A power distribution network elasticity evaluation method based on mechanical mapping

Abstract

The application provides a power distribution network elasticity evaluation method based on mechanical mapping, which firstly establishes a mechanical elasticity and power distribution network elasticity mapping relationship for two stages of disaster resistance and post-disaster recovery, respectively, determines resistance elasticity coefficient and recovery elasticity coefficient expression based on power distribution network elasticity indexes, and the power distribution network elasticity indexes include active power shortage in the resistance stage, average load loss speed, average load loss duration, active power shortage in the recovery stage, average load recovery speed and average load recovery duration; then, the power distribution network topology information and fault conditions are input, and a power distribution network system load curve is simulated; finally, the power distribution network elasticity indexes are calculated based on the power distribution network system load curve, and then the resistance elasticity coefficient and the recovery elasticity coefficient are calculated, so as to evaluate the power distribution network elasticity level. The application comprehensively quantifies the resistance elasticity coefficient and the recovery elasticity coefficient through six elasticity indexes, excavates the power distribution network elasticity connotation, and realizes comprehensive and effective evaluation of the power distribution network elasticity level.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method for assessing the resilience of distribution networks based on mechanical mapping. Background Technology

[0002] The frequent occurrence of extreme disasters poses a significant challenge to the safe and stable operation of power systems. As the final link connecting the power system to users, the distribution network bears the crucial responsibility of directly distributing electricity to end users. Distribution networks suffer from problems such as weak grid structure, poor equipment quality, and low maintenance levels, making them more susceptible to extreme natural disasters compared to transmission networks. Consequently, the distribution network's ability to respond to extreme disasters has attracted widespread attention both domestically and internationally.

[0003] Resilience measures a system's ability to mitigate losses during severe disturbances or faults by altering its state and to quickly return to normal operation after the fault ends. Distribution network resilience assessment primarily evaluates the system's ability to prevent, withstand, and rapidly recover from disturbances under extreme disaster events. Currently, existing distribution network resilience assessment methods lack high accuracy because their resilience evaluation indicators cannot comprehensively quantify the network's resilience level. Summary of the Invention

[0004] To improve the accuracy of distribution network resilience assessment, this invention provides a distribution network resilience assessment method based on mechanical mapping.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical method: a distribution network resilience assessment method based on mechanical mapping, comprising:

[0006] Step S1: Establish the mapping relationship between mechanical elasticity and distribution network elasticity for the two stages of disaster resistance and post-disaster recovery, and determine the expressions for the resistance elasticity coefficient and recovery elasticity coefficient based on the distribution network elasticity index. The distribution network elasticity index includes active power deficit, average load loss rate, and average load loss duration in the resistance stage, and active power deficit, average load recovery rate, and average load recovery duration in the recovery stage.

[0007] Step S2: Input the distribution network topology information and fault conditions, and simulate to obtain the load curve of the distribution network system;

[0008] Step S3: Calculate the distribution network resilience index based on the distribution network system load curve, and then calculate the resistance resilience coefficient and recovery resilience coefficient to assess the distribution network resilience level.

[0009] Furthermore, in step S1, the load curve of the distribution network system is divided into three stages—pre-disaster, during-disaster, and post-disaster—according to the time scale of the disaster occurrence process. Based on the relationship between stress and strain on a spring in mechanics, the relationship between power and elasticity of the distribution network system in each stage is mapped as follows:

[0010]

[0011] In the formula: F is the external force applied to the spring; k is the spring elastic coefficient; L is the length of the spring after being subjected to force; L0 is the initial length of the spring; P is the system power of each stage of the distribution network; m is the elastic coefficient of each stage of the distribution network; S is the final state of each stage of the distribution network; S0′ is the initial state of each stage of the distribution network.

[0012] Furthermore, in step S1, when determining the expressions for the resilience coefficient and recovery coefficient based on the distribution network resilience index:

[0013] First, combine equation (1) to determine the expression for the resilience coefficient of the distribution network during the disaster resistance stage, which is:

[0014]

[0015] In the formula: P d To withstand power in the distribution network system; ΔW d To counteract the active power deficit of the system during the phase; ΔT d L0(t) represents the duration of the resistance phase; L1(t) represents the load curve of the distribution network system without disaster; L1(t) represents the load curve of the distribution network system with disaster and with recovery strategies implemented; m d S1 represents the resilience coefficient of the distribution network; S2 represents the load of the distribution network system before or after disaster recovery; S0 represents the load of the distribution network system before or after disaster recovery.

[0016] Combining equation (1), the expression for the recovery resilience coefficient of the distribution network during the post-disaster recovery phase is determined as follows:

[0017]

[0018] In the formula: P h To restore power to the distribution network system; ΔW h To address the system's active power deficit during the recovery phase; ΔT h L1(t) represents the duration of the recovery phase; L2(t) represents the load curve of the distribution network system that has experienced a disaster and adopted a recovery strategy; L3(t) represents the load curve of the distribution network system that has experienced a disaster and has not adopted a recovery strategy; m h S1 represents the distribution network recovery resilience coefficient; S0 represents the distribution network system load before or after disaster recovery; S2 represents the distribution network system load before or after disaster recovery.

[0019] Next, the calculation formulas for six distribution network resilience indicators—active power deficit during the resistance phase, average rate of load loss, average duration of load loss, active power deficit during the recovery phase, average load recovery rate, and average load recovery duration—were determined as follows:

[0020]

[0021] In the formula: I loss To counteract the active power deficit during the resistance phase; V loss The mean rate of loss of load; T loss Mean time of load loss; I rec The active power deficit during the recovery phase; V rec T represents the average load recovery rate. rec Mean recovery time of the load;

[0022] Finally, combining equations (2), (3), and (4), we obtain the expressions for the resilience coefficient and recovery coefficient based on the distribution network resilience index, as follows:

[0023]

[0024] Preferably, in step S3, the resistance elasticity coefficient ranges from -1 to 0. The larger the resistance elasticity coefficient, the stronger the resistance elasticity of the distribution network system and the stronger its ability to cope with extreme disaster events. A resistance elasticity coefficient of 0 indicates that there is no load loss when encountering an extreme disaster event, while a resistance elasticity coefficient of -1 indicates that the extreme disaster event causes the distribution network system to collapse. The recovery elasticity coefficient ranges from 0 to 1. The larger the recovery elasticity coefficient, the better the elastic recovery strategy and the higher the elasticity level of the distribution network system. A recovery elasticity coefficient of 1 indicates that the distribution network system can instantly restore the system load to the ideal value before the disaster. A recovery elasticity coefficient of 0 indicates that the distribution network system has not taken any recovery strategy and the distribution network system has no elasticity.

[0025] This invention provides a method for assessing the resilience of distribution networks based on mechanical mapping. This method maps the elasticity of a spring in mechanics to the resilience of the distribution network during and after extreme disasters. It comprehensively quantifies the resistance elasticity coefficient and the recovery elasticity coefficient using active power deficit, average rate of load loss, and average duration of load loss during the resistance phase, and active power deficit, average load recovery rate, and average load recovery time during the recovery phase. These resistance elasticity coefficients and recovery elasticity coefficients are then used to assess the resilience level of the distribution network during and after the disaster. This method, which comprehensively quantifies the resistance elasticity coefficient and the recovery elasticity coefficient using six elasticity indicators (active power deficit, average rate of load loss, average duration of load loss, active power deficit, average load recovery rate, and average load recovery time during the recovery phase), can fully explore the resilience connotation of the distribution network, quickly achieve a comprehensive assessment of the distribution network's resilience level, and effectively improve the accuracy of distribution network resilience level assessment. Attached Figure Description

[0026] Figure 1 This is a flowchart of the distribution network resilience assessment method based on mechanical mapping involved in this invention;

[0027] Figure 2 This is a schematic diagram of the load curve of the power distribution network system of the present invention;

[0028] Figure 3 This is a schematic diagram of the distribution network elasticity model based on mechanical mapping during the disaster resistance phase of this invention.

[0029] Figure 4 This is a schematic diagram of the distribution network elasticity model based on mechanical mapping during the post-disaster recovery phase of this invention.

[0030] Figure 5 This is a topology diagram of an IEEE 33-node distribution network system in an embodiment of the present invention;

[0031] Figure 6 The above are load curves of the power distribution network system under three scenarios, Case 1, Case 2 and Case 3, obtained through simulation in the embodiments of the present invention. Detailed Implementation

[0032] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0033] As described in the background section, most existing resilience assessment methods lack in-depth understanding of the connotation of resilience and cannot achieve comprehensive quantification of the resilience level of distribution networks. Therefore, it is necessary to clarify the connotation of distribution network resilience and its assessment indicators based on the definition of resilience in mechanics, and to propose a method for assessing the resilience level of distribution networks to achieve a comprehensive evaluation. To this end, this invention proposes a distribution network resilience assessment method based on mechanical mapping. This method comprehensively quantifies the resistance resilience coefficient and recovery resilience coefficient by considering the active power deficit during the resistance phase, the average rate of load shedding, the average duration of load shedding, the active power deficit during the recovery phase, the average load recovery rate, and the average load recovery duration. This process delves into the connotation of distribution network resilience, achieving a comprehensive assessment of the distribution network resilience level and further improving the accuracy of the assessment.

[0034] Specifically, such as Figure 1 As shown, the distribution network resilience assessment method based on mechanical mapping provided by the present invention includes the following steps.

[0035] Step S1: Establish the mapping relationship between mechanical elasticity and distribution network elasticity for the two stages of disaster resistance and post-disaster recovery, and determine the expressions for the resistance elasticity coefficient and recovery elasticity coefficient based on the distribution network elasticity index. The distribution network elasticity index includes active power deficit, average load loss rate, and average load loss duration in the resistance stage, and active power deficit, average load recovery rate, and average load recovery duration in the recovery stage.

[0036] S11, Based on the disaster's progression and time scale Figure 2 The system load curve shown is divided into three stages: pre-disaster, during-disaster, and post-disaster. In mechanics, the spring constant is defined as the ratio of stress to strain experienced by an object. For example... Figure 3 As shown, the disaster phase can be likened to the compression process of a spring. Initially, the spring's tension F = 0, and the spring is at its original length. When the spring is compressed to L, the tension is the product of the spring's compression and its elastic modulus. Figure 4 As shown, the post-disaster phase is analogized to the elongation process of a spring. Initially, the tension F = 0, and the spring is at its original length. When the spring is stretched to L, the tension is the product of the spring's elongation and its elastic modulus. Based on the relationship between stress and strain on a spring in mechanics, the elasticity of the power distribution network during and after the disaster is mapped. The mapping relationship is as follows:

[0037]

[0038] In the formula: F is the external force applied to the spring; k is the spring elastic coefficient; L is the length of the spring after being subjected to force; L0 is the initial length of the spring; P is the system power of each stage of the distribution network; m is the elastic coefficient of each stage of the distribution network; S is the final state of each stage of the distribution network; S0′ is the initial state of each stage of the distribution network.

[0039] S12, determine the expressions for the resistance elasticity coefficient and the recovery elasticity coefficient based on the distribution network elasticity index.

[0040] First, combine equation (1) to determine the expression for the resilience coefficient of the distribution network during the disaster resistance stage, which is:

[0041]

[0042] In the formula: P d To withstand power in the distribution network system; ΔW d To counteract the active power deficit of the system during the phase; ΔT d L0(t) represents the duration of the resistance phase; L1(t) represents the load curve of the distribution network system without disaster; L1(t) represents the load curve of the distribution network system with disaster and with recovery strategies implemented; m d S1 represents the resilience coefficient of the distribution network; S2 represents the load of the distribution network system before or after disaster recovery; and S0 represents the load of the distribution network system before or after disaster recovery.

[0043] Combining equation (1), the expression for the recovery resilience coefficient of the distribution network during the post-disaster recovery phase is determined as follows:

[0044]

[0045] In the formula: P h To restore power to the distribution network system; ΔW h To address the system's active power deficit during the recovery phase; ΔT h L1(t) represents the duration of the recovery phase; L2(t) represents the load curve of the distribution network system that has experienced a disaster and adopted a recovery strategy; L3(t) represents the load curve of the distribution network system that has experienced a disaster and has not adopted a recovery strategy; m h S1 represents the distribution network recovery resilience coefficient; S2 represents the distribution network system load before or after disaster recovery; and S3 represents the distribution network system load before or after disaster recovery.

[0046] Next, the calculation formulas for six distribution network resilience indicators—active power deficit during the resistance phase, average rate of load loss, average duration of load loss, active power deficit during the recovery phase, average load recovery rate, and average load recovery duration—were determined as follows:

[0047]

[0048] In the formula: I loss To counteract the active power deficit during the resistance phase; V loss The mean rate of loss of load; T loss Mean time of load loss; I rec The active power deficit during the recovery phase; V rec T represents the average load recovery rate.rec This represents the average load recovery time.

[0049] Finally, combining equations (2), (3), and (4), we obtain the expressions for the resilience coefficient and recovery coefficient based on the distribution network resilience index, as follows:

[0050]

[0051] Step S2: Input the distribution network topology information and fault conditions, and simulate to obtain the load curve of the distribution network system.

[0052] The IEEE 33-bus distribution network system was used for the case study test. The system topology diagram is as follows: Figure 5 As shown in Table 1, the IEEE 33-node distribution network system comprises 33 nodes, with 32 sectionalizing switches and 5 tie switches. In a normal scenario, the sectionalizing switches are closed, and the tie switches are open. Assuming the disaster is a typhoon lasting 8 hours, three scenarios are considered: Case 1, Case 2, and Case 3. Case 1 has a greater impact from the natural disaster, with most lines experiencing faults. Cases 2 and 3 have smaller and similar impacts from the natural disaster, therefore, the number of faulty lines in Cases 2 and 3 is far less than in Case 1. The line repair speed for Cases 1 and 2 is 1 line per hour, while the repair speed for Case 3 is 2 lines per hour. The repair sequence follows the order of the faulty lines. The line fault situations under the three cases are shown in Table 1.

[0053] Table 1. Three Scenario Settings

[0054]

[0055] The simulation yielded the load curves of the distribution network system under three scenarios: Case 1, Case 2, and Case 3, as shown below. Figure 6 As shown, in Figure 6In the three scenarios, the system load curves generally show a trend of first decreasing and then increasing. This is because in the initial stage, the system encounters a disaster, the load decreases, and the load curve shows a downward trend. Subsequently, the faults are gradually repaired, the load begins to increase, and the load curve shows an upward trend. Finally, the faulty lines in all three cases are repaired, and the system load returns to the pre-disaster state. Compared with Case 2 and Case 3, Case 1's disaster is more severe, and the distribution network system has more faults. Therefore, during the disaster phase, Case 1's system load curve is the lowest, consistently lower than that of Case 2 and Case 3. Case 2 and Case 3 encounter the same extreme natural disaster scenario and have the same line fault situation, so the load curves of the two scenarios overlap during the disaster resistance phase. Compared with Case 2, Case 3's fault repair speed is faster; therefore, during the post-disaster recovery phase, Case 3's load curve is higher than that of Case 2. Overall, Case 3 has the best load curve, followed by Case 2. Due to the severity of the disaster, Case 1 has the worst load curve.

[0056] Step S3: Based on the load curve of the distribution network system, calculate six distribution network resilience indicators: active power deficit during the resistance phase, average rate of load loss, average duration of load loss, active power deficit during the recovery phase, average load recovery rate, and average load recovery duration. The results are shown in Table 2.

[0057] Table 2 Calculation results of distribution network resilience index

[0058]

[0059] For the resilience phase during a disaster, the active power deficit, average rate of load loss, and average duration of load loss are mainly used to describe the resilience level during the change phase. Generally, the larger the active power deficit, the faster the load loss rate, and the longer the average duration of load loss during the resilience phase, the greater the impact of the extreme natural disaster on the distribution network, and the lower the resilience level of the distribution network. Among the three scenarios set in this invention's implementation, Case 1 has the worst resilience level, while Case 2 and Case 3 have the same resilience level. For the above three indicators, the calculated results for Case 1 are 14.1715, 0.4175, and 8, respectively, while the calculated results for Case 2 and Case 3 are consistent, with calculated results of 5.005, 0.2388, and 8, respectively. In the post-disaster recovery phase, the active power deficit, average load recovery rate, and average load recovery time are used to describe the resilience level during the recovery phase. Unlike the resilience phase during a disaster, the three indicators for the recovery phase cannot fully describe the recovery capacity level during the recovery phase. From the perspective of active power deficit during the system recovery phase, if the disaster scenario is severe, the active power deficit during the recovery phase will certainly be large, but this does not necessarily mean that the recovery capability during the recovery phase is poor. Similarly, the other two indicators cannot fully describe the resilience level during the recovery phase; they can only provide a reference for comparing the recovery elasticity level under the same disaster conditions. For the three scenarios set in the embodiments of this invention, it is certain that Case 3 has a better elasticity level during the recovery phase than Case 2. This can also be seen from the calculation results of the three indicators: the calculation results of the three indicators for Case 3 are 2.625, 0.637, and 3, respectively, while the calculation results for Case 2 are 7.855, 0.382, and 5, respectively. For Case 3, the results of the three indicators are the worst, but this does not mean that the elasticity level during the recovery phase is the worst. Therefore, in order to further compare the elasticity levels during the resistance phase and the recovery phase, it is also necessary to calculate the elasticity coefficients of the resistance phase and the recovery phase, as follows.

[0060] Substituting the calculated results of the active power deficit, average rate of load loss, average duration of load loss during the resistance phase, and active power deficit, average recovery rate, and average recovery duration of load during the recovery phase into equation (5), we can calculate the resistance elasticity coefficient and recovery elasticity coefficient under the three scenarios. The results are shown in Table 3.

[0061] Table 3 Calculation results of elastic coefficient

[0062]

[0063] Table 3 shows that the resilience coefficients for the three scenarios are -0.530, -0.327, and -0.327, respectively. This indicates that Case 1 has the lowest resilience, while Case 2 and Case 3 have the same resilience. Comparing the scenario settings, Case 1 has more faulty lines, thus exhibiting the lowest resilience level during the resistance phase. Case 2 and Case 3 have the same fault conditions, therefore exhibiting the same resilience level during the disaster phase. Regarding the recovery resilience coefficient, Case 3 has a faster repair speed than Case 2, resulting in a recovery resilience index of 0.542, which is greater than the calculated recovery resilience index of 0.177 for Case 2. Since Case 1 experiences more load loss during the disaster, it has a larger recovery space during the recovery phase and demonstrates better recovery performance. Therefore, Case 1 has the highest recovery resilience coefficient of 0.561 among the three scenarios. In summary, the resilience coefficient ranges from -1 to 0. A larger resilience coefficient indicates stronger resilience of the distribution network system and a stronger ability to cope with extreme disaster events. A resilience coefficient of 0 indicates that no load loss occurs when an extreme disaster event occurs, while a resilience coefficient of -1 indicates that the distribution network system collapses due to an extreme disaster event. The recovery resilience coefficient ranges from 0 to 1. A larger recovery resilience coefficient indicates a better elastic recovery strategy and a higher level of resilience in the distribution network system. A recovery resilience coefficient of 1 indicates that the distribution network system can instantly restore the system load to the ideal value before the disaster. A recovery resilience coefficient of 0 indicates that the distribution network system has not taken any recovery strategy and has no resilience.

[0064] The above embodiments are preferred implementations of the present invention. In addition, the present invention can be implemented in other ways. Any obvious substitutions without departing from the concept of the present technical solution are within the protection scope of the present invention.

Claims

1. A method for assessing the resilience of a distribution network based on mechanical mapping, characterized in that, Includes the following steps: Step S1: Establish the mapping relationship between mechanical elasticity and distribution network elasticity for the two stages of disaster resistance and post-disaster recovery, and determine the expressions for the resistance elasticity coefficient and recovery elasticity coefficient based on the distribution network elasticity index. The distribution network elasticity index includes active power deficit, average load loss rate, and average load loss duration in the resistance stage, and active power deficit, average load recovery rate, and average load recovery duration in the recovery stage. When determining the expressions for the resilience coefficient and recovery coefficient based on the distribution network resilience index: First, based on the established mapping relationship between mechanical elasticity and distribution network elasticity, the expression for the resistance elasticity coefficient of the distribution network during the disaster resistance stage is determined as follows: （2） In the formula: To withstand power in the power distribution network system; To counteract the system's active power deficit during the phase; Duration of the resistance phase; The load curve for a distribution network system in the absence of disasters; Load curves for distribution network systems that have experienced disasters and have adopted recovery strategies; The resilience coefficient of the distribution network; To withstand the load on the power distribution network system after a disaster or before recovery; To withstand the load on the power distribution network system before or after a disaster; Based on the established mapping relationship between mechanical elasticity and distribution network elasticity, the expression for the recovery elasticity coefficient of the distribution network during the post-disaster recovery phase is determined as follows: （3） In the formula: To restore power to the power distribution network system; To address the system's active power deficit during the recovery phase; This refers to the duration of the recovery phase; Load curves for distribution network systems that have experienced disasters and have adopted recovery strategies; Load curves for distribution network systems that have experienced disasters and for which no recovery strategies have been adopted; The resilience coefficient of the distribution network; To withstand the load on the power distribution network system before or after a disaster, To withstand the load on the power distribution network system after a disaster or before recovery; Next, the calculation formulas for six distribution network resilience indicators—active power deficit during the resistance phase, average rate of load loss, average duration of load loss, active power deficit during the recovery phase, average load recovery rate, and average load recovery duration—were determined as follows: （4） In the formula: To counteract the active power deficit during the resistance phase; Mean rate of loss of load; Mean time of load loss; The active power deficit during the recovery phase; The average load recovery rate; Mean recovery time of the load; Finally, combining equations (2), (3), and (4), we obtain the expressions for the resilience coefficient and recovery coefficient based on the distribution network resilience index, as follows: （5） Step S2: Input the distribution network topology information and fault conditions, and simulate to obtain the load curve of the distribution network system; Step S3: Calculate the distribution network resilience index based on the distribution network system load curve, and then calculate the resistance resilience coefficient and recovery resilience coefficient to assess the distribution network resilience level.

2. The distribution network resilience assessment method based on mechanical mapping according to claim 1, characterized in that: In step S1, the load curve of the distribution network system is divided into three stages—pre-disaster, during-disaster, and post-disaster—according to the time scale of the disaster occurrence process. Based on the relationship between stress and strain on a spring in mechanics, the relationship between the power and elasticity of the distribution network system in each stage is mapped as follows: （1） In the formula: The external force applied to the spring; The spring constant; This is the length of the spring after it is subjected to force; This is the initial length of the spring; This refers to the system power at each stage of the distribution network. These are the elasticity coefficients for each stage of the power distribution network; This represents the final state of each stage of the power distribution network. This represents the initial state of the distribution network at each stage.

3. The distribution network resilience assessment method based on mechanical mapping according to claim 2, characterized in that: In step S3, the resistance elasticity coefficient ranges from -1 to 0. The larger the resistance elasticity coefficient, the stronger the resistance elasticity of the distribution network system and the stronger its ability to cope with extreme disaster events. A resistance elasticity coefficient of 0 indicates that there is no load loss when encountering an extreme disaster event. A resistance elasticity coefficient of -1 indicates that the extreme disaster event causes the distribution network system to collapse. The recovery elasticity coefficient ranges from 0 to 1. The larger the recovery elasticity coefficient, the better the elastic recovery strategy and the higher the elasticity level of the distribution network system. A recovery elasticity coefficient of 1 indicates that the distribution network system can instantly restore the system load to the ideal value before the disaster. A recovery elasticity coefficient of 0 indicates that the distribution network system has not taken any recovery strategy and the distribution network system has no elasticity.

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