Data operation and maintenance method and control system based on secondary equipment

Abstract

The invention discloses a data operation and maintenance method and control system based on secondary equipment, and the method comprises the steps: collecting a plurality of pieces of time sequence data during normal operation and a plurality of pieces of time sequence data during fault in the secondary equipment, and constructing a training set and a test set; intercepting the normalized time sequence data according to the window length to obtain a plurality of input sequences; constructing and training an LSTM neural network model, and stopping training until the prediction accuracy of the LSTM neural network model in the test set reaches a preset precision requirement; and comparing the obtained output sequence with model parameters, and generating data for storage. According to the method, archiving storage and data sharing of the operation and maintenance data are realized; an information fusion technology of a relay protection test result and mobile operation and maintenance inspection is further realized, data sharing is facilitated, and the working efficiency is improved; meanwhile, the secondary professional digital management level is improved, and safe and stable operation of a large power grid is supported.

Description

Technical Field

[0001] The present invention relates to the technical field of feeder automation, and in particular to a data operation and maintenance method and a control system based on secondary equipment. Background Art

[0002] With the emergence of smart grids, the intelligence level of substation secondary equipment has been rapidly improved, and its number is also gradually increasing. There are also higher requirements for the professional and technical level of relevant personnel in the operation, management, and maintenance of equipment. Only by doing a good job in the operation and maintenance of smart grid secondary equipment can the service life of smart grids be increased and the smooth application of smart grids be ensured.

[0003] The number of substations is developing rapidly. The operation and maintenance quality and management level of secondary equipment are directly related to the production efficiency of the enterprise and the safe and stable operation of the equipment. At present, each team mainly relies on manual operation to control the relay protection relay to carry out the maintenance of relay protection devices. On the one hand, the level of maintenance personnel is uneven, and the quality of commissioning is difficult to guarantee. Although there are guiding documents such as commissioning operation instructions to guide team members to carry out relevant testing work, the configuration of test parameters according to the operation instructions is more dependent on the technical level of the commissioning personnel, and 100% correctness cannot be guaranteed. Some projects require repeated testing many times, resulting in low efficiency in the maintenance of relay protection devices. On the other hand, the workload of recording secondary equipment test data is large and the debugging efficiency is low. A large number of relay protection devices are repeatedly tested, the data is very large, and there is a lack of automatic analysis. After the test is completed, the report needs to be manually sorted, and the paper report is easily lost and damaged, which is not conducive to archiving and data sharing. Therefore, it is necessary to establish an automatic testing model for relay protection devices based on mobile Internet technology, and propose information fusion technology for relay protection test results and mobile operation and maintenance inspection, so as to facilitate data sharing, improve work efficiency, enhance the level of secondary professional digital management, and support the safe and stable operation of large power grids. Summary of the invention

[0004] Technical purpose: In view of the defects in the prior art, the present invention discloses a data operation and maintenance method and control system based on secondary equipment. The LSTM neural network model is obtained through training, and then the historical time series data in the secondary equipment is used to obtain the predicted output results within a period of time, thereby realizing the archiving and sharing of operation and maintenance data; further realizing the information fusion technology of relay protection test results and mobile operation and maintenance inspection, facilitating data sharing and improving work efficiency; at the same time, improving the level of secondary professional digital management, and supporting the safe and stable operation of large power grids.

[0005] Technical solution: In order to achieve the above technical objectives, the present invention adopts the following technical solution.

[0006] A data operation and maintenance method based on secondary equipment includes the following steps:

[0007] Step S1: Use the mobile operation and maintenance job template in the mobile operation and maintenance and relay protection instrument to collect the time series data of several normal operations and several faults in the secondary equipment, build a training set and a test set; and send them to the mobile operation and maintenance APP;

[0008] Step S2: normalize all the time series data in the training set and the test set respectively, and truncate the normalized time series data according to the window length S to obtain several input sequences X;

[0009] Step S3, constructing and training an LSTM neural network model, and stopping the training until the prediction accuracy of the LSTM neural network model in the test set reaches a preset accuracy requirement, thereby obtaining a trained LSTM neural network model;

[0010] Step S4, obtaining the historical time series data in the secondary device to be detected, normalizing it in step S2, and inputting it into the LSTM neural network model trained in step S3; comparing the obtained output sequence with the model parameters, generating data and saving it in the relay protection instrument;

[0011] Step S5: The relay protection instrument tests the instantiation work and returns the result to the mobile terminal APP after the test is completed; the mobile operation and maintenance inspection module parses the file sent back by the relay protection instrument and displays the test results; after the mobile operation and maintenance inspection task is submitted, the inspection data is submitted to the relay protection integration platform to archive the test results and generate an inspection report.

[0012] Preferably, the time series data in step S1 includes the position state of the switch in the secondary device within a period of time, the grid current, and the grid voltage; the expression formula of the time series data is:

[0013] {(State1,V1,I1),(State2,V2,I2),...,(State t ,V t ,I t ),...,(State T ,V T ,I T )},1≤t≤Twhere,State t is the position state of the switch at the tth time point, V t is the grid voltage at the tth time point, I t is the grid current at the tth time point; T is the time series length.

[0014] Preferably, the expression formula of the input sequence X in step S2 is:

[0015] X={X1,X2,...,X s,...,X S}=

[0016] {(State1,V1,I1),(State2,V2,I2),...,(State s ,V s ,I s ),...,(State S ,V S ,I S )},1≤s≤S

[0017] Among them, State s is the position state of the switch at the sth time point, V s is the grid voltage at the sth time point,

[0018] I s is the grid current at the sth time point; the window length S is less than the time series length T.

[0019] Preferably, step S3 comprises the following steps:

[0020] Step S31, the LSTM neural network model is composed of S LSTM networks in parallel, and its input is the grouped training set, that is, a number of input sequences X; the output is the output sequence Y, that is, the prediction sequence;

[0021] Step S32, according to the position state of the switch in all output sequences Y, the grid voltage and the grid current, respectively fitting the model parameters of the LSTM neural network model, including the position state threshold of the switch, the grid voltage threshold and the grid current threshold;

[0022] Step S33, input the grouped test set into the LSTM neural network model to obtain an output sequence corresponding to each input sequence, and determine whether the position state of the switch, the grid voltage and the grid current corresponding to the last time point in the output sequence exceed the position state threshold of the switch, the grid voltage threshold and the grid current threshold fitted in step S32, if so, determine that the input sequence belongs to the time series data when a fault occurs, if not, determine that the input sequence belongs to the time series data when normal operation occurs;

[0023] Step S34, determine whether the fault prediction accuracy in the test set reaches the preset accuracy requirement. If so, stop training and obtain the trained LSTM neural network model; if not, return to step S31 to continue the model sequence and fit new model parameters.

[0024] Preferably, the calculation process of the output sequence Y in step S31 includes:

[0025] Step S311: The initialization unit state of the LSTM neural network model is preset to INIT0, and the input sequence X is combined with INIT0 to generate a set SN, SN = {[X1,h0], [X2,h0], ..., [X s ,h0],...,[X S ,h0]}, where h0 is the hidden state of the LSTM neural network model;

[0026] Step S312: After the set SN enters S LSTM networks, the memory information set M, the forgetting information ratio set FO and the output sequence Y are calculated; wherein the memory information set M = {M1, M2, ..., M s ,...,M S},M s For X s After the sth LSTM network remembers part of the information, the forgotten information ratio set FO={FO1,FO2,...,FO s ,...,FO S}, FO s For X s The corresponding proportion information of the forgotten content, the output sequence Y = {Y1,Y2,...,Y s ,...,Y S},Y s For X s The corresponding output:

[0027] Step S313: Obtain a unit state set U={U1, U2, ..., U s ,...,U S}, where U s is the state of the sth unit, that is, X s The corresponding unit status;

[0028] Step S314: s As the memory state of the first input sequence, when the second input sequence is input into the LSTM neural network model, U s Assign the initialization unit state to INIT0 and return to step S311 to perform calculation until the output sequence of each input sequence is calculated.

[0029] Preferably, the model parameters are fitted using the least squares method to obtain a fitting curve of the model parameters and time. When the model parameters are used, the model parameter values ​​at corresponding time points are searched on the fitting curve.

[0030] A fault prediction control system based on secondary equipment comprises a plurality of secondary equipment, power distribution terminals connected to the secondary equipment in a one-to-one correspondence, relay protection instruments connected to the power distribution terminals and the secondary equipment in a one-to-one correspondence, a relay protection integration platform and a human-machine interactive display screen, wherein the relay protection integration platform is connected to the human-machine interactive display screen and all the relay protection instruments; the secondary equipment is used to obtain grid current and grid voltage from the power distribution terminals, the relay protection instruments are used to collect timing data and feed it back to the relay protection integration platform, and the relay protection integration platform executes any of the above-mentioned data operation and maintenance methods based on secondary equipment, and displays the data analysis results through the human-machine interactive display screen.

[0031] Preferably, the secondary equipment includes a switch, the switch is connected to the distribution terminal, the distribution terminal is connected to the relay, and the relay is connected to the switch and relay protection integrated platform; wherein the relay obtains the grid current and grid voltage from the distribution terminal according to the interface acquisition function of the switch; the timing data includes the position status of the switch in the secondary equipment over a period of time, the grid current, and the grid voltage.

[0032] Beneficial effect: The present invention obtains an LSTM neural network model through training, and then obtains the output results within a predicted period of time for the historical time series data in the secondary equipment. It can not only predict whether a fault will occur on the feeder, which is convenient for the staff to conduct early screening, but also obtain the cause of the fault, that is, predict whether the fault is related to the position state of the switch, the grid voltage, or the grid current, which greatly improves the maintenance efficiency of the staff and reduces the time cost.

[0033] The protection device function automatic verification relay completes automatic testing according to the protection device intelligent test model, and can automatically read the protection device action behavior, automatically check the debugging data, and automatically generate a test report. The testing workload of maintenance personnel is reduced from 4 hours / unit to 1.5 hours / unit.

[0034] The protection device test data is collected by locating the test device through the mobile terminal, establishing a data connection with the relay protection instrument through the Bluetooth communication module, collecting the test results, and generating a test report. The efficiency of manually collating the test report has been improved from the original 1 hour / device to 10 minutes / device.

[0035] The protection equipment intelligent test management mobile terminal is connected to the relay protection instrument to collect test results, and at the same time pushes the test result information to the inspection management module of the relay protection integration platform to uniformly manage the maintenance and debugging data and related reports, and the archiving rate of maintenance and debugging reports is increased to 90%. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the method of the present invention;

[0037] Figure 2 is a system block diagram of the present invention;

[0038] Figure 3 It is an implementation flow chart of the present invention. DETAILED DESCRIPTION

[0039] The following further describes and explains a data operation and maintenance method and system based on secondary equipment of the present invention in conjunction with the accompanying drawings.

[0040] As attached Figure 1 As shown, a data operation and maintenance method based on secondary equipment includes the following steps:

[0041] Step S1, collecting several normal operation time series data and several fault time series data of the secondary equipment, constructing a training set and a test set, and both the training set and the test set include the normal operation time series data and the fault time series data;

[0042] In some embodiments of the present invention, the ratio of the training set to the test set may be 8:2 or 7:3, and the specific value is selected according to the actual situation.

[0043] Among them, the secondary equipment includes switches, the switches are connected to the distribution terminals, the distribution terminals are connected to the relay protection instrument, and the relay protection instrument is connected to the switch and relay protection integrated platform; among them, the relay protection instrument obtains the grid current and grid voltage from the distribution terminal according to the interface acquisition function of the switch; the time series data includes the position status of the switch in the secondary equipment within a period of time, the grid current, and the grid voltage; the expression formula of the time series data is:

[0044] {(State1,V1,I1),(State2,V2,I2),...,(State t ,V t ,I t ),...,(State T ,V T ,I T )},1≤t≤Twhere,State t is the position state of the switch at the tth time point, V t is the grid voltage at the tth time point, I t is the grid current at the tth time point; T is the time series length;

[0045] Step S2: normalize all the time series data in the training set and the test set respectively, and truncate the normalized time series data according to the window length S to obtain several input sequences X, where the window length S is less than the time series length T; the expression formula of the input sequence X is:

[0046] X={X1,X2,...,Xs ,...,X S}=

[0047] {(State1,V1,I1),(State2,V2,I2),...,(State s ,V s ,I s ),...,(State S ,V S ,I S )},1≤s≤S

[0048] Among them, State s is the position state of the switch at the sth time point, V s is the grid voltage at the sth time point,

[0049] I s is the grid current at the sth time point;

[0050] Step S3, constructing and training an LSTM neural network model, and stopping the training until the fault prediction accuracy of the LSTM neural network model in the test set reaches a preset accuracy requirement, thereby obtaining a trained LSTM neural network model;

[0051] Step S3 includes the following steps:

[0052] Step S31, the LSTM neural network model includes S parallel LSTM networks, whose input is the grouped training set, that is, a number of input sequences X; the output is the output sequence Y, that is, the prediction sequence, including:

[0053] Step S311: The initialization unit state of the LSTM neural network model is preset to INIT0, and the input sequence X is combined with INIT0 to generate a set SN, SN = {[X1,h0], [X2,h0], ..., [X s ,h0],...,[X S ,h0]}, where h0 is the hidden state of the LSTM neural network model;

[0054] Step S312: After the set SN enters S LSTM networks, the memory information set M, the forgetting information ratio set FO and the output sequence Y are calculated; wherein the memory information set M = {M1, M2, ..., M s ,...,M S},

[0055] M s For X s After the sth LSTM network remembers part of the information, the proportion of forgotten information is set

[0056] FO={FO1,FO2,...,FO s ,...,FO S}, FO s For X s The corresponding proportion information of the forgotten content, the output sequence Y = {Y1,Y2,...,Y s ,...,Y S},Y s For X s The corresponding output:

[0057] Step S313: Obtain a unit state set U={U1, U2, ..., U s ,...,U S}, where U s is the state of the sth unit, that is, X s The corresponding unit status;

[0058] Step S314: s As the memory state of the first input sequence, when the second input sequence is input into the LSTM neural network model, U s Assign the initialization unit state to INIT0 and return to step S311 to perform calculation until the output sequence of each input sequence is calculated;

[0059] Step S32, according to the position state of the switch in all the output sequences Y, the grid voltage and the grid current, respectively fit the model parameters of the LSTM neural network model, including the position state threshold of the switch, the grid voltage threshold and the grid current threshold; the position state threshold of the switch, the grid voltage threshold and the grid current threshold in the model parameters of the present invention are a numerical range, that is, the numerical range of the position state of the switch, the grid voltage and the grid current during normal operation. When a fault is about to occur somewhere, the position state of the corresponding switch, the grid voltage and the grid current will fluctuate in value, that is, they are not within the values ​​of the position state of the switch, the grid voltage and the grid current during normal operation. Therefore, in the present invention, fault prediction is performed according to the model parameters obtained by fitting.

[0060] In the present invention, the model parameters are fitted by the least square method to obtain a fitting curve of the model parameters and time. When the model parameters are used, the model parameter values ​​at corresponding time points are found on the fitting curve.

[0061] Step S33, input the grouped test set into the LSTM neural network model to obtain an output sequence corresponding to each input sequence, and determine whether the position state of the switch, the grid voltage and the grid current corresponding to the last time point in the output sequence exceed the position state threshold of the switch, the grid voltage threshold and the grid current threshold fitted in step S32, if so, determine that the input sequence belongs to the time series data when a fault occurs, if not, determine that the input sequence belongs to the time series data when normal operation occurs;

[0062] Step S34: determine whether the fault prediction accuracy in the test set reaches the preset accuracy requirement. If so, stop training and obtain the trained LSTM neural network model; if not, return to step S31 to continue the model sequence and fit new model parameters;

[0063] In the present invention, if the LSTM neural network model fails to meet the preset accuracy requirements, the ratio of the training set and the data set can be readjusted, or the data in the training set and the data set can be expanded.

[0064] Step S4, obtaining the historical time series data in the secondary equipment to be detected, normalizing it in step S2, and inputting it into the LSTM neural network model trained in step S3; comparing the obtained output sequence with the model parameters, predicting whether a fault will occur on the corresponding feeder and the cause of the fault, that is, predicting whether the fault is related to the position state of the switch, the grid voltage, or the grid current.

[0065] The present invention obtains an LSTM neural network model through training, and then obtains the output results within a period of time predicted for the historical time series data in the secondary equipment. Figure 3 As shown, the implementation process of the present invention includes: 1) the mobile operation and maintenance job template formulates a test template according to the operation instruction and sends it to the mobile operation and maintenance inspection module, and the relay protection instrument test template formulates a test template according to the operation instruction and sends it to the relay protection instrument. 2) When doing a certain inspection, the mobile operation and maintenance inspection module currently inspects the project and sends it to the relay protection instrument in the form of json. 3) The relay protection instrument performs the test instantiation work for testing, and returns the result to the mobile terminal APP after the test is completed. The mobile operation and maintenance inspection module parses the file returned by the relay protection instrument and displays the test results. 4) After the mobile operation and maintenance inspection task is submitted, the inspection data is submitted to the relay protection integration platform, the test results are archived and an inspection report is generated. Not only can it predict whether a fault will occur on the feeder, which is convenient for the staff to screen in advance, but also the cause of the fault can be obtained, that is, it is predicted whether the fault is related to the position state of the switch, or the grid voltage, or the grid current, which greatly improves the maintenance efficiency of the staff and reduces the time cost.

[0066] As attached Figure 2 As shown, the present invention also discloses a control system based on data operation and maintenance of secondary equipment, including several secondary equipment, distribution terminals connected one-to-one with the secondary equipment, relay protection instruments connected one-to-one with the distribution terminals and the secondary equipment, a relay protection integrated platform and a human-machine interactive display screen, the relay protection integrated platform is connected to the human-machine interactive display screen and all relay protection instruments; the secondary equipment is used to obtain the grid current and grid voltage from the distribution terminal, the relay protection instrument is used to collect timing data and feed it back to the relay protection integrated platform, the relay protection integrated platform executes any of the above-mentioned data operation and maintenance methods based on secondary equipment, and displays the prediction results through the human-machine interactive display screen. The entire control system realizes communication through CAN communication and 4G wireless network.

[0067] The secondary equipment includes switches, which are connected to the power distribution terminal, which is connected to the relay protection instrument, which is connected to the switch and relay protection integrated platform; the relay protection instrument obtains the grid current and grid voltage from the power distribution terminal according to the interface acquisition function of the switch; the time series data includes the position status of the switch in the secondary equipment within a period of time, the grid current and the grid voltage;

[0068] The system provided by the present invention has simple wiring, is easy to install, is applicable to the existing feeder automation system, and has low additional production cost.

[0069] 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 principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A data operation and maintenance method based on secondary equipment, characterized in that: The following steps are involved: Step S1, using the mobile operation and maintenance job template in the mobile operation and maintenance and relay protection instrument to collect the time series data of several normal operations and several time series data of failures in the secondary equipment, and construct a training set and a test set; Send to mobile operation and maintenance APP; Step S2: normalize all the time series data in the training set and the test set respectively, and truncate the normalized time series data according to the window length S to obtain several input sequences X; Step S3, constructing and training an LSTM neural network model, and stopping the training until the prediction accuracy of the LSTM neural network model in the test set reaches a preset accuracy requirement, thereby obtaining a trained LSTM neural network model; Step S4, obtaining the historical time series data in the secondary device to be detected, normalizing it in step S2, and inputting it into the LSTM neural network model trained in step S3; comparing the obtained output sequence with the model parameters, generating data and saving it in the relay protection instrument; Step S5: The relay protection instrument tests the instantiation work and returns the result to the mobile terminal APP after the test is completed; The mobile operation and maintenance inspection module analyzes the files sent back by the relay protection instrument and displays the test results; After the mobile operation and maintenance inspection task is submitted, the inspection data will be submitted to the integrated relay protection platform to archive the test results and generate an inspection report.

2. According to claim 1, a data operation and maintenance method based on secondary equipment is characterized in that: The time series data in step S1 includes the position state of the switch in the secondary device within a period of time, the grid current, and the grid voltage; the expression formula of the time series data is: {(State1, V1, I1), (State2, V2, I2),..., (State, V t , I t ),..., (State T , V T , I T ),}, 1 ≤ t ≤ T where,​ State t is the position state of the switch at the tth time point, V t is the grid voltage at the tth time point, I t is the grid current at the tth time point; T is the time series length.

3. The data operation and maintenance method based on secondary equipment according to claim 1 is characterized in that: The expression formula of the input sequence X in step S2 is: X={X1,X2,…,X s ,…,X S }= {(State1, V1, I1), (State2, V2, I2),...,(State s , V s , I s ),...,(State S , V S , I S ),..., (State )}, 1 ≤ s ≤ S where, State s is the position state of the switch at the sth time point, V s is the grid voltage at the sth time point, I s is the grid current at the sth time point; the window length S is less than the time series length T.

4. The data operation and maintenance method based on secondary equipment according to claim 1, characterized in that: Step S3 includes the following steps: Step S31, the LSTM neural network model is composed of S LSTM networks in parallel, and its input is the grouped training set, that is, a number of input sequences X; the output is the output sequence Y, that is, the prediction sequence; Step S32, according to the position state of the switch in all output sequences Y, the grid voltage and the grid current, respectively fitting the model parameters of the LSTM neural network model, including the position state threshold of the switch, the grid voltage threshold and the grid current threshold; Step S33, input the grouped test set into the LSTM neural network model to obtain an output sequence corresponding to each input sequence, and determine whether the position state of the switch, the grid voltage and the grid current corresponding to the last time point in the output sequence exceed the position state threshold of the switch, the grid voltage threshold and the grid current threshold fitted in step S32, if so, determine that the input sequence belongs to the time series data when a fault occurs, if not, determine that the input sequence belongs to the time series data when normal operation occurs; Step S34, determine whether the prediction accuracy in the test set reaches the preset accuracy requirement. If so, stop training and obtain the trained LSTM neural network model; if not, return to step S31 to continue the model sequence and fit new model parameters.

5. A data operation and maintenance method based on secondary equipment according to claim 4, characterized in that: The calculation process of the output sequence Y in step S31 includes: Step S311: The initialization unit state of the LSTM neural network model is preset to INIT0, and the input sequence X is combined with INIT0 to generate a set SN, SN = {[X1,h0], [X2,h0], ..., [X s ,h0],...,[X S ,h0]}, where h0 is the hidden state of the LSTM neural network model; Step S312: After the set SN enters S LSTM networks, the memory information set M, the forgetting information ratio set FO and the output sequence Y are calculated; wherein the memory information set M = {M1, M2, ..., M s ,...,M S },M s For X s After the sth LSTM network remembers part of the information, the forgotten information ratio set FO={FO1,FO2,...,FO s ,...,FO S }, FO s For X s The corresponding proportion information of the forgotten content, the output sequence Y = {Y1,Y2,...,Y s ,...,Y S },Y s For X s The corresponding output: Step S313: Obtain a unit state set U={U1, U2, ..., U s ,...,U S }, where U s is the state of the sth unit, that is, X s The corresponding unit status; Step S314: s As the memory state of the first input sequence, when the second input sequence is input into the LSTM neural network model, U s Assign the initialization unit state to INIT0 and return to step S311 to perform calculation until the output sequence of each input sequence is calculated.

6. A data operation and maintenance method based on secondary equipment according to claim 4, characterized in that: The model parameters are fitted using the least squares method to obtain a fitting curve between the model parameters and time. When the model parameters are used, the model parameter values ​​at the corresponding time points are found on the fitting curve.

7. A data operation and maintenance control system based on secondary equipment, characterized in that: It includes several secondary devices, distribution terminals connected to the secondary devices in a one-to-one correspondence, relay protection instruments connected to the distribution terminals and secondary devices in a one-to-one correspondence, a relay protection integration platform and a human-computer interaction display screen, and the relay protection integration platform is connected to the human-computer interaction display screen and all relay protection instruments; the secondary devices are used to obtain grid current and grid voltage from the distribution terminals, the relay protection instruments are used to collect timing data and feed it back to the relay protection integration platform, and the relay protection integration platform executes a data operation and maintenance method based on secondary devices as described in any one of claims 1-6, and displays the prediction results through the human-computer interaction display screen.

8. The data operation and maintenance control system based on secondary equipment according to claim 7, characterized in that: The secondary equipment includes switches, which are connected to distribution terminals, which are connected to relays, and which are connected to the integrated platform of switches and relay protection. The relays obtain grid current and grid voltage from the distribution terminals based on the interface acquisition function of the switches. The timing data includes the position status of the switches, grid current, and grid voltage in the secondary equipment over a period of time.

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