Mathematical model construction method for external short-circuit fault of T-type DC transformer

Abstract

The invention discloses a method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer, comprising the following steps: establishing a T-type DC transformer topology; keeping the transformer ratio and output voltage constant through common point voltage control, DC power control, AC power control and SPWM modulation; establishing a mathematical model of an external short-circuit fault of a T-type DC transformer: simplifying the transformer into a linear time-varying circuit by using a submodule equivalent method; deriving the short-circuit current by using a loop current method from the perspectives of a single-phase high-voltage bridge arm power supply acting alone, a single-phase multiplexed bridge arm power supply acting alone, a single-phase low-voltage bridge arm power supply acting alone, and a low-voltage side power supply acting alone, and summing the short-circuit currents generated by each power supply to obtain a complex frequency domain expression of the short-circuit current. The invention can predict the instantaneous short-circuit current impact value of an external short-circuit fault of a T-type DC transformer.

Description

Technical Field

[0001] The invention relates to an external short-circuit fault of a T-type direct current transformer, and in particular to a method for constructing a mathematical model of an external short-circuit fault of a T-type direct current transformer. Background Art

[0002] With the large number of new energy sources connected to the grid, traditional power systems can no longer meet the needs of new energy generation. DC grid technology based on flexible DC transmission is currently the most effective technical solution to the problem of new energy generation, and power electronic DC transformers can achieve interconnection between DC lines of different voltage levels and types, and are the core power equipment in DC grids.

[0003] Compared with isolated DC transformers, non-isolated DC transformers have the advantages of high conversion efficiency, low cost, small size and weight, and have broad application prospects. Among them, T-type DC transformers can use multiplexed bridge arms to maintain the power balance of matching power supplies, and are non-isolated DC transformers with high energy utilization. Therefore, studying the fault analysis method of this transformer is crucial for predicting the impact of faults and maintaining the stable operation of DC power grids. DC transformer faults include internal faults and external faults. Among them, external faults are often manifested as polar short circuits on the DC side. At the moment of polar short circuit faults, the DC side will generate short-circuit impact currents several times greater than normal operating conditions, which directly affects the normal operation of the DC transmission system and even causes immeasurable damage to the transformer and DC power grid. At present, the research on mathematical models for external short circuit faults of T-type DC transformers is still blank. Therefore, it is of great practical significance to establish a mathematical model for external short circuit faults of T-type DC transformers and predict the impact value of short circuit current on the DC side at the moment of faults. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned background technology and provide a method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer, thereby solving the problem in the prior art that the instantaneous short-circuit current impact value of an external short-circuit fault of a T-type DC transformer cannot be predicted, and providing a theoretical basis for further analysis, diagnosis and protection of external short-circuit faults of the transformer.

[0005] The technical solution adopted by the present invention to solve the technical problem is a method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer, comprising the following steps:

[0006] Step S1: Establish a T-type DC transformer topology structure;

[0007] Step S2: through common point voltage control, DC power control, AC power control and SPWM modulation, each bridge arm submodule of the T-type DC transformer topology structure outputs an ideal voltage and power, so that the transformer ratio and output voltage remain constant;

[0008] Step S3: Establish a mathematical model of external short-circuit fault of T-type DC transformer: Use submodule equivalent method to simplify the transformer into a linear time-varying circuit; Use loop current method to derive short-circuit current from the perspectives of single-phase high-voltage bridge arm power supply acting alone, single-phase multiplexed bridge arm power supply acting alone, single-phase low-voltage bridge arm power supply acting alone, and low-voltage side power supply acting alone, and use superposition principle to add up the short-circuit current generated by each power supply to obtain the short-circuit current The complex frequency domain expression of .

[0009] Furthermore, the T-type DC transformer topology structure is composed of three identical phase units, each phase unit is composed of a high-voltage bridge arm H, a low-voltage bridge arm L, and a reused bridge arm F; each bridge arm is composed of multiple series-connected sub-modules and an inductor, and the multiple series-connected sub-modules are connected in series with the inductor, wherein the sub-modules in the high-voltage bridge arm H and the reused bridge arm F are all half-bridge sub-modules, and the sub-modules in the low-voltage bridge arm L are all full-bridge sub-modules.

[0010] Further, the common point voltage control method is:

[0011] The DC voltage of the low-voltage bridge arm L is controlled to be 0, that is, the common point voltage is equal to the low-voltage side voltage, specifically:

[0012] For the high-voltage bridge arm H, control the DC voltage of the y-phase high-voltage bridge arm for:

[0013] (1)

[0014] in, is the DC voltage of the y-phase high-voltage bridge arm, where y represents any one of the three phases A, B, and C. is the high voltage side voltage, is the voltage on the low voltage side;

[0015] For the multiplexing bridge arm F, control the DC voltage of the y-phase multiplexing bridge arm for:

[0016] (2)

[0017] in, is the DC voltage of the y-phase multiplexing bridge arm.

[0018] Further, the DC power control method is:

[0019] For phase A of the step-up transformer, the load power is calculated from the high voltage side according to the three-phase circuit, and the load power is:

[0020] (3)

[0021] in, is the load power, is the high voltage side voltage, is the DC current of the high voltage bridge arm of phase A;

[0022] Based on the fact that the DC power of the reuse bridge arm and the high-voltage bridge arm is equal in magnitude and opposite in direction, the following equation is listed: Assuming that the forward direction is the bridge arm absorbing power:

[0023] (4)

[0024] in, is the DC current of the A-phase multiplexing bridge arm, is the DC current of the high voltage bridge arm of phase A, is the DC voltage of the high voltage bridge arm of phase A, is the DC voltage of the A-phase multiplexing bridge arm;

[0025] The DC current of the low-voltage bridge arm of phase A is directly obtained by Kirchhoff's current law;

[0026] set up is the DC current of the low-voltage bridge arm of phase A. Ideally, the DC power on the low-voltage side is equal to the load power, so the power on the low-voltage side is:

[0027] (5)

[0028] in, is the low voltage side power, is the reference value of the high voltage bridge arm current; is the voltage on the low voltage side; is the load power, is the DC current of the low voltage bridge arm of phase A;

[0029] Using the high-voltage bridge arm current reference value obtained by formula (5), the high-voltage bridge arm DC current is controlled at the reference value about;

[0030] Combining equations (1), (2), 3), and (4) to obtain the DC current of the A phase multiplexing bridge arm for:

[0031] (6)

[0032] According to formula (6), the reference value of the multiplexed bridge arm current is obtained: for:

[0033] (7)

[0034] The DC current of the multiplexed bridge arm is controlled at the reference value about.

[0035] Further, the AC power control method is:

[0036] Assuming that the d-axis voltage component of the high-voltage bridge arm H is 0 and the q-axis voltage component of the reused bridge arm F is 0, the DC power balance between the reused bridge arm F and the high-voltage bridge arm H can be established as follows:

[0037] (9)

[0038] in, is the d-axis voltage of the multiplexed bridge arm, is the q-axis voltage of the high-voltage bridge arm, is the d-axis current of the multiplexed bridge arm, is the q-axis current of the high-voltage bridge arm, is the AC active power, is the DC power;

[0039] Since the active component of AC power is equal to DC power, and DC power is transmitted through AC circulation, the circulating power of the AC circuit itself is the active component of AC power. Assuming that the energy transferred from the high voltage side to the low voltage side is positive, we have:

[0040] (10)

[0041] in, is the active power of the high voltage bridge arm of phase A, is the active power of the A-phase multiplexing bridge arm, is the instantaneous voltage of the high-voltage bridge arm of phase A, is the instantaneous voltage of the A-phase multiplexing bridge arm, is the instantaneous current of the high voltage bridge arm of phase A, is the instantaneous current of the A-phase multiplexing bridge arm, is the instantaneous DC voltage of the high-voltage bridge arm of phase A, is the instantaneous DC voltage of the A-phase multiplexing bridge arm, is the instantaneous AC voltage of the A-phase high-voltage bridge arm, is the instantaneous AC voltage of the A-phase multiplexing bridge arm, is the instantaneous DC current of the A-phase high-voltage bridge arm, is the instantaneous DC current of the A-phase multiplexing bridge arm, is the circulating current of the AC circuit;

[0042] Set the transformation ratio for:

[0043] (11)

[0044] DC component of active power in high voltage bridge arm and the DC component of the active power of the multiplexed bridge arm They are:

[0045] (12)

[0046] in, is the circulating active power;

[0047] Substituting formula (11) into formula (12), we can obtain:

[0048] (13)

[0049] According to the active power formula and superposition theorem, we can get:

[0050] (14)

[0051] in, is the d-axis voltage of the multiplexed bridge arm, is the q-axis voltage of the high-voltage bridge arm, is the d-axis current of the high-voltage bridge arm, is the d-axis current of the multiplexed bridge arm, is the q-axis current of the high-voltage bridge arm, is the q-axis current of the multiplexed bridge arm; is the high voltage bridge arm inductance, To reuse the bridge arm inductance, is the AC frequency;

[0052] Combining the above formulas, the d-axis voltage of the multiplexed bridge arm can be calculated , d-axis current , q-axis current And the q-axis voltage of the high-voltage bridge arm , d-axis current , q-axis current .

[0053] Further, in step S3, the short-circuit current is derived using the loop current method from the perspective of the single-phase high-voltage bridge arm power supply acting alone, and the specific method is:

[0054] For phase A, when the high-voltage bridge arm power supply acts alone, the equivalent power supplies of all bridge arms except the high-voltage bridge arm are set to zero, and the branches of phases B and C are transformed equivalently to obtain the complex frequency domain fault equivalent circuit. Assume that the branch impedance for:

[0055] (15)

[0056] In the formula, L is the bridge arm inductance, R is the equivalent resistance of the bridge arm line, is the equivalent submodule capacitance of the X bridge arm, s is the complex frequency;

[0057] Since the three phase units are symmetrical, the loop current equation can be written as:

[0058] (16)

[0059] In the formula, is the capacitor voltage of the high voltage bridge arm of phase A, is the inductor current of the high voltage bridge arm of phase A, is the short-circuit branch equivalent resistance, It indicates the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone; is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of high-voltage bridge arm, reused bridge arm and short-circuit branch, loop 2 is a loop composed of reused bridge arm, low-voltage bridge arm and high-voltage side, loop 3 is a loop composed of high-voltage bridge arm, reused bridge arm and other equivalent branches, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel;

[0060] Solving equation (16) yields:

[0061] (17)

[0062] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone.

[0063] Further, in step S3, the short-circuit current is derived using the loop current method from the perspective of the single-phase multiplexed bridge arm power supply acting alone, and the specific method is:

[0064] For phase A, when the multiplexed bridge arm power supply acts alone, the equivalent power supplies of all bridge arms except the multiplexed bridge arm are set to zero, and the branches of phases B and C are equivalently transformed to obtain the complex frequency domain fault equivalent circuit. Suppose the branch impedance for:

[0065] (15)

[0066] In the formula, L is the bridge arm inductance, R is the equivalent resistance of the bridge arm line, is the equivalent submodule capacitance of the X bridge arm, s is the complex frequency;

[0067] Since the three phase units are symmetrical, the loop current equation can be written as:

[0068] (18)

[0069] In the formula, is the capacitor voltage of the A-phase reset bridge arm, is the inductor current of the reset bridge arm of phase A, is the short-circuit branch equivalent resistance, is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of high-voltage bridge arm, reused bridge arm and short-circuit branch, loop 2 is a loop composed of reused bridge arm, low-voltage bridge arm and high-voltage side, loop 3 is a loop composed of high-voltage bridge arm, reused bridge arm and other equivalent branches, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel;

[0070] Solving equation (18) yields:

[0071] (19)

[0072] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase multiplexed bridge arm power supply acts alone.

[0073] Further, in step S3, the short-circuit current is derived using the loop current method from the perspective of the single-phase low-voltage bridge arm power supply acting alone, and the specific method is:

[0074] For phase A, when the low-voltage bridge arm power supply acts alone, the equivalent power supplies of all bridge arms except the low-voltage bridge arm are set to zero, and the branches of phases B and C are equivalently transformed to obtain the complex frequency domain fault equivalent circuit. Suppose the branch impedance for:

[0075] (15)

[0076] In the formula, L is the bridge arm inductance, R is the equivalent resistance of the bridge arm line, is the equivalent submodule capacitance of the X bridge arm, s is the complex frequency;

[0077] Since the three phase units are symmetrical, the loop current equation can be written as:

[0078] (20)

[0079] In the formula, is the capacitor voltage of the low voltage bridge arm of phase A, is the inductor current of the low voltage bridge arm of phase A, is the short-circuit branch equivalent resistance, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage bridge arm power supply acts alone; is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of high-voltage bridge arm, reused bridge arm and short-circuit branch, loop 2 is a loop composed of reused bridge arm, low-voltage bridge arm and high-voltage side, loop 3 is a loop composed of high-voltage bridge arm, reused bridge arm and other equivalent branches, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel;

[0080] Solving equation (20) yields:

[0081] (twenty one)

[0082] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage bridge arm power supply acts alone.

[0083] Further, in step S3, the short-circuit current is derived using the loop current method from the perspective of the low-voltage side power supply acting alone, and the specific method is:

[0084] For phase A, when the low-voltage power supply acts alone, the equivalent power supplies of all bridge arms are set to zero, and the branches of phases B and C are transformed equivalently to obtain the complex frequency domain fault equivalent circuit. Suppose the branch impedance for:

[0085] (15)

[0086] In the formula, L is the bridge arm inductance, R is the equivalent resistance of the bridge arm line, is the equivalent submodule capacitance of the X bridge arm, s is the complex frequency;

[0087] Writing the KVL equation gives:

[0088] (twenty two)

[0089] In the formula, is the short-circuit branch equivalent resistance, is the current flowing through a phase multiplexing bridge arm, is the low voltage side voltage, is the low-voltage side voltage in the complex frequency domain;

[0090] Solving equation (22) yields:

[0091] (twenty three)

[0092] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage side power supply acts alone.

[0093] Further, in step S3, the short-circuit currents generated by each power source are summed up using the superposition principle, and the short-circuit current expression obtained by the summation is subjected to an inverse Laplace transform to obtain the short-circuit current The complex frequency domain expression of is as follows:

[0094] After adding equations (17), (19), (21), and (23), substitute equation (15) into the summation equation, amplify the sum three times according to the three-phase symmetry, and let R approach 0, the short-circuit current can be obtained. Complex frequency domain expression:

[0095] (twenty four)

[0096] When an external short circuit occurs, the current at the short-circuit port is .

[0097] Compared with the prior art, the advantages of the present invention are as follows:

[0098] The present invention combines the equivalent method with the loop current method, uses the submodule equivalent method to simplify the transformer into a linear time-varying circuit, transforms the fault equivalent circuit of the T-type DC transformer under normal working conditions into the complex frequency domain through Laplace transform, derives the short-circuit current using the loop current method, and then obtains the complex frequency domain equation of the short-circuit current through inverse transformation, and obtains the complex frequency domain expression of the short-circuit current impact value at the moment of the fault, which provides a theoretical basis for further analysis, diagnosis and protection of the transformer external short-circuit fault. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 It is a topological diagram of a single-phase T-type DC transformer according to an embodiment of the present invention.

[0100] Figure 2 The single-phase T-type DC transformer of the present invention is an AC / DC equivalent circuit diagram, wherein (a) is a DC equivalent circuit diagram, and (b) is an AC equivalent circuit diagram.

[0101] Figure 3 It is a topological diagram of a three-phase T-type DC transformer according to an embodiment of the present invention.

[0102] Figure 4 It is an equivalent circuit diagram of an external short-circuit fault of a T-type DC transformer in an embodiment of the present invention.

[0103] Figure 5 It is a complex frequency domain equivalent circuit diagram of an external short circuit fault when the high-voltage bridge arm power supply in an embodiment of the present invention acts alone.

[0104] Figure 6 It is a complex frequency domain simplified circuit diagram of an external short circuit fault when the high-voltage bridge arm power supply of an embodiment of the present invention acts alone.

[0105] Figure 7 It is a simplified circuit diagram in the complex frequency domain of an external short circuit fault when the multiplexed bridge arm power supply in an embodiment of the present invention acts alone. Figure 8 It is a complex frequency domain simplified circuit diagram of an external short circuit fault when the low-voltage bridge arm power supply in an embodiment of the present invention acts alone.

[0106] Fig. 9 It is a complex frequency domain simplified circuit diagram of an external short circuit fault when the low-voltage side power supply in an embodiment of the present invention acts alone.

[0107] Fig.10 It is a comparison diagram of the short-circuit current instantaneously measured and the short-circuit current result obtained by calculation according to the embodiment of the present invention. DETAILED DESCRIPTION

[0108] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0109] Step S1: Establish a T-type DC transformer topology structure, which is an existing three-phase T-type DC transformer topology structure. The topology consists of three identical phase units, each of which consists of a high-voltage bridge arm H, a low-voltage bridge arm L, and a reused bridge arm F. Each bridge arm consists of a plurality of series-connected submodules and an inductor, and a plurality of series-connected submodules are connected in series with the inductor, wherein the submodules in the high-voltage bridge arm H and the reused bridge arm F are half-bridge submodules, and the submodules in the low-voltage bridge arm L are full-bridge submodules. L The inductance of each bridge arm. The two sides of the transformer are connected to the DC transmission system of different voltage levels. The high-voltage bridge arm H, the low-voltage bridge arm L, and the reused bridge arm F are used to connect the transmission systems of different voltage levels on the high and low voltage sides to achieve matching between systems of different voltage levels in the DC power grid. The single-phase topology of the T-type DC transformer is as follows: Figure 1 As shown in the figure, HVDC represents the low voltage side voltage and LVDC represents the high voltage side voltage. The three-phase topology of the T-type DC transformer is as follows: Figure 3 shown.

[0110] Step S2: Through common point voltage control, DC power control, AC power control and SPWM modulation, each bridge arm submodule outputs an ideal voltage and power, so that the transformer ratio and output voltage remain constant.

[0111] The principle of T-type DC transformer to achieve DC transformation is to balance the energy of the bridge arm so that each output can withstand the DC voltage of the voltage difference between the high and low voltage sides, so as to achieve DC voltage matching between two DC systems with different voltage levels, so as to achieve interconnection between two systems with different voltage levels. After the DC system on one side emits electrical energy, part of this electrical energy is absorbed by the DC system on the other side, and the other part is absorbed by the bridge arm between the two systems. In order to improve the energy conversion efficiency and stabilize the transformation ratio of the transformer, it is necessary to release the electrical energy absorbed by the bridge arm between the systems, and the bridge arm itself must maintain energy conservation, that is, the released electrical energy is equal to the absorbed electrical energy. The energy transfer between the bridge arms is achieved through AC circulation, that is, the AC circuit is used to transmit active power, so that the DC power and AC active power of the same bridge arm are equal in magnitude and opposite in direction, so as to achieve energy conservation. If each bridge arm sub-module is equivalent to the sum of the DC power supply and the AC power supply, the DC equivalent circuit and AC equivalent circuit of the single-phase transformer are obtained as follows: Figure 2 As shown, and are the high voltage side voltage and the low voltage side voltage respectively, and They are the equivalent DC voltage and AC voltage of the submodule of bridge arm x (x is H, F, L), Does not exist.

[0112] is the bridge arm x inductance. The three-phase transformer topology is as follows Figure 3 As shown, and are the high voltage side voltage and the low voltage side voltage respectively, and They are the equivalent DC voltage and AC voltage of the A-phase bridge arm x submodule, respectively. According to the analysis of the AC / DC equivalent circuit, taking the step-up transformer as an example, the reused bridge arm F absorbs electric energy in the form of DC components, and then transmits the electric energy in the form of AC active components through the AC circuit to the reused bridge arm F in equal amounts through the public point and enters the high-voltage bridge arm H. The high-voltage bridge arm H absorbs this electric energy through the AC circuit, and then sends the electric energy back to the reused bridge arm F in equal amounts in the form of DC power. The low-voltage bridge arm L does not participate in the energy exchange, and it only needs to maintain energy self-consistency. Based on the above working principle, the T-type DC transformer can maintain a constant output voltage and transformation ratio.

[0113] To achieve the above working conditions, it is necessary to control the IGBT switch devices of each bridge arm so that each bridge arm can output the corresponding voltage and power. The control system is divided into three parts: common point voltage control, DC power control and AC power control.

[0114] The common point voltage control ensures that the common point DC voltage of the three bridge arms is stable at a certain value. Since the low-voltage bridge arm L does not participate in energy exchange, the AC and DC powers are both 0, but there is current flowing through the DC circuit. Therefore, the DC voltage of the low-voltage bridge arm L must be 0, that is, the common point voltage is equal to the low-voltage side voltage. Therefore, for the high-voltage bridge arm H, the DC voltage of the y-phase high-voltage bridge arm is controlled. for:

[0115] (1)

[0116] in, is the DC voltage of the high-voltage bridge arm of phase y (representing A, B, and C in the three-phase), is the high voltage side voltage, is the voltage on the low voltage side;

[0117] For the multiplexing bridge arm F, control the DC voltage of the y-phase multiplexing bridge arm for:

[0118] (2)

[0119] in, is the DC voltage of the y-phase multiplexing bridge arm.

[0120] DC power control is equivalent to DC current control, and its purpose is to determine the DC current of each bridge arm. Taking the A phase of the step-up transformer as an example, the load is connected to the high-voltage side of the symmetrical three-phase circuit. Therefore, the load power should be calculated from the high-voltage side according to the three-phase circuit, and the load power is:

[0121] (3)

[0122] in, is the load power, is the DC current of the high-voltage bridge arm of phase A. From the perspective of energy conservation, the reused bridge arm will transfer energy to the high-voltage bridge arm. Therefore, the DC power of the two bridge arms should be equal in magnitude and opposite in direction. Therefore, the following equation can be listed: (assuming that the forward direction is the bridge arm absorbing power)

[0123] (4)

[0124] in, is the DC current of the A-phase multiplexing bridge arm.

[0125] The DC current of the low-voltage bridge arm can be directly obtained by the KCL law (Kirchhoff's current law).

[0126] set up is the DC current of the low-voltage bridge arm of phase A. Ideally, the DC power on the low-voltage side is equal to the load power, so the power on the low-voltage side is:

[0127] (5)

[0128] in, is the low voltage side power, is the reference value of the high voltage bridge arm current, is the DC current of the A-phase low-voltage bridge arm.

[0129] Using the high-voltage bridge arm current reference value obtained by equation (5), the PID controller controls the high-voltage bridge arm DC current at the reference value about.

[0130] Combining equations (1), (2), 3), and (4), we can get the DC current of the A-phase multiplexing bridge arm: for:

[0131] (6)

[0132] According to formula (6), the reference value of the multiplexed bridge arm current can be obtained: for:

[0133] (7)

[0134] The PID controller controls the DC current of the multiplexed bridge arm to a reference value. about.

[0135] Using the KCL theorem, we can get the DC current of the low-voltage bridge arm of phase A: :

[0136] (8)

[0137] Low voltage bridge arm DC current is the DC current of the high voltage bridge arm With the multiplexed bridge arm DC current The sum of the low voltage bridge arm DC current No additional control link is required.

[0138] AC power control is AC circulating current control, which ensures that the AC power active component and DC power on the bridge arm are equal in magnitude and opposite in direction. The dq coordinate system can be used to calculate the AC power active component to simplify the calculation. Assuming that the d-axis voltage component of the high-voltage bridge arm H is 0 and the q-axis voltage component of the reused bridge arm F is 0, the DC power balance of the reused bridge arm F and the high-voltage bridge arm H can be established as follows:

[0139] (9)

[0140] in, is the d-axis voltage of the multiplexed bridge arm, is the q-axis voltage of the high-voltage bridge arm, is the d-axis current of the multiplexed bridge arm, is the q-axis current of the high-voltage bridge arm, is the AC active power, is the DC power.

[0141] Since the active component of AC power is equal to DC power, and DC power is transmitted through AC circulation, the circulating power of the AC circuit itself is the active component of AC power. Assuming that the energy transferred from the high voltage side to the low voltage side is positive, we have:

[0142] (10)

[0143] in, is the active power of the high voltage bridge arm of phase A, is the active power of the A-phase multiplexing bridge arm, is the instantaneous voltage of the high-voltage bridge arm of phase A, is the instantaneous voltage of the A-phase multiplexing bridge arm, is the instantaneous current of the high voltage bridge arm of phase A, is the instantaneous current of the A-phase multiplexing bridge arm, is the instantaneous DC voltage of the high-voltage bridge arm of phase A, is the instantaneous DC voltage of the A-phase multiplexing bridge arm, is the instantaneous AC voltage of the A-phase high-voltage bridge arm, is the instantaneous AC voltage of the A-phase multiplexing bridge arm, is the instantaneous DC current of the A-phase high-voltage bridge arm, is the instantaneous DC current of the A-phase multiplexing bridge arm, is the circulating current in the AC circuit.

[0144] Set the transformation ratio for:

[0145] (11)

[0146] DC component of active power in high voltage bridge arm and the DC component of the active power of the multiplexed bridge arm They are:

[0147] (12)

[0148] in, is the circulating active power.

[0149] Substituting formula (11) into formula (12), we can obtain:

[0150] (13)

[0151] According to the active power formula and superposition theorem, we can get:

[0152] (14)

[0153] in, is the d-axis voltage of the multiplexed bridge arm, is the q-axis voltage of the high-voltage bridge arm, is the d-axis current of the high-voltage bridge arm, is the d-axis current of the multiplexed bridge arm, is the q-axis current of the high-voltage bridge arm, is the q-axis current of the multiplexed bridge arm; is the high voltage bridge arm inductance, To reuse the bridge arm inductance, is the AC frequency.

[0154] Combining the above formulas, the d-axis voltage of the multiplexed bridge arm can be calculated , d-axis current , q-axis current And the q-axis voltage of the high-voltage bridge arm , d-axis current , q-axis current .

[0155] After establishing the above control links, the ideal PWM signal can be output to the IGBT device through SPWM modulation, completing the establishment of the T-type DC transformer control system.

[0156] Step S3: Establish a mathematical model of external short-circuit fault of T-type DC transformer

[0157] Under the control link, the capacitors of each bridge arm submodule will maintain equal voltage and the same capacitance, and the number of equivalent submodules turned on in a single cycle remains unchanged. Assuming that all submodules in the bridge arm are completely balanced, that is, the capacitor voltage and current are equal, then one equivalent submodule can replace all submodules.

[0158] Taking the high-voltage side short-circuit fault as an example, after establishing the equivalent sub-module, assuming that the capacitance and inductance of each bridge arm equivalent sub-module are the same, the equivalent circuit of the external short-circuit fault of the T-type DC transformer is as follows: Figure 4 As shown, L is the bridge arm inductance, R is the equivalent resistance of the bridge arm line, and the load end branch represents the ground short-circuit branch formed after a short circuit occurs. is the short-circuit branch equivalent resistance, is the current of the y-phase bridge arm x, is the short-circuit current on the high-voltage side. Figure 4 It can be seen that when the load-end branch on the high-voltage side is short-circuited, the transformer will lose its transformer function. At the same time, the sub-module capacitors and inductors of the high-voltage, reused, and low-voltage bridge arms will discharge a large amount to the short-circuit side, forming a discharge loop, causing a short-circuit current that is several times higher than the current on the high-voltage side under normal operating conditions. .

[0159] For short circuit current , the complex frequency domain analysis method is used for derivation. Based on the assumptions made in the previous article and the equivalence of the sub-modules, the circuit in the complex frequency domain can be regarded as a linear time-varying circuit. Therefore, the superposition theorem can be used to quantitatively analyze the fault circuit. After the fault circuit is Laplace transformed, it is necessary to first analyze the impact of each branch power supply separately. Therefore, it is necessary to use the loop current method to derive the short-circuit current from the perspectives of single-phase high-voltage bridge arm power supply alone, single-phase multiplexed bridge arm power supply alone, single-phase low-voltage bridge arm power supply alone, and low-voltage side power supply alone. The short-circuit current generated by each power supply is added using the superposition principle, and finally the short-circuit current expression obtained by the sum is inverse Laplace transformed to obtain the short-circuit current The complex frequency domain expression of .

[0160] Taking phase A as an example, when the high-voltage bridge arm power supply acts alone, before the fault occurs, is the capacitor voltage of the y-phase bridge arm x, is the inductor current of the y-phase bridge arm x, and the complex frequency domain fault equivalent circuit is as follows: Figure 5 As shown. Among them, It represents the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone. Except for the high-voltage bridge arm, the equivalent power supplies of other bridge arms are all set to zero. After the branches of phases B and C are equivalently transformed, the equivalent circuit diagram obtained is as follows Figure 6 As shown, is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of the high-voltage bridge arm, the reused bridge arm and the short-circuit branch, loop 2 is a loop composed of the reused bridge arm, the low-voltage bridge arm and the high-voltage side, and loop 3 is a loop composed of the high-voltage bridge arm, the reused bridge arm and other equivalent branches. is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of the two-phase parallel connection. Assume the branch impedance for:

[0161] (15)

[0162] In the formula, L is the bridge arm inductance, R is the equivalent resistance of the bridge arm line, is the equivalent submodule capacitance of the X bridge arm, s is the complex frequency.

[0163] Since the three phase units are symmetrical, the loop current equation can be written as:

[0164] (16)

[0165] In the formula, is the capacitor voltage of the high voltage bridge arm of phase A, is the inductor current of the high voltage bridge arm of phase A, is the short-circuit branch equivalent resistance, It indicates the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone.

[0166] Solving equation (16) yields:

[0167] (17)

[0168] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone.

[0169] When the A-phase multiplexed bridge arm power supply acts alone, the calculation principle is the same as when the high-voltage bridge arm power supply acts alone. The complex frequency domain fault equivalent circuit is as follows: Figure 7 As shown, the overall circuit is very similar to the equivalent circuit when the high-voltage bridge arm power supply acts alone, except that the equivalent power supplies of other bridge arms are all set to zero except for the reused bridge arm. It indicates the short-circuit current formed on the short-circuit side when the A-phase multiplexed bridge arm power supply acts alone. is the current of loop 1, is the current of loop 2, is the current of loop 3, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel, and the loop current equation can be written as:

[0170] (18)

[0171] In the formula, is the capacitor voltage of the A-phase reset bridge arm, is the inductor current of the reset bridge arm of phase A, is the equivalent resistance of the short-circuit branch.

[0172] Solving equation (18) yields:

[0173] (19)

[0174] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase multiplexed bridge arm power supply acts alone.

[0175] When the A-phase low-voltage bridge arm power supply acts alone, the calculation principle is the same as before. The complex frequency domain fault equivalent circuit is as follows: Figure 8 As shown in the figure, except for the low-voltage bridge arm, the equivalent power supplies of other bridge arms are all set to zero. It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage bridge arm power supply acts alone. is the current of loop 1, is the current of loop 2, is the current of loop 3, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel, and the loop current equation can be written as:

[0176] (20)

[0177] In the formula, is the capacitor voltage of the low voltage bridge arm of phase A, is the inductor current of the low voltage bridge arm of phase A, is the equivalent resistance of the short-circuit branch.

[0178] Solving equation (20) yields:

[0179] (twenty one)

[0180] In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage bridge arm power supply acts alone.

[0181] When the low voltage power supply acts alone, the calculation principle is the same as above. The complex frequency domain fault equivalent circuit is as follows: Fig. 9 As shown. Among them, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage side power supply acts alone. is the current flowing through a phase reuse bridge arm, is the low voltage side voltage, is the low-voltage side voltage in the complex frequency domain. At this time, all the power supplies in the bridge arm are set to zero, and the KVL equation can be written as:

[0182] (twenty two)

[0183] Solving equation (22) yields:

[0184] (twenty three)

[0185] If the bridge arm capacitor releases all the electric energy, only the low-voltage side DC power supply outputs current to the grounding branch, so the grounding current has a minimum value. After adding equations (17), (19), (21), and (23), the sum is magnified three times according to the three-phase symmetry, and equation (15) is substituted into the summation. Considering that the equivalent resistance of the bridge arm transmission line is small, let R approach, and the short-circuit current can be obtained. Complex frequency domain expression:

[0186] (twenty four)

[0187] When an external short circuit occurs, the current at the short-circuit side port is .

[0188] The present invention is actually tested and verified on a T-type DC step-up transformer with a low-voltage side voltage of 1kV and a transformation ratio of 3 in Simulink. The high-voltage side is connected to a load, which is composed of a resistor and a capacitor in parallel, and the AC frequency is 50Hz. After the simulation model is allowed to run normally for 2s, a short-circuit fault occurs on the high-voltage side. At this time, the load end of the high-voltage side is directly short-circuited, and the short-circuit branch directly connects the two ends of the high-voltage side through the grounding resistor. The short-circuit current measured at this moment is compared with the short-circuit current calculated, and the result is as follows: Fig.10 The gray line represents the calculated short-circuit current value, and the black line represents the measured short-circuit current value. Fig.10 It can be seen that when the short-circuit current reaches the peak value about 0.008s after the fault occurs, the short-circuit current calculated value and the simulation value are basically consistent. It can be seen that the above mathematical model can make an approximate prediction of the impact of the short-circuit current, and the changes in the short-circuit current measured value and the calculated value are relatively similar in a short time before and after reaching the peak value. Therefore, the model can predict the state when the short-circuit current reaches the peak at the moment when the external short-circuit fault occurs in the T-type DC transformer, that is, the short-circuit current impact value at the moment when the external short-circuit fault occurs in the T-type DC transformer is predicted.

[0189] Those skilled in the art may make various modifications and variations to the present invention. If these modifications and variations are within the scope of the claims of the present invention and their equivalents, then these modifications and variations are also within the protection scope of the present invention.

[0190] The contents not described in detail in the specification are prior art known to those skilled in the art.

Claims

1. A method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer, characterized in that: The following steps are involved: Step S1: Establish a T-type DC transformer topology structure; Step S2: through common point voltage control, DC power control, AC power control and SPWM modulation, each bridge arm submodule of the T-type DC transformer topology structure outputs an ideal voltage and power, so that the transformer ratio and output voltage remain constant; The common point voltage control method is: The DC voltage of the low-voltage bridge arm L is controlled to be 0, that is, the common point voltage is equal to the low-voltage side voltage, specifically: For the high-voltage bridge arm H, control the DC voltage of the y-phase high-voltage bridge arm for: (1) in, is the DC voltage of the y-phase high-voltage bridge arm, where y represents any one of the three phases A, B, and C. is the high voltage side voltage, is the voltage on the low voltage side; For the multiplexing bridge arm F, control the DC voltage of the y-phase multiplexing bridge arm for: (2) in, is the DC voltage of the y-phase multiplexing bridge arm; The DC power control method is: For phase A of the step-up transformer, the load power is calculated from the high voltage side according to the three-phase circuit, and the load power is: (3) in, is the load power, is the high voltage side voltage, is the DC current of the high voltage bridge arm of phase A; Based on the fact that the DC power of the reuse bridge arm and the high-voltage bridge arm is equal in magnitude and opposite in direction, the following equation is listed: Assuming that the forward direction is the bridge arm absorbing power: (4) in, is the DC current of the A-phase multiplexing bridge arm, is the DC current of the high voltage bridge arm of phase A, is the DC voltage of the high voltage bridge arm of phase A, is the DC voltage of the A-phase multiplexing bridge arm; The DC current of the low-voltage bridge arm of phase A is directly obtained by Kirchhoff's current law; set up is the DC current of the low-voltage bridge arm of phase A. Ideally, the DC power on the low-voltage side is equal to the load power, so the power on the low-voltage side is: (5) in, is the low voltage side power, is the reference value of the high voltage bridge arm current; is the voltage on the low voltage side; is the load power, is the DC current of the low voltage bridge arm of phase A; Using the high-voltage bridge arm current reference value obtained by formula (5), the high-voltage bridge arm DC current is controlled at the reference value about; Combining equations (1), (2), 3), and (4) to obtain the DC current of the A phase multiplexing bridge arm for: (6) According to formula (6), the reference value of the multiplexed bridge arm current is obtained: for: (7) The DC current of the multiplexed bridge arm is controlled at the reference value about; Step S3: Establish a mathematical model of external short-circuit fault of T-type DC transformer: Use submodule equivalent method to simplify the transformer into a linear time-varying circuit; Use loop current method to derive short-circuit current from the perspectives of single-phase high-voltage bridge arm power supply acting alone, single-phase multiplexed bridge arm power supply acting alone, single-phase low-voltage bridge arm power supply acting alone, and low-voltage side power supply acting alone, and use superposition principle to add up the short-circuit current generated by each power supply to obtain the short-circuit current The complex frequency domain expression of .

2. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 1, characterized in that: The T-type DC transformer topology structure consists of three identical phase units, each of which consists of a high-voltage bridge arm H, a low-voltage bridge arm L, and a reused bridge arm F; each bridge arm consists of a plurality of series-connected sub-modules and an inductor, and the plurality of series-connected sub-modules are connected in series with the inductor, wherein the sub-modules in the high-voltage bridge arm H and the reused bridge arm F are both half-bridge sub-modules, and the sub-modules in the low-voltage bridge arm L are all full-bridge sub-modules.

3. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 1, characterized in that: The AC power control method is: Assuming that the d-axis voltage component of the high-voltage bridge arm H is 0 and the q-axis voltage component of the reused bridge arm F is 0, the equation can be established by the DC power balance between the reused bridge arm F and the high-voltage bridge arm H: (9) in, is the d-axis voltage of the multiplexed bridge arm, is the q-axis voltage of the high-voltage bridge arm, is the d-axis current of the multiplexed bridge arm, is the q-axis current of the high-voltage bridge arm, is the AC active power, is the DC power; Since the active component of AC power is equal to DC power, and DC power is transmitted through AC circulation, the circulating power of the AC circuit itself is the active component of AC power. Assuming that the energy transferred from the high voltage side to the low voltage side is positive, we have: (10) in, is the active power of the high voltage bridge arm of phase A, is the active power of the A-phase multiplexing bridge arm, is the instantaneous voltage of the high-voltage bridge arm of phase A, is the instantaneous voltage of the A-phase multiplexing bridge arm, is the instantaneous current of the high voltage bridge arm of phase A, is the instantaneous current of the A-phase multiplexing bridge arm, is the instantaneous DC voltage of the high-voltage bridge arm of phase A, is the instantaneous DC voltage of the A-phase multiplexing bridge arm, is the instantaneous AC voltage of the A-phase high-voltage bridge arm, is the instantaneous AC voltage of the A-phase multiplexing bridge arm, is the instantaneous DC current of the A-phase high-voltage bridge arm, is the instantaneous DC current of the A-phase multiplexing bridge arm, is the circulating current of the AC circuit; Set the transformation ratio for: (11) DC component of active power in high voltage bridge arm and the DC component of the active power of the multiplexed bridge arm They are: (12) in, is the circulating active power; Substituting formula (11) into formula (12), we can obtain: (13) According to the active power formula and superposition theorem, we can get: (14) in, is the d-axis voltage of the multiplexed bridge arm, is the q-axis voltage of the high-voltage bridge arm, is the d-axis current of the high-voltage bridge arm, is the d-axis current of the multiplexed bridge arm, is the q-axis current of the high-voltage bridge arm, is the q-axis current of the multiplexed bridge arm; is the high voltage bridge arm inductance, To reuse the bridge arm inductance, is the AC frequency; Combining the above formulas, the d-axis voltage of the multiplexed bridge arm can be calculated , d-axis current , q-axis current And the q-axis voltage of the high-voltage bridge arm , d-axis current , q-axis current .

4. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 1, characterized in that: In step S3, the short-circuit current is derived using the loop current method from the perspective of the single-phase high-voltage bridge arm power supply acting alone. The specific method is: For phase A, when the high-voltage bridge arm power supply acts alone, the equivalent power supplies of all bridge arms except the high-voltage bridge arm are set to zero, and the branches of phases B and C are transformed equivalently to obtain the complex frequency domain fault equivalent circuit. Assume that the branch impedance for: (15) In the formula, is the bridge arm inductance, is the equivalent resistance of the bridge arm line, for Bridge arm equivalent submodule capacitance, is the complex frequency; Since the three phase units are symmetrical, the loop current equation can be written as: (16) In the formula, is the capacitor voltage of the high voltage bridge arm of phase A, is the inductor current of the high voltage bridge arm of phase A, is the short-circuit branch equivalent resistance, It indicates the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone; is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of high-voltage bridge arm, reused bridge arm and short-circuit branch, loop 2 is a loop composed of reused bridge arm, low-voltage bridge arm and high-voltage side, loop 3 is a loop composed of high-voltage bridge arm, reused bridge arm and other equivalent branches, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel; Solving equation (16) yields: (17) In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase high-voltage bridge arm power supply acts alone.

5. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 4, characterized in that: In step S3, the short-circuit current is derived using the loop current method from the perspective of the single-phase multiplexed bridge arm power supply acting alone. The specific method is: For phase A, when the multiplexed bridge arm power supply acts alone, the equivalent power supplies of all bridge arms except the multiplexed bridge arm are set to zero, and the branches of phases B and C are equivalently transformed to obtain the complex frequency domain fault equivalent circuit. Suppose the branch impedance for: (15) In the formula, is the bridge arm inductance, is the equivalent resistance of the bridge arm line, for Bridge arm equivalent submodule capacitance, is the complex frequency; Since the three phase units are symmetrical, the loop current equation can be written as: (18) In the formula, is the capacitor voltage of the A-phase multiplexing bridge arm, is the inductor current of the A-phase multiplexing bridge arm, is the short-circuit branch equivalent resistance, is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of high-voltage bridge arm, reused bridge arm and short-circuit branch, loop 2 is a loop composed of reused bridge arm, low-voltage bridge arm and high-voltage side, loop 3 is a loop composed of high-voltage bridge arm, reused bridge arm and other equivalent branches, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel; Solving equation (18) yields: (19) In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase multiplexed bridge arm power supply acts alone.

6. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 5, characterized in that: In step S3, the short-circuit current is derived using the loop current method from the perspective of the single-phase low-voltage bridge arm power supply acting alone. The specific method is: For phase A, when the low-voltage bridge arm power supply acts alone, the equivalent power supplies of all bridge arms except the low-voltage bridge arm are set to zero, and the branches of phases B and C are equivalently transformed to obtain the complex frequency domain fault equivalent circuit. Suppose the branch impedance for: (15) In the formula, is the bridge arm inductance, is the equivalent resistance of the bridge arm line, for The equivalent submodule capacitance of the bridge arm, is the complex frequency; Since the three phase units are symmetrical, the loop current equation can be written as: (20) In the formula, is the capacitor voltage of the low voltage bridge arm of phase A, is the inductor current of the low voltage bridge arm of phase A, is the short-circuit branch equivalent resistance, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage bridge arm power supply acts alone; is the current of loop 1, is the current of loop 2, is the current of loop 3, loop 1 is a loop composed of high-voltage bridge arm, reused bridge arm and short-circuit branch, loop 2 is a loop composed of reused bridge arm, low-voltage bridge arm and high-voltage side, loop 3 is a loop composed of high-voltage bridge arm, reused bridge arm and other equivalent branches, is the total voltage of the high-voltage bridge arm in the complex frequency domain, is the equivalent impedance of two phases in parallel; Solving equation (20) yields: (21) In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage bridge arm power supply acts alone.

7. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 6, characterized in that: In step S3, the short-circuit current is derived using the loop current method from the perspective of the low-voltage side power supply acting alone. The specific method is: For phase A, when the low-voltage power supply acts alone, the equivalent power supplies of all bridge arms are set to zero, and the branches of phases B and C are transformed equivalently to obtain the complex frequency domain fault equivalent circuit. Suppose the branch impedance for: (15) In the formula, is the bridge arm inductance, is the equivalent resistance of the bridge arm line, for Bridge arm equivalent submodule capacitance, is the complex frequency; Writing the KVL equation gives: (22) In the formula, is the short-circuit branch equivalent resistance, is the current flowing through a phase reuse bridge arm, is the low voltage side voltage, is the low-voltage side voltage in the complex frequency domain; Solving equation (22) yields: (23) In the formula, It indicates the short-circuit current formed on the short-circuit side when the A-phase low-voltage side power supply acts alone.

8. The method for constructing a mathematical model of an external short-circuit fault of a T-type DC transformer according to claim 7, characterized in that: In step S3, the short-circuit currents generated by each power source are summed up using the superposition principle, and the short-circuit current expression obtained by the summation is subjected to an inverse Laplace transform to obtain the short-circuit current The complex frequency domain expression of is as follows: After adding equations (17), (19), (21), and (23), substitute equation (15) into the summation equation, amplify the sum three times according to the three-phase symmetry, and let R approach 0, the short-circuit current can be obtained. Complex frequency domain expression: (24) When an external short circuit occurs, the current at the short-circuit port is .

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