A SSC analysis method considering the effect of LCC-HVDC receiving system control loop

Abstract

The application relates to the technical field of high-voltage direct current transmission, and discloses an SSC analysis method considering the action of a control link of an LCC-HVDC receiving end system, which comprises the following steps: based on the output characteristics of an LCC inverter, a conventional LCC inverter quasi-static mathematical model is established; then, by performing Kirchhoff law analysis on a simplified circuit model of the LCC-HVDC receiving end system, a phase-locked loop dynamic equation is obtained; finally, by analyzing a fixed off-angle control link and a VDCOL provided on the inverter side of the LCC-HVDC system, mathematical models of the fixed off-angle and the VDCOL are obtained. By considering the influence of the control link on the steady-state synchronous stability of the LCC inverter, the analysis result of the steady-state synchronous characteristic is basically consistent with the actual simulation result, the output of the conventional LCC inverter model is taken as the input of the phase-locked loop, the fixed off-angle control and the VDCOL, the output of the phase-locked loop, the fixed off-angle control and the VDCOL is taken as the input of the conventional LCC inverter model, a closed loop system is formed, and the steady-state synchronous process of the LCC-HVDC receiving end system can be clearly observed.

Description

Technical Field

[0001] This invention relates to the field of high voltage direct current transmission technology, specifically to an SSC analysis method that considers the role of control links in the receiving-end system of LCC-HVDC. Background Technology

[0002] Guided by new energy strategic goals, my country is accelerating the construction of a new power system characterized by a high proportion of renewable energy and power electronic equipment. In the field of inter-regional power transmission, high-voltage direct current (HVDC) transmission technology based on grid-commutated converters remains dominant due to its maturity. In particular, ultra-high-voltage direct current (UHVDC) transmission, with its significant advantages in long-distance transmission, large-capacity throughput, and low losses, and its ability to effectively avoid the power angle stability risks associated with AC interconnection, has become a key focus of current power grid construction, and the scale of related projects is experiencing rapid growth.

[0003] With the large-scale advancement of ultra-high voltage direct current (UHVDC) transmission projects, the steady-state synchronization characteristics of LCC-HVDC (Line Commutated Converter-High Voltage Direct Current) receiving-end systems have gradually become a focus of academic attention. However, research on the inverter side (receiving end) faces significant challenges: on the one hand, there is an inherent strong coupling mechanism between active and reactive power, making decoupling control difficult, which makes the mechanism analysis of synchronization characteristics lack intuitiveness; on the other hand, the interweaving and superposition of multiple control loops within the LCC-HVDC receiving-end system further increases the dimension and complexity of analyzing the system's steady-state synchronization characteristics.

[0004] Therefore, how to clearly and accurately describe the steady-state synchronization characteristics of the LCC-HVDC receiving-end system has become a key issue. Based on this, scholars at home and abroad have begun to study the steady-state synchronization characteristics of the LCC-HVDC receiving-end system. Currently, some studies focus on establishing quasi-static mathematical models of LCC inverters for analysis. However, conventional quasi-static mathematical models of LCC inverters usually ignore the control loop, resulting in a large error between the conventional quasi-static mathematical models of LCC inverters and the actual system, which cannot accurately describe the steady-state synchronization characteristics of the LCC-HVDC receiving-end system. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide an SSC (Steady-state synchronization characteristic) analysis method that considers the role of control elements in the LCC-HVDC receiving-end system. Since control elements objectively exist in the LCC-HVDC receiving-end system and influence synchronization characteristics, this method fully considers the role of the LCC-HVDC receiving-end control elements, thus clearly and accurately describing the steady-state synchronization characteristics of the LCC-HVDC receiving-end system. The technical solution is as follows:

[0006] A method for SSC analysis considering the role of control elements in the LCC-HVDC receiving-end system includes the following steps:

[0007] Step 1: Based on the output characteristics of the LCC inverter, establish a conventional quasi-static mathematical model of the LCC inverter; the quasi-static mathematical model uses the lead firing angle β and DC current I as the basis for the model. dc and the effective value of the bus voltage at the grid connection point V L As input, with power factor angle Turn-off angle γ, DC voltage V dc and the effective value of the bus current at the grid connection point I L For output;

[0008] Step 2: Determine the control loop, which includes phase-locked loop control, constant turn-off angle control, and low-voltage current limiting control, based on the power factor angle output in Step 1. RMS value of bus current at grid connection point I L Based on the parameters of the simplified circuit model of the LCC-HVDC receiving-end system, and through Kirchhoff's laws, the dynamic equation of the phase-locked loop and the effective value of the bus voltage at the grid connection point, V, are obtained. L ;

[0009] Step 3: Based on the turn-off angle γ and DC voltage V output in Step 1 dc By analyzing the constant turn-off angle control loop and the voltage-dependent current order limiter (VDCOL) control loop of the LCC-HVDC receiving-end system, the mathematical models, lead firing angle β, and DC current I of the constant turn-off angle control loop and the low-voltage current order limiter control loop are obtained. dc ;

[0010] The phase-locked loop dynamic equation is used to update the effective value V of the grid connection point bus voltage in step 2. L The mathematical models of the constant turn-off angle control loop and the low-voltage current limiting control loop are used in step 3 to update the advance firing angle β and the DC current I. dc The updated effective value V of the grid connection point bus voltage in step 2 LAnd the updated lead firing angle β and DC current I in step 3. dc This serves as the input to the conventional quasi-static mathematical model of the LCC inverter in step 1, forming an analytical closed loop.

[0011] The beneficial effects of this invention are:

[0012] This invention considers the impact of control loops on the steady-state synchronization characteristics of the LCC-HVDC receiving-end system, making the analysis results of the steady-state synchronization characteristics basically consistent with the actual simulation results. Furthermore, the output of the conventional LCC inverter model is used as the input of the phase-locked loop, constant turn-off angle control, and low-voltage current limiting control loops, while the outputs of the phase-locked loop, constant turn-off angle control, and low-voltage current limiting control loops are used as the input of the conventional LCC inverter model, forming a closed-loop system. The synchronization process of the LCC-HVDC receiving-end system can be clearly observed. Attached Figure Description

[0013] Figure 1 A schematic diagram of an LCC inverter model considering the role of the control loop.

[0014] Figure 2 This is a schematic diagram of a conventional LCC inverter model.

[0015] Figure 3 A simplified circuit model diagram of the LCC-HVDC receiving-end system.

[0016] Figure 4 The control structure diagram for fixed shut-off angle control.

[0017] Figure 5 This is the control structure diagram for low-voltage current limiting control; where G and T are the gain and time of the low-pass filter, respectively.

[0018] Figure 6 The waveform diagram shows the advance trigger angle β calculated by the fixed shut-off angle control of this invention.

[0019] Figure 7 The DC current I calculated for the low-voltage current limiting control of this invention dc The waveform diagram.

[0020] Figure 8 The effective value V of the grid connection point bus voltage calculated by the quasi-static mathematical model of this invention. L The waveform diagram.

[0021] Figure 9 The waveform of the shut-off angle γ calculated by the quasi-static mathematical model of this invention is shown.

[0022] Figure 10 The DC voltage V calculated by the quasi-static mathematical model of this invention dc The waveform diagram.

[0023] Figure 11 The power factor angle calculated by the quasi-static mathematical model of this invention The waveform diagram.

[0024] Figure 12 The effective value I of the bus current at the grid connection point calculated by the quasi-static mathematical model of this invention. L The waveform diagram. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0026] like Figure 1 As shown, the LCC inverter model considering the role of control loops includes a conventional LCC inverter model, a phase-locked loop (PLL) control loop, a constant turn-off angle control loop, and a low-voltage current-limiting control loop. The conventional LCC inverter model is used to establish a conventional quasi-static mathematical model of the LCC inverter. The PLL is used to obtain the PLL dynamic equations and the effective value V of the grid connection point bus voltage. L The constant turn-off angle control loop and the low-voltage current limiting control loop are used to obtain their respective mathematical models, lead firing angle β, and DC current I. dc Its conventional LCC inverter model is as follows: Figure 2 As shown, the simplified circuit model of the LCC-HVDC receiving-end system is as follows: Figure 3 As shown, the control structure diagrams for constant turn-off angle control and low-voltage current limiting control are respectively as follows: Figure 4 and Figure 5 As shown.

[0027] Step 1: Based on the output characteristics of the LCC inverter and the conventional LCC inverter model, establish a conventional quasi-static mathematical model of the LCC inverter.

[0028] Figure 2 This is a schematic diagram of a conventional LCC inverter model, with a lead firing angle β and DC current I. dc Effective value of bus voltage at grid connection point V L As input, with turn-off angle γ and DC voltage V dc Power factor angle Effective value of bus current at grid connection point I L This is the output.

[0029] In one alternative embodiment, the conventional quasi-static mathematical model of an LCC inverter is:

[0030] Based on the LCC inverter input's lead firing angle β and DC current I... dc Effective value of bus voltage at grid connection point V L Determine the power factor angle of the LCC inverter output. The exact expressions for the turn-off angle γ, power factor angle, and turn-off angle are as follows:

[0031] ;

[0032] In the formula, k and x c These represent the equivalent commutation reactance of the transformer turns ratio and the transformer leakage reactance on the inverter side, respectively.

[0033] Secondly, based on the calculated turn-off angle γ, the LCC inverter input lead firing angle β, and the effective value of the grid connection point bus voltage V... L Determine the DC output voltage V of the LCC inverter. dc The precise expression for DC voltage is:

[0034] ;

[0035] Combined with the calculated power factor angle and DC voltage V dc The effective value of the bus current I at the grid connection point is calculated based on the conservation of AC and DC active power on the inverter side. L The power conservation expression is:

[0036] ;

[0037] In the formula, P dc and P ac These represent the active power on the DC side and the active power on the AC side of the inverter, respectively, and the effective value of the bus current at the grid connection point, I. L The precise expression is:

[0038] ;

[0039] In summary, the quasi-static mathematical model of a conventional LCC inverter is obtained:

[0040] ;

[0041] Figure 1 and Figure 2 ①②③④ in the middle correspond to the four formulas above, respectively.

[0042] It should be noted that in this embodiment, although parameters other than the input parameters are used to calculate the effective values ​​of DC voltage and grid connection point bus current, it is not difficult to see that the effective values ​​of DC voltage and grid connection point bus current can also be completely represented by the input parameters:

[0043] ;

[0044] Therefore, by reasonably selecting the mathematical expressions of the output parameters, there is no coupling between the various output parameters in the conventional quasi-static mathematical model of LCC inverters, which makes the steady-state synchronization characteristic analysis of conventional LCC inverters very clear.

[0045] Step 2, based on the power factor angle output from the conventional LCC inverter model in Step 1. Effective value of bus current at grid connection point I L In addition to system parameters, Kirchhoff's laws were used to analyze the simplified circuit model of the LCC-HVDC receiving-end system, resulting in the dynamic equation of the phase-locked loop and the effective value of the bus voltage at the grid connection point, V. L .

[0046] Figure 3 This is a simplified circuit model diagram of the LCC-HVDC receiving-end system. The grid side is equivalent to an infinite voltage source connected in series with the line impedance, and connected to the LCC inverter and AC filter at the grid connection point. Furthermore, the AC filter can filter out AC harmonics from the LCC inverter output, further improving stability and operational reliability. Since the main analysis focuses on the dynamic characteristics of the inverter side, the dynamic process at the rectifier-side sending end is ignored, and the rectifier side and DC line are equivalent to a controlled current source.

[0047] In one alternative embodiment, defining the structure and parameters of the system includes:

[0048] Define the grid connection point of the LCC inverter as PCC, and the grid connection point is represented by the equivalent admittance Y. g ∠θ g The transmission line is connected to an infinite power grid, and the connection point is equivalent to admittance B. c ∠θ c The AC filter is connected to the ground.

[0049] Define the voltage of an infinite power grid as V. g ∠0°, the equivalent current injected into the busbar is I L ∠(δ+ The effective value of the line voltage at the grid connection point of the LCC inverter is V. L ∠δ; where δ is the power angle of the LCC inverter, i.e., the phase difference between the grid connection point and the infinite power grid. The power factor angle is V. L I is the effective value of the bus voltage at the grid connection point. L This represents the effective value of the bus current at the grid connection point.

[0050] Based on the simplified circuit model of the LCC-HVDC receiving-end system, and synthesizing Kirchhoff's voltage and current laws, the nodal admittance equation for the grid connection point is obtained as follows:

[0051] ;

[0052] The voltage at the grid connection point of the LCC inverter is obtained as follows:

[0053] ;

[0054] In the formula, Y g and B c Equivalent admittance Y g and B c The modulus of θ; g θ is the admittance angle of the line impedance between the power grid and the grid connection point. c θ is the admittance angle of the filter.

[0055] Effective value of LCC inverter grid connection point bus voltage V in phase-locked loop synchronous reference coordinate system L d-axis component V Ld and q-axis component V Lq They are respectively:

[0056] ;

[0057] Figure 1 ⑤ corresponds to the above formula.

[0058] In the formula, Y t For complex conduction Y t The modulus, θ t For complex conduction Y t Admittance angle;

[0059] Complex Admittance Y t Represented as:

[0060] ;

[0061] It should be noted that, in this embodiment, the LCC inverter operates as follows:

[0062] The LCC inverter obtains the voltage phase at its grid connection point PCC through a phase-locked loop, and uses this phase as a reference to inject a phase angle into the bus. The amplitude is I L The current, of which That is, the power factor angle, therefore the dynamic equation of the phase-locked loop is:

[0063] ;

[0064] In the formula, K p-PLL K is the proportional gain coefficient in the phase-locked loop; i-PLL This is the integral gain coefficient in the phase-locked loop.

[0065] Step 3, based on the turn-off angle γ and DC voltage V output in Step 1 dcBy analyzing the constant turn-off angle control and low-voltage current limiting control loops of the LCC-HVDC receiving-end system, the mathematical models, lead-fire angle β, and DC current I of the constant turn-off angle control and low-voltage current limiting control loops are obtained. dc .

[0066] Figure 4 and Figure 5 These are the control structure diagrams for the constant turn-off angle control and low-voltage current limiting control of the LCC-HVDC receiving-end system, respectively.

[0067] In this embodiment, the control loop of the LCC-HVDC receiving end system operates as follows:

[0068] The difference between the shut-off angle and the shut-off angle reference value in step 1 is used by the PI controller to determine the trigger lead angle. The mathematical model expression for the fixed shut-off angle control is:

[0069] ;

[0070] in, This is a reference value for the shut-off angle. This refers to the proportional gain coefficient in a constant off-angle controller. is the integral gain coefficient in the fixed off-angle controller, and s is the Laplace operator.

[0071] In a 12-pulse inverter, the 12 thyristors have different turn-off angles. For the system to operate normally, each thyristor must not be mis-turned on. Therefore, it is necessary to compare the minimum turn-off angle with the reference value of the turn-off angle.

[0072] The DC voltage output in step 1 is passed through a low-pass filter and input to the VDCOL controller to determine the DC current I. dc A low-pass filter can filter out AC harmonics in DC voltage. The mathematical model for low-voltage current limiting control is as follows:

[0073] ;

[0074] in, , V dl and V dh These are the lower and upper limits of the DC voltage in the controller, I. dl and I dh These are the lower and upper limits of the DC current in the controller, respectively, V dN and I dN These are the rated values ​​for DC voltage and DC current, respectively. Once a drop in DC bus voltage is detected, the low-voltage current limiting unit will immediately activate, dynamically reducing the DC current command value according to the magnitude of the voltage drop, thereby ensuring the safe and stable operation of the system.

[0075] The key parameter settings for the power grid and equipment are shown in Table 1.

[0076] Table 1 Key Parameters

[0077] .

[0078] By analyzing the conventional LCC inverter model, phase-locked loop control, constant off-angle control, and low-voltage current limiting control, the output of the conventional LCC inverter model is used as the input to the phase-locked loop, constant off-angle control, and low-voltage current limiting control loops. The outputs of the phase-locked loop, constant off-angle control, and low-voltage current limiting control loops are used as the input to the conventional LCC inverter model. This not only allows for accurate analysis of the steady-state values ​​of various parameters of the LCC-HVDC receiving-end system, but also forms a closed-loop system, and the steady-state synchronization process of the LCC-HVDC receiving-end system can be clearly observed.

[0079] In actual high-voltage direct current transmission systems, the steady-state values ​​of the output and input parameters of the LCC-HVDC receiving-end system are shown in Table 2.

[0080] Table 2 Output and Input Parameters

[0081] .

[0082] Figures 6-8 The leading firing angle β and DC current I calculated for the example of this invention are respectively: dc Effective value of bus voltage at grid connection point V L Waveform. By incorporating the phase-locked loop dynamic equation, the fixed turn-off angle control mathematical model, and the low-voltage current-limiting control mathematical model into the conventional LCC inverter quasi-static mathematical model, a complete quasi-static mathematical model of the LCC-HVDC receiving-end system is obtained. The lead-flash angle β and the effective value of the grid-connected bus voltage V are set. L DC current I dc The initial values ​​are 1.57 rad, 155 kV and 2 kA, respectively, and are used as the first inputs to the LCC inverter model to enable the entire closed-loop system to run.

[0083] Figures 9-12 The turn-off angle γ and DC voltage V calculated for the example of this invention are respectively dc Power factor angle Effective value of bus current at grid connection point I L Waveform. Based on the initial input of the LCC inverter model and combined with the conventional quasi-static mathematical model of the LCC inverter, the turn-off angle γ and DC voltage V are calculated. dc Power factor angle Effective value of bus current at grid connection point I LThe initial values ​​are 1.38 rad, 50 kV, 1.41 rad, and 1.38 kA, respectively, and are used as the initial inputs to the phase-locked loop, constant turn-off control, and low-voltage current limiting control. Subsequently, under the action of each control link, the lead trigger angle β and the effective value of the grid connection point bus voltage V are calculated. L DC current I dc And by using this as the second input to the LCC inverter model, it is easy to see that as long as the first input or output of the LCC inverter model is given, the system can run on its own until the system reaches a steady state value.

[0084] By plotting the calculated data and comparing it with the steady-state values ​​of the output and input parameters of the LCC-HVDC receiving-end system, it can be seen that this method can accurately calculate the steady-state values ​​of each parameter of the LCC-HVDC receiving-end system and clearly observe the steady-state process of the LCC-HVDC receiving-end system.

[0085] As can be seen from the above embodiments and figures, compared with existing methods, the method for analyzing the steady-state synchronization characteristics of the LCC-HVDC receiving-end system provided by the present invention can clearly and intuitively analyze the steady-state process of the LCC-HVDC receiving-end system.

Claims

1. A SSC analysis method considering the role of the control loop in the LCC-HVDC receiver-end system, wherein the SSC analysis is a steady-state synchronization characteristic analysis, characterized in that, Includes the following steps: Step 1: Based on the output characteristics of the LCC inverter, establish a conventional quasi-static mathematical model of the LCC inverter; the quasi-static mathematical model uses the lead firing angle β and DC current I as the basis for the model. dc and the effective value of the bus voltage at the grid connection point V L As input, with power factor angle Turn-off angle γ, DC voltage V dc and the effective value of the bus current at the grid connection point I L For output; Step 2: Determine the control loop, which includes phase-locked loop control, constant turn-off angle control, and low-voltage current limiting control, based on the power factor angle output in Step 1. RMS value of bus current at grid connection point I L Based on the parameters of the simplified circuit model of the LCC-HVDC receiving-end system, and through Kirchhoff's laws, the dynamic equation of the phase-locked loop and the effective value of the bus voltage at the grid connection point, V, are obtained. L ; Step 3: Based on the turn-off angle γ and DC voltage V output in Step 1 dc By analyzing the constant turn-off angle control and low-voltage current limiting control loops of the LCC-HVDC receiving-end system, the mathematical models, lead-fire angle β, and DC current I of the constant turn-off angle control and low-voltage current limiting control loops are obtained. dc ; The phase-locked loop dynamic equation is used to update the effective value V of the grid connection point bus voltage in step 2. L The mathematical models of the constant turn-off angle control loop and the low-voltage current limiting control loop are used in step 3 to update the advance firing angle β and the DC current I. dc The updated effective value V of the grid connection point bus voltage in step 2 L And the updated lead firing angle β and DC current I in step 3. dc This serves as the input to the conventional quasi-static mathematical model of the LCC inverter in step 1, forming an analytical closed loop.

2. The SSC analysis method considering the role of the control link in the LCC-HVDC receiving-end system according to claim 1, characterized in that, In step 1, the establishment of a conventional quasi-static mathematical model for an LCC inverter is specifically as follows: Step 1.1: Based on the lead firing angle β and DC current I input to the LCC inverter... dc Effective value of bus voltage at grid connection point V L Determine the power factor angle of the LCC inverter output. The exact expressions for the turn-off angle γ, power factor angle, and turn-off angle are as follows: ； In the formula, k and x c These represent the equivalent commutation reactances of the transformer turns ratio and leakage reactance on the inverter side, respectively. Step 1.2: Based on the calculated turn-off angle γ, the LCC inverter input lead firing angle β, and the effective value of the grid connection point bus voltage V... L Determine the DC output voltage V of the LCC inverter. dc The precise expression for DC voltage is: ； Step 1.3: Combine the calculated power factor angle and DC voltage V dc The effective value of the bus current I at the grid connection point is calculated based on the conservation of AC and DC active power on the inverter side. L The precise expression for the effective value of the bus current at the grid connection point is: 。 3. The SSC analysis method considering the role of the control link in the LCC-HVDC receiving-end system according to claim 2, characterized in that, In step 2, the simplified circuit model of the LCC-HVDC receiving-end system includes: the grid connection point via the equivalent admittance Y g ∠θ g Connected to an infinite power grid, and via equivalent admittance B c ∠θ c The AC filter is grounded; the infinite mains voltage is defined as V. g ∠0°, the equivalent current injected into the grid connection point is I L ∠(δ+ The line voltage at the grid connection point is V. L ∠δ; By writing the nodal admittance equation for the grid connection point, the expression for the grid connection point voltage is obtained as follows: ； In the formula, δ is the power angle of the inverter, i.e., the phase difference between the grid connection point and the infinite power grid; Y g and B c Equivalent admittance Y g and B c The modulus of θ; g θ is the line admittance angle between the power grid and the grid connection point. c The admittance angle of the filter; Effective value of LCC inverter grid connection point bus voltage V in phase-locked loop synchronous reference coordinate system L d-axis component V Ld and q-axis component V Lq They are respectively: ； In the formula, Y t For complex conduction Y t The modulus, θ t For complex conduction Y t Admittance angle; Complex Admittance Y t Represented as: 。 4. The SSC analysis method considering the role of the control loop in the LCC-HVDC receiving-end system according to claim 3, characterized in that, Step 3 specifically involves: Step 3.1: Input the turn-off angle γ output in Step 1 into the fixed turn-off angle controller to determine the trigger lead angle. The mathematical model expression for the fixed shut-off angle control is: ； in, This is a reference value for the shut-off angle. This refers to the proportional gain coefficient in a constant off-angle controller. s is the integral gain coefficient in the fixed shut-off angle controller, and s is the Laplace operator; Step 3.2: Convert the DC voltage V output in Step 1... dc The input is passed through a low-pass filter to the VDCOL controller to determine the DC current I. dc The mathematical model for low-pressure current limiting control is as follows: ； Where a and b are intermediate variables in the calculation; and , V dl and V dh These are the lower and upper limits of the DC voltage in the VDCOL controller, respectively. dl and I dh These are the lower and upper limits of the DC current in the controller, respectively, V dN and I dN These are the rated values ​​for DC voltage and DC current, respectively. Once a drop in DC bus voltage is detected, the low-voltage current limiting unit is immediately activated to dynamically reduce the DC current command value based on the magnitude of the voltage drop, in order to ensure the safe and stable operation of the system.

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