CN112487710B - Power distribution network protection configuration optimization method and system - Google Patents
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Abstract
The invention discloses a power distribution network protection configuration optimization method and a system, which belong to the technical field of relay protection of power systems and comprise the following steps: according to a real-time operation mode, the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers are obtained, and an initial group of the outgoing line unit is randomly generated based on tide distribution; calculating fitness functions of all groups and recording optimal chromosomes; selecting crossed and mutated individuals to form a new generation population; calculating the fitness function of the new population, and recording the final individuals; judging whether the maximum iteration number is reached, ending the cycle if the maximum iteration number is reached, outputting the optimal individual, and otherwise, carrying out the cross mutation operation again. The method and the device for identifying the main line and the branch line by combining the real-time tide have the advantages that the reliability of the setting value of the power distribution network is improved, the power failure range of the power distribution network is reduced, and the safe and reliable operation of the power distribution network is ensured.
Description
Technical Field
The invention relates to the technical field of relay protection of power systems, in particular to a power distribution network protection configuration optimization method and system.
Background
The power distribution network is used as the last link of a power transmission and distribution system, closely contacts with terminal power utilization users, and the safe and stable operation of the power distribution network is the guarantee of high-quality and high-reliability power utilization of the users, so that the relay protection of the power distribution network serving as the first defense line of the safe operation of the power distribution network is particularly important. The distribution network switch is divided into four types of outlet switch, main line segment switch, branch switch and user demarcation switch. The configuration of the overhead distribution line protection in China is generally divided into secondary protection and tertiary protection according to actual setting conditions, and as the grid structure of the distribution network is complex, T wiring paths are more and change frequently, the fixed value of each level of switch is not accurate enough in actual setting, and the coordination among different levels is realized mainly by time level difference. Taking a certain ground distribution network as an example, three-level protection is mainly adopted, namely zero-level protection, one-level protection and two-level protection, each level adopts three-section overcurrent protection, and the time limit of the I section of each level of protection in actual setting is 0s; the time limit obtained by matching the II-stage time limit of the zero-level protection with the backup protection of the upper-level transformer is generally 0.6s, and the time limit of the II-stage time limit of the first-level protection and the second-level protection obtained by adopting a time level difference mechanism of 0.2s is respectively 0.4s and 0.2s; the time limit of the III section of the zero-level protection and the time limit obtained by matching the backup protection of the upper-level transformer are generally 1.0s, and the time limit of the III section of the first-level protection and the time limit of the III section of the second-level protection are respectively 0.8s and 0.6s by adopting a time level difference mechanism of 0.2 s.
Because of no unified standard, the protection configuration in actual setting is realized by human, the configuration is not reasonable, and the set value and time fixed value of each level of protection cannot completely adapt to the requirements of an actual power grid, so that the capability of guaranteeing the reliability of electricity utilization is greatly affected. The positions and the fixed values of the protection at each level are reasonably configured, when the power distribution network line breaks down, not only can the orderly tripping of each protection switch be realized, the power failure range is reduced, but also the power supply reliability of the power distribution network can be improved, so that the optimization of the protection configuration of the power distribution network line protection becomes a key research point.
Disclosure of Invention
The invention aims to overcome the defects in the background technology and improve the reliability of the setting value of the power distribution network.
In order to achieve the above object, on the one hand, a power distribution network protection configuration optimization method is adopted, which comprises the following steps:
s1, acquiring the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers;
S2, according to the opening and closing states and protection configuration of each breaker, generating an initial population of the outgoing line units randomly based on real-time tide distribution;
S3, calculating an fitness function of the initial population and recording an optimal individual;
s4, selecting individuals to carry out combination intersection and mutation according to the fitness of the individuals in the problem domain to obtain a new generation population;
S5, calculating a fitness function of the new generation population and recording an optimal individual;
S6, judging whether the target iteration times are reached, if yes, executing the step S7, and if not, executing the step S4;
And S7, ending the circulation and outputting the optimal individual.
Further, according to the opening and closing state and the protection configuration of each breaker, and based on real-time power flow distribution, an initial population of the outlet units is randomly generated, including:
determining a main line and a branch line of the power distribution network based on the real-time power flow;
adopting binary codes, and determining protection configuration codes of a main line and branch lines according to the opening and closing states and the protection configurations of the circuit breakers;
and combining the protection configuration codes of the main line and the protection configuration codes of the branch lines to obtain the coded individuals of the outlet units, and forming an initial population of the outlet units.
Further, the determining the trunk line and the branch line of the power distribution network based on the real-time power flow includes:
Starting from the outlet switch, searching all loads along the direction of each branch tide after encountering T connection, and taking the load and the largest load as a main line;
after all the main lines of the outlet units are found out, the rest are used as branch lines.
Further, the adoption of binary codes, according to the opening and closing state and the protection configuration of each breaker, determines the protection configuration codes of the trunk line and the branch line, and comprises the following steps:
grading operation is carried out on the circuit breakers which are in a closed state in the trunk line and the branch line and are provided with protection;
And (3) encoding the primary switch into 0, and encoding the secondary switch into 1 to respectively obtain the protection configuration code of the trunk line and the protection configuration code of the branch line.
Further, the fitness function of the initial population is the inverse of the objective function, and the objective function is: min (C), wherein C is annual outage loss cost of the power system, c= (a 1K+a2bd)WENS, K is power generation ratio, a 1 is power generation ratio weighting coefficient, a 2 is average power price conversion multiple method weighting coefficient, b is the ratio of unit outage power electricity price to average power price, d is average power price, and W ENS is expected shortage power supply amount of the power system;
The constraint conditions are as follows:
Wherein:
r is a system reliability index under a certain protection switch configuration mode;
R 0 is a reliability index required by planning;
V i is the i-th node voltage;
v imax is the maximum voltage allowed by node i;
V imin is the minimum voltage allowed by node i;
I i is the I-th branch current;
I imax is the maximum current allowed by the ith branch;
F max is the annual average maximum failure rate of the line.
Further, before the obtaining the opening and closing states of the circuit breakers of the outlet unit and the protection configuration of the circuit breakers, the method further includes:
Scanning an operation mode file, comparing the operation mode file obtained by scanning with the switch opening and closing state of the current operation mode file of the outlet unit, and judging whether the operation mode file is changed or not;
If yes, executing the step S2;
If not, the cycle is ended.
On the other hand, the power distribution network protection configuration optimizing system comprises an acquisition module, an initial population forming module, a first calculation module, a cross variation operation module, a second calculation module, a judgment module and an output module, wherein:
The acquisition module is used for acquiring the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers;
The initial population forming module is used for randomly generating an initial population of the outgoing line unit based on real-time tide distribution according to the opening and closing states and the protection configuration of each breaker;
The first calculation module is used for calculating the fitness function of the initial population and recording the optimal individuals;
The cross mutation operation module is used for selecting individuals to carry out combination cross and mutation according to the fitness of the individuals in the problem domain to obtain a new generation population;
the second calculation module is used for calculating the fitness function of the new generation population and recording the optimal individuals;
the judging module is used for judging whether the set iteration times are reached;
the output module is used for ending the circulation and outputting the optimal individual when the output result of the judging module is yes;
And the second calculation module is used for re-executing the steps when the output result of the judgment module is NO.
Further, the initial population forming module comprises a determining unit, a coding unit and a combining unit, wherein:
the determining unit is used for determining a main line and a branch line of the power distribution network based on the real-time power flow;
the coding unit is used for determining a protection configuration code of the main line and a protection configuration code of the branch line according to the opening and closing states and the protection configuration of each breaker by adopting binary codes;
The combination unit is used for combining the protection configuration codes of the main line and the protection configuration codes of the branch lines to obtain the coded individuals of the outlet units, so as to form an initial population of the outlet units.
Further, the determining unit is specifically configured to:
Starting from the outlet switch, searching all loads along the direction of each branch tide after encountering T connection, and taking the load and the largest load as a main line;
after all the main lines of the outlet units are found out, the rest are used as branch lines.
Further, the encoding unit is specifically configured to:
grading operation is carried out on the circuit breakers which are in a closed state in the trunk line and the branch line and are provided with protection;
And (3) encoding the primary switch into 0, and encoding the secondary switch into 1 to respectively obtain the protection configuration code of the trunk line and the protection configuration code of the branch line.
Further, the fitness function of the initial population is the inverse of the objective function, and the objective function is: min (C), wherein C is annual outage loss cost of the power system, c= (a 1K+a2bd)WENS, K is power generation ratio, a 1 is power generation ratio weighting coefficient, a 2 is average power price conversion multiple method weighting coefficient, b is the ratio of unit outage power electricity price to average power price, d is average power price, and W ENS is expected shortage power supply amount of the power system;
The constraint conditions are as follows:
Wherein:
r is a system reliability index under a certain protection switch configuration mode;
R 0 is a reliability index required by planning;
V i is the i-th node voltage;
v imax is the maximum voltage allowed by node i;
V imin is the minimum voltage allowed by node i;
I i is the I-th branch current;
I imax is the maximum current allowed by the ith branch;
F max is the annual average maximum failure rate of the line.
Compared with the prior art, the invention has the following technical effects: the hierarchical protection switch technology based on the improved genetic algorithm solves the problem that the set value cannot adapt to the actual tide caused by the manual non-unified standard hierarchical protection switch; and the main line and the branch line are identified by combining the real-time tide, so that the reliability of the setting value of the power distribution network is improved, the power failure range of the power distribution network is reduced, and the safe and reliable operation of the power distribution network is ensured.
Drawings
The following detailed description of specific embodiments of the invention refers to the accompanying drawings, in which:
FIG. 1 is a flow chart diagram of a method of optimizing protection configuration of a power distribution network;
FIG. 2 is a flow chart of another method of optimizing protection configuration of a power distribution network;
FIG. 3 is a schematic diagram of a power distribution network protection configuration optimization result;
Fig. 4 is a block diagram of a distribution network protection configuration optimization system.
Detailed Description
For a further description of the features of the present invention, refer to the following detailed description of the invention and the accompanying drawings. The drawings are for reference and illustration purposes only and are not intended to limit the scope of the present invention.
As shown in fig. 1, this embodiment discloses a power distribution network protection configuration optimization method, which includes the following steps:
s1, acquiring the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers;
S2, according to the opening and closing states and protection configuration of each breaker, generating an initial population of the outgoing line units randomly based on real-time tide distribution;
S3, calculating an fitness function of the initial population and recording an optimal individual;
s4, selecting individuals to carry out combination intersection and mutation according to the fitness of the individuals in the problem domain to obtain a new generation population;
S5, calculating a fitness function of the new generation population and recording an optimal individual;
S6, judging whether the target iteration times are reached, if yes, executing the step S7, and if not, executing the step S4;
And S7, ending the circulation and outputting the optimal individual.
It should be noted that, the initial population number of the randomly generated outgoing line units in this embodiment includes, but is not limited to, 600, and the target iteration number in this embodiment is the number corresponding to the time when the value of the objective function is minimum, where the inverse of the objective function is the fitness function.
As a further preferable embodiment, the step S2 is as follows: according to the opening and closing state and protection configuration of each breaker and based on real-time tide distribution, an initial population of outlet units is randomly generated, and the method comprises the following subdivision steps:
determining a main line and a branch line of the power distribution network based on the real-time power flow;
adopting binary codes, and determining protection configuration codes of a main line and branch lines according to the opening and closing states and the protection configurations of the circuit breakers;
and combining the protection configuration codes of the main line and the protection configuration codes of the branch lines to obtain the coded individuals of the outlet units, and forming an initial population of the outlet units.
As a further preferable aspect, the determining the trunk line and the branch line of the power distribution network based on the real-time power flow includes:
Starting from the outlet switch, searching all loads along the direction of each branch tide after encountering T connection, and taking the load and the largest load as a main line;
after all the main lines of the outlet units are found out, the rest are used as branch lines.
It should be noted that, the formation of the initial population is generated by adopting a random function, and because the distribution network has more branches, the main line needs to be determined first, and the main line is determined by adopting real-time tide, so that the main line of the outlet unit is obtained, and the rest is branch lines. According to the method, the device and the system, the identification of the trunk line and the branch line is fully combined with real-time tide, the reliability of the setting value of the power distribution network is greatly improved, the power outage range of the power distribution network is reduced, and the safe and reliable operation of the power distribution network is guaranteed.
As a further preferable solution, the determining, by binary code, a protection configuration code of a trunk line and a protection configuration code of a branch line according to the opening and closing states and the protection configurations of the circuit breakers includes:
grading operation is carried out on the circuit breakers which are in a closed state in the trunk line and the branch line and are provided with protection;
And (3) encoding the primary switch into 0, and encoding the secondary switch into 1 to respectively obtain the protection configuration code of the trunk line and the protection configuration code of the branch line.
The specific process of grading operation of the circuit breaker in the application is as follows: and the corresponding protection configuration switch stage number when the objective function is minimum is the stage number of the circuit breaker in the outgoing line unit, and the grading operation is completed.
In this embodiment, the binary code is adopted, and because the circuit breakers configured by the outgoing line units of the power distribution network are more, the codes are relatively complicated and affect the convergence effect, and in this embodiment, the classification operation is only performed on the closed switches configured with protection in the outgoing line units, if the primary switch is the primary switch, the code is 0, and the secondary switch code is 1, so that the protection configuration code of the trunk line and the protection configuration code of the branch line are respectively obtained, and the total code of the outgoing line units is obtained by combining as one chromosome.
As a further preferable scheme, the fitness function of the initial population is the inverse of an objective function, and the objective function is: min (C), wherein C is annual outage loss cost of the power system, c= (a 1K+a2bd)WENS, K is power generation ratio, a 1 is power generation ratio weighting coefficient, a 2 is average power price conversion multiple method weighting coefficient, b is the ratio of unit outage power electricity price to average power price, d is average power price, and W ENS is expected shortage power supply amount of the power system;
The constraint conditions are as follows:
Wherein:
r is a system reliability index under a certain protection switch configuration mode;
R 0 is a reliability index required by planning;
V i is the i-th node voltage;
v imax is the maximum voltage allowed by node i;
V imin is the minimum voltage allowed by node i;
I i is the I-th branch current;
I imax is the maximum current allowed by the ith branch;
F max is the annual average maximum failure rate of the line.
It should be noted that the configuration problem of the protection switch of the power distribution network, namely the configuration protection problem of the circuit breaker, belongs to the nonlinear and discrete multi-objective combination optimization problem, the power distribution network is used as the tail end of the power network, the safe and stable operation of the power distribution network directly influences the requirements of users in terms of power quality, power supply reliability and the like, the less the loss caused by power failure of the users is represented as the higher the power supply reliability of the power distribution network, so the minimum power failure loss is selected as an objective function.
As a further preferable embodiment, as shown in fig. 2, in step S1: before obtaining the opening and closing states of the circuit breakers of the outlet unit and the protection configuration of the circuit breakers, the method further comprises the following steps:
Scanning an operation mode file, comparing the operation mode file obtained by scanning with the switch opening and closing state of the current operation mode file of the outlet unit, and judging whether the operation mode file is changed or not;
If yes, executing the step S2;
If not, the loop is ended, that is, if the scanned operation file is consistent with the current file, the circuit breaker of the outgoing line unit can be regarded as consistent in grading. .
According to the embodiment, the operation mode of the power distribution network switch is automatically identified, a technology for automatically identifying the matching point of the power distribution network based on a real-time tide and intelligent optimization algorithm is provided, then the intelligent setting of the power distribution network fixed value is realized by automatically matching with a protection fixed value scheme, so that the verification of the existing operation fixed value is realized, an auxiliary decision is provided for switching of a power distribution network fixed value area, the adaptability of the fixed value under the change of the tide and the change of the operation mode can be checked in real time, and the result of the selection rule of the zero-level switch, the first-level switch and the second-level switch in the branch line mode obtained by the method is shown in fig. 3.
It should be noted that, in this embodiment, the matching point is defined as a good-level, a first-level, and a second-level matching point; the primary and secondary coordination points can be ring main units, switching stations or intelligent circuit breakers with microcomputer protection functions and fixed value free setting functions on 10 (20) kilovolt distribution lines.
As shown in fig. 4, the embodiment discloses a power distribution network protection configuration optimization system, which includes an acquisition module 10, an initial population forming module 20, a first calculation module 30, a cross mutation operation module 40, a second calculation module 50, a judgment module 60 and an output module 70, wherein:
the acquisition module 10 is used for acquiring the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers;
The initial population forming module 20 is configured to randomly generate an initial population of the outgoing line units according to the opening and closing states and protection configurations of the circuit breakers and based on real-time power flow distribution;
The first calculation module 30 is configured to calculate an fitness function of the initial population and record the optimal individuals;
The crossover mutation operation module 40 is used for selecting individuals to perform combination crossover and mutation according to the fitness of the individuals in the problem domain to obtain a new generation population;
the second calculation module 50 is used for calculating the fitness function of the new generation population and recording the optimal individuals;
The judging module 60 is configured to judge whether the set iteration number is reached;
the output module 70 is configured to end the cycle and output the optimal individual when the output result of the judging module 60 is yes;
the second calculation module 70 is configured to re-execute the steps when the output result of the determination module 60 is no.
As a further preferred aspect, the initial population forming module 20 includes a determining unit, a coding unit, and a combining unit, wherein:
the determining unit is used for determining a main line and a branch line of the power distribution network based on the real-time power flow;
the coding unit is used for determining a protection configuration code of the main line and a protection configuration code of the branch line according to the opening and closing states and the protection configuration of each breaker by adopting binary codes;
The combination unit is used for combining the protection configuration codes of the main line and the protection configuration codes of the branch lines to obtain the coded individuals of the outlet units, so as to form an initial population of the outlet units.
As a further preferable aspect, the determining unit is specifically configured to:
Starting from the outlet switch, searching all loads along the direction of each branch tide after encountering T connection, and taking the load and the largest load as a main line;
after all the main lines of the outlet units are found out, the rest are used as branch lines.
As a further preferable aspect, the encoding unit is specifically configured to:
grading operation is carried out on the circuit breakers which are in a closed state in the trunk line and the branch line and are provided with protection;
And (3) encoding the primary switch into 0, and encoding the secondary switch into 1 to respectively obtain the protection configuration code of the trunk line and the protection configuration code of the branch line.
As a further preferable scheme, the fitness function of the initial population is the inverse of an objective function, and the objective function is: min (C), wherein C is annual outage loss cost of the power system, c= (a 1K+a2bd)WENS, K is power generation ratio, a 1 is power generation ratio weighting coefficient, a 2 is average power price conversion multiple method weighting coefficient, b is the ratio of unit outage power electricity price to average power price, d is average power price, and W ENS is expected shortage power supply amount of the power system;
The constraint conditions are as follows:
Wherein:
r is a system reliability index under a certain protection switch configuration mode;
R 0 is a reliability index required by planning;
V i is the i-th node voltage;
v imax is the maximum voltage allowed by node i;
V imin is the minimum voltage allowed by node i;
I i is the I-th branch current;
I imax is the maximum current allowed by the ith branch;
F max is the annual average maximum failure rate of the line.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (4)
1. The power distribution network protection configuration optimization method is characterized by comprising the following steps of:
s1, acquiring the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers;
S2, according to the opening and closing states and protection configuration of each breaker, generating an initial population of the outgoing line units randomly based on real-time tide distribution;
S3, calculating an fitness function of the initial population and recording an optimal individual;
s4, selecting individuals to carry out combination intersection and mutation according to the fitness of the individuals in the problem domain to obtain a new generation population;
S5, calculating a fitness function of the new generation population and recording an optimal individual;
S6, judging whether the target iteration times are reached, if yes, executing the step S7, and if not, executing the step S4;
s7, ending the circulation and outputting an optimal individual;
According to the opening and closing state and protection configuration of each breaker and based on real-time tide distribution, the initial population of the outgoing line unit is randomly generated, and the method comprises the following steps:
determining a main line and a branch line of the power distribution network based on the real-time power flow;
adopting binary codes, and determining protection configuration codes of a main line and branch lines according to the opening and closing states and the protection configurations of the circuit breakers;
Combining the protection configuration codes of the main line and the protection configuration codes of the branch lines to obtain coded individuals of the outlet units, and forming an initial population of the outlet units;
the determining the main line and the branch line of the power distribution network based on the real-time power flow comprises the following steps:
Starting from the outlet switch, searching all loads along the direction of each branch tide after encountering T connection, and taking the load and the largest load as a main line;
After all the main lines of the outlet units are found out, the rest are taken as branch lines;
the adoption of binary codes, the protection configuration codes of the main line and the branch line are determined according to the opening and closing states and the protection configuration of each breaker, and the method comprises the following steps:
grading operation is carried out on the circuit breakers which are in a closed state in the trunk line and the branch line and are provided with protection;
And (3) encoding the primary switch into 0, and encoding the secondary switch into 1 to respectively obtain the protection configuration code of the trunk line and the protection configuration code of the branch line.
2. The power distribution network protection configuration optimization method according to claim 1, wherein the fitness function of the initial population is the inverse of an objective function, and the objective function is: min (C), wherein C is annual outage loss cost of the power system, c= (a 1K+a2bd)WENS, K is power generation ratio, a 1 is power generation ratio weighting coefficient, a 2 is average power price conversion multiple method weighting coefficient, b is the ratio of unit outage power electricity price to average power price, d is average power price, and W ENS is expected shortage power supply amount of the power system;
The constraint conditions are as follows:
Wherein:
r is a system reliability index under a certain protection switch configuration mode;
R 0 is a reliability index required by planning;
V i is the i-th node voltage;
v imax is the maximum voltage allowed by node i;
V imin is the minimum voltage allowed by node i;
I i is the I-th branch current;
I imax is the maximum current allowed by the ith branch;
F max is the annual average maximum failure rate of the line.
3. The power distribution network protection configuration optimization method according to claim 1 or 2, further comprising, before the obtaining the opening and closing states of the circuit breakers of the outgoing line unit and the protection configuration of the circuit breakers:
Scanning an operation mode file, comparing the operation mode file obtained by scanning with the switch opening and closing state of the current operation mode file of the outlet unit, and judging whether the operation mode file is changed or not;
If yes, executing the step S2;
If not, the cycle is ended.
4. The utility model provides a distribution network protection configuration optimizing system which is characterized in that, including obtaining module, initial population formation module, first calculation module, cross variation operation module, second calculation module, judgement module and output module, wherein:
The acquisition module is used for acquiring the opening and closing states of all the circuit breakers of the outgoing line unit and the protection configuration of all the circuit breakers;
The initial population forming module is used for randomly generating an initial population of the outgoing line unit based on real-time tide distribution according to the opening and closing states and the protection configuration of each breaker;
The first calculation module is used for calculating the fitness function of the initial population and recording the optimal individuals;
The cross mutation operation module is used for selecting individuals to carry out combination cross and mutation according to the fitness of the individuals in the problem domain to obtain a new generation population;
the second calculation module is used for calculating the fitness function of the new generation population and recording the optimal individuals;
the judging module is used for judging whether the set iteration times are reached;
the output module is used for ending the circulation and outputting the optimal individual when the output result of the judging module is yes;
the second calculation module is used for re-executing when the output result of the judgment module is NO;
the initial population forming module comprises a determining unit, a coding unit and a combining unit, wherein:
the determining unit is used for determining a main line and a branch line of the power distribution network based on the real-time power flow;
the coding unit is used for determining a protection configuration code of the main line and a protection configuration code of the branch line according to the opening and closing states and the protection configuration of each breaker by adopting binary codes;
the combination unit is used for combining the protection configuration codes of the main line and the protection configuration codes of the branch lines to obtain coded individuals of the outlet line units, so as to form an initial population of the outlet line units;
The determining unit is specifically configured to:
Starting from the outlet switch, searching all loads along the direction of each branch tide after encountering T connection, and taking the load and the largest load as a main line;
After all the main lines of the outlet units are found out, the rest are taken as branch lines;
the coding unit is specifically configured to:
grading operation is carried out on the circuit breakers which are in a closed state in the trunk line and the branch line and are provided with protection;
And (3) encoding the primary switch into 0, and encoding the secondary switch into 1 to respectively obtain the protection configuration code of the trunk line and the protection configuration code of the branch line.
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