of 10In×(1 - 20%) ---- 10In×(1 + 20%), and a short-circuit short-time delay setting value of 30 - 60ms;

[0157] If a molded case DC circuit breaker is selected, then Id4 < 10In < Id3, and the rated current of the selected DC circuit breaker can be obtained;

[0158] If a molded case selective DC circuit breaker is selected, then the upper limit of the instantaneous tripping value 18In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value 18In×(1 - 20%) > Id4; if the instantaneous tripping does not meet the selectivity requirement, then the upper limit of the short-time delay tripping value 10In×(1 + 20%) < Id3;

[0159] S3: Digital modeling of DC system cable calculation;

[0160] Digital modeling of the DC system requires accurate calculation and modeling of the cable cross-section; the cable cross-section should be selected according to two conditions: the long-term allowable current-carrying capacity of the cable and the allowable voltage drop of the circuit. The formula is as follows:

[0161] I pc ≥I ca1 [[ID=26]]

[0162]

[0163] I<0000146>=max(I ca1 ,I ca2 )

[0164] In the formula: I pc is the allowable current-carrying capacity of the cable, A; I ca1 is the long-term working calculation current of the circuit, A; S cac is the calculated cross-section of the cable, mm 2 ; l is the resistivity coefficient, taking 0.0184Ω·mm 2 / m for copper conductor; L is the cable length, m; I ca is the calculated current for allowable voltage drop, A; ΔU p is the allowable voltage drop of the circuit, V; I ca1 is the long-term working calculation current of the circuit, A; I ca2 is the short-term working calculation current of the circuit, A

[0165] S3.1: Calculation and modeling of battery circuit cables;

[0166] In the formula: I ca1 The battery discharge rate current during the power outage period, in A; I ca2 The initial impulse discharge current (1 minute) of the accident is expressed in A.

[0167] I ca1 =I d1h =K c ×C 10

[0168]

[0169] S3.2: Calculation and modeling of the cable from the DC feeder to the DC distribution panel;

[0170]

[0171] S3.3: According to the regulations, the load current of the DC cabinet to the terminal circuit in a centralized radial power supply shall be calculated according to I... d calculate;

[0172]

[0173] S3.4: Calculation and modeling of DC power distribution cables to other protective shields;

[0174] According to the regulations, the load current from the DC cabinet to the terminal circuit in a layered radial power supply system is I. d calculate;

[0175] Condition one:

[0176] Condition two: The value is either condition one or condition two, or the relation value.

[0177] S4: Digital modeling results;

[0178] S4.1 DC load statistical calculation modeling results;

[0179] DC load statistical calculation modeling and analysis mainly involves classifying and calculating all loads. Based on the fault discharge time of each equipment load, the statistical device automatically outputs the calculated capacity, load current and normal current. Finally, the discharge current is obtained for each 30-minute period in the total fault discharge time from the initial 1 minute to 240 minutes.

[0180] S4.2 Results of cable cross-section and DC micro-fracture modeling using gradient descent algorithm;

[0181] By leveraging machine algorithms and digital modeling techniques, the complex calculations of various levels of cables and the coordination of different levels of DC micro-interrupts in DC systems can be simplified and digitally represented.

[0182] Input the cross-sectional parameters of the three-level cables from the battery to the DC main panel, from the DC main panel to the DC sub-panel, and from the DC sub-panel to the end load into the configuration diagram; input the rated current parameters of the four-level DC miniature circuit breakers for the battery outlet circuit breaker, the DC main panel outlet circuit breaker, the DC sub-panel outlet circuit breaker, and the end load outlet circuit breaker into the configuration diagram; through machine algorithms, iterate using the gradient descent algorithm, and finally select the optimal calculation result that meets the requirements;

[0183] By verifying the data of rated current and tripping current of each level of DC micro-interrupt calculated from the digital results, as well as the calculated cross-section of the cable, the sensitivity and level coordination are verified, thereby validating the effectiveness and accuracy of this digital modeling.

[0184] In S1.2, m is the number of data points in the dataset, which is also the number of samples, and X... (i) Y represents the data point for the rated current of each stage of the DC miniature circuit breaker in the DC system. (i) These are experimental data from the manufacturer for different models of DC miniature circuit breakers, h θ (X (i) ) is the intermediate optimized value of the short-circuit current at the outlet of the next-level circuit breaker and the short-circuit current at the outlet of the current-level circuit breaker after iterative calculation, where θ is the different cable cross-section values.

[0185] In formula S2.2.1: I sc Main transformer protection cabinet output short-circuit current, A; U n The nominal voltage of the DC power supply system is taken as 220V; ∑R i R is the sum of the circuit resistances, in Ω; r is the internal resistance of the valve-regulated lead-acid battery, in mΩ; L1 The internal resistance of the cable connecting the battery and the rectifier panel is given in Ω; R s2 R is the internal resistance of the DC circuit breaker in the DC feeder panel, in Ω; L2 The internal resistance of the cable connecting the DC feeder panel and the main transformer protection cabinet is given in Ω; R s3 To protect the internal resistance of the DC circuit breaker inside the cabinet, Ω.

[0186] In S2.2.1, according to the 5044 DC specification, the third-level DC circuit breaker should be a type B DC circuit breaker, that is, a type B DC circuit breaker should be installed on the protection cabinet in the main control room. This satisfies the differential coordination requirement.

[0187] 7×I n <I d4 (where I) nThis refers to the rated current of the third-level (Type B) circuit breaker in a three-level circuit breaker configuration, typically configured with 3A or 4A, and a maximum of 6A; I d4 This refers to the short-circuit current at the final outlet, which is the short-circuit current at the outlet of the protection cabinet.

[0188] In S2.2.2, the selection of the fourth-level DC circuit breaker:

[0189] Refer to the selection of the third-level DC circuit breaker in the configuration of a three-level DC circuit breaker. It is also a type B DC circuit breaker. The short-circuit current in the calculation is Id5, which is the short-circuit current at the end of the fourth-level DC circuit breaker.

[0190] In S2.2.2, the selection of the third-level DC circuit breaker:

[0191] The calculation method for the second-level DC circuit breaker in the configuration of a three-level DC circuit breaker can be referenced. That is, compare three types of DC circuit breakers: CH type DC circuit breaker, C type DC circuit breaker and three-section DC circuit breaker to meet the level coordination. The upper limit of the instantaneous tripping value short circuit current is Id5 (the short circuit current at the output end of the DC circuit breaker in the local intelligent control cabinet or prefabricated cabin panel cabinet), and the lower limit of the instantaneous tripping value short circuit current is Id4 (the short circuit current at the output of the DC circuit breaker in the prefabricated cabin DC distribution cabinet).

[0192] In S2.2.2, the selection of the second-stage DC circuit breaker:

[0193] According to the regulations, the second-stage DC circuit breaker should be a molded case DC circuit breaker. The calculation of the short-circuit current in the DC system can refer to Formula I. SC =U n / ∑R i , Equation ∑R i =r+R L1 +R S2 +R L2 +R S3 Calculations are performed. The short-circuit current at the DC circuit breaker outlet from the DC feeder cabinet to the DC distribution cabinet in the main control room is Id3, and the short-circuit current at the DC circuit breaker outlet in the DC distribution cabinet is Id4.

[0194] In S2.2, the DC circuit breaker configuration of the substation mainly includes load-side circuit breakers, distribution-side circuit breakers, feeder-side circuit breakers, and battery-side circuit breakers.

[0195] This paper presents a digital modeling method for DC systems based on a gradient descent machine learning algorithm. By leveraging machine learning and digital modeling techniques, it simplifies and digitally represents the complex calculations of various levels of cables and the differential coordination of different levels of DC micro-circuit breakers in DC systems. The method inputs the cross-sectional parameters of the three-level cables (battery to DC main panel, DC main panel to DC sub-panel, and DC sub-panel to end load) into the configuration diagram. Similarly, it inputs the rated current parameters of the four-level DC micro-circuit breakers (battery outlet circuit breaker, DC main panel outlet circuit breaker, DC sub-panel outlet circuit breaker, and end load outlet circuit breaker) into the configuration diagram. Through machine learning and iterative gradient descent, the optimal calculation result that meets the requirements is ultimately selected.

[0196] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising a reference structure" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A digital modeling method for DC systems based on gradient descent machine learning algorithm, comprising the following steps: S1: Machine algorithm analysis; By predicting and analyzing data, especially unknown new data, we can achieve accurate statistical predictions and solutions for data. S1.1: Perform gradient descent algorithm on the existing data; First, the coefficient vector is initialized, and then the coefficient vector values ​​are iteratively updated step by step to minimize the objective function until convergence. Gradient descent is an iterative algorithm that selects an appropriate initial value x(0), iterates continuously, updates the value of x, and minimizes the objective function until convergence. Since the negative gradient direction is the direction that makes the function value decrease the fastest, the value of x is updated in the negative gradient direction at each step of the iteration, thereby achieving the purpose of reducing the function value. The gradient descent algorithm mainly consists of: Input: Objective function f(x), gradient function g(x) = Calculation accuracy ; Output: The minimum point of f(x) ; K1 takes an initial value Set k=0; K2 calculation ; K3 calculates the gradient ,when When the iteration stops, let Otherwise, let ,beg ,make ; K4 ,calculate , when or When the iteration stops, let ; K5 Otherwise, set k=k+1 and go to K3; S1.2: Simulate DC circuit breaker step differences and cable calculations using the gradient descent algorithm; Under normal circumstances, the short-circuit current of a DC system can be expressed by the mathematical relationship between the cable cross-section and the resistance of the DC circuit breaker. The rated tripping current value of the DC miniature circuit breaker should ensure that the trip unit can reliably not operate when the next-level circuit breaker outlet is short-circuited and that the trip unit can reliably operate when the current-level circuit breaker outlet is short-circuited. Considering the closest intermediate value as the optimal value, the function set in this way is a differentiable function. When calculating the short-circuit current of a DC system, it is necessary to assume a value for the rated current of the DC circuit breaker, from which the resistance value of the DC circuit breaker can be derived; an initial value should be set for the rated tripping current of each stage of the DC circuit breaker. This allows us to derive the coefficients of the mathematical relationship; and define a cost function. This is manifested in the common form of root mean square error as follows: In equation (1), It can be expressed as a differentiable function as: ,in , , The median value of the parameters corresponding to the three levels of cable cross-sections; The parameter value for converting the rated current of the corresponding DC miniature circuit breaker into a resistance value; Cost function In this context, there are three variables: , , This represents three different levels of cable cross-sections: from the battery circuit to the DC main cabinet, from the DC main cabinet to the DC distribution cabinet, and from the DC distribution cabinet to the end. Where m is the number of data points in the dataset, which is also the number of samples. This refers to the data points for the rated current of each level of DC miniature circuit breaker in a DC system. These are experimental data from the manufacturer for different models of DC miniature circuit breakers. It is an intermediate optimized value between the short-circuit current at the outlet of the next-stage circuit breaker and the short-circuit current at the outlet of the current-stage circuit breaker, calculated through iterative calculations. These are different cable cross-sectional values; S2: Digital modeling for calculating the differential calculation of DC system feeder circuit breakers; S2.1: Digital modeling of DC feeder load; Digital modeling involves assigning load factors, normal current, and fault discharge time to the loads with the above characteristics, and then modeling the scale of equipment involved in the DC system. S2.2: Modeling of differential coordination of DC circuit breakers; Digital modeling of DC circuit breaker differential coordination mainly targets the configuration of three-level DC circuit breakers and the configuration of four-level DC circuit breakers. S2.2.1: Configuration of three-level DC circuit breakers; The configuration of three-level DC circuit breakers mainly involves the differential coordination between the second and third level DC circuit breakers and the selection of circuit breakers, which is the protection coordination of the DC circuit breaker outlet from the DC feeder cabinet to any protection cabinet in the main control room. Q1 Calculation of the third-level DC circuit breaker: Calculation of short-circuit current in DC system: Q2 Calculation of the second-level DC circuit breaker: The formula for calculating short-circuit current in a DC system can be referenced. , Remove from the sum of the loop resistances The internal resistance of the DC circuit breaker in the main transformer protection cabinet is used to calculate the short-circuit current. The short-circuit current at the end of the DC feeder cabinet S2 circuit breaker is Id3. The short-circuit current at the output of the main transformer protection cabinet is measured in A. The nominal voltage of the DC power supply system is taken as 220 V. The sum of the loop resistances, in Ω; The internal resistance of a valve-regulated lead-acid battery is given in mΩ. The internal resistance of the cable connecting the battery and the rectifier panel is given in Ω. The internal resistance of the DC circuit breaker in the DC feeder panel is Ω; The internal resistance of the cable connecting the DC feeder panel and the main transformer protection cabinet is Ω; To protect the internal resistance of the DC circuit breaker inside the cabinet, Ω; According to the 5044 DC specification, the second-stage DC circuit breaker can be configured as a type C DC circuit breaker. This section compares three types of DC circuit breakers to ensure proper coordination: The instantaneous tripping range of the CH type DC circuit breaker is: 14In×(1-20%)---- 14In×(1+20%); The instantaneous tripping range of the C-type DC circuit breaker is: 10In×(1-20%)---- 10In×(1+20%); Three-stage DC circuit breaker short-circuit short-delay setting value: 10In×(1-20%)---- 10In×(1+20%), time constant 5ms, short-circuit instantaneous trip current value 1680A; If CH is selected, the upper limit of the instantaneous tripping value is 14In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value is 14In×(1 - 20%) < Id4; If a C-type miniature circuit breaker is selected, the upper limit of the instantaneous tripping value is 10In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value is 10In×(1 - 20%) > Id4; If neither the CH type nor the C type satisfies the grading coordination, a three-stage circuit breaker can be selected, that is, the upper limit of the short-time delay tripping value is 10In×(1 + 20%) < Id3; S2.2.2: Configuration of four-pole DC circuit breakers; In the configuration of four-pole DC circuit breakers, the main ones are the second stage and the third stage, referring to the grading coordination and the configuration type of the DC circuit breakers on the DC feeder panel in the main control room and the DC distribution panel in the equipment area, as well as the grading coordination between the third stage and the fourth stage, that is, the coordination between the DC circuit breaker on the DC distribution panel and the DC circuit breaker on the terminal intelligent control panel or the DC circuit breaker in the distribution area; most of the equipment in the intelligent substation is in the distribution area, so most of the DC loads of the whole station are concentrated in the DC distribution panel; and because the distance between the DC distribution panel and the DC feeder panel in the main control room is closer than the layout of the conventional intelligent substation, when a short circuit occurs at the outlet of the DC distribution panel, the short-circuit current may be within the instantaneous action area of the upper-level DC circuit breaker, causing越级tripping; Here, two types of DC circuit breakers will be compared to meet the grading coordination: The molded case DC circuit breaker has an instantaneous tripping range of: 10In, a limit short-time withstand current of 20 - 30 kA, and a time of 15 ms; The molded case selective DC circuit breaker has an instantaneous tripping value of 18In×(1 - 20%) ---- 18In×(1 + 20%), a short-circuit short-time delay current setting value of 10In×(1 - 2%) ---- 10In×(1 + 20%), and a short-circuit short-time delay setting value of 30 - 60 ms; If a molded case DC circuit breaker is selected, then Id4 < 10In < Id3, and the rated current of the selected DC circuit breaker can be obtained; If a molded case selective DC circuit breaker is selected, the upper limit of the instantaneous tripping value is 18In×(1 + 20%) < Id3, and the lower limit of the instantaneous tripping value is 18In×(1 - 20%) > Id4; if the instantaneous tripping does not meet the selectivity requirements, the upper limit of the short-time delay tripping value is 10In×(1 + 20%) < Id3; S3: Digital modeling of DC system cable calculation; Digital modeling of the DC system requires accurate calculation and modeling of the cable cross-section; the cable cross-section should be selected according to two conditions: the long-term allowable current-carrying capacity of the cable and the allowable voltage drop of the circuit. The formula is as follows: In the formula: The allowable current carrying capacity of the cable is A; Calculate the current (A) for long-term operation of the circuit; For the calculated cross-section of the cable, mm 2 ; The resistivity is taken as 0.0184 Ω·mm for copper conductors. 2 / m; The length of the cable is in meters (m). Calculate the current (A) to account for the allowable voltage drop; The allowable voltage drop of the circuit is V; Calculate the current (A) for long-term operation of the circuit; Calculate the current A for short-time operation of the circuit. S3.1: Cable calculation and modeling for the battery circuit; In the formula: The battery discharge rate current during the power outage period, in A; The initial discharge current (A) in the first minute after the accident. ; ; S3.2: Cable calculation and modeling from the DC feeder to the DC distribution panel; ; S3.3: According to the regulations, the load current of the DC cabinet with centralized radial power supply to the terminal circuit shall be calculated as follows: calculate; ； S3.4: Cable calculation and modeling from the DC distribution to other protection panels; According to regulations, the load current from the DC cabinet to the terminal circuit in a layered radial power supply system is... calculate; Condition 1: ; Condition two: The value is either condition one or condition two, or the relation value. S4: Digital modeling results; S4.1 Results of DC load statistical calculation and modeling; DC load statistical calculation modeling and analysis mainly involves classifying and calculating all loads. Based on the fault discharge time of each equipment load, the statistical device automatically outputs the calculated capacity, load current and normal current. Finally, the discharge current is obtained for each 30-minute period in the total fault discharge time from the initial 1 minute to 240 minutes. S4.2 Results of cable cross-section and DC micro-fracture modeling using gradient descent algorithm; By leveraging machine algorithms and digital modeling techniques, the complex calculations of various levels of cables and the coordination of different levels of DC micro-interrupts in DC systems can be simplified and digitally represented. Input the cross-sectional parameters of the three-level cables from the battery to the DC main panel, from the DC main panel to the DC sub-panel, and from the DC sub-panel to the end load into the configuration diagram; input the rated current parameters of the four-level DC miniature circuit breakers for the battery outlet circuit breaker, the DC main panel outlet circuit breaker, the DC sub-panel outlet circuit breaker, and the end load outlet circuit breaker into the configuration diagram; through machine algorithms, iterate using the gradient descent algorithm, and finally select the optimal calculation result that meets the requirements; By verifying the data of rated current and tripping current of each level of DC micro-interrupt calculated from the digital results, as well as the calculated cross-section of the cable, the sensitivity and level coordination are verified, thereby validating the effectiveness and accuracy of this digital modeling.

2. The digital modeling method for DC systems based on gradient descent machine algorithm according to claim 1, characterized in that, In S2.2.1, according to the 5044 DC specification, the third-level DC circuit breaker should be configured as a type B DC circuit breaker, that is, a type B DC circuit breaker should be configured on the protection cabinet in the main control room to meet the level coordination requirements. ,in This refers to the rated current of the third-level B-type circuit breaker in a three-level circuit breaker configuration, which can be configured as 3A, 4A, or up to 6A. This is the short-circuit current at the very end of the circuit, which is the short-circuit current at the outlet of the protection cabinet.

3. The digital modeling method for DC systems based on gradient descent machine algorithm according to claim 1, characterized in that, In S2.2.2, the fourth-level DC circuit breaker is selected as follows: Refer to the selection of the third-level DC circuit breaker in the configuration of a three-level DC circuit breaker. It is also a type B DC circuit breaker. The short-circuit current in the calculation is Id5, which is the short-circuit current at the end of the fourth-level DC circuit breaker.

4. The digital modeling method for DC systems based on gradient descent machine algorithm according to claim 1, characterized in that, In S2.2.2, the selection of the third-stage DC circuit breaker is as follows: The calculation method for the second-level DC circuit breaker in the configuration of a three-level DC circuit breaker can be referenced. That is, compare three types of DC circuit breakers: CH type DC circuit breaker, C type DC circuit breaker and three-section DC circuit breaker to meet the level coordination. The upper limit of the instantaneous tripping value short circuit current is Id5, which is the short circuit current at the output end of the DC circuit breaker of the local intelligent control cabinet or the prefabricated cabin panel cabinet. The lower limit of the instantaneous tripping value short circuit current is Id4, which is the short circuit current at the output of the DC circuit breaker of the DC distribution cabinet in the prefabricated cabin.

5. The digital modeling method for DC systems based on gradient descent machine algorithm according to claim 1, characterized in that, In section S2.2.2, the selection of the second-stage DC circuit breaker: According to the regulations, the second-stage DC circuit breaker should be a molded case DC circuit breaker. The calculation of the short-circuit current of the DC system can refer to the formula... , The calculations are performed; the short-circuit current at the DC circuit breaker outlet from the DC feeder cabinet to the DC distribution cabinet in the main control room is Id3, and the short-circuit current at the DC circuit breaker outlet in the DC distribution cabinet is Id4.

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