Voltage security region assessment method for HVDC transmission system

Abstract

The present invention relates to the field of power system operation control technology, and specifically to a voltage security domain evaluation method for a high-voltage direct current transmission system. The method comprises: analyzing the reactive voltage characteristics of a converter of a high-voltage direct current transmission system, and establishing a corresponding converter model; establishing a corresponding optimal power flow problem based on the converter model; then solving the corresponding optimal power flow problem to obtain an equivalent reactive voltage control characteristic of a converter station of the high-voltage direct current transmission system; analyzing the equivalent reactive voltage control characteristic of the converter station and expressing it in piecewise linear form to obtain an approximate expression of a corresponding reactive voltage characteristic; replacing the optimal power flow problem with the corresponding approximate expression of the reactive voltage characteristic, and establishing a corresponding voltage security domain optimization problem in combination with the set upper and lower limit constraints of the variables; then solving the corresponding voltage security domain optimization problem to obtain a corresponding voltage security domain. The voltage security domain evaluation method of the present invention can improve the accuracy and efficiency of voltage security domain calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of power system operation control, and in particular to a voltage safety domain assessment method for a high voltage direct current transmission system. Background Art

[0002] As one of the most popular technologies for long-distance transmission of large-scale electricity, the high-voltage direct current (HVDC) system based on line-commutated converters (LCCs) and voltage-source-commutated converters (VSCs) has the advantages of low cost, low loss, good stability, high transmission efficiency and good controllability, and has unique advantages in the grid connection of new energy sources such as wind power. However, the high-voltage direct current transmission system will have a great impact on the reactive voltage of the nearby power grid, so it is very important to realize the safety prevention control of the power grid and the online evaluation of the safety margin of the power grid. Among them, the security region refers to the set of state variables such as injected power, voltage, phase angle, etc. that meet the system safety constraints. The security region analysis method mainly calculates the boundary expression of the security region of the operating point, and then compares the position of the current operating point in the security region to draw a conclusion on whether the system is safe.

[0003] In response to the problem of voltage safety domain assessment, a Chinese patent with publication number CN113517713B discloses "A static voltage safety domain assessment method and device suitable for AC / DC hybrid systems", which includes: firstly, calculating the power flow of the system under normal conditions based on the mathematical model of the AC / DC system; Taylor expanding the system power balance equation, ignoring the high-order terms that have little effect on voltage changes to obtain a fast calculation formula for voltage changes; based on various serious accidents in the area, the voltage changes are calculated by equating them to corresponding disturbances; the maximum value of the voltage changes under various accidents is taken, and the static voltage safety domain of each node is determined according to the specified upper and lower voltage limits.

[0004] The voltage safety domain evaluation method in the above-mentioned existing scheme mainly considers the operating characteristics of the AC / DC hybrid system, and is applied to the power flow calculation method of the AC / DC system. The applicant found that, unlike the AC / DC hybrid system, most of the reactive power consumed by the DC converter stations at the transmitting and receiving ends of the high-voltage DC transmission system is provided by the filter, so that when a DC isolation fault occurs at the transmitting end, the redundant filter group cannot be immediately shut down, and the transmission line at the transmitting end will be in a light-load state, which will cause the voltage surge of the entire power grid to affect the nearby new energy stations, and ultimately lead to a series of power grid accidents. In other words, the high-voltage DC transmission system has complex reactive voltage control characteristics at the control end and the controlled end, as well as difficulties in solving the optimal power flow problem considering safety constraints, which makes it difficult to ensure the accuracy of the voltage safety domain calculation. At the same time, in the optimal power flow problem considering transient stability constraints in the high-voltage DC transmission system, the nonlinear constraints are too complex, resulting in low efficiency in the voltage safety domain calculation. Therefore, how to design a method that can take into account both the accuracy and efficiency of voltage safety domain calculation is a technical problem that needs to be solved urgently. Summary of the invention

[0005] In view of the deficiencies of the above-mentioned prior art, the technical problem to be solved by the present invention is: how to provide a voltage security domain evaluation method for a high-voltage direct current transmission system, so as to effectively solve the problems of complex reactive voltage control characteristics at the control end and the controlled end of the high-voltage direct current transmission system, difficulty in solving the optimal power flow problem considering safety constraints, and complex nonlinear constraints in the optimal power flow problem considering transient stability constraints, thereby improving the accuracy and efficiency of voltage security domain calculation.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] The voltage security domain assessment method for a high voltage direct current transmission system comprises the following steps:

[0008] S1: Analyze the reactive voltage characteristics of the HVDC converter and establish the corresponding converter model;

[0009] S2: Establish the corresponding optimal power flow problem based on the converter model; then solve the corresponding optimal power flow problem to obtain the equivalent reactive voltage control characteristics of the converter station of the high-voltage direct current transmission system;

[0010] S3: Analyze the equivalent reactive voltage control characteristics of the converter station and express them in piecewise linear form to obtain the corresponding approximate expression of reactive voltage characteristics;

[0011] S4: Replace the optimal power flow problem with the corresponding reactive power voltage characteristic approximate expression, and establish the corresponding voltage safety region optimization problem in combination with the set upper and lower limit constraints of the variables; then solve the corresponding voltage safety region optimization problem to obtain the corresponding voltage safety region.

[0012] Preferably, the voltage safety domain assessment method for a high voltage direct current transmission system further comprises:

[0013] S5: When the voltage safety domain is less than the set minimum voltage safety domain width threshold, the corresponding minimum dynamic reactive power reserve is calculated based on the minimum voltage safety domain width threshold to correct the voltage safety domain.

[0014] Preferably, in step S1, the converter model includes a line-commutated converter model and a voltage-source-commutated converter model;

[0015] The line commutated converter model is expressed by the following formula:

[0016]

[0017]

[0018]

[0019]

[0020] Where: U represents voltage; I represents current; T represents tap ratio; X represents impedance of line-commutated converter; P represents active power of line-commutated converter; Q represents reactive power of line-commutated converter; α represents trigger angle; Indicates the working angle; the superscripts DC and AC indicate the variables related to direct current and alternating current, respectively; the subscript LCC indicates the parameters related to the line commutation converter;

[0021] The voltage source commutated converter model is expressed by the following formula:

[0022]

[0023]

[0024] Where: P represents the active power of the line-commutated converter; Q represents the reactive power of the line-commutated converter; U represents the voltage; M represents the duty cycle of PWM; X represents the impedance of the line-commutated converter; δ represents the generator power angle, which ranges from [0,2π]; the superscripts DC and AC represent the relevant variables of direct current and alternating current, respectively; the subscript VSC represents the relevant parameters of the voltage source commutated converter.

[0025] Preferably, in the line commutated converter model:

[0026]

[0027] α min ≤α≤α min +xα max -xαmin ;

[0028] γ min ≤γ≤ max -xγ max +xγ min

[0029] In the formula: x represents a virtual variable, which takes 1 or 0; α min Indicates the minimum value of the trigger angle; α max represents the maximum value of the trigger angle; γ represents the arc extinction angle, γ min Indicates the minimum value of the arc extinction angle, γ max Indicates the maximum value of the arc extinction angle;

[0030] In the voltage source commutated converter model:

[0031] M min ≤M≤M max ;

[0032]

[0033]

[0034] Where: M min Indicates the minimum value of the duty cycle; M max Indicates the maximum value of the duty cycle; Indicates the maximum value of the apparent power of the voltage source commutated converter; It represents the minimum value of the AC voltage of the voltage source commutated converter; Indicates the maximum value of the AC voltage of a voltage source commutated converter.

[0035] Preferably, in step S2, the optimal power flow problem is expressed by the following formula, and the corresponding equivalent reactive voltage control characteristic is obtained by solving the problem through a step search algorithm;

[0036]

[0037]

[0038]

[0039]

[0040] Where: Q EX Indicates the lower limit of external exchange power; Indicates the upper limit of external switching power; Indicates the lower voltage limit of the AC busbar of the line commutation converter; Indicates the voltage upper limit of the AC busbar of the line-commutated converter; It represents the lower limit of the AC bus of the voltage source commutated converter; It represents the upper limit of the AC bus of the voltage source commutated converter; Indicates the voltage value of the external AC bus; Indicates the voltage value of the external commutation bus; Q EX Indicates external exchange power; Indicates the AC bus voltage of the line-commutated converter; represents the AC bus voltage of the voltage source commutated converter; Indicates the voltage value of the external AC bus.

[0041] Preferably, in step S3, the equivalent reactive voltage control characteristics of the converter station are analyzed by an adaptive linearized boundary regression method, thereby realizing piecewise linear expression;

[0042] The adaptive linearization boundary regression method includes: firstly, dividing the curve of the equivalent reactive voltage control characteristic into several segments according to the set step size, and calculating the slope of each segment; then combining multiple segments into one segment and recalculating the slope. If the change of the slope is less than the set threshold, then one segment of the curve can be regarded as a linearized segment.

[0043] Preferably, in step S3, the reactive voltage characteristic approximate expression is expressed by the following formula:

[0044]

[0045] Where: V 0 Indicates reactive power change The corresponding voltage value when S V Represents the reactive voltage sensitivity in steady state; V 0,cur Indicates the voltage value of the current state; Indicates the change in reactive power; Represents the reactive voltage sensitivity matrix during fault; V s Indicates reactive power change after a fault The corresponding voltage value after s,cur Indicates the current voltage value at the time of fault; Indicates the change in reactive power after a fault.

[0046] Preferably, in step S4, the voltage safety region optimization problem is expressed by the following formula:

[0047]

[0048]

[0049]

[0050] Where: λ represents the weight coefficient of the voltage safety region; Indicates the steady-state voltage value; Indicates the upper limit of the operating voltage in steady state; Indicates the lower limit of the operating voltage in steady state; The transmission value representing the line transmission power; Indicates the upper limit of the line transmission power transmission value; Indicates the lower limit of the line transmission power transmission value; Represents the upper and lower limit constraints of voltage.

[0051] Preferably, in step S4, when solving the voltage safety region optimization problem, it is converted into the following formula for solution:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Where: Indicates the transmission power of the base state line; Indicates the sensitivity corresponding to the lower limit of line transmission power; Indicates the sensitivity corresponding to the upper limit of line transmission power; G Q Represents reactive power sensitivity; S V Indicates reactive voltage sensitivity; Indicates the upper limit of line transmission power; Indicates the external exchange voltage value; and They represent the minimum and maximum values ​​of the externally injected reactive power in the base state respectively; and Respectively represent the base voltage values ​​of the line-commutated converter and the voltage-source-commutated converter; A, B, C, D, and E respectively represent the set coefficient values; Indicates the change in reactive power; Indicates the upper limit of reactive power change; Indicates the lower limit of reactive power change; the superscript cur indicates the current value; (·) - and(·) + denote negative and positive elements respectively; the symbol Δ denotes the deviation from the current value of the corresponding variable, Indicates the base value of reactive power output of the corresponding station in the current state. Indicates the change in base-state line transmission power; Represents the upper and lower limit constraints of voltage.

[0058] Preferably, in step S5, the minimum dynamic reactive power reserve is calculated by the following formula:

[0059]

[0060]

[0061]

[0062] Where: F(V) refers to the required voltage safety region; ΔC refers to the change value of reactive power and other control variables; Indicates the sensitivity coefficient of the setting.

[0063] Compared with the prior art, the voltage safety domain assessment method of the present invention has the following beneficial effects:

[0064] The present invention establishes a corresponding converter model by analyzing the reactive voltage characteristics of the converter of the high-voltage direct current transmission system, and then establishes and solves the corresponding optimal power flow problem based on the converter model to obtain the equivalent reactive voltage control characteristics of the converter station, so that the problems of complex reactive voltage control characteristics at the control end and the controlled end of the high-voltage direct current transmission system and the difficulty in solving the optimal power flow problem considering safety constraints can be effectively solved, thereby improving the accuracy of subsequent voltage safety domain calculations.

[0065] The present invention analyzes the equivalent reactive voltage control characteristics of the converter station and expresses it in piecewise linear form to obtain an approximate expression of the reactive voltage characteristics, and then replaces the optimal power flow problem with the approximate expression of the reactive voltage characteristics. Finally, the corresponding voltage safety domain optimization problem is established and solved in combination with the upper and lower limit constraints of the variables to obtain the corresponding voltage safety domain, so that the problem of complex nonlinear constraints in the optimal power flow problem considering transient stability constraints can be effectively solved, thereby greatly improving the solution efficiency of the voltage safety domain under the premise of ensuring the accuracy of the voltage safety domain calculation.

[0066] When the voltage safety domain is less than a set minimum voltage safety domain width threshold, the present invention calculates the corresponding minimum dynamic reactive reserve through the minimum voltage safety domain width threshold to correct the voltage safety domain, so as to solve the problem that the voltage safety domain is too small to meet the operating requirements in certain extreme scenarios, thereby improving the accuracy and effectiveness of the voltage safety domain calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0068] Figure 1 The logical block diagram of the voltage security domain assessment method for high voltage direct current transmission system;

[0069] Figure 2 A hierarchical structure diagram of a power system connected with high voltage direct current;

[0070] Figure 3 (a) shows the case when the transformer ratio is 1.08. Figure 3 (b) shows the case when the transformer ratio is 1.12;

[0071] Figure 4 A schematic diagram showing the relationship between different voltage safety zones;

[0072] Figure 5 Schematic diagram of the adaptive linear regression algorithm for the lower bound of reactive exchange range;

[0073] Figure 6 (a) and Figure 6 (b) Voltage safety region simulation results of two commutation converters before and after N-1 fault;

[0074] Figure 7 This is a simulation result diagram of the graded reactive voltage safety domain within the 24-hour operation time;

[0075] Figure 8 Schematic diagram of load shedding before and after optimization in extreme scenarios. DETAILED DESCRIPTION

[0076] The following is a further detailed description through specific implementation methods:

[0077] Example:

[0078] This embodiment discloses a voltage safety domain assessment method for a high voltage direct current transmission system.

[0079] like Figure 1 As shown, the voltage security domain assessment method for a high voltage direct current transmission system comprises the following steps:

[0080] S1: Analyze the reactive voltage characteristics of the HVDC converter and establish the corresponding converter model;

[0081] S2: Establish the corresponding optimal power flow problem based on the converter model; then solve the corresponding optimal power flow problem to obtain the equivalent reactive voltage control characteristics of the converter station of the high-voltage direct current transmission system;

[0082] S3: Analyze the equivalent reactive voltage control characteristics of the converter station and express them in piecewise linear form to obtain the corresponding approximate expression of reactive voltage characteristics;

[0083] S4: Replace the optimal power flow problem with the corresponding reactive voltage characteristic approximate expression, and establish the corresponding voltage security domain optimization problem in combination with the set upper and lower limit constraints of the variables; then solve the corresponding voltage security domain optimization problem to obtain the corresponding voltage security domain. In this embodiment, the voltage security domain optimization problem is called hierarchical voltage / reactive security boundaries, i.e. HVVSB (Hierarchical Voltage / VAR security boundaries), which is also referred to as HVVSB or HVVSBs model in the future.

[0084] S5: When the voltage safety domain is less than the set minimum voltage safety domain width threshold, the corresponding minimum dynamic reactive power reserve is calculated based on the minimum voltage safety domain width threshold to correct the voltage safety domain.

[0085] The present invention establishes a corresponding converter model by analyzing the reactive voltage characteristics of the converter of the high-voltage direct current transmission system, and then establishes and solves the corresponding optimal power flow problem based on the converter model to obtain the equivalent reactive voltage control characteristics of the converter station, so that the complex reactive voltage control characteristics of the control end and the controlled end of the high-voltage direct current transmission system and the difficulty in solving the optimal power flow problem considering safety constraints can be effectively solved, thereby improving the accuracy of subsequent voltage safety domain calculations. Secondly, the present invention analyzes the equivalent reactive voltage control characteristics of the converter station and expresses it in a piecewise linear manner to obtain an approximate expression of the reactive voltage characteristics, and then replaces the optimal power flow problem with the approximate expression of the reactive voltage characteristics, and finally establishes and solves the corresponding voltage safety domain optimization problem in combination with the upper and lower limit constraints of the variables to obtain the corresponding voltage safety domain, so that the problem of complex nonlinear constraints in the optimal power flow problem considering transient stability constraints can be effectively solved, thereby greatly improving the efficiency of solving the voltage safety domain under the premise of ensuring the accuracy of the voltage safety domain calculation. Finally, when the voltage safety domain is less than the set minimum voltage safety domain width threshold, the present invention calculates the corresponding minimum dynamic reactive reserve through the minimum voltage safety domain width threshold to correct the voltage safety domain, so as to solve the problem that the voltage safety domain is too small to meet the operating requirements in certain extreme scenarios, thereby improving the accuracy and effectiveness of the voltage safety domain calculation.

[0086] In the specific implementation process, the converter model includes a line commutated converter model and a voltage source commutated converter model;

[0087] First, the operation state of the LCC (Line Commutated Converter)-HVDC (High Voltage Direct Current Transmission) converter station at the sending and receiving ends can be automatically converted to different states, respectively. But once a system failure occurs, for example, if the voltage control capability of the system decreases and the voltage distribution at the sending end drops sharply, then the LCC will automatically change its control mode to the constant firing angle (CFA) mode or CC mode for quasi-steady state after the event or disturbance, respectively;

[0088] Secondly, the virtual variable x (x = 0, 1) can be used to describe the control characteristics of the LCC, as shown in formula (1), where x = 1 and x = 0 represent the states before and after the accident. For example, for DC current, in the pre-emergency state, it is equal to the fixed current value In the aftermath state, You can take the interval The value in .

[0089]

[0090] In the formula: x represents a virtual variable, which takes 1 or 0; α min Indicates the minimum value of the trigger angle; α max represents the maximum value of the trigger angle; γ represents the arc extinction angle, γ min Indicates the minimum value of the arc extinction angle, γ max Indicates the maximum value of the arc extinction angle.

[0091] For the line-commutated converter-dominated HVDC transmission system, the expressions of the voltage, active power and reactive power on the DC side of the LCC-HVDC converter under different quasi-steady-state conditions can be controlled by the trigger angle of the thyristor and the power factor angle of the LCC to control the converter and voltage on the AC side in equations (1), (2) and (3).

[0092] The line commutated converter model is expressed by the following formula:

[0093]

[0094]

[0095]

[0096]

[0097] Where: U represents voltage; I represents current; T represents tap ratio; X represents impedance of line-commutated converter; P represents active power of line-commutated converter; Q represents reactive power of line-commutated converter; α represents trigger angle; Indicates the working angle; the superscripts DC and AC represent the related variables of direct current and alternating current respectively; the subscript LCC represents the related parameters of the line commutation converter.

[0098] The VSC is controlled by M and δ, subject to the constraints of the control capacity limitation (5) and the power exchange between the AC and DC grids (6), and the value range of δ is [0,2π]. Therefore, the reactive power of the VSC can be controlled under any active power consumption and absorption values. In addition, the AC voltage in different scenarios should also be kept within a certain range, as shown in Equation (7).

[0099] M min ≤M≤M max (5);

[0100]

[0101]

[0102] Where: M min Indicates the minimum value of the duty cycle; M max Indicates the maximum value of the duty cycle; Indicates the maximum value of the apparent power of the voltage source commutated converter; It represents the minimum value of the AC voltage of the voltage source commutated converter; Indicates the maximum value of the AC voltage of a voltage source commutated converter.

[0103] The active and reactive power injection of VSC in quasi-steady state can be described by equations (8) and (9) respectively. The control method of VSC converter station can be divided into active power control and reactive power control according to the nature of the controlled object. Active power controlled objects include active power, DC voltage and frequency, which are directly or indirectly related to active power; reactive power control objects include reactive power and AC voltage, which are directly or indirectly related to reactive power. According to the deviation between the reference value and the measured value of the controlled object, the phase angle of the converter voltage regulation angle and the PWM modulation ratio M are adjusted. The active power and reactive power transmitted by the VSC converter station are used to control the controlled objects in equations (8) and (9).

[0104] The voltage source commutated converter model is expressed by the following formula:

[0105]

[0106]

[0107] Where: P represents the active power of the line-commutated converter; Q represents the reactive power of the line-commutated converter; U represents the voltage; M represents the duty cycle of PWM; X represents the impedance of the line-commutated converter; δ represents the generator power angle, which ranges from [0,2π]; the superscripts DC and AC represent the relevant variables of direct current and alternating current, respectively; the subscript VSC represents the relevant parameters of the voltage source commutated converter.

[0108] The present invention can better establish and solve the corresponding optimal power flow problem through the line commutated converter model and the voltage source commutated converter model, so that it can effectively solve the complex reactive voltage control characteristics of the control end and the controlled end of the high-voltage direct current transmission system and the difficulty in solving the optimal power flow problem considering safety constraints, thereby further improving the accuracy of subsequent voltage safety domain calculations.

[0109] In the specific implementation process, for any given voltage value of the converter station AC bus, it is difficult to control the voltage amplitude to remain at a given value regardless of whether LCC or VSC is used; the AC bus of LCC and VSC stations cannot be regarded as a "PV" type bus or a relaxed bus unless the converter station has sufficient voltage / reactive power control capabilities in all scenarios. Therefore, in order to obtain the equivalent reactive voltage control characteristics of the converter station (i.e., the equivalent external voltage / reactive power control characteristics), a stepwise search method can be applied by repeatedly solving the optimal power flow (OPF) problem given in equations (10) to (13).

[0110] The optimal power flow problem is expressed by the following formula, and the corresponding equivalent reactive voltage control characteristics are obtained by solving the step search algorithm;

[0111]

[0112]

[0113]

[0114]

[0115] Where: Q EX Indicates the lower limit of external exchange power; Indicates the upper limit of external switching power; Indicates the lower voltage limit of the AC busbar of the line commutation converter; Indicates the voltage upper limit of the AC busbar of the line-commutated converter; It represents the lower limit of the AC bus of the voltage source commutated converter; It represents the upper limit of the AC bus of the voltage source commutated converter; Indicates the voltage value of the external AC bus; Indicates the voltage value of the external commutation bus; Q EXIndicates external exchange power; Indicates the AC bus voltage of the line-commutated converter; represents the AC bus voltage of the voltage source commutated converter; Indicates the voltage value of the external AC bus.

[0116] The present invention obtains the corresponding equivalent reactive voltage control characteristics by solving the search algorithm, which can effectively solve the problems of complex reactive voltage control characteristics at the control end and the controlled end of the high-voltage direct current transmission system and the difficulty in solving the optimal power flow problem considering safety constraints, thereby further improving the accuracy of subsequent voltage safety domain calculations.

[0117] In order to facilitate the calculation of the (graded) voltage safety domain of the system, the boundary of the equivalent reactive voltage control characteristic of the HVDC converter station should be linearized first. However, the shape of the boundary may change with different operating conditions. For example, when the transformer ratio changes, the shape of the external voltage and reactive exchange safety area of ​​the HVDC converter station is not fixed. Since there is no universal fitting expression, the number of linearized segments is also unknown. Therefore, it is necessary to find a suitable piecewise linearization method to represent it.

[0118] In the specific implementation process, the equivalent reactive voltage control characteristics of the converter station are analyzed by an adaptive linearization boundary regression method to achieve piecewise linear expression; the adaptive linearization boundary regression method includes: firstly, dividing the curve of the equivalent reactive voltage control characteristics into several segments according to the set step size, and calculating the slope of each segment; then combining multiple segments into one segment and recalculating the slope. If the change in the slope is less than the set threshold, then a segment of the curve can be regarded as a linearized segment.

[0119] The reactive voltage characteristic is approximated by the following formula:

[0120]

[0121] Where: V 0 Indicates reactive power change The corresponding voltage value when S V Represents the reactive voltage sensitivity in steady state; V 0,cur Indicates the voltage value of the current state; Indicates the change in reactive power; Represents the reactive voltage sensitivity matrix during fault; V s Indicates reactive power change after a fault The corresponding voltage value after s,cur Indicates the current voltage value at the time of fault; Indicates the change in reactive power after a fault.

[0122] The adaptive linearized boundary regression method used in the present invention is an existing mature method. The adaptive linearized boundary regression method can be explained by Table 1, and the specific symbols have the following meanings: Indicates the number of curve endpoints; a i is the i-th line segment boundary point on the curve; and Point a i The x and y coordinates of Ω L Indicates that The set of linear regression lines of elements; f nΩ and t nΩ Respectively represent lines The starting bus and the ending bus.

[0123] Table 1 Adaptive linearization boundary regression method

[0124]

[0125]

[0126] The present invention analyzes the equivalent reactive voltage control characteristics of the converter station through an adaptive linearized boundary regression method, and then realizes piecewise linear expression, so that it can effectively solve the problem of complex nonlinear constraints in the optimal power flow problem considering transient stability constraints, thereby greatly improving the solution efficiency of the voltage safety domain.

[0127] In the specific implementation process, the voltage safety domain optimization problem is expressed by the following formula:

[0128]

[0129]

[0130]

[0131] Where: λ represents the weight coefficient of the voltage safety region; Indicates the steady-state voltage value; Indicates the upper limit of the operating voltage in steady state; Indicates the lower limit of the operating voltage in steady state; The transmission value representing the line transmission power; Indicates the upper limit of the line transmission power transmission value; Indicates the lower limit of the line transmission power transmission value; Represents the upper and lower limit constraints of voltage.

[0132] The voltage safety region optimization problem can be expressed as shown in (15)-(17), and its purpose is to obtain the vector V with different weight coefficients. 0The maximum safety margin (15). If the vector V 0 is controlled within its safety boundary, then as long as the uncertain variables remain within their own prediction error intervals, the safe operation of the system can be guaranteed (16). Here, represents uncertain variables, including system load and power output of renewable generators. Although considering the prediction error may lead to conservative calculation results of the graded voltage safety region, it is also worth considering a certain range of prediction errors to ensure robustness in practical applications, because even for short-term predictions, the prediction accuracy cannot reach 100%.

[0133] Now the HVVSB model (i.e., Hierarchical Voltage / VAR security boundaries, i.e., the voltage security domain optimization problem in the present invention) has been established. In order to solve it effectively, the nonlinear interval optimization problem can be further transformed into a conventional optimization problem;

[0134]

[0135]

[0136]

[0137] The sensitivity of the branch transmission power level can be calculated as shown in (18)-(19).

[0138] The maximum value within the prediction error interval can be derived as shown in (20):

[0139]

[0140] Considering the prediction error of active power level, the relevant constraints can be further transformed as shown in (21), where the superscript “cur” represents the current value; (A) - and (A) + represent the negative and positive elements of the matrix A respectively; the symbol Δ represents the deviation from the current value of the corresponding variable.

[0141]

[0142] Under normal operating conditions, S V represents the sensitivity matrix of the control variables relative to the state variables, that is, can be substituted into (21) to derive an equivalent transformation expression as shown in (22).

[0143]

[0144] Similar to (22), the constraints can be equivalently transformed as shown in (23) and (24).

[0145]

[0146]

[0147] After the N-1 fault, if the vector V0 is controlled near its current value, the increase or decrease of the V0 value caused by the stock price increase can be expressed by formula (25).

[0148]

[0149] In the specific implementation process, when solving the voltage safety region optimization problem, it is converted into the following formula for solution:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] Where: Indicates the transmission power of the base state line; Indicates the sensitivity corresponding to the lower limit of line transmission power; Indicates the sensitivity corresponding to the upper limit of line transmission power; G Q Represents reactive power sensitivity; S V Indicates reactive voltage sensitivity; Indicates the upper limit of line transmission power; Indicates the external exchange voltage value; and They represent the minimum and maximum values ​​of the externally injected reactive power in the base state respectively; and Respectively represent the base voltage values ​​of the line-commutated converter and the voltage-source-commutated converter; A, B, C, D, and E respectively represent the set coefficient values; Indicates the change in reactive power; Indicates the upper limit of reactive power change; Indicates the lower limit of reactive power change; the superscript cur indicates the current value; (·) - and(·) + denote negative and positive elements respectively; the symbol Δ denotes the deviation from the current value of the corresponding variable, Indicates the base value of reactive power output of the corresponding station in the current state. Indicates the change in base-state line transmission power; Represents the upper and lower limit constraints of voltage.

[0156] Through the above steps, the present invention can accurately and efficiently solve the voltage safety region optimization problem and obtain the voltage safety region.

[0157] In the specific implementation process, the hierarchical voltage safety region boundary assessment problem considering dynamic reactive power reserve is linearized into the following form (14):

[0158]

[0159] The original problem can be completely linearized and rearranged into a new compact equivalent form by adding additional equations, as shown in equation (27):

[0160]

[0161] When the optimal solution is obtained by solving equation (27), the decision variable V can be rearranged into the following form (28):

[0162]

[0163] Where the subscript "B" represents the corresponding rows and columns associated with the optimal basis matrix, and the non-optimal basis matrix part of the vector V is a zero matrix. Then, substitute (28) into the constraints of (27), as shown in (29).

[0164]

[0165] If the system retains more dynamic reactive power, that is, the matrix C becomes C→C+ΔC, then the optimal value F(V) becomes F(V)→F(V)+ΔF(V). The relationship between ΔF(V) and ΔC can be approximately obtained, as shown in (30).

[0166]

[0167] The system's dynamic reactive power reserve is closely related to the graded reactive power voltage safety domain.

[0168] If the system requires a minimum voltage safety domain width V REQ , the minimum dynamic reactive power reserve is calculated by formula (31):

[0169]

[0170] in,

[0171] Where: F(V) refers to the required voltage safety region; ΔC refers to the change value of reactive power and other control variables; Indicates the set sensitivity coefficient, which is used to reflect the voltage change The relationship between the change ΔC of the controlled variable C.

[0172] It should be noted that if (27) is an infeasible problem, that is, the system is in an extreme scenario where there is no graded voltage safety domain, then its range can be expanded by setting upper and lower limits on ΔC, and the required minimum dynamic reactive power reserve can be calculated from (31).

[0173] Through the above steps, the present invention can effectively calculate the corresponding minimum dynamic reactive power reserve to correct the voltage safety domain, so as to solve the problem that the voltage safety domain is too small to meet the operation requirements in some extreme scenarios, thereby improving the accuracy and effectiveness of the voltage safety domain calculation.

[0174] In order to better illustrate the advantages of the present invention, this embodiment also discloses the following experiment.

[0175] In this experiment, the typical structure of the hybrid AC / DC system can be divided into three subsystems, such as Figure 2 The AC and DC grids can be considered as the main system, while the LCC and VSC stations are subsystems. The boundaries between these systems include the AC and DC buses. The specific information is shown in Table 2, Table 3, Table 4, Table 5, and Table 6.

[0176] Table 2 Improved 118-node system HVDC information

[0177]

[0178]

[0179] Table 3 Parameters of line commutation converter on the rectifier side of LCC-HVDC

[0180]

[0181] Table 4 Parameters of line commutation converter on the inverter side of LCC-HVDC

[0182]

[0183] Table 5 Parameters of voltage source commutated converter on the rectifier side of VSC-HVDC

[0184]

[0185] Table 6 VSC-HVDC inverter side voltage source commutated converter parameters

[0186]

[0187] like Figure 3 (a) and Figure 3 As shown in (b), for a given external voltage value in the current state, the corresponding reactive power exchange range can be calculated using equations (6) to (9). Then, the given voltage value is gradually increased and decreased, and the calculation is repeated to obtain the corresponding upper and lower bounds. Figure 3 In the figure, the area enclosed by the curve represents the voltage / reactive feasible operation domain.

[0188] In order to clearly demonstrate the application of the proposed voltage security region assessment method, Figure 4 The relationship between different types of safety margins in the two-dimensional projection space is illustrated. The white area is the safety region, where all safety operating limits are guaranteed to be met at all points. In order to further consider certain prediction errors of uncertain variables, a robust safety region (gray area) smaller than the white area is defined. Then, the decoupled HVVSB model (voltage safety domain optimization problem) guarantees independent control between V1 and V2, that is, the values ​​of these two variables can be controlled within the range of r1 and r2, respectively, without considering the detailed operation and control information of other variables, corresponding to the black area.

[0189] In order to better illustrate the voltage safety domain evaluation method of the present invention, Figure 5 shows the process of finding the safety margin of reactive power exchange. The program starts with the minimum voltage value a1 of the external grid; as an initial step, a1a2 is set as the first regression line l1. Then, the slope of the straight line a1a3 is calculated. If the difference between the tangent angles of a1a2 and a1a3 is less than a given threshold, the two lines are considered as one line, otherwise a2a3 is set as the new regression line l2. Since the difference between the tangent angles of a2a5 and a2a6 is greater than a given threshold, the step-by-step search continues until point a6. Therefore, the third regression line starts from point a6. Once the maximum voltage value of the external grid is reached, the program ends.

[0190] Select a certain point A and B inside and outside the HVVSB (voltage safety domain optimization problem in the present invention) of VSC-HVDC (voltage source commutated converter-high voltage direct current transmission), set a three-phase short circuit fault at bus No. 96, the fault start time is 0.2s, the clearing time is 0.3s, and the voltage curve records bus No. 82 on the VSC rectifier side. After the fault at operating point A was found, the voltage curve at point A was stable, the steady-state voltage reached 1.01pu, and the bus voltage at point B fluctuated around 0.82pu, and the safety could not guarantee the operating point B. Similarly, select a point C and a point D inside and outside the HVVSB of LCC-HVDC-1 (experimental scenario 1), set a three-phase short circuit fault at bus No. 43, the fault start time was 0.2s, the clearing time was 0.3s, and the voltage curve of bus No. 34 on the rectifier side of LCC-1 was recorded. After the fault of the operating point C, the voltage curve of point C is stable, and the steady-state voltage reaches 1.028pu, while the bus voltage of point B fluctuates greatly after the fault. The simulation results show that when the operating point voltage is within the HVVSBs (graded voltage / safe reactive power boundary), the voltage of LCC-HVDC-1 and VSC-HVDC can ensure safe operation. It can be seen that the HVVSB proposed in the present invention can be used for voltage control in a decoupled manner, because all operating points within the HVVSB are safe.

[0191] Specifically, for two VSC stations, although there is an area where reactive power can be decoupled and controlled, the converter station does not have sufficient voltage / VAR control capability; therefore, the true safety boundary is not rectangular in shape due to the relatively strong relationship between the voltages of the two stations. The two LCC-HVDC converter stations have sufficient voltage / VAR control capability; therefore, the true safety boundary forms a rectangular shape similar to the HVVSB. In other words, the voltage / VAR control relationship affects the shape of the true safety boundary, and the HVVSB is found by finding the largest rectangle that lies within the true safety boundary.

[0192] Figure 6 (a) and Figure 6 (b) The voltage safety domain simulation results of the two commutation converters before and after N-1 fault. Figure 6 In the figure, the dots represent the 2000 simulation results generated for the fault scenarios, and the two lines represent the corresponding physical operating limits of HVVSB and the corresponding variables, respectively.

[0193] Figure 7 The 24-hour simulation results of HVVSB are shown.

[0194] In this simulation test, renewable energy generation and system load forecasting were considered. First, 100 simulation points were generated uniformly distributed on the voltage interval [0.95,1.05]pu. For each scenario, each scenario corresponds to a time interval of 15 minutes (a total of 96 scenarios in 24 hours). Then, all physical operating restrictions were simulated for all 9,600 simulation points, including all scenarios before and after the fault occurred. The safe operating points that meet all physical operating restrictions (in terms of the voltage of the LCC-HVDC-1 converter station) under all scenarios are marked inside the solid line, and other unsafe operating points are marked outside the solid line, such as Figure 7 shown.

[0195] In practical systems, a minimum HVVSB width threshold is usually guaranteed to compensate for potential interference, load fluctuations, and N-1 failures. It is assumed that the required HVVSB width of all substations is less than 0.01pu, otherwise the system may shed load to ensure safe operation. Figure 8 The 24-hour system load is shown, with the two lines representing the system status with and without dynamic reserve optimization. In some extreme scenarios where the system load is relatively heavy and there is a lack of dynamic reserve under normal operating conditions, such as the 11:15-11:45 power flow scenario, in order to ensure the minimum HVVSB width of 0.01pu for all stations, the system needs to reduce the load by about 2.15% when no additional dynamic reactive reserve optimization is performed in these extreme cases.

[0196] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A voltage safety region assessment method for a high voltage direct current transmission system, characterized in that: The following steps are involved: S1: Analyze the reactive voltage characteristics of the HVDC converter and establish the corresponding converter model; S2: Establish the corresponding optimal power flow problem based on the converter model; then solve the corresponding optimal power flow problem to obtain the equivalent reactive voltage control characteristics of the converter station of the high-voltage direct current transmission system; In step S2, the optimal power flow problem is expressed by the following formula, and the corresponding equivalent reactive voltage control characteristic is obtained by solving it through a step search algorithm; Where: Q EX Indicates the lower limit of external exchange power; Indicates the upper limit of external switching power; Indicates the lower voltage limit of the AC busbar of the line commutation converter; Indicates the voltage upper limit of the AC busbar of the line-commutated converter; It represents the lower limit of the AC bus of the voltage source commutated converter; It represents the upper limit of the AC bus of the voltage source commutated converter; Indicates the voltage value of the external AC bus; Indicates the voltage value of the external commutation bus; Q EX Indicates external exchange power; Indicates the AC bus voltage of the line-commutated converter; represents the AC bus voltage of the voltage source commutated converter; Indicates the voltage value of the external AC bus; S3: Analyze the equivalent reactive voltage control characteristics of the converter station and express them in piecewise linear form to obtain the corresponding approximate expression of reactive voltage characteristics; The equivalent reactive voltage control characteristics of the converter station are analyzed by the adaptive linearization boundary regression method, and then the piecewise linearization expression is realized; The adaptive linearization boundary regression method includes: firstly, dividing the curve of the equivalent reactive voltage control characteristic into several segments according to the set step size, and calculating the slope of each segment; then combining multiple segments into one segment and recalculating the slope. If the change of the slope is less than the set threshold, the segment of the curve can be regarded as a linearized segment; The reactive voltage characteristic is approximated by the following formula: Where: V 0 Indicates reactive power change The corresponding voltage value when S V Represents the reactive voltage sensitivity in steady state; V 0,cur Indicates the voltage value of the current state; Indicates the change in reactive power; Represents the reactive voltage sensitivity matrix during fault; V s Indicates reactive power change after a fault The corresponding voltage value after s,cur Indicates the current voltage value at the time of fault; Indicates the change in reactive power after a fault; S4: Replace the optimal power flow problem with the corresponding reactive power voltage characteristic approximate expression, and establish the corresponding voltage safety region optimization problem in combination with the set upper and lower limit constraints of the variables; then solve the corresponding voltage safety region optimization problem to obtain the corresponding voltage safety region; In step S4, the voltage safety region optimization problem is expressed by the following formula: Where: λ represents the weight coefficient of the voltage safety region; Indicates the upper limit of the operating voltage in steady state; Indicates the lower limit of the operating voltage in steady state; The transmission value representing the line transmission power; Indicates the upper limit of the line transmission power transmission value; Indicates the lower limit of the line transmission power transmission value; Represents the upper and lower limit constraints of voltage.

2. The voltage safety region assessment method for a high voltage direct current transmission system according to claim 1, characterized in that: Also includes: S5: When the voltage safety domain is less than the set minimum voltage safety domain width threshold, the corresponding minimum dynamic reactive power reserve is calculated based on the minimum voltage safety domain width threshold to correct the voltage safety domain.

3. The voltage safety region assessment method for a high voltage direct current transmission system according to claim 1, characterized in that: In step S1, the converter model includes a line commutated converter model and a voltage source commutated converter model; The line commutated converter model is expressed by the following formula: Where: U represents voltage; I represents current; T represents tap ratio; X L Indicates the impedance of the line; Indicates the active power of the line-commutated converter; represents the reactive power of the line commutation converter; α represents the firing angle; Indicates the working angle; the superscripts DC and AC indicate the variables related to direct current and alternating current, respectively; the subscript LCC indicates the parameters related to the line commutation converter; The voltage source commutated converter model is expressed by the following formula: Where: represents the active power of the voltage source commutated converter; represents the reactive power of the voltage source commutated converter; U represents the voltage; M represents the duty cycle of PWM; X L represents the impedance of the line; δ represents the generator power angle, which ranges from [0,2π]; the superscripts DC and AC represent the relevant variables of direct current and alternating current, respectively; the subscript VSC represents the relevant parameters of the voltage source commutated converter.

4. The voltage safety region assessment method for a high voltage direct current transmission system according to claim 3, characterized in that: In the line-commutated converter model: In the formula: x represents a virtual variable, which takes 1 or 0; α min Indicates the minimum value of the trigger angle; α max Indicates the maximum value of the trigger angle; β indicates the arc extinction angle, γ min Indicates the minimum value of the arc extinction angle, γ max Indicates the maximum value of the arc extinction angle; In the voltage source commutated converter model: M min ≤M≤M max ; Where: M min Indicates the minimum value of the duty cycle; M max Indicates the maximum value of the duty cycle; Indicates the maximum value of the apparent power of the voltage source commutated converter; It represents the minimum value of the AC voltage of the voltage source commutated converter; Indicates the maximum value of the AC voltage of a voltage source commutated converter.

5. The voltage safety region assessment method for a high voltage direct current transmission system according to claim 1, characterized in that: In step S4, when solving the voltage safety region optimization problem, it is converted into the following formula for solution: Where: Indicates the transmission power of the base state line; Indicates the sensitivity corresponding to the lower limit of line transmission power; Indicates the sensitivity corresponding to the upper limit of line transmission power; G Q Represents reactive power sensitivity; S V Indicates reactive voltage sensitivity; Indicates the upper limit of line transmission power; Indicates the external exchange voltage value; and They represent the minimum and maximum values ​​of the externally injected reactive power in the base state respectively; and Respectively represent the base voltage values ​​of the line-commutated converter and the voltage-source-commutated converter; A, B, C, D, and E represent the set coefficient values; Indicates the change in reactive power; Indicates the upper limit of reactive power change; Indicates the lower limit of reactive power change; the superscript cur indicates the current value; (·) - and(·) + denote negative and positive elements respectively; the symbol Δ denotes the deviation from the current value of the corresponding variable, Indicates the base value of reactive power output of the corresponding station in the current state. Indicates the change in base-state line transmission power; Represents the upper and lower limit constraints of voltage.

6. The voltage safety region assessment method for a high voltage direct current transmission system according to claim 1, characterized in that: In step S5, the minimum dynamic reactive power reserve is calculated by the following formula: Where: F(V) refers to the required voltage safety region; ΔC refers to the change value of reactive power and other control variables; Indicates the sensitivity coefficient of the setting.

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