A distribution system risk assessment method and system considering the impact of severe weather

Abstract

The present invention discloses a distribution system risk assessment method and system considering the influence of severe weather in the technical field of distribution system risk assessment, aiming to solve the problem of low assessment efficiency of existing distribution system risk assessment technology when considering the influence of severe weather. The method comprises the following steps: calculating an estimated value of expected power shortage of the distribution system during normal weather periods in a year, and an estimated value of a low-order part and a high-order part of the expected power shortage during severe weather periods, and adding them to obtain an estimated value of the expected power shortage of the distribution system throughout the year; judging the risk level of the distribution system according to the estimated value of the expected power shortage of the distribution system, and the like. The present invention evaluates the ability of the distribution system to resist conventional severe weather by calculating the expected energy shortage (EENS) risk index of the distribution system throughout the year.

Description

Technical Field

[0001] The present invention relates to a method and system for risk assessment of a power distribution system taking into account the influence of severe weather, and belongs to the technical field of risk assessment of power distribution systems. Background Art

[0002] Research on risk assessment of distribution systems has not been active for a long time. Traditional methods can be used to take into account both high accuracy and high computational efficiency of risk indicators. This is because the smaller scale and lower line failure rate of traditional distribution systems (i.e., distribution systems that do not include distributed energy or microgrids) result in a smaller number of accident states and a very low probability of second-order and higher accident states. In this case, it is only necessary to enumerate and analyze a small number of first- and second-order accident states to obtain more accurate risk indicators. Secondly, traditional distribution systems are generally closed-loop designs and open-loop operations; their power flow distribution is a simple radial distribution. This makes the analysis of accident states a simple and time-saving connectivity analysis.

[0003] However, global climate change has brought severe challenges to the risk assessment of distribution systems. The frequent occurrence of extreme meteorological disasters and the vulnerability of distribution systems in severe weather have prompted people to realize the need to consider the impact of severe weather on power grid security in risk assessment. Existing methods are difficult to balance high assessment accuracy and high assessment efficiency. First, the high failure rate of overhead lines in severe weather significantly increases the probability of high-order accident states. In order to obtain accurate risk indicators, it is necessary to take into account high-order accident states, which significantly increases the number of state analyses. In addition, with the development of the power industry, traditional distribution systems are gradually transforming to new distribution systems (i.e., distribution systems containing distributed energy or microgrids). The power flow distribution of new distribution systems containing distributed energy and a large number of switchgear is flexible and involves bidirectional flow of power flow, and its complexity is much higher than that of traditional distribution systems. The state analysis algorithm of the distribution system needs to gradually change from simple and time-saving connectivity analysis to complex and time-consuming power flow analysis.

[0004] Therefore, there is an urgent need for a risk assessment method that can take into account the impact of severe weather and achieve both high accuracy and high efficiency. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and to provide a distribution system risk assessment method and system taking into account the impact of severe weather. The ability of the distribution system to resist conventional severe weather is assessed by calculating the expected energy not supplied (EENS) risk index of the distribution system throughout the year.

[0006] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0007] In one aspect, the present invention provides a method for risk assessment of a power distribution system taking into account the impact of severe weather, comprising:

[0008] Calculate an estimate of the expected shortfall in power supply to the distribution system during normal weather periods and the lower-order portion of the expected shortfall in power supply during severe weather periods during a year;

[0009] Calculate an estimate of the high-order portion of the distribution system's expected shortfalls during periods of severe weather during a year;

[0010] The estimated value of the expected power shortage during normal weather periods, the estimated value of the low-order part and the high-order part of the expected power shortage during severe weather periods are added together to obtain the estimated value of the expected power shortage of the distribution system throughout the year;

[0011] The risk level of the distribution system is determined according to the estimated value of the expected power shortage of the distribution system. The larger the estimated value of the expected power shortage of the distribution system is, the higher the risk level of the distribution system is.

[0012] Among them, the low-order part is the contribution of the low-order accident state to the expected power shortage, the high-order part is the contribution of the high-order accident state to the expected power shortage, and the accident state is the state of the distribution system when the line is out of service.

[0013] Furthermore, the order of the accident state is determined by the number of outage lines in the power distribution system. When the number of outage lines in the power distribution system is n, it is an n-th order accident state.

[0014] The low-order accident state is a state where the order is not higher than a set order threshold, and the high-order accident state is a state where the order is higher than a set order threshold.

[0015] Further, the estimated value of the expected power shortage during normal weather periods and the low-order portion of the expected power shortage during severe weather periods are calculated, including:

[0016] Obtain power flow data of the distribution system, annual severe weather time series data, and risk parameters of the lines;

[0017] Based on the distribution system structure and switch layout, the distribution system lines are equivalent to reduce the dimension of the distribution system, and the risk parameters of the equivalent lines after dimensionality reduction are calculated;

[0018] Based on the risk parameters of the distribution system after dimensionality reduction and the equivalent line after dimensionality reduction, the accident state space is divided into a low-order accident state space and a high-order accident state space according to the order threshold;

[0019] The load shedding power of each low-order accident state in the low-order accident state subspace at all load levels is calculated using power flow analysis software;

[0020] According to the load shedding power, the load shedding power increment and the load shedding power increment correction amount of all low-order accident states are calculated;

[0021] The load shedding power increment and load shedding power increment correction of all low-order accident states are used to calculate the estimated value of the expected power shortage of the distribution system during normal weather periods and the low-order part of the expected power shortage during severe weather periods.

[0022] Furthermore, the flow data includes an annual load curve, the severe weather time series data includes the occurrence time and duration of severe weather within a year, the lines include overhead lines and non-overhead lines, and the risk parameters include failure rate and repair rate.

[0023] Furthermore, the distribution system lines are equivalent based on the distribution system structure and switch layout to reduce the dimension of the distribution system, and the risk parameters of the equivalent lines after dimensionality reduction are calculated, including:

[0024] The lines in the power distribution system that satisfy the series logic are equivalent to one line, where the lines that satisfy the series logic represent that the outage of any one line in the line set will cause the outage of the remaining lines;

[0025] The calculation expression of the risk parameter of the equivalent circuit is:

[0026]

[0027] Among them, λ eq is the failure rate of the equivalent circuit, μ eq is the repair rate of the equivalent line, λ i is the failure rate of the ith line, λ j is the failure rate of the jth line, μ i is the repair rate of the ith line, μ j is the repair rate of the jth line, i≠j;

[0028] When the number of lines in the power distribution system that satisfy the series logic is 2, the calculation is performed directly using formula (1);

[0029] When the number of lines that meet the series logic in the distribution system is greater than 2, two of the lines are first equivalent to one line through formula (1), and then the equivalent line is equivalent to the remaining lines according to formula (1) in turn until all lines are equivalent to one line, and the parameters used in the subsequent equivalent calculation are all the equivalent parameters obtained in the previous calculation.

[0030] Furthermore, the load reduction power is directly calculated by power flow calculation software;

[0031] The calculation expression of the load reduction power increment is:

[0032]

[0033] Where c represents the accident state, which is represented by the set of outage equivalent lines, ΔI cl represents the load shedding power increment under the accident state c at load level l, n c represents the number of outage equivalent lines corresponding to the accident state c, that is, the order of the accident state c, w is the low-order accident state corresponding to the accident state c, I w is the load reduction power of the low-order accident state corresponding to the accident state c, represents the set of low-order accident states of order k corresponding to the accident state c,

[0034] The calculation expression of the load reduction power increment correction amount is:

[0035]

[0036] Among them, ΔI' cl represents the load reduction power increment correction amount of state c at load level l, A represents the set of all lines in the system that may be out of service; Ac represents the set of elements in A but not in c; a eqi represents the availability of equivalent line i under normal weather conditions;

[0037] The availability rate a of the equivalent line i under normal weather conditions eqi The calculation expression is:

[0038]

[0039] Among them, μ eqi is the repair rate of equivalent line i under normal weather conditions, λ eqi is the failure rate of equivalent line i under normal weather conditions;

[0040] The calculation expression of the estimated value of the expected power shortage of the power distribution system during normal weather periods is:

[0041]

[0042] Among them, R EENSn is the expected power shortage of the distribution system during normal weather periods, l is the load level, c L is the low-order state subspace, L d is the set of all load levels, c represents the accident state, C is the accident state space, n L is the order threshold, P c is the probability of occurrence of accident state c during normal weather period, I cl represents the load shedding power in the accident state c at load level l, Dl represents the duration of load level l during normal weather periods, A represents the set of all equivalent lines in the distribution system that may be out of service, u eqi represents the unavailability rate of equivalent line i under normal weather conditions, ΔI cl represents the load shedding power increment under the accident state c at load level l, represents the set of accident states with outage order k;

[0043] The unavailability rate u of the equivalent line i under normal weather conditions is eqi The calculation expression is:

[0044]

[0045] Among them, μ eqi is the repair rate of equivalent line i under normal weather conditions, λ eqi is the failure rate of equivalent line i under normal weather conditions;

[0046] The calculation expression of the low-order part of the expected power shortage of the distribution system during the bad weather period is:

[0047]

[0048] Among them, R EENSs1 The low-level portion of the distribution system that is expected to be short of power during periods of severe weather. Indicates the probability of occurrence of accident state c in bad weather; ΔI' ce It represents the load reduction power increment correction value under load level e in state c, D e Indicates the duration of severe weather.

[0049] Furthermore, the estimated value of the high-order part of the expected power shortage during the severe weather period is calculated, including:

[0050] S1. extracting a high-order accident state sample from the high-order accident state subspace;

[0051] S2. Determine whether the outage branch corresponding to the high-order accident state sample is a feeder. If all the outage branches are feeders, set the load reduction power increment correction amount of the high-order accident state sample to 0, and go to S5; if not all the outage branches are feeders, go to S3;

[0052] S3. Using power flow analysis to obtain the load shedding power of the high-order accident state at the load level during the bad weather period;

[0053] S4, calculating the load reduction power increment correction amount under the load level during the severe weather period for the high-order accident state;

[0054] S5. Calculate an estimated value of the high-order portion of the expected power shortage during the severe weather period;

[0055] S6, calculating the variance coefficient according to the estimated value of the high-order part of the expected power shortage;

[0056] S7: If the variance coefficient of the estimated value of the expected power shortage for the whole year is greater than or equal to the preset algorithm termination threshold, go to S1; if it is less than the preset algorithm termination threshold, output the high-order estimated value of the expected power shortage during the bad weather period.

[0057] Furthermore, the calculation expression for the estimated value of the high-order part of the expected power shortage during the severe weather period is:

[0058]

[0059] Among them, R EENSs2 P is the high-level department that expects power shortage during severe weather periods. c ' represents the probability of occurrence of accident state c in bad weather, P L ' is the cumulative probability of low-order accident states under severe weather conditions, Card(A) represents the number of elements in set A, and Card(·) represents the number of elements in the set; C H is the high-order accident state subspace, c(i) represents the i-th accident state sample, N represents the number of accident state samples required to meet the termination criterion, ΔI' c(i)e represents the load reduction power increment correction of sample c(i) at load level e;

[0060] Among them, the cumulative probability of low-order accident state in severe weather is P L The calculation expression of ' is:

[0061]

[0062] Among them, u eqi ' represents the unavailability rate of the ith equivalent line in bad weather; a eqj ' represents the availability of the jth equivalent line in bad weather, n L is the order threshold.

[0063] Unavailability rate u of equivalent line i in bad weather eqi The calculation expression of ' is:

[0064]

[0065] Among them, u eqi ' is the repair rate of equivalent line i in severe weather, λ eqi ' is the failure rate of equivalent line i in severe weather.

[0066] Availability a of equivalent line j in bad weather eqj The calculation expression of ' is:

[0067]

[0068] Among them, μ j ' is the repair rate of equivalent line j in bad weather, λ j ' is the failure rate of equivalent line j in bad weather

[0069] The calculation expression for calculating the variance coefficient based on the estimated value of the high-order part of the expected power shortage is:

[0070]

[0071] Among them, β is the variance coefficient of the high-order part estimate of the expected power shortage, is the high-order estimate of the expected power shortage, for expectations; for The variance of .

[0072] Furthermore, the calculation expression of the estimated value of the expected power shortage of the power distribution system throughout the year is:

[0073]

[0074] c(i)∈C H

[0075] Among them, R EENS is the expected power shortage of the distribution system throughout the year, R EENSn is the expected power shortage of the distribution system during normal weather periods, R EENSs1 R is the low-order part of the expected power shortage during bad weather periods. EENSs2 This is the high-level portion of power shortage expected during severe weather periods.

[0076] On the other hand, the present invention also provides a power distribution system risk assessment system considering the impact of severe weather, comprising:

[0077] Memory for storing computer programs;

[0078] A processor is used to execute the computer program to implement the steps of any of the above-mentioned methods for risk assessment of a power distribution system considering the impact of severe weather.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] The present invention proposes a risk index calculation model that can consider the correlation between severe weather and load time series, and evaluates the ability of the distribution system to resist conventional severe weather by calculating the estimated value of the risk index of the expected annual short supply (EENS) of the distribution system by enumeration, wherein the conventional means that the probability of occurrence of severe weather is high and the intensity is the average level of previous years, which makes up for the lack of a calculation method for the expected annual short supply of the distribution system in the existing distribution system, thereby providing favorable data support for improving the ability of the distribution system to resist conventional severe weather, and greatly improving the risk of the distribution system;

[0081] The present invention establishes a steady-state probability model based on a homogeneous Markov process. Compared with the traditional steady-state probability model, this model can consider the temporal correlation between severe weather and load levels, so that the evaluation results are more in line with the actual situation. Compared with other models that can consider temporal correlation, this model simplifies its own complexity by giving reasonable assumptions, so that the evaluation has a higher efficiency; through the extended branch set decoupling technology, the characteristics of the impact of feeder outages in the distribution system can be used to reduce the number of state analyses, thereby improving the calculation efficiency of risk indicators. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 A schematic flow chart of a method for risk assessment of a power distribution system taking into account the impact of severe weather in an embodiment of the present invention;

[0083] Figure 2 Schematic diagram of comparison of a power distribution system before and after dimensionality reduction in an embodiment of the present invention, wherein a is a schematic diagram of the structure of the power distribution system before dimensionality reduction, and b is a schematic diagram of the structure of the power distribution system after dimensionality reduction;

[0084] Figure 3 A schematic diagram of overhead line state transition considering the timing of severe weather in an embodiment of the present invention;

[0085] Figure 4 Schematic diagram of the structure of a power distribution system using decoupling technology in an embodiment of the present invention, wherein a is the initial structure of the power distribution system, and b is a schematic diagram of the structure of the power distribution system after dimensionality reduction for decoupling determination. DETAILED DESCRIPTION

[0086] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0087] Embodiment 1:

[0088] like Figure 1 As shown, the risk assessment method for a power distribution system taking into account the impact of severe weather provided by an embodiment of the present invention includes two parts: an enumeration process and a simulation process.

[0089] The enumeration process is used to calculate an estimate of the expected shortfall in power supply during normal weather periods and the low-order portion of the expected shortfall in power supply during severe weather periods during a year, including:

[0090] The first step is to obtain the power flow data of the distribution system, the annual severe weather time series data and the risk parameters of the line. The power flow data includes the annual load curve, the severe weather time series data includes the occurrence time and duration of severe weather in a year, the line includes overhead lines and non-overhead lines, and the risk parameters include failure rate and repair rate.

[0091] The second step is to perform equivalence on the distribution system lines based on the distribution system structure and switch layout to reduce the dimension of the distribution system, and calculate the risk parameters of the equivalent lines after dimensionality reduction, including:

[0092] Since the number of power system accident states increases exponentially with the expansion of the system scale, reducing the system dimension is an important way to improve the evaluation efficiency. The distribution system usually only arranges switches (including circuit breakers and disconnectors) on key lines. This feature determines that the dimension of the distribution system can be reduced by treating multiple lines as one line.

[0093] Figure 2 The schematic diagram of the dimensionality reduction technology of the distribution system based on the switch arrangement is shown in Figure 1. When all lines in the system are operating normally, the circuit breakers and disconnectors are normally closed; the tie switches are normally open. When the trunk line 1 is out of service, the circuit breaker on its left side is immediately disconnected, causing all load nodes in the system to lose power. In order to minimize the impact of load shedding, the power system operator manually or automatically disconnects the disconnector on the right side of the trunk line 1 and restores the power supply of LP3 to LP6 by closing the tie switch. In this case, lines 1, 4, 5, and 6 are out of service. Similarly, when any one of the feeders 4 to 6 fails, in order to ensure the safety of users and maintenance personnel, the power grid operator needs to disconnect the circuit breaker on the left side of the trunk line 1 and the disconnector on the right side. In this case, lines 1, 4, 5, and 6 are out of service. According to the above analysis, any failure of lines 1, 4, 5, and 6 will cause the other lines in them to stop operating. From a risk perspective, these lines can be equivalent to one line, namely E1. By analogy, lines 2, 7, 8, and 9 can be equivalent to line E2. Load nodes LP1 and LP2 are equivalent to LP1-2; LP4 and LP5 are equivalent to LP4-5.

[0094] Since the equivalent lines satisfy the series logic from the risk perspective before they are equivalent to one line (that is, the shutdown of any one of them will cause the shutdown of the remaining lines), the risk parameter calculation model of the equivalent line is derived based on the series logic, and its expression is:

[0095]

[0096] Among them, λ eq is the failure rate of the equivalent circuit, μ eq is the repair rate of the equivalent line, λ i is the failure rate of the ith equivalent circuit, λ j is the failure rate of the jth equivalent circuit, μ i is the repair rate of the ith equivalent circuit, μ j is the repair rate of the jth equivalent line, i≠j.

[0097] When the number of lines in the power distribution system that satisfy the series logic is 2, the calculation is performed directly using formula (1);

[0098] When the number of lines that meet the series logic in the distribution system is greater than 2, two of the lines are first equivalent to one line through formula (1), and then the equivalent line is equivalent to the remaining lines according to formula (1) in turn until all lines are equivalent to one line, and the parameters used in the subsequent equivalent calculation are all the equivalent parameters obtained in the previous calculation.

[0099] The following steps are all based on the risk parameters of the distribution system and equivalent lines after dimensionality reduction.

[0100] The third step is to divide the accident state space into a low-order accident state space and a high-order accident state space according to a preset order threshold. The low-order accident state space contains all low-order accident states, and the high-order accident state space contains all high-order accident states.

[0101] The accident state is the state of the distribution system when the line is out of service. The order of the accident state is determined by the number of outage lines in the distribution system. When the number of outage lines in the distribution system is n, it is an n-order accident state. A low-order accident state is a state whose order is not higher than the set order threshold, and a high-order accident state is a state whose order is higher than the set order threshold.

[0102] Step 4: Calculate the load shedding power of each low-order accident state in the low-order accident state subspace at all load levels using power flow analysis software. In this embodiment, the power flow analysis software uses the matpower toolkit.

[0103] Step 5: Calculate the load shedding power increment and the load shedding power increment correction amount according to the load shedding power in the low-order accident state.

[0104] The calculation expression of load shedding power increment in low-order accident state is:

[0105]

[0106] Where c represents the accident state, which is represented by the set of outage equivalent lines, ΔI cl represents the load shedding power increment under the accident state c at load level l, n c represents the number of outage equivalent lines corresponding to the accident state c, that is, the order of the accident state c, w is the low-order accident state corresponding to the accident state c, I w is the load reduction power of the low-order accident state corresponding to the accident state c, represents the set of low-order accident states of order k corresponding to the accident state c,

[0107] The calculation expression of the load reduction power increment correction amount in the low-order accident state is:

[0108]

[0109] Among them, ΔI' cl represents the load reduction power increment correction amount of state c at load level l, A represents the set of all equivalent lines in the system that may be out of service; Ac represents the set of elements in A but not in c; a eqi Represents the availability of equivalent line i under normal weather conditions.

[0110] Specifically, the availability rate a of equivalent line i under normal weather conditions is eqi The calculation expression is:

[0111]

[0112] Among them, μ eqi is the repair rate of equivalent line i under normal weather conditions, λ eqi is the failure rate of equivalent line i under normal weather conditions

[0113] Step 6: By calculating the load power increment reduction and the load power increment reduction correction, the estimated value of the expected power shortage of the distribution system during normal weather periods and the low-order part of the expected power shortage during severe weather periods are obtained.

[0114] The calculation expression for the estimated value of the expected power shortage of the distribution system during normal weather periods is:

[0115]

[0116] Among them, R EENSn is the expected power shortage of the distribution system during normal weather periods, l is the load level, c L is the low-order state subspace, L d is the set of all load levels, c represents the accident state, G is the accident state space, n L is the order threshold, P cis the probability of occurrence of accident state c during normal weather period, I cl represents the load shedding power in the accident state c at load level l, D l represents the duration of load level l during normal weather periods, A represents the set of all lines in the distribution system that may be out of service, and u eqi represents the unavailability rate of equivalent line i under normal weather conditions, ΔI cl represents the load shedding power increment under the accident state c at load level l, Represents the set of accident states with outage order k.

[0117] Unavailability rate u of equivalent line i under normal weather conditions eqi The calculation expression is:

[0118]

[0119] Among them, μ eqi is the repair rate of equivalent line i under normal weather conditions, λ eqi is the failure rate of equivalent line i under normal weather conditions.

[0120] The severe weather involved refers to weather that can affect the risk parameters of overhead lines (such as typhoons, thunderstorms, blizzards, etc.). The occurrence period of severe weather in a year and the fluctuation of load levels have significant temporal characteristics (for example, typhoons occur more frequently in summer and autumn; annual peak loads occur more frequently in summer and winter). Ignoring the temporal correlation between severe weather and load levels will cause the load levels set during the state simulation process to be inconsistent with the actual situation, resulting in large errors in the evaluation results.

[0121] Traditional steady-state probability models are difficult to consider the temporal nature of severe weather, but the current state duration models that can consider temporal factors significantly increase the computational burden of risk assessment. In response to the above problems, the present invention proposes a steady-state probability model for components and systems based on a homogeneous Markov process.

[0122] The assumptions of the model include:

[0123] (1) The intensity of severe weather conditions experienced by all overhead lines at the same time is the same;

[0124] (2) Severe weather only occurs during certain periods of the year and is of regular intensity, that is, the average level of severe weather intensity over the years;

[0125] (3) The weather intensity remains constant during the duration of severe weather.

[0126] The above assumptions will not affect the effectiveness of the first-stage risk assessment. The reasons are as follows: First, the spatial scope of the distribution system is usually small, and the weather intensity is approximately equal everywhere within its scope. Second, according to statistical regularity, severe weather is likely to occur at a certain time of the year and the intensity is likely to be regular. Third, although the assumption that the weather intensity remains constant deviates from the actual situation, it can basically meet the accuracy requirements of the scheme screening work. In fact, establishing overly sophisticated component and system risk models will significantly increase the computational burden without having much impact on the screening results of the planning scheme.

[0127] Based on the above assumptions, Figure 3 The state transition of overhead lines within one year considering the timing of severe weather is shown. The division of time periods is used to distinguish weather conditions, where the weather conditions of normal weather period 1 and normal weather period 2 are the same. λ and μ are the failure rate and repair rate of overhead lines under normal weather, respectively; λ' and μ' are the failure rate and repair rate of overhead lines under severe weather, respectively. Since the intensity of severe weather is constant, λ' and μ' are constants. The duration of a severe weather period can be the sum of the duration of several severe weather events. Taking Taizhou City, Zhejiang Province as an example, a certain area of ​​the city is hit by typhoons once or twice a year on average, so the duration of severe weather can be set to the sum of the duration of one or two typhoons. The month in which the severe weather period occurs determines the load level of the distribution system during the duration of the severe weather.

[0128] Overhead lines in Figure 3 The state transitions in the three time periods all obey the homogeneous Markov process. The following takes the state transition process in time period 1 as an example to establish the probability model of the overhead line. According to the Fokker-Planck equation, we can get:

[0129]

[0130] Where a(t) represents the probability that the overhead line is in normal operation after time t from time 0 (i.e., the initial time) of the process (i.e., the availability rate); u(t) represents the probability that the overhead line is in an outage state after time t from time 0 (i.e., the unavailability rate).

[0131] Assuming that the initial probability distribution is a(0)=1, that is, the overhead line must be in working state at the beginning of the process, then by solving the differential equations, we can get:

[0132]

[0133] Where a(t) and u(t) are the steady-state probabilities of the homogeneous Markov process when t→∞. According to the properties of the homogeneous Markov process, the steady-state probability is independent of the probability distribution at the initial moment of the process. When the risk parameter is a constant, the time required for the probability distribution of the overhead line to enter the steady state is very short. For example, when the failure rate of the overhead line is 1.5 times / year and the average repair time is 10 hours, the values ​​of a(t) and u(t) are approximately equal to the time required for the steady-state probability, which is less than 24 hours. Based on this, the state probability of the overhead line at any time throughout the year can be approximated as the steady-state probability.

[0134] According to the above analysis, the steady-state probability model of overhead lines based on homogeneous Markov processes consists of three parts, namely, the steady-state probability distribution of overhead lines in normal weather, the steady-state probability distribution of overhead lines in bad weather, and the time periods covered by normal weather and bad weather (including duration and month). The significance of determining the month is to be able to reasonably match weather conditions with load levels.

[0135] The state probability distribution of overhead lines at any time during normal weather periods is:

[0136]

[0137] Where a represents the steady-state operation probability of the overhead line under normal weather conditions; u represents the steady-state outage probability of the overhead line under normal weather conditions; μ represents the repair rate of the overhead line under normal weather conditions; and λ represents the failure rate of the overhead line under normal weather conditions.

[0138] The steady-state probability distribution of overhead lines at any time during the bad weather period is:

[0139]

[0140] Where a' represents the steady-state operation probability of overhead lines in bad weather; u' represents the steady-state outage probability of overhead lines in bad weather; μ' represents the repair rate of overhead lines in bad weather; λ' represents the failure rate of overhead lines in bad weather.

[0141] Figure 3 In the data, the length of the normal weather period is the sum of the length of the normal weather period 1 and the normal weather period 2; the rest is the duration of the bad weather. In the specific risk assessment work, the normal weather period and the bad weather period can be divided according to the meteorological laws of the area where the system being assessed is located. One principle of division is to combine the time of several bad weather events in a season into a whole period.

[0142] The steady-state probability model of non-overhead lines based on homogeneous Markov processes only needs to include a part, namely the steady-state probability distribution of non-overhead lines throughout the year. This is because non-overhead lines are not affected by weather conditions, and their risk parameters in normal weather are consistent with those in severe weather. When μ and λ are used to represent the repair rate and failure rate of all components (including overhead lines and non-overhead lines) in normal weather, respectively; μ' and λ' are used to represent the repair rate and failure rate of all components (including overhead lines and non-overhead lines) in severe weather, respectively, the probability model of non-overhead lines throughout the year can be expressed by any one of the state probability distribution formula of overhead lines at any time during normal weather periods and the steady-state probability distribution formula of overhead lines at any time during severe weather periods.

[0143] Based on the steady-state probability model of the component, the steady-state probability model of the system can be further obtained. Similar to the component model, the system model also contains three parts, namely the steady-state probability distribution of the system under normal weather, the steady-state probability distribution of the system under bad weather, and the time periods covered by normal weather and bad weather, where the time periods of normal weather and bad weather are consistent with the component model.

[0144] Assuming that the outages of components are independent of each other, the probability distribution of the system state at any time during normal weather periods is:

[0145]

[0146] In the formula, u eqi represents the unavailability rate of the ith component under normal weather conditions; a eqj represents the availability of the jth component under normal weather conditions.

[0147] The state probability distribution of the system at any time during the bad weather period is:

[0148]

[0149] In the formula, u eqi ' represents the unavailability rate of the i-th component in bad weather; a eqj ' represents the availability of the jth component in bad weather. For non-overhead lines, a eqj with a eqj 'Equal;u eqi with u eqi 'equal.

[0150] Therefore, the calculation expression for the low-order part of the expected power shortage of the distribution system during severe weather periods is:

[0151]

[0152] Among them, R EENSs1P is the low-order portion of the distribution system that is expected to be short of power during severe weather periods. c ' represents the probability of occurrence of accident state c in bad weather; ΔI' ce It represents the load reduction power increment correction value under load level e in state c, D e Indicates the duration of severe weather.

[0153] In addition, the branch set decoupling technology uses the weak coupling of power flows between branches in the transmission system to improve the efficiency of transmission system risk assessment. In the theoretical derivation of this technology, branch independence is first defined. This independence is a kind of independence at the power flow level, that is, when two branch sets c 1 and c 2 When the outage does not change the power flow on the same branch, c 1 and c 2 Then, based on the independence of branches, the superposition of load reduction power was derived, that is, when two branches are combined c 1 and c 2 When they are independent of each other, we can get Among them, s(c 1 ) and s(c 2 ) represent c 1 and c 2 Any non-empty subset of ; and Respectively represent s(c 1 ) and s(c 2 ), that is, the load shedding power of the corresponding accident state. The meaning of "corresponding" is that the outage of a group of branches will inevitably lead to the occurrence of an accident state. The accident state can be represented by the set of outage branches. In the case of superposition of load shedding power, the state c can be further obtained. 1 ∪c 2 The conclusion that the load power increment correction is 0 (i.e. ).

[0154] During the application process, the branch set decoupling technology can quickly determine whether the set of outage branches corresponding to an accident state can be decoupled. When the branch set corresponding to the state can be decoupled, the power flow analysis of the state can be omitted. However, there is a strong power flow coupling between the branches of the distribution system. This is closely related to the structure of the distribution system. The distribution system is mostly a closed-loop design and open-loop operation, and presents a radial structure during operation. Strong power flow coupling is established between the feeders through the trunk line; and strong power flow coupling is established between the trunk lines due to the head-to-tail connection. Based on this, the structural characteristics of the distribution system limit the application of branch set decoupling technology in the risk assessment of the distribution system. In fact, power flow independence is a sufficient but not necessary condition for the state load reduction power to meet the superposition. When the state load reduction power meets the superposition, the corresponding state analysis can be omitted to improve the evaluation efficiency. There are just a large number of states that meet the superposition of load reduction power in the distribution system. Based on this phenomenon, the present invention combines the theory of branch set decoupling technology and the structural characteristics of the distribution system to propose an extended branch set decoupling technology (i.e., EBSD technology) to improve the calculation efficiency of the risk indicators of the distribution system.

[0155] In order to continue to use the two terms "independence" and "decoupling", the present invention extends the definition of branch independence from the power flow level to the load shedding power level as follows: Let c 1 and c 2 represents two non-empty branch sets that have no common elements. When established, c 1 and c 2 Independence (also called c 1 ∪c 2 Can be decoupled into c 1 and c 2 ); otherwise, c 1 and c 2 Not independent. According to the above definition and the state reduction load power increment theorem, c 1 ∪c 2 When decoupling is possible, c 1 ∪c 2 The corresponding load reduction power increment correction amount of the accident state is 0, that is,

[0156] The application idea of ​​the extended branch set decoupling technology is to quickly determine whether the branch set corresponding to an accident state can be decoupled. When the branch set corresponding to the state can be decoupled, the power flow analysis of the state can be omitted. According to the definition of branch independence, one method to determine branch independence is to obtain load shedding power through state analysis, and further determine whether the impact satisfies superposition based on the state load shedding power. However, this method violates the original intention of improving evaluation efficiency by reducing the number of state analyses.

[0157] In fact, the power distribution system has the following two properties (the proof process is omitted):

[0158] (1) When switches are installed on the feeders, any two feeder sets satisfy the load shedding power superposition property. When switches are not installed on the feeders, the load shedding power superposition property does not necessarily hold.

[0159] (2) When switches are installed on the feeder, any feeder set and its subordinate trunk set meet the superposition of impact. When switches are not installed on the feeder, the superposition of load reduction power may not be established.

[0160] According to the above properties, the corresponding two branch independence criteria (that is, decoupling criteria) can be obtained as follows:

[0161] (1) When all feeders in two groups of feeders are equipped with switches, the two groups of feeders are independent of each other. From another perspective, when all the outage branches in an accident state are feeders equipped with switches, the outage branch set in the accident state can be decoupled.

[0162] (2) When switches are installed on a group of feeders, the set of feeders is independent of the set of lower-level trunk lines.

[0163] Figure 4 The above branch independence criterion is illustrated by an example of a distribution system. The system consists of two sets of trunk lines {1,2,3} and {4,5,6}; two sets of feeders {7,8,9} and {10,11,12}; two generator sets and a tie line. Among them, the tie line switch is normally open; the feeder switch and the trunk switch are normally closed. Since there is no switch on feeder 9, the dimensionality reduction technology in Section 4.3.1 can be used to first make feeder 9 and trunk line 3 equivalent to trunk line 3. Any two feeder sets in the distribution system after dimensionality reduction obviously satisfy the superposition of load shedding power. For example, for the feeder sets {7,8} and {12}, there exists I {7,8} +I {12} =I {7,8,12} =15;I {7} +I {12} =I {7,12} =9;I {8} +I {12} =I {8,12}=10. According to the definition of branch independence, any two feeder sets in the reduced-dimensional distribution system are independent of each other. On the other hand, the feeder set in the reduced-dimensional distribution system and its corresponding subordinate trunk set also satisfy the superposition of load shedding power. For example, when the tie switch is always disconnected, the flow direction in trunks 4 to 6 is from trunk 4 to trunk 6, that is, trunks 5 and 6 are downstream of the flow of trunk 4. Since trunk 4 and its corresponding feeder 10 are in the same flow section, the trunk set {5,6} is the subordinate trunk set of the feeder set {10}. For the sets {5,6} and {10}, there exists I {5,6} +I {10} =I {5,6,10} =20;I {5} +I {10} =I {5,10} =20;I {6} +I {10} =I {6,10} =13. According to the definition of branch independence, any set of feeders in the distribution system after dimensionality reduction is independent of its corresponding set of subordinate trunks. However, for the distribution system considering power transfer, the opening and closing of the tie switch will change the flow direction in the trunk, thereby causing the change of the upstream and downstream relationship between the feeder and the trunk. In addition, for the distribution system including distributed power sources, the scheduling strategy of the power source will also cause the change of the upstream and downstream relationship between the feeder and the trunk.

[0164] Through the analysis of the example system, it can be seen that due to the influence of the switch mechanism of the distribution system and the distributed power generation scheduling strategy, the application complexity of the second criterion is relatively high. Therefore, the extended branch set decoupling technology only uses the first criterion as the branch independence criterion during the application process. In addition, the distribution system dimensionality reduction technology and the extended branch set decoupling technology are complementary in improving the evaluation efficiency. When the proportion of feeders without switches increases, the effect of the dimensionality reduction technology is enhanced. On the contrary, when the proportion of feeders with switches increases, the effect of the extended branch set decoupling technology is enhanced.

[0165] Based on the above branch set decoupling technology, the simulation process is used to calculate the estimated value of the high-order part of the distribution system's expected power shortage during severe weather periods in a year, including:

[0166] S1. Extract a high-order accident state sample from the high-order accident state subspace.

[0167] S2. Determine whether the outage branch corresponding to the high-order accident state sample is a feeder. If all the outage branches are feeders, set the load reduction power increment correction amount of the high-order accident state sample to 0, and go to S5; if not all the outage branches are feeders, go to S3;

[0168] S3. Using power flow analysis software to obtain the load shedding power of the high-order accident state at the load level during the bad weather period;

[0169] S4, calculating the load reduction power increment correction amount under the load level during the severe weather period for the high-order accident state;

[0170] S5. Calculate the estimated value of the high-order part of the expected power shortage during the bad weather period, and the calculation expression is:

[0171]

[0172] Among them, R EENSs2 P is the high-level department that expects power shortage during severe weather periods. c ' represents the probability of occurrence of accident state c in bad weather, P L ' is the cumulative probability of low-order accident states under severe weather, Card(A) represents the number of elements in set A, CH is the high-order accident state subspace, c(i) represents the i-th accident state sample, N represents the number of accident state samples required to meet the termination criterion, ΔI' c(i)e It represents the load reduction power increment correction of sample c(i) at load level e.

[0173] Among them, the cumulative probability of low-order accident state in severe weather is P L The calculation expression of ' is:

[0174]

[0175] Among them, u i ' represents the unavailability rate of the ith line in bad weather; a j ' represents the availability of the jth line in bad weather.

[0176] Unavailability rate u of equivalent line i in bad weather eqi The calculation expression of ' is:

[0177]

[0178] Among them, u eqi ' is the repair rate of equivalent line i in severe weather, λ eqi ' is the failure rate of equivalent line i in severe weather.

[0179] Availability a of equivalent line j in bad weather eqj The calculation expression of ' is:

[0180]

[0181] Among them, μ j' is the repair rate of equivalent line j in bad weather, λ j ' is the failure rate of equivalent line j in bad weather

[0182] S6. Calculate the variance coefficient based on the estimated value of the high-order part of the expected power shortage, and the calculation expression is:

[0183]

[0184] Where β is the variance coefficient of the high-order part estimate of the expected power shortage, is the high-order estimate of the expected power shortage, for expectations; for The variance of .

[0185] S7: If the variance coefficient of the estimated value of the expected power shortage for the whole year is greater than or equal to the preset algorithm termination threshold, go to S1; if it is less than the preset algorithm termination threshold, output the high-order estimated value of the expected power shortage during the bad weather period.

[0186] Finally, the estimated value of the expected power shortage during normal weather periods, the estimated value of the low-order part of the expected power shortage during severe weather periods, and the estimated value of the high-order part are added together to obtain the estimated value of the expected power shortage of the distribution system throughout the year. The calculation expression is:

[0187]

[0188] c(i)∈C H

[0189] Among them, R EENS is the expected power shortage of the distribution system throughout the year, R EENSn is the expected power shortage of the distribution system during normal weather periods, R EENSs1 R is the low-order part of the expected power shortage during bad weather periods. EENSs2 This is the high-level portion of power shortage expected during severe weather periods.

[0190] The risk level of the distribution system is judged according to the estimated value of the expected power shortage of the distribution system. The larger the estimated value of the expected power shortage of the distribution system is, the higher the risk level of the distribution system is.

[0191] Embodiment 2:

[0192] Based on Example 1, this embodiment further provides a distribution system risk assessment system considering the impact of severe weather, including:

[0193] Memory for storing computer programs;

[0194] A processor is used to execute the computer program to implement the steps of the distribution system risk assessment method considering the impact of severe weather as described in Example 1.

[0195] The present invention first uses a distribution system dimensionality reduction technology based on switch layout to equate multiple lines in the evaluated distribution system to one, thereby improving the calculation efficiency of EENS risk indicators in the subsequent process. Unlike the transmission system, the distribution system usually only arranges switches (including circuit breakers and disconnectors) on important lines. Therefore, the shutdown of a line will cause the shutdown of multiple related lines. From a risk perspective, these lines can be equivalent to one line.

[0196] Then, according to the risk parameters of equivalent components after system dimension reduction, a steady-state probability model of components and systems based on homogeneous Markov process was established. This model takes into account the temporal correlation between the period of occurrence of regular severe weather and the load level and simplifies its own complexity by using reasonable assumptions, so that accurate risk indicators can be obtained with high efficiency.

[0197] In order to further improve the calculation efficiency of EENS indicators, an extended branch set decoupling technology (Extended Branch Set Decoupling, EBSD) is proposed on the basis of branch set decoupling technology (Branch Set Decoupling, BSD) and the contingency space partitioning technology (Contingency Space Partition, CSP) is introduced. These two technologies can significantly reduce the number of state analysis without reducing the evaluation accuracy. Considering the trend of complexity of the distribution system, the present invention uses power flow analysis instead of traditional analysis (i.e., connectivity analysis) to obtain the impact of the accident state of the distribution system. In addition, in order to consider the temporal correlation between severe weather and load, a new risk indicator calculation model is proposed.

[0198] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A distribution system risk assessment method considering the impact of severe weather, characterized in that: include: Calculate an estimate of the expected shortfall in power for the distribution system during normal weather periods and the lower-order portion of the expected shortfall in power during severe weather periods during a year, including; Obtain power flow data of the distribution system, annual severe weather time series data, and risk parameters of the lines; Based on the distribution system structure and switch layout, the distribution system lines are equivalent to reduce the distribution system dimension, and the risk parameters of the equivalent lines after dimensionality reduction are calculated; Based on the distribution system after dimensionality reduction, the accident state space is divided into low-order accident state space and high-order accident state space according to the order threshold; Calculate the load shedding power at all load levels for each low-order accident state in the low-order accident state subspace; According to the load shedding power, the load shedding power increment and the load shedding power increment correction amount of all low-order accident states are calculated; The estimated value of the expected power shortage of the distribution system during normal weather periods and the low-order part of the expected power shortage during bad weather periods are calculated respectively by using the load reduction power increment and the load reduction power increment correction of all low-order accident states; Calculate a high-level estimate of the expected shortfalls in the distribution system during severe weather events over the course of a year, including: S1. extracting a high-order accident state sample from the high-order accident state subspace; S2. Determine whether the outage branch corresponding to the high-order accident state sample is a feeder. If all the outage branches are feeders, set the load reduction power increment correction amount of the high-order accident state sample to 0, and go to S5; if not all the outage branches are feeders, go to S3; S3. Using power flow analysis software to obtain the load shedding power of the high-order accident state at the load level during the bad weather period; S4, calculating the load reduction power increment correction amount under the load level during the severe weather period for the high-order accident state; S5. Calculate an estimated value of the high-order portion of the expected power shortage during the severe weather period; S6. Calculate the variance coefficient β based on the estimated value of the high-order part of the expected power shortage EENS ; S7. If the variance coefficient of the estimated value of the expected power shortage throughout the year is greater than or equal to the preset algorithm termination threshold β EENS_con , then go to S1, if it is less than the preset algorithm termination threshold, calculate the high-order part estimate of the expected power shortage during the bad weather period The estimated value of the expected power shortage during normal weather periods, the estimated value of the low-order part and the high-order part of the expected power shortage during severe weather periods are added together to obtain the estimated value of the expected power shortage of the distribution system throughout the year; The risk level of the distribution system is determined according to the estimated value of the expected power shortage of the distribution system. The larger the estimated value of the expected power shortage of the distribution system is, the higher the risk level of the distribution system is. Among them, the low-order part is the contribution of the low-order accident state to the expected power shortage, the high-order part is the contribution of the high-order accident state to the expected power shortage, and the accident state is the state of the distribution system when the line is out of service.

2. The method for risk assessment of power distribution system considering the impact of severe weather according to claim 1, characterized in that: The order of the accident state is determined by the number of outage lines in the power distribution system. When the number of outage lines in the power distribution system is n, it is an n-order accident state. The low-order accident state is a state in which the order is not higher than a set order threshold, and the high-order accident state is a state in which the order is higher than the set order threshold.

3. The risk assessment method for power distribution system considering the impact of severe weather according to claim 1 is characterized in that: The flow data includes an annual load curve, the severe weather time series data includes the occurrence time and duration of severe weather in a year, the lines include overhead lines and non-overhead lines, and the risk parameters include failure rate and repair rate.

4. The method for risk assessment of power distribution system considering the impact of severe weather according to claim 1, characterized in that: Based on the structure of the distribution system and the switch arrangement, the distribution system lines are equivalent to reduce the dimension of the distribution system, and the risk parameters of the equivalent lines after dimensionality reduction are calculated, including: the lines in the distribution system that meet the series logic are equivalent to one line, where the lines that meet the series logic indicate that the outage of any one line in the line set will cause the outage of the remaining lines; The calculation expression of the risk parameter of the equivalent circuit is: Among them, λ eq is the failure rate of the equivalent circuit, μ eq is the repair rate of the equivalent line, λ i is the failure rate of the ith line, λ j is the failure rate of the jth line, μ i is the repair rate of the ith line, μ j is the repair rate of the jth line, i≠j; When the number of lines in the power distribution system that satisfy the series logic is 2, the calculation is performed directly using formula (1); When the number of lines that meet the series logic in the distribution system is greater than 2, two of the lines are first equivalent to one line through formula (1), and then the equivalent line is equivalent to the remaining lines according to formula (1) in turn until all lines are equivalent to one line, and the parameters used in the subsequent equivalent calculation are all the equivalent parameters obtained in the previous calculation.

5. The method for risk assessment of power distribution system considering the impact of severe weather according to claim 1, characterized in that: The load shedding power is directly calculated by power flow calculation software; The calculation expression of the load reduction power increment is: Where c represents the accident state, which is represented by the set of outage equivalent lines, ΔI cl represents the load shedding power increment under the accident state c at load level l, n c represents the number of outage equivalent lines corresponding to the accident state c, that is, the order of the accident state c, w is the low-order accident state corresponding to the accident state c, I w is the load reduction power of the low-order accident state corresponding to the accident state c, represents the set of low-order accident states of order k corresponding to the accident state c, The calculation expression of the load reduction power increment correction amount is: Among them, ΔI c ' l represents the load reduction power increment correction amount of state c at load level l, A represents the set of all equivalent lines in the system that may be out of service; Ac represents the set of elements in A but not in c; a eqi represents the availability of equivalent line i under normal weather conditions; The availability rate a of the equivalent line i under normal weather conditions eqi The calculation expression is: Among them, μ eqi is the repair rate of equivalent line i under normal weather conditions, λ eqi is the failure rate of equivalent line i under normal weather conditions; The calculation expression of the estimated value of the expected power shortage of the power distribution system during normal weather periods is: Among them, R EENSn is the expected power shortage of the distribution system during normal weather periods, l is the load level, c L is the low-order state subspace, L d is the set of all load levels, c represents the accident state, C is the accident state space, n L is the order threshold, P c is the probability of occurrence of accident state c during normal weather period, I cl represents the load shedding power in the accident state c at load level l, D l represents the duration of load level l during normal weather periods, A represents the set of all equivalent lines in the distribution system that may experience outages, and u eqi represents the unavailability rate of equivalent line i under normal weather conditions, ΔI cl represents the load shedding power increment under the accident state c at load level l, represents the set of accident states with outage order k; The unavailability rate u of the equivalent line i under normal weather conditions is eqi The calculation expression is: Among them, μ eqi is the repair rate of equivalent line i under normal weather conditions, λ eqi is the failure rate of equivalent line i under normal weather conditions; The calculation expression of the low-order part of the expected power shortage of the distribution system during the bad weather period is: Among them, R EENSs1 P is the low-order portion of the distribution system that is expected to be short of power during severe weather periods. c ' represents the probability of occurrence of accident state c in bad weather; ΔI c ' e It represents the load reduction power increment correction value under load level e in state c, D e Indicates the duration of severe weather.

6. The method for risk assessment of power distribution system considering the impact of severe weather according to claim 1, characterized in that: The calculation expression for the estimated value of the high-order part of the expected power shortage during severe weather periods is: Among them, R EENSs2 is the high-order portion of the expected power shortage during severe weather periods, P c ' represents the probability of occurrence of accident state c in bad weather, P L ' is the cumulative probability of low-order accident states under severe weather conditions, Card(A) represents the number of elements in set A, C H is the high-order accident state subspace, c(i) represents the i-th accident state sample, N represents the number of accident state samples required to meet the termination criterion, ΔI′ c(i)e represents the load reduction power increment correction of sample c(i) at load level e, n L is the order threshold; Among them, the cumulative probability of low-order accident state in severe weather is P L The calculation expression of ' is: In the formula, u eqi ' represents the unavailability rate of the i-th equivalent line in bad weather, a eqj ' represents the availability of the jth equivalent line in bad weather, n L is the order threshold; The unavailability rate u of the equivalent line i in bad weather eqi The calculation expression of ' is: Among them, u eqi ' is the repair rate of equivalent line i in severe weather, λ eqi ' is the failure rate of equivalent line i in bad weather; The availability rate a of the equivalent line j in bad weather eqj The calculation expression of ' is: Among them, μ eqj ' is the repair rate of equivalent line j in bad weather, λ eqj ' is the failure rate of equivalent line j in bad weather; The calculation expression for calculating the variance coefficient based on the estimated value of the high-order part of the expected power shortage is: In the formula, β EENS is the variance coefficient of the estimated value of the high-order part of the expected power shortage, is the high-order estimate of the expected power shortage, for expectations; for The variance of .

7. The method for risk assessment of power distribution system considering the impact of severe weather according to claim 1, characterized in that: The calculation expression of the estimated value of the expected power shortage of the power distribution system throughout the year is: Among them, R EENS is the expected power shortage of the distribution system throughout the year, R EENSn is the expected power shortage of the distribution system during normal weather periods, R EENSs1 R is the low-order part of the expected power shortage during bad weather periods. EENSs2 This is the high-level portion of power shortage expected during severe weather periods.

8. A power distribution system risk assessment system considering the impact of severe weather, characterized in that: include: Memory for storing computer programs; A processor is used to execute the computer program to implement the steps of the distribution system risk assessment method considering the impact of severe weather as described in any one of claims 1 to 7.

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