Equivalent method of HVDC system considering commutation failure process and controller action

Abstract

The equivalent method of DC power transmission system considering commutation failure process and controller action belongs to the technical field of DC power transmission technology, and solves the problems of poor calculation accuracy and low efficiency in the prior art when the DC power transmission system is equivalent; the technical scheme of the present application equivalent to a voltage-controlled power supply realizes accurate expression of DC voltage, DC current and AC current values of any order; the LCC-HVDC dynamic behavior characteristics are described by a switching function to obtain the interaction mechanism of the AC / DC system under commutation failure and the analytical expression of the power frequency quantity and each harmonic. The present application can overcome the shortcomings of slow calculation speed, low accuracy, and not taking into account the control action and the influence of commutation failure in the prior art, and is suitable for the equivalent scheme of the converter station of the UHV AC / DC hybrid system, and has the advantages of simple and easy steps, clear and explicit, etc., and has great popularization significance.

Description

Technical Field

[0001] This invention belongs to the field of DC power transmission technology and relates to an equivalent method for DC power transmission systems that considers the commutation failure process and the role of the controller. Background Technology

[0002] Due to the dynamic switching behavior of the converter valves in LCC-HVDC (DC transmission system based on grid-commutated converters), the nonlinear coordination mechanism of the multiple controllers of the DC converter valves, and the unpredictable commutation failure events that may occur on the inverter side, the accurate transient response of DC transmission systems can currently only be obtained through electromagnetic transient numerical simulation under detailed modeling. The solution is a numerical solution and is limited to the "one scenario, one situation" limitation of fault-by-fault scenario simulation. This is also the current inevitability that LCC-HVDC tuning must rely on electromagnetic transient numerical simulation, making it impossible to quantitatively analyze the faults of AC-DC hybrid systems from a physical mechanism perspective, and making it difficult to achieve subsequent protection and control optimization configuration.

[0003] Traditional AC system fault analysis strives for an analytical expression of fault characteristics. However, due to the lack of mathematical means to solve high-order nonlinear time-varying differential equations, directly obtaining analytical solutions for the DC transmission system response under fault conditions is impractical. Therefore, a simplified equivalent model of the DC transmission system is necessary. Currently, there are four main equivalent models for analyzing different application scenarios and time scales of LCC-HVDC: 1) Quasi-steady-state model: Based on the idea of ​​quasi-steady-state circuit average values, this model describes the behavior of the DC transmission system over large time scales; 2) Electromagnetic transient model: This model has the smallest computational step size, the highest accuracy, and is suitable for the most detailed modeling of small time scales in offline simulation numerical calculations; 3) State-space model: Utilizing the property that the circuit topology remains linear within the switching interval, this model uses algebraic differential equations to describe the AC / DC transmission system within the circuit topology switching interval; 4) Dynamic phasor model: Based on dynamic phasor simulation calculations using modulation theory.

[0004] Quasi-steady-state models are simple to calculate, but lack accuracy. State-space models are relatively accurate, but involve large computational loads, difficult equation solving, and insufficient precision in characterizing control effects. Electromagnetic transient models are the most accurate modeling method, calculating the dynamic behavior of nonlinear systems with extremely small simulation steps, achieving the highest numerical accuracy in the simulation field. Therefore, they have become the default equivalent scheme for most time-domain simulation software such as PSCAD and EMTDC. However, they require detailed model building, resulting in low computational efficiency and failing to fully meet engineering design needs. Furthermore, analysis based on numerical solutions cannot meet the requirements for analyzing the mechanism of AC / DC systems during commutation failure, and is also difficult to guide the design of relay protection systems for AC / DC hybrid systems. Dynamic phasor methods have many advantages, such as directly describing the nonlinearity of DC systems, possessing concise mathematical expressions, and low computational complexity. However, their research is still immature in areas such as the standard derivation of switching functions, the acquisition of switching functions involved in the commutation failure process, the optimization of simulation calculation processes based on dynamic phasor methods, and the simulation interface for AC / DC hybrid systems.

[0005] Chinese invention patent document CN106856334A, published on June 16, 2017, entitled "A Power System State Estimation Method Considering Flexible DC Control Characteristics," avoids the adverse effects on state estimation caused by changes in control mode without corresponding changes in settings in the control system through dynamic monitoring of the flexible DC control mode. However, this document does not solve the aforementioned problem. Therefore, there is a need to develop an equivalent method for DC transmission systems that has high computational accuracy and efficiency, and can accurately simulate the commutation failure process and the controller's role. Summary of the Invention

[0006] The purpose of this invention is to design an equivalent method for DC transmission systems that considers the commutation failure process and the role of the controller, so as to solve the problems of poor calculation accuracy and low efficiency in the existing technology when performing equivalent calculations on DC transmission systems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] An equivalent method for DC transmission systems that considers commutation failure processes and controller actions includes the following steps:

[0009] S1. Establish the AC / DC coupling model of the six-pulse converter using switching functions;

[0010] S2. Determine the arbitrary-order analytical expression of the voltage or current switching function composed of the basic component, the delayed triggering component, and the commutation overlap component.

[0011] S3. Explicitly model the six-pulse converter control system, that is, explicitly construct a state variable for the PI element of each controller, and write differential equations based on the corresponding control block diagram for numerical integration.

[0012] S4. By analyzing the commutator valve conduction mechanism during commutation failure, the impact of commutation failure on the switching function is considered, thereby correcting the equivalent model of the six-pulse converter.

[0013] S5. Connect the two modified six-pulse converter equivalent models in series to construct a twelve-pulse converter equivalent model.

[0014] The technical solution of this invention treats the DC transmission system as a voltage-controlled power source, enabling precise expression of DC voltage, DC current, and AC current values ​​of any order. By characterizing the dynamic behavior of LCC-HVDC through switching functions, the interaction mechanism of the AC / DC system under commutation failure and the analytical expression of power frequency quantities and harmonics are obtained, overcoming the shortcomings of existing technical solutions such as slow calculation speed, coarse accuracy, and failure to consider control effects and the impact of commutation failure.

[0015] Furthermore, the AC / DC coupling model described in step S1 is determined by the following analytical expression of the switching function:

[0016] 1) The voltage coupling of an AC / DC system is described by the following switching function:

[0017] u dc =s va u a +s vb u b +s vc u c (1)

[0018] 2) The AC / DC current coupling situation can be described by the following switching function.

[0019] i a =s ia i dc i b =s ib i dc i c =s ic i dc (2)

[0020] In the formula, u dc i is the DC-side voltage of the six-pulse converter. dc For direct current, u a ,u b ,u c These are the three-phase voltages on the AC side, s va ,s vb,s vc These are the switching functions for the three-phase voltages a, b, and c on the AC side, respectively, s ia ,s ib ,s ic These are the switching functions for the three phases a, b, and c on the AC side, respectively.

[0021] Furthermore, the arbitrary-order analytical expression of the voltage or current switching function described in step S2 is as follows:

[0022] xy > k = δ(xy) > k + α(xy) > k + μ(xy) > k (3)

[0023] In the formula, xy > k This is the k-th order analytical expression for the voltage or current switching function, where the subscript x represents the voltage or current switching function and the subscript y represents phase a, b, or c. δ(xy) > k These are the basic components; α(xy) > k For delayed triggering components; μ(xy) > k For the commutation overlap component, k is a positive integer.

[0024] Furthermore, the fundamental components include: the fundamental components of the k-th order analytical expression of the three-phase voltage or current switching function a, b, and c, and their calculation formulas are as follows:

[0025]

[0026] In the formula, δ(xa) > k , δ(xb) > k , δ(xc) > k These are the basic components of the k-th order analytical expression of the three-phase voltage or current switching function for phases a, b, and c, respectively.

[0027] Furthermore, the delayed triggering component includes: the delayed triggering component of the k-th order analytical expression of the three-phase voltage or current switching function a, b, and c, and their calculation formulas are as follows:

[0028]

[0029]

[0030] In the formula, <S​​​​​​​​​​​α(xa) > k , α(xb) > k , α(xc) > k These are the delayed triggering components of the k-th order analytical expressions of the three-phase voltage or current switching functions of phases a, b, and c, respectively. h >(k,α zy ) k An auxiliary function, α, defined to simplify the formula. zy Let z be the delayed firing angle during the commutation process, and z = a, b, c, y = a, b, c.

[0031] Furthermore, the commutation overlap components include: the commutation overlap components of the k-th order analytical expressions of the three-phase current switching functions a, b, and c, and their calculation formulas are as follows:

[0032]

[0033]

[0034] In the formula, μ(ia) > k , μ(ib) > k , μ(ic) > k The commutation components of the k-th order analytical expression of the three-phase current switching functions a, b, and c are respectively, μ. zy This refers to the commutation overlap angle during the phase transition process. h >(k,α zy ,μ zy ) k Auxiliary functions are defined to simplify the formula.

[0035] Furthermore, the commutation overlap component also includes the commutation overlap component of the k-th order analytical expression of the three-phase voltage switching function a, b, and c, and their calculation formulas are as follows:

[0036]

[0037] w >(k,α zy ) = 0.5 h >(k,α zy (10)

[0038] In the formula, μ(ia) > k , μ(ib) > k , μ(ic) > k ​​​​​​​​​​​​These are the commutation components of the k-th order analytical expression of the three-phase voltage switching functions a, b, and c, respectively. w >(k,α zy Auxiliary functions are defined to simplify formulas.

[0039] Furthermore, the differential equation described in step S3 is a constant current controlled differential equation, and its calculation formula is as follows:

[0040]

[0041] In the formula, Idref and Idmeas are the reference value and measured value of DC current, respectively; KI and KP are the integral coefficient and proportional coefficient, respectively; αord is the firing angle command value; and x1 and x2 are intermediate variables.

[0042] Furthermore, the method described in step S4 for considering the impact of commutation failure on the switching function, thereby correcting the equivalent model of the six-pulse converter, is as follows: at time t b From the beginning of +μ until the time interval t4+μ, the switching functions of the starting phase, the target phase, and the third phase corresponding to the commutation failure are corrected as follows:

[0043]

[0044]

[0045]

[0046] In the formula, S m ,S y ,S z These are the initial phase switching functions, the target phase switching functions, and the third phase switching functions when a commutation failure occurs, respectively. m ,S' y ,S' z These are the corrected switching functions for the starting phase when commutation failure occurs, the corrected switching functions for the target phase when commutation failure occurs, and the corrected switching functions for the third phase when commutation failure occurs.

[0047] Furthermore, the equivalent model of the twelve-pulse converter described in step S5 is constructed as follows:

[0048]

[0049] In the formula, The fundamental angular frequency, the phase difference between the two six-pulse converters Determine the k-th switching function for the YY converter and the YD converter, respectively. ​

[0050] The advantages of this invention are:

[0051] The technical solution of this invention equates the DC transmission system to a voltage-controlled power source, enabling precise expression of DC voltage, DC current, and AC current values ​​of any order. By characterizing the dynamic behavior of LCC-HVDC through switching functions, it derives the interaction mechanism of the AC / DC system under commutation failure, as well as the analytical expressions of power frequency quantities and harmonics. This invention overcomes the shortcomings of existing technical solutions, such as slow calculation speed, coarse accuracy, and failure to consider control effects and the impact of commutation failure. It is applicable to the equivalent scheme of converter stations in UHV AC / DC hybrid systems, and has advantages such as simple and easy implementation, clarity, and significant potential for widespread application. Attached Figure Description

[0052] Figure 1 This is a flowchart of an equivalent method for DC transmission systems that considers the commutation failure process and the role of the controller, according to an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram of a constant current controller according to an embodiment of the present invention;

[0054] Figure 3 This is an electrical schematic diagram of a six-pulse converter according to an embodiment of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0057] Example 1

[0058] like Figure 1 As shown, the equivalent method for a DC transmission system considering the commutation failure process and the controller's action includes the following steps:

[0059] 1. Using a six-pulse converter as the basic research unit (including YY converter and YD converter), an AC / DC coupling model is established using switching functions.

[0060] The AC / DC coupling model is determined by the following analytical expression of the switching function:

[0061] 1) The voltage coupling of an AC / DC system is described by the following switching function:

[0062] u dc =s va u a +s vb u b +s vc u c (1)

[0063] 2) The AC / DC current coupling situation can be described by the following switching function.

[0064] i a =s ia i dc i b =s ib i dc i c =s ic i dc (2)

[0065] In the formula, u dc i is the DC-side voltage of the six-pulse converter. dc For direct current, u a ,u b ,u c These are the three-phase voltages on the AC side, s va ,s vb ,s vc These are the switching functions for the three-phase (a, b, c) voltages on the AC side, s ia ,s ib ,s ic These are the current switching functions for the three phases (a, b, c) on the AC side, respectively.

[0066] 2. Determine the analytical expression of the voltage and current switching functions of any order.

[0067] 1) The k-th order analytical expression of the voltage-current switching function consists of three parts: the basic component, the delayed triggering component, and the commutation overlap component, and is determined by the following switching function:

[0068] xy > k = δ(xy) > k + α(xy) > k + μ(xy) > k x = v, i; y = a, b, c (3)

[0069] In the formula, xy > k ​​​​​This is the k-th order analytical expression for the voltage or current switching function. The subscript x indicates the voltage (V) or current (i) switching function, and the subscript y indicates the three phases a, b, and c, and so on. δ(xy) > k These are the basic components; α ( xy )> k For delayed triggering components; μ(xy) > k This refers to the commutation overlap component.

[0070] 2) The basic components of the k-th order analytical expression of the three-phase voltage or current switching function of phases a, b, and c are determined by the following switching functions:

[0071]

[0072] In the formula, δ(xa) > k , δ(xb) > k , δ(xc) > k These are the basic components of the k-th order analytical expression of the three-phase voltage or current switching function for phases a, b, and c, respectively.

[0073] 3) The delayed triggering component of the k-th order analytical expression of the three-phase voltage or current switching function of phases a, b, and c is determined by the following switching function:

[0074]

[0075]

[0076] In the formula, α(xa) > k , α(xb) > k , α(xc) > k The delayed triggering components of the k-th order analytical expression of the three-phase voltage or current switching functions a, b, and c are respectively, α zy The delayed firing angle is the angle used during the commutation process of the z-phase and y-phase. h >(k,α zy ) k Auxiliary functions defined to simplify the formulas: z = a, b, c; y = a, b, c.

[0077] 4) The commutation components of the k-th order analytical expression of the three-phase current switching functions a, b, and c are determined by the following switching functions:

[0078]

[0079] ​​​​​​​​​​

[0080] In the formula, μ(ia) > k , μ(ib) > k , μ(ic) > k These are the commutation components of the k-th order analytical expression of the three-phase current switching functions a, b, and c, respectively, and α. zy μ is the delay firing angle during the commutation process of the z-phase and y-phase. zy This refers to the commutation overlap angle during the commutation process of the z-phase and y-phase. h >(k,α zy ,μ zy ) k Auxiliary functions are defined to simplify the formula.

[0081] 5) The commutation components of the k-th order analytical expression of the three-phase voltage switching function a, b, and c are determined by the following switching function:

[0082]

[0083] w >(k,α zy ) = 0.5 h >(k,α zy (10)

[0084] In the formula, μ(ia) > k , μ(ib) > k , μ(ic) > k The commutation components of the k-th order analytical expression of the three-phase voltage switching function for phases a, b, and c are respectively, α zy μ is the delay firing angle during the commutation process of the z-phase and y-phase. zy Let be the commutation overlap angle during the commutation process of phase z and phase y. w >(k,α zy Auxiliary functions are defined to simplify formulas.

[0085] 3. Perform explicit modeling of the control system, that is, explicitly construct a state variable for each controller's PI element, and write differential equations based on the corresponding control block diagram for numerical integration.

[0086] like Figure 2 As shown, the constant current control differential equation is as follows:

[0087]

[0088] In the formula, the relevant variables are as follows: Figure 2 ​​​​​​​​​​As shown, Idref and Idmeas are the DC current reference value and measured value, respectively; KI and KP are the integral coefficient and proportional coefficient, respectively; αord is the trigger angle command value; tk is the time; T is the integral time constant; and x1 and x2 are intermediate variables.

[0089] 4. By analyzing the commutator valve conduction mechanism during commutation failure, the impact of commutation failure on the switching function is explicitly considered, and the equivalent model is modified.

[0090] When a large disturbance occurs in the inverter-side AC system of an LCC-HVDC converter, commutation failure on the inverter side is inevitable. This is because when a disturbance occurs in the inverter-side AC system, the AC voltage of the inverter-side converter bus is prone to voltage drop or phase shift of the commutation voltage, both of which can promote the commutation failure process of the converter valve.

[0091] Commutation failure directly alters the timing conduction patterns of each converter valve. When commutation failure occurs, the conduction pattern of the thyristors differs from the 2-3 conduction state under steady-state operation. Depending on the timing of the commutation failure and the valve group involved, the converter valves on the inverter side will exhibit relatively complex conduction modes.

[0092] In reality, when a single commutation failure occurs on the inverter side, the conduction of each valve is not independent. If a commutation failure occurs between two phases, it will directly affect the subsequent four commutation processes. All switching functions within this influence timeframe are fundamentally different from the switching functions of the 2-3 conduction state.

[0093] Therefore, in order to improve the accuracy of the equivalent model, the simulation algorithm itself must explicitly consider the impact of commutation failure events on the switching function. It is necessary to directly analyze the conduction mechanism of the converter valve under typical commutation failure, so as to clarify the impact of commutation failure on the equivalent model and correct the equivalent model.

[0094] like Figure 3 As shown, for simplicity, it is assumed that the commutation failure occurs at time tb (corresponding to the triggering time of valve VT3), which corresponds to the commutation process from valve VT1 to valve VT3. The time range of the impact of a single commutation failure is time t. b The duration of +μ from the start to the time interval t4+μ spans 5 commutation pulses and 4 commutation intervals (2 / 3 of the commutation cycle T in steady state). After that, if there are no new disturbances or pulse signal loss, the DC system will resume normal operation and normal sequential commutation.

[0095] At time t bFrom the start of +μ until the time interval t4+μ, the switching functions of the three phases (m phase, i.e., the starting phase when commutation failure occurs), y phase, i.e., the target phase when commutation failure occurs), and z phase (the third phase when commutation failure occurs) are corrected as follows:

[0096]

[0097]

[0098]

[0099] In the formula, S m ,S y ,S z S' represents the switching functions for phase m, phase y, and phase z (without considering the impact of commutation failure and without correction). m ,S' y ,S' z These are the corrected switching functions for the m-phase, y-phase, and z-phase commutation failures, respectively.

[0100] 5. Constructing an equivalent model of a twelve-pulse converter

[0101] A typical twelve-pulse converter generally consists of two six-pulse converters connected in series with a phase difference. Therefore, the switching function of a twelve-pulse converter can be viewed as a combination of two independent six-pulse converters. Modeling the twelve-pulse converter bridge can be achieved by modeling the two independent six-pulse converter bridges separately. A complete twelve-pulse converter's k-th switching function... 12 > k The following is confirmed:

[0102]

[0103] In the formula, The fundamental angular frequency, the phase difference between the two six-pulse converters Determine the k-th switching function for the YY converter and the YD converter, respectively.

[0104] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.​

Claims

1. An equivalent method for DC transmission systems considering commutation failure processes and controller actions, characterized in that, Includes the following steps: S1. Establish the AC / DC coupling model of the six-pulse converter using switching functions; S2. Determine the arbitrary-order analytical expression of the voltage or current switching function composed of the basic component, the delayed triggering component, and the commutation overlap component. S3. Explicitly model the six-pulse converter control system, that is, explicitly construct a state variable for the PI element of each controller, and write differential equations based on the corresponding control block diagram for numerical integration; the differential equations adopt constant current control differential equations, and their calculation formulas are as follows: （11） In the formula, Idref and Idmeas are the reference value and measured value of DC current, respectively; KI and KP are the integral coefficient and proportional coefficient, respectively; αord is the trigger angle command value; tk is time; T is the integral time constant; and x1 and x2 are intermediate variables. S4. By analyzing the commutator valve conduction mechanism during commutation failure, and considering the impact of commutation failure on the switching function, the equivalent model of the six-pulse converter is modified. The specific method is as follows: at time... The beginning until Within the time period, the switching functions for the starting phase, the target phase, and the third phase corresponding to the commutation failure are corrected as follows: （12） （13） （14） In the formula, These are the initial phase switching function, the target phase switching function, and the third phase switching function when a commutation failure occurs, respectively. These are the corrected switching functions for the initial phase when commutation failure occurs, the corrected switching function for the target phase when commutation failure occurs, and the corrected switching function for the third phase when commutation failure occurs. S5. Connect the two corrected six-pulse converter equivalent models in series to construct a twelve-pulse converter equivalent model; The equivalent model of the twelve-pulse converter is constructed as follows: （15） In the formula, The fundamental angular frequency, the phase difference between the two six-pulse converters , Determine the k-th switching function for the YY converter and the YD converter, respectively.

2. The equivalent method for DC transmission systems considering commutation failure process and controller action according to claim 1, characterized in that, The AC / DC coupling model described in step S1 is determined by the following analytical expression of the switching function: 1) The voltage coupling of an AC / DC system is described by the following switching function: （1） 2) The AC / DC current coupling situation can be described by the following switching function. （2） In the formula, This refers to the DC-side voltage of the six-pulse converter. It is direct current. These are the three-phase voltages on the AC side. These are the switching functions for the three-phase voltages a, b, and c on the AC side, respectively. These are the switching functions for the three phases a, b, and c on the AC side, respectively.

3. The equivalent method for DC transmission systems considering commutation failure process and controller action according to claim 2, characterized in that, The arbitrary-order analytical expression of the voltage or current switching function described in step S2 is as follows: （3） In the formula, This is the k-th order analytical expression for the voltage or current switching function, where the subscript x represents the voltage or current switching function and the subscript y represents phase a, b, or c. These are the basic components; For delayed triggering components; For the commutation overlap component, k is a positive integer.

4. The equivalent method for DC transmission systems considering commutation failure process and controller action according to claim 3, characterized in that, The fundamental components include: the fundamental components of the k-th order analytical expression of the three-phase voltage or current switching function a, b, and c, and their calculation formulas are as follows: （4） In the formula, These are the basic components of the k-th order analytical expression of the three-phase voltage or current switching function for phases a, b, and c, respectively.

5. The equivalent method for DC transmission systems considering commutation failure process and controller action according to claim 4, characterized in that, The delayed triggering components include: the delayed triggering components of the k-th order analytical expression of the three-phase voltage or current switching function a, b, and c, and their calculation formulas are as follows: （5） （6） In the formula, These are the delayed triggering components of the k-th order analytical expressions of the three-phase voltage or current switching functions of phases a, b, and c, respectively. Auxiliary functions defined to simplify formulas. The delayed firing angle during the commutation process, , .

6. The equivalent method for DC transmission systems considering commutation failure process and controller action according to claim 5, characterized in that, The commutation overlap components include the commutation overlap components of the k-th order analytical expressions of the three-phase current switching functions a, b, and c, and their calculation formulas are as follows: （7） （8） In the formula, These are the commutation components of the k-th order analytical expressions of the three-phase current switching functions a, b, and c, respectively. This refers to the commutation overlap angle during the phase transition process. Auxiliary functions are defined to simplify the formula.

7. The equivalent method for DC transmission systems considering commutation failure process and controller action according to claim 6, characterized in that, The commutation overlap component also includes the commutation overlap component of the k-th order analytical expression of the three-phase voltage switching function a, b, and c, and their calculation formulas are as follows: （9） （10） In the formula, These are the commutation components of the k-th order analytical expression of the three-phase voltage switching functions a, b, and c, respectively. Auxiliary functions are defined to simplify the formula.

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