Method for calculating maximum transmission capacity of weak sending end direct current system considering transient overvoltage constraint

Abstract

The invention discloses a method for calculating the maximum transmission capacity of a weak sending end direct current system considering transient overvoltage constraint, and belongs to the control technology of a high-voltage direct current system. According to the method, transient power characteristics of the alternating current and direct current hybrid system after direct current blocking are considered firstly, so that the influence range of each parameter on transient overvoltage is determined, the mathematical relationship among direct current, direct current voltage and transient overvoltage is constructed, and a direct current maximum transmission capacity calculation model is constructed based on transient overvoltage constraint; and solving is carried out through an improved genetic algorithm. According to the method, the DC maximum transmission capacity can be calculated off line, related results can provide a certain reference for making stable measures after DC locking, and a DC maximum transmission power real-time calculation method suitable for AC / DC faults will be further researched subsequently.

Description

Technical Field

[0001] The present invention belongs to high voltage direct current (HVDC) system control technology, and in particular relates to a method for calculating the maximum transmission capacity of a weak sending-end direct current (HVDC) system taking transient overvoltage constraints into account. Background Art

[0002] With the continued advancement of the "dual carbon" energy transition strategy, the penetration rate of renewable energy in the sending-end power grid continues to increase, further reducing the fault immunity of the weak sending-end AC system, which already has a weak grid structure and insufficient reactive voltage support capacity. Since DC systems consume a large amount of reactive power during normal operation, once a DC blocking fault occurs, the unbalanced reactive power after the fault will interact between the AC and DC systems, causing transient overvoltages on the commutation busbars, triggering large-scale disconnection of new energy units at the sending end, and severely restricting the DC channel's transmission capacity. Currently, the maximum transmission capacity of DC transmission channels is far less than the rated power, and transient overvoltages at the sending end have become the primary factor limiting the improvement of DC power transmission levels. Therefore, accurately assessing the maximum DC transmission capacity by considering transient overvoltage constraints is a key step in guiding the formulation of stability strategies for AC / DC hybrid systems and providing early warning of operational safety risks.

[0003] Regarding transient overvoltages at the sending end caused by DC blocking faults, actual DC blocking fault cases in power grids have revealed that large reactive power surges during transient conditions are the root cause of wind turbine disconnections. Based on the mechanism of wind turbine disconnections caused by transient overvoltages on the sending-end commutation bus after DC blocking, corresponding mitigation measures have been proposed. However, existing research has only qualitatively analyzed transient overvoltages after DC blocking, and no research has been conducted on quantitative calculation methods for transient overvoltage peaks.

[0004] "Calculation Method for Transient Overvoltage Caused by DC Interlock and Analysis of Influencing Factors (Wang Feng, Liu Tianqi, Ding Yuanyuan, et al.)" proposed a transient overvoltage calculation method that takes into account the short-circuit ratio and DC interlock capacity, but it is not applicable under low short-circuit ratio conditions. To expand the scope of the transient overvoltage calculation method, it is necessary to establish a relationship between transient overvoltage and resonant frequency. The reactive short-circuit ratio was used to measure the peak transient overvoltage after DC interlock. "Calculation Method for Transient Overvoltage in Sending-End System Under DC Bipolar Interlock Fault (Li Xinyue, Li Fengting, Yin Chunya, et al.)" derived an expression for the transient voltage rise after DC bipolar interlock based on an equivalent model of the sending-end system. The impedance ratio was used to characterize the peak transient overvoltage at any node in the sending-end system after the fault. However, these studies only considered the effects of the reactive component and the system equivalent reactance when calculating the transient overvoltage amplitude, and did not consider the effects of the active component and the system equivalent resistance on the transient overvoltage amplitude. Summary of the Invention

[0005] Purpose of the invention: In view of the deficiencies in the prior art, the present invention aims to provide a method for calculating the maximum transmission capacity of a weak-sending-end DC system taking into account transient overvoltage constraints.

[0006] Technical Solution: A method for calculating the maximum transfer capacity of a weak-sending DC system taking transient overvoltage constraints into account. This method first considers the transient power characteristics of the AC / DC hybrid system after DC blocking, thereby determining the impact of various parameters on transient overvoltage. This method includes establishing a mathematical relationship between DC current, DC voltage, and transient overvoltage, and then constructing a DC maximum transfer capacity calculation model based on transient overvoltage constraints. The model is then solved using an improved genetic algorithm.

[0007] The optimization objective function of the model is expressed as:

[0008] F=P dnmax =max(U d I d )

[0009] Where: P dnmax represents the maximum DC transmission power under transient overvoltage constraint, I d 、U d is the DC current and voltage;

[0010] DC steady-state operation inequality constraints: including the constraints of converter transformer capacity, active power P dn Constraint, reactive power Q dn Constraint, DC voltage U d Constraint and DC current I d constraint:

[0011]

[0012] P dnmin ≤P dn ≤P dnmax

[0013] Q dnmin ≤Q dn ≤Q dnmax

[0014] U dmin ≤U d ≤U dmax

[0015] I dmin ≤I d ≤I dmax

[0016] U Lrmin ≤U Lr,pu ≤U Lrmax

[0017] Where STmin and S Tmax are the minimum and maximum values of the converter transformer capacity, P dnmin represents the minimum DC transmission power under transient overvoltage constraint, Q dn min and Q dnmax The corresponding is the converter reactive power Q dn The minimum and maximum values of U Lrmin and U Lrmax Indicates the commutation bus voltage U Lr,pu The minimum and maximum values of

[0018] DC steady-state operation equation constraints: Consider transient overvoltage limits, active power, reactive power, and transient overvoltage constraints:

[0019] P dn =U d I d

[0020]

[0021]

[0022] Where, N is the number of 6-pulse commutation bridges, T r Indicates the rectifier side converter transformer ratio, U Lrn Indicates the commutation bus voltage on the rectifier side, Q drn Rated reactive power of rectifier, A, B, C represent commutation bus voltage U Lr,pu The coefficients that satisfy this linear relationship.

[0023] Furthermore, the solution process of the DC maximum transmission capacity calculation model includes:

[0024] (1) Dynamic elite retention mechanism: The top n individuals in terms of fitness are selected from a population of size N to form an elite set and directly added to the next generation candidate pool. The remaining Nn individuals generate offspring through crossover mutation.

[0025] (2) Differential evolution crossover mechanism: Randomly select three different individual vectors x from the parent individuals r1 、x r2 、x r3 Calculate the differential perturbation to obtain the mutant individual vector v i , expressed as:

[0026] v i =x r1 +F(x r2 -x r3 )

[0027] Where: F is the scaling factor;

[0028] The mutation individual vector v i and the parent individual vector x ri Cross to get the test individual vector u i , for each dimension j according to the crossover probability P c After comparison, the better vector is selected as the offspring individual:

[0029]

[0030] (3) Adaptive crossover and mutation probability: Adaptively adjust the crossover probability P at different stages according to the population fitness c and mutation probability P m :

[0031]

[0032] Where: k1, k2 are constants f max is the maximum fitness of the population; f avg is the average fitness of the population; f c max For higher fitness among individuals participating in crossover:

[0033]

[0034] Where: k3, k4 are constants; f m is the fitness of the mutant individual.

[0035] Furthermore, the transient overvoltage after DC blocking is affected by P dr and Q dr Therefore, the combined influence of U d and I d P dr and U Lr Impact: I d Is the impact of P dr The dominant factor, increasing U d Can effectively improve P dr While reducing Q dr , increase I d P dr and Q dr The effect is opposite. This method also considers that the transient overvoltage after DC blocking is affected by P dr and Q dr Taking into account the joint influence of U d and I d P dr and U Lr The influence of transient overvoltage is calculated to obtain the maximum transmission power of the DC system under transient overvoltage constraints.

[0036] In combination with the above scheme, this method is analyzed in combination with the equivalent circuit of the AC / DC hybrid system after DC blocking, including constructing the following relationship:

[0037] P ac , Q ac is the active and reactive power of the AC system, Q C The reactive power generated by the reactive power compensation device; U L is the commutation bus voltage; I d 、U d For DC current and voltage, there are the following expressions:

[0038]

[0039] In the formula, the subscript r represents the electrical quantity of the sending end system, the subscript d represents the DC system, a represents the AC system, and P dr Indicates the DC system power, Q dr Indicates the reactive power of the DC system;

[0040] The transient overvoltage caused by DC blocking is ΔP r , ΔQ r , SCR and k jointly determine:

[0041]

[0042] Define the impedance ratio of the equivalent impedance of the sending end system as k, then the equivalent impedance of the AC system is expressed as:

[0043]

[0044] The short-circuit ratio SCR is used to characterize the strength of the sending-end system, expressed as the ratio of the AC system short-circuit capacity to the DC transmission capacity P. dn The relationship between the commutation bus voltage and the short-circuit ratio is obtained as follows:

[0045]

[0046] The transient overvoltage after DC blocking is determined by ΔP r , ΔQ r , SCR and k, so the influence of the above parameters on transient overvoltage should be further analyzed. Specifically, the lower the short-circuit ratio of the sending-end system, the higher the risk of transient overvoltage exceeding the limit after DC blocking. As the short-circuit ratio decreases, the influence of surplus active power and impedance ratio on the amplitude of transient overvoltage at the sending end will become more obvious.

[0047] The method includes the transient overvoltage peak calculation process after DC blocking to obtain the DC current I d and DC voltage U d For P dr and Qdr The influence of , and the coefficients A, B and C in the DC steady-state operation equation constraints are obtained:

[0048] Reactive power Q generated by the sending end AC filter and capacitor bank Cr with U Lr The relationship can be expressed as:

[0049]

[0050] Q Crn It is the rated reactive power generated by the sending-end AC filter group and capacitor group under rated voltage conditions;

[0051] When the AC / DC hybrid system is operating normally, the power balance and the reactive power relationship at the sending end are expressed as:

[0052] Q drn =Q Crn +Q acrn

[0053] When a DC complete blocking fault occurs, Q dr When it drops to 0 instantaneously, the surplus reactive power of the AC system is:

[0054]

[0055] The above formula can be rearranged to:

[0056]

[0057] ΔP after DC blocking r is the transmission power in steady-state operation, there is:

[0058]

[0059] The active power and reactive power at the sending end during DC steady-state operation are expressed as:

[0060] P dr =U d I d

[0061]

[0062] Where: N is the number of 6-pulse rectifier bridges; T r is the transformation ratio of the converter transformer of the rectifier station;

[0063] During steady-state operation, the reactive exchange between AC and DC systems is very small, and Q acrN And the transient overvoltage equation after DC blocking is sorted out as follows:

[0064]

[0065] Beneficial Effects: This invention effectively assesses the DC transmission capacity of the sending-end power grid and provides early warning of operational safety risks. It also analyzes the transient power characteristics of the AC / DC hybrid system after a DC blocking fault, demonstrating that the transient overvoltage amplitude is related to surplus power, AC system strength, and impedance ratio, and establishes a quantitative relationship expression for the transient overvoltage. The method provided by this invention enables offline calculation of the maximum DC transmission capacity. The results can provide a reference for formulating safety measures after DC blocking. Further research will be conducted on a real-time calculation method for the maximum DC transmission power applicable to AC / DC faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is the equivalent model of AC / DC hybrid system;

[0067] Figure 2 It is the equivalent circuit of the AC / DC hybrid system after DC blocking;

[0068] Figure 3 Different SCR, ΔP r with U Lr The relationship between (ΔQ r =540Mvar);

[0069] Figure 4 Different SCR, ΔQ r with U Lr The relationship between (ΔP r =1000MW);

[0070] Figure 5 is the effect of surplus active power on transient overvoltage peak;

[0071] Figure 6 Different SCR, k and U Lr The relationship between (ΔP r =1000MW,ΔQ r =540Mvar);

[0072] Figure 7 It is the effect of impedance ratio on transient overvoltage peak (SCR=2.5). DETAILED DESCRIPTION

[0073] Starting from the transient power characteristics of the AC / DC hybrid system after DC blocking, the present invention analyzes the influence of surplus power, system strength and impedance ratio on transient overvoltage. On this basis, a quantitative relationship expression between DC current, DC voltage and transient overvoltage is derived. Further, based on the steady-state operating characteristics of the DC system, the influence of DC current and DC voltage on DC power is analyzed. Then, a calculation model for the maximum DC transmission capacity is constructed taking into account transient overvoltage constraints, and an improved genetic algorithm is used to optimize the solution. Finally, simulation verification is carried out in test systems and actual systems.

[0074] 1. Analysis of transient overvoltage mechanism caused by DC blocking

[0075] The equivalent model of AC / DC hybrid system is as follows: Figure 1 As shown in the figure: subscript r represents the electrical quantity of the sending end system. ac , Q ac is the active and reactive power of the AC (subscript a) system; Z eq is the equivalent impedance of the AC system; C is the capacitance value; Q C The reactive power generated by the reactive power compensation device; U L is the commutation bus voltage; I d 、U d is the DC current and voltage. Figure 1 The relationship between AC and DC electrical quantities can be expressed as:

[0076]

[0077] The equivalent circuit of the sending end system after DC blocking is as follows: Figure 2 As shown. The power imbalance of the sending-end system and the commutation bus voltage after DC blocking are shown in equations (2) and (3). Where subscript n represents the electrical quantity in steady-state operation, i.e. rated condition; R eqr and X eqr are the equivalent resistance and equivalent reactance of the sending end system respectively.

[0078]

[0079] Define the impedance ratio (X / R) of the equivalent impedance of the sending end system as k, then the equivalent impedance of the AC system is expressed as:

[0080]

[0081] Substituting equation (4) into equation (3) and converting it to per-unit value, the commutation bus voltage considering the impedance ratio is:

[0082]

[0083] The short circuit ratio (SCR) can characterize the strength of the sending end system and is expressed as the ratio of the AC system short circuit capacity to the DC transmission capacity (S ac / P dN ), by substituting into formula (5), the relationship between the commutation bus voltage and the short-circuit ratio can be obtained as follows:

[0084]

[0085] From formula (6), we can see that the transient overvoltage after DC blocking is ΔP r , ΔQ r , SCR and k, so the influence of the above parameters on transient overvoltage should be further analyzed.

[0086] 2. Analyze the impact of various parameters on transient overvoltage

[0087] In order to clarify the influence of each parameter on transient overvoltage, after squaring both sides of equation (6), the partial derivative of each parameter is obtained:

[0088]

[0089] From equations (7) to (9), we can see that ΔP r , ΔQ r with U Lr Positive correlation, SCR and U Lr Negative correlation, so ΔP r and ΔQ r The larger the value is and the smaller the SCR is, the higher the transient overvoltage caused by DC blocking will be. In a certain DC system operating condition, SCR, k and P dN are all constant values, so the transient overvoltage peak under DC blocking is affected by ΔP r and ΔQ r For scenarios with large short circuits, ΔP r The impact on the voltage amplitude can be ignored. However, as the proportion of new energy access at the sending end continues to increase, the short-circuit ratio of the sending end system continues to decrease, and ΔP r The impact on transient overvoltage peak cannot be ignored. Taking the CIGRE HVDC standard test system parameters as an example, when ΔQ r When and k are determined, SCR, ΔP r and U Lr The relationship as Figure 3 As shown. When ΔP r When and k are determined, SCR, ΔQ r and U Lr The relationship as Figure 4 shown.

[0090] According to formula (6)-formula (9), Figure 3 and Figure 4 It can be seen that after a DC blocking fault, the transient overvoltage of the sending-end AC system is jointly affected by the surplus active power, reactive power, and the short-circuit capacity of the sending-end AC system. Comparing Figure 3 and Figure 4 it can be seen that when the short-circuit capacity is the same, the influence of the surplus reactive power on the transient overvoltage is greater than that of the surplus active power. Therefore, most existing studies ignore the influence of the surplus active power on the transient overvoltage amplitude. However, according to Figure 3 it is known that as the system strength decreases, the contribution of the surplus active power to the transient overvoltage peak cannot be ignored. The influence of the surplus active power on the transient overvoltage peak under different system strengths is as Figure 5 shown, and the calculation results of the transient overvoltage peak are shown in Table 1.

[0091] Table 1 Calculation results of transient overvoltage peaks under different system strengths

[0092]

[0093] According to Figure 5 and Table 1, it can be seen that as the short-circuit ratio of the sending-end system decreases, the deviation of the transient overvoltage peak with / without considering the surplus active power increases exponentially. Therefore, the transient overvoltage peak calculated by ignoring the influence of the surplus active power under weak system conditions will be too conservative, affecting the accuracy of the system operation risk assessment.

[0094] For Equation (10), the relationship between k and U Lr is non-monotonic, and there is a unique critical point k0. When k < k0, k and U Lr are positively correlated, and when k ≥ k0, k and U Lr are negatively correlated. When ΔP r and ΔQ r are determined, the relationship between SCR, k, and U Lr is as Figure 6 shown.

[0095] From Equation (6), Equation (10), and Figure 6 it can be seen that the impedance ratio also affects the transient overvoltage of the sending-end system after DC blocking. As the SCR decreases, the influence of k on U Lr increases. When k and SCR are large, their influence on the transient overvoltage is small. Therefore, existing studies do not consider the influence of the impedance ratio on the transient overvoltage amplitude. However, with the large-scale access of new energy to the sending-end power grid, the sending-end system strength and impedance ratio decrease, and the influence of the impedance ratio on the transient overvoltage peak cannot be ignored. The influence of different impedance ratios on the transient overvoltage peak is as Figure 7 shown, and the calculation results of the transient overvoltage peak are shown in Table 2.

[0096] Table 2 Calculation results of transient overvoltage peak under different impedance ratios

[0097]

[0098] according to Figure 7 As can be seen from Table 2, the impact of the impedance ratio on the transient voltage peak gradually increases as the short-circuit ratio decreases. Even in extremely low short-circuit ratio scenarios, the impact of a relatively large impedance ratio on transient overvoltage cannot be ignored. Therefore, ignoring the influence of the impedance ratio in weak system conditions will result in an overly conservative transient overvoltage peak, affecting the accuracy of system operation risk assessment.

[0099] In summary, the lower the short-circuit ratio of the sending-end system, the higher the risk of exceeding the transient overvoltage limit after DC blocking. Furthermore, as the short-circuit ratio decreases, the impact of surplus active power and impedance ratio on the magnitude of the sending-end transient overvoltage becomes increasingly significant. Therefore, the present invention considers the surplus active power term and impedance ratio when analyzing transient overvoltage peaks, and uses these factors to calculate the maximum DC transmission capacity under transient overvoltage constraints.

[0100] 3. DC maximum transmission capacity model and solution based on transient overvoltage constraints

[0101] (3.1) Calculation of transient overvoltage peak after DC blocking

[0102] Figure 2 When the DC system in the system is blocked, the reactive power Q generated by the AC filter and capacitor bank at the sending end is Cr with U Lr The relationship can be expressed as:

[0103]

[0104] Q CrN It is the rated reactive power generated by the sending-end AC filter group and capacitor group under rated voltage conditions.

[0105] When the AC / DC hybrid system is operating normally, the power balance and the reactive power relationship at the sending end can be expressed as:

[0106] Q drn =Q Crn +Q acrn (12)

[0107] When a DC complete blocking fault occurs, Q dr It drops to 0 instantaneously. According to formula (2), the surplus reactive power of the AC system is:

[0108]

[0109] Substituting formula (12) into formula (13) yields:

[0110]

[0111] ΔP after DC blocking r is the transmission power in steady-state operation. Substituting equation (14) into equation (5), we get:

[0112]

[0113] The active power and reactive power at the sending end during DC steady-state operation can be expressed as:

[0114] P dr =U d I d (16)

[0115]

[0116] Where: N is the number of 6-pulse rectifier bridges; T r is the transformation ratio of the converter transformer in the rectifier station.

[0117] During steady-state operation, the reactive exchange between AC and DC systems is very small, and Q acrN Substituting equations (16) and (17) into equation (15), the transient overvoltage equation after DC blocking is obtained as follows:

[0118]

[0119] In formula (18):

[0120]

[0121] When the operating conditions of the AC / DC hybrid system are determined, S cr 、U LrN , N and T r are all fixed values, so the U d and I d Substituting into equation (13) can obtain the transient overvoltage peak value after DC blocking offline.

[0122] (3.2) Analysis of the dominant factors affecting DC power

[0123] Substituting formula (16) into formula (17) and sorting it out, we can get:

[0124]

[0125] From formula (17) and formula (20), we can see that P dr and Q dr There is strong coupling between them and both are affected by DC electrical quantities. It is necessary to further clarify the influence of DC electrical quantities on DC power.

[0126] I in formula (17)d and U d A sensitivity analysis yields:

[0127]

[0128] According to formula (21), I d With Q dr Positive correlation, U d With Q dr Therefore, the larger the DC current and the smaller the DC voltage, the greater the reactive power consumption of the rectifier. dr Much greater than I d and U d To further determine the impact of Q dr The dominant factor of , the ratio of the two partial derivatives in formula (21) can be obtained:

[0129]

[0130] When formula (22) is greater than or equal to 1 (i.e. ) when I d To influence Q dr The dominant factor. When formula (22) is less than 1 (i.e. ) when U d To influence Q dr leading factor.

[0131] I in formula (20) d and U d A sensitivity analysis yields:

[0132]

[0133] According to formula (21), I d With P dr Positive correlation, Q dr With P dr Therefore, the larger the DC current and the smaller the rectifier reactive power consumption, the larger the DC transmission capacity. dr The dominant factor of , the ratio of the two partial derivatives in formula (23) can be obtained:

[0134]

[0135] Formula (24) is always true if it is greater than 1. Obviously, I d Is the impact of P dr In summary, increasing U d Can effectively improve P dr While reducing Q dr , increase I d P dr and Qdr The effect is opposite. From the analysis in the second part above, we can know that the transient overvoltage after DC blocking is affected by P dr and Q dr Therefore, the combined influence of U d and I d P dr and U Lr The influence of transient overvoltage is calculated to obtain the maximum transmission power of the DC system under transient overvoltage constraints.

[0136] (3.3) Calculation model for DC maximum transmission capacity

[0137] Considering the transient overvoltage caused by the most serious fault (DC blocking) of the DC system, the maximum DC transmission capacity is obtained through the objective function, inequality constraints and equality constraints.

[0138] To balance economic efficiency and equipment safety, and to ensure that system equipment is not damaged after a DC blocking fault, an optimization model was constructed with maximum DC transmission power as the goal, transient overvoltage and DC steady-state operation as constraints, and steady-state DC voltage and DC current as optimization variables. The optimization objective function is expressed as:

[0139] F=P dNmax =max(U d I d )(29)

[0140] Where: P dNmax represents the maximum DC transmission power under transient overvoltage constraints.

[0141] 1) Inequality constraints

[0142] The DC steady-state operation inequality constraints include converter transformer capacity constraints, active power constraints, reactive power constraints, DC voltage constraints and DC current constraints.

[0143]

[0144] P dNmin ≤P dN ≤P dNmax (31)

[0145] Q dNmin ≤Q dN ≤Q dNmax (32)

[0146] U dmin ≤U d ≤U dmax (33)

[0147] I dmin ≤I d ≤Idmax (34)

[0148] U Lrmin ≤U Lr,pu ≤U Lrmax (35)

[0149] 2) Equality constraints

[0150] The equality constraint needs to consider the transient overvoltage limit, active power, reactive power and the transient overvoltage analytical expression obtained above.

[0151] P dN =U d I d (36)

[0152]

[0153] The above constraints are combined with equation (18) as the transient overvoltage equality constraint.

[0154] (3) Model solution

[0155] The calculation model of the maximum DC transmission capacity is highly nonlinear, and traditional mathematical programming methods are difficult to accurately solve. Therefore, the present invention introduces an improved genetic algorithm (GA) based on differential evolution crossover to solve the problem, so as to obtain the maximum DC transmission capacity under transient overvoltage constraints. The GA algorithm is an intelligent optimization algorithm obtained by simulating the biological evolution process. Although the traditional GA algorithm has advantages such as strong global search capabilities, it has a long calculation time and is prone to premature convergence and falling into local optimal solutions. In response to the above problems, this paper adopts elite retention, differential evolution crossover mechanism and adaptive crossover mutation probability to improve the traditional genetic algorithm, while retaining the global search capability of GA, significantly improving the convergence efficiency and solution quality. The improved GA is mainly divided into the following aspects:

[0156] (1) Elite retention strategy

[0157] In order to prevent individuals with high fitness from being randomly selected and eliminated, a dynamic elite retention mechanism is introduced. The top n individuals with the highest fitness are selected from a population of size N to form an elite set and directly added to the next generation candidate pool. The remaining Nn individuals generate offspring through crossover mutation.

[0158] (2) Differential evolution crossover mechanism

[0159] The differential evolution mechanism is introduced into the crossover operation to avoid the reduction of population diversity and the reduction of global exploration ability. Three different individual vectors x are randomly selected from the parent individuals. r1 、x r2 、x r3 Calculate the differential perturbation to obtain the mutant individual vector vi , which can be expressed as:

[0160] v i =x r1 +F(x r2 -x r3 )(39)

[0161] Where: F is the scaling factor.

[0162] The mutation individual vector v i and the parent individual vector x ri Cross to get the test individual vector u i , for each dimension j according to the crossover probability P c After comparison, the better vector is selected as the offspring individual:

[0163]

[0164] (3) Adaptive crossover and mutation probability

[0165] The crossover and mutation probabilities of traditional GA are fixed, which makes it difficult to adapt to the optimization process at different stages. In order to improve the global search and local search capabilities of the algorithm to avoid premature convergence, the crossover probability P at different stages is adaptively adjusted according to the population fitness. c and mutation probability P m :

[0166]

[0167] Where: k1, k2 are constants f max is the maximum fitness of the population; f avg is the average fitness of the population; f c max is the higher fitness among individuals participating in crossover.

[0168]

[0169] Where: k3, k4 are constants; f m is the fitness of the mutant individual.

[0170] Example analysis: To verify the effectiveness of the proposed method for calculating the maximum DC transmission capacity, the CIGRE HVDC standard test system is first used for verification, where the system rated parameters are shown in Table 3.

[0171] Table 3 Rated parameters of CIGRE HVDC standard test system

[0172]

[0173] When the AC / DC hybrid system is in steady-state operation, the reactive power exchange between the AC / DC systems is very small, so the influence of the reactive power exchange between the AC / DC systems is ignored in the solution process.

[0174] The proposed method for calculating the maximum DC transmission capacity takes into account the effects of active power and impedance ratio on the transient overvoltage amplitude. The calculation results of the maximum transmission capacity with and without considering active power and impedance ratio at different short-circuit capacities are shown in Table 4.

[0175] Table 4 Results of DC maximum transmission capacity under different short-circuit capacities (test system)

[0176]

[0177] The calculation results for the maximum DC transmission capacity in Table 4 show that the maximum DC transmission capacity without considering the effects of active power and impedance ratio deviates by more than 20% compared to the case with these factors, and the deviation increases exponentially with decreasing impedance ratio. The main reason for this increased deviation is that as short-circuit capacity and impedance ratio decrease, their influence on transient overvoltage peaks increases further, resulting in a greater transient voltage rise under the same power disturbance. Consequently, the calculated maximum DC transmission power deviation increases.

[0178] For the DC maximum transmission capacity calculated above, in order to verify the accuracy of the calculation results of the DC maximum transmission capacity under different short-circuit capacities, the transient overvoltage results of the commutation bus under different DC transmission capacities are shown in Table 5.

[0179] Table 5 Transient overvoltage results under different DC transmission capacities (test system)

[0180]

[0181] Table 5 shows that, under different DC transmission capacities, the transient overvoltage amplitudes, ignoring the effects of active power and impedance ratio, all exceeded 1.3 pu, with an error exceeding 5%. This poses a risk of grid disconnection for the sending-end renewable energy units after DC blocking. However, for DC transmission power with active power and impedance ratio, the transient overvoltage peaks under different short-circuit capacities remained within the specified limits, with an error within 3%, effectively avoiding the risk of large-scale grid disconnection for the sending-end renewable energy units after DC blocking. The primary cause of the transient overvoltage error is the discrepancy between the calculated DC system reactive power and the actual reactive power in the simulation. Furthermore, the solution uses offline calculated values, resulting in a conservative maximum DC transmission capacity. This also increases the transient overvoltage deviation after DC blocking at very low short-circuit capacities.

[0182] In order to further verify the accuracy of the proposed calculation method for the maximum DC transmission capacity, a ±800kV Tianzhong (Harbin-Zhengzhou) DC transmission system was built for verification. The system rated parameters are shown in Table 7. Under different short-circuit capacities, ΔP is not considered / considered. r The calculation results of the maximum transmission capacity under and k are shown in Table 8.

[0183] Table 7 Rated parameters of the DC transmission system in Tianzhong

[0184]

[0185] Table 8 Transient overvoltage results of commutation busbars under different DC transmission capacities (actual system)

[0186]

[0187] From the comparison results of the DC maximum transmission capacity calculation shown in Table 8, it can be seen that ignoring the effects of active power and impedance ratio will lead to an error of more than 20% in the calculation results of the DC maximum transmission capacity, and the error will increase exponentially with the decrease of the impedance ratio, which is consistent with the analysis results in Section 4.1.

[0188] In order to verify the accuracy of the calculation results of the maximum DC transmission capacity under different short-circuit capacities, the transient overvoltage amplitude after DC blocking was obtained by simulation based on the DC transmission capacity calculated above. The statistical results of the commutation bus transient overvoltage under different DC transmission capacities are shown in Table 9.

[0189] Table 9 Transient overvoltage results under different DC transmission capacities (actual system)

[0190]

[0191] To effectively assess the DC transmission capacity of the sending-end power grid and provide early warning of operational safety risks, this paper proposes a method for calculating the maximum DC transmission capacity that takes into account transient overvoltage constraints. The conclusions are as follows:

[0192] 1) The transient power characteristics of the AC / DC hybrid system after a DC blocking fault are analyzed. It is found that the transient overvoltage amplitude is related to the surplus power, AC system strength and impedance ratio, and a quantitative relationship expression for the transient overvoltage is established.

[0193] 2) The dominant factors affecting DC power were analyzed, and a calculation model for the maximum DC transmission capacity taking into account transient overvoltage constraints was established, and an improved genetic algorithm was used to solve it.

[0194] 3) Simulation results show that under the maximum DC transmission power calculated by the proposed method, the transient overvoltage after DC blocking does not exceed 1.3 pu, and the transient overvoltage error is within 3%, which verifies the effectiveness of the proposed method for calculating the maximum DC transmission capacity.

[0195] 4) The method described in this invention can calculate the maximum DC transmission capacity offline. The relevant results can provide a certain reference for formulating stability measures after DC blocking. The real-time calculation method of the maximum DC transmission power applicable to AC and DC faults will be further studied in the future.

Claims

1. A method for calculating the maximum transmission capacity of a weak-sending-end DC system taking into account transient overvoltage constraints, characterized in that: The method first considers the transient power characteristics of the AC / DC hybrid system after DC blocking, thereby determining the influence of various parameters on transient overvoltage. This includes constructing the mathematical relationship between DC current, DC voltage and transient overvoltage, and then building a DC maximum transmission capacity calculation model based on transient overvoltage constraints. The model is then solved using an improved genetic algorithm. The optimization objective function of the model is expressed as: F=P dnmax =max(U d I d ) Where: P dnmax represents the maximum DC transmission power under transient overvoltage constraint, I d 、U d is the DC current and voltage; DC steady-state operation inequality constraints: including the constraints of converter transformer capacity, active power P dn Constraint, reactive power Q dn Constraint, DC voltage U d Constraint and DC current I d constraint: P dnmin ≤P dn ≤P dnmax Q dnmin ≤Q dn ≤Q dnmax IN dmin ≤U d ≤U dmax I dmin ≤I d ≤I dmax IN Lrmin ≤U Lr,pu ≤U Lrmax Where S Tmin and S Tmax are the minimum and maximum values of the converter transformer capacity, P dnmin represents the minimum DC transmission power under transient overvoltage constraint, Q dnmin and Q dnmax The corresponding is the converter reactive power Q dn The minimum and maximum values of U Lrmin and U Lrmax Indicates the commutation bus voltage U Lr,pu The minimum and maximum values of DC steady-state operation equation constraints: Consider transient overvoltage limits, active power, reactive power, and transient overvoltage constraints: P dn =U d AND d Where, N is the number of 6-pulse commutation bridges, T r Indicates the rectifier side converter transformer ratio, U Lrn Indicates the commutation bus voltage on the rectifier side, Q drn Rated reactive power of rectifier, A, B, C represent commutation bus voltage U Lr,pu The coefficients that satisfy this linear relationship.

2. The method for calculating the maximum transmission capacity of a weak-sending-end DC system according to claim 1, characterized in that: The solution process of the DC maximum transmission capacity calculation model includes: (1) Dynamic elite retention mechanism: The top n individuals in terms of fitness are selected from a population of size N to form an elite set and directly added to the next generation candidate pool. The remaining Nn individuals generate offspring through crossover mutation. (2) Differential evolution crossover mechanism: Randomly select three different individual vectors x from the parent individuals r1 、x r2 、x r3 Calculate the differential perturbation to obtain the mutant individual vector v i , expressed as: v i =x r1 +F(x r2 -x r3 ) Where: F is the scaling factor; The mutation individual vector v i and the parent individual vector x ri Cross to get the test individual vector u i , for each dimension j according to the crossover probability P c After comparison, the better vector is selected as the offspring individual: (3) Adaptive crossover and mutation probability: Adaptively adjust the crossover probability P at different stages according to the population fitness c and mutation probability P m : Where: k1, k2 are constants f max is the maximum fitness of the population; f avg is the average fitness of the population; f c max For higher fitness among individuals participating in crossover: Where: k3, k4 are constants; f m is the fitness of the mutant individual.

3. The method for calculating the maximum transmission capacity of a weak-sending-end DC system according to claim 1, characterized in that: The transient overvoltage after DC blocking is affected by P dr and Q dr Therefore, the combined influence of U d and I d P dr and U Lr Impact: I d Is the impact of P dr The dominant factor, increasing U d Can effectively improve P dr While reducing Q dr , increase I d P dr and Q dr The effect is opposite. This method also considers that the transient overvoltage after DC blocking is affected by P dr and Q dr Taking into account the joint influence of U d and I d P dr and U Lr The influence of transient overvoltage is calculated to obtain the maximum transmission power of the DC system under transient overvoltage constraints.

4. The method for calculating the maximum transmission capacity of a weak-sending-end DC system according to claim 1, characterized in that: This method is combined with the equivalent circuit of the AC / DC hybrid system after DC blocking for analysis, including the construction of the following relationship: P ac , Q ac is the active and reactive power of the AC system, Q C The reactive power generated by the reactive power compensation device; U L is the commutation bus voltage; I d 、U d For DC current and voltage, there are the following expressions: In the formula, the subscript r represents the electrical quantity of the sending end system, the subscript d represents the DC system, a represents the AC system, and P dr Indicates the DC system power, Q dr Indicates the reactive power of the DC system; The transient overvoltage caused by DC blocking is ΔP r , ΔQ r , SCR and k jointly determine: Define the impedance ratio of the equivalent impedance of the sending end system as k, then the equivalent impedance of the AC system is expressed as: The short-circuit ratio SCR is used to characterize the strength of the sending-end system, expressed as the ratio of the AC system short-circuit capacity to the DC transmission capacity P. dn The relationship between the commutation bus voltage and the short-circuit ratio is obtained as follows: The transient overvoltage after DC blocking is determined by ΔP r , ΔQ r , SCR and k, so the influence of the above parameters on transient overvoltage should be further analyzed. Specifically, the lower the short-circuit ratio of the sending-end system, the higher the risk of transient overvoltage exceeding the limit after DC blocking. As the short-circuit ratio decreases, the influence of surplus active power and impedance ratio on the amplitude of transient overvoltage at the sending end will become more obvious.

5. The method for calculating the maximum transmission capacity of a weak-sending-end DC system according to claim 1, characterized in that: The method includes the transient overvoltage peak calculation process after DC blocking to obtain the DC current I d and DC voltage U d For P dr and Q dr The influence of , and the coefficients A, B and C in the DC steady-state operation equation constraints are obtained: Reactive power Q generated by the sending end AC filter and capacitor bank Cr with U Lr The relationship can be expressed as: Q Crn It is the rated reactive power generated by the sending-end AC filter group and capacitor group under rated voltage conditions; When the AC / DC hybrid system is operating normally, the power balance and the reactive power relationship at the sending end are expressed as: Q drn =Q Crn +Q acrn When a DC complete blocking fault occurs, Q dr When it drops to 0 instantaneously, the surplus reactive power of the AC system is: The above formula can be rearranged to: ΔP after DC blocking r is the transmission power in steady-state operation, there is: The active power and reactive power at the sending end during DC steady-state operation are expressed as: P dr =U d AND d Where: N is the number of 6-pulse rectifier bridges; T r is the transformation ratio of the converter transformer of the rectifier station; During steady-state operation, the reactive exchange between AC and DC systems is very small, and Q acrN And the transient overvoltage equation after DC blocking is sorted out as follows:

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