Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method for monitoring the chargeable allowance of an electric vehicle in a transformer area considering N-1 safety, can provide technical support for a power distribution network to accept large-scale electric vehicle safety charging, can be further used for optimal scheduling auxiliary decision in future electric vehicle-power grid interaction, and can help to realize the double-carbon target in the traffic field.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a method for monitoring the chargeable allowance of an electric automobile in a transformer area considering N-1 safety comprises the following steps:
step 1, constructing an EV-containing power distribution system security domain model of a platform area view angle;
step 2, performing DSSR visualization by taking the power of the distribution system of the transformer area EV as a viewing angle according to the security domain model established in the step 1;
step 3, calculating the chargeable margin index of the distribution system of the distribution area EV based on the security domain model according to the DSSR visualization in the step 2;
and 4, constructing a power distribution internet of things cloud-edge cooperative framework, and monitoring the charging condition of the distribution area EV power distribution system according to the chargeable allowance index of the distribution area EV power distribution system calculated in the step 3.
Further, the step 1 includes the steps of:
1.1, constructing a state space model containing an EV power distribution system:
wherein the content of the first and second substances,
is a working point;
for the net power at the node 1 to be,
is a node
iThe net power of the power is that of the power,
is a node
Net power;
as a station area node
The load power of the access;
generating power for a distributed power supply;
charging load power for the EV power distribution system; at the same time
The constraint conditions of (1) are:
wherein the content of the first and second substances,
for distribution transformers
The capacity of (a) is set to be,
the power reverse feeding upper limit coefficient;
for distribution transformer
A heavy duty factor;
step 1.2, constructing a normal operation constraint model of the EV power distribution system; the normal operation constraint model comprises normal operation line capacity constraint and normal operation main transformer capacity constraint,
wherein, the normal operation line capacity constraint is as follows:
wherein the content of the first and second substances,
is a line
The power of (a) is determined,
as a line
The set of all the nodes downstream is,
is a line
The capacity of (a) is set to be,
for all linesThe set of (a) and (b),
is a node
Net power;
the capacity constraint of a normally-operated main transformer is as follows:
wherein the content of the first and second substances,
is a main transformer
The power of (a) is determined,
for the main change of
The set of all the nodes downstream is,
for the main change of
The rated capacity of the battery pack is set,
the method comprises the following steps of (1) collecting all main transformers;
step 1.3, an EV power distribution system N-1 safety criterion constraint model;
the N-1 safety criterion constraint modeling comprises N-1 line capacity constraint and N-1 main transformer capacity constraint,
wherein the N-1 line capacity constraint is:
wherein the content of the first and second substances,
as a line
The power of (a) is determined,
is a branch
A downstream node set of (2);
as a line
The capacity of (a) is set to be,
is the set of all lines;
is a component on the line;
the N-1 main transformer capacity constraint is as follows:
wherein the content of the first and second substances,
is a main transformer
The power of (a) is determined,
for the main change of
Is to be transmitted to the downstream node set of,
is a main transformer
The rated capacity of the air conditioner (c),
the method comprises the following steps of (1) collecting all main transformers;
step 1.4, according to the state space model, the normal operation constraint model and the N-1 safety criterion constraint model:
wherein the content of the first and second substances,
is the first
In a hyperplane
The coefficient of (a).
Further, the step 2 includes the steps of:
step 2.1, judging the number of the concerned areas needing to be selected, if the number of the concerned areas is 2, performing step 2.2, and if the number of the concerned areas is 3, performing step 2.3;
2.2, performing DSSR two-dimensional visualization by taking the power of the distribution system of the transformer area EV as a viewing angle;
and 2.3, performing DSSR three-dimensional visualization by taking the power of the distribution system of the station area EV as a viewing angle.
Moreover, the specific implementation method of the step 2.2 is as follows: for containing
Distribution network of each distribution area, and the distribution area concerned is selected
And platform area
Get it
The system power distribution at the moment, the fixed variable becomes constant:
wherein, the first and the second end of the pipe are connected with each other,
is a platform area
The net power of the power is that of the power,
system for controlling a power supply
tTime zone
The net power of the power converter,
is a platform area
iThe power of all the loads is set to be,
is a system
tTime zone
iThe power of all the loads is set to be,
is a platform area
iThe output power of all of the distributed power sources,
is a system of
tTime zone
iThe output power of all of the distributed power sources,
is a platform area
jThe power consumed by all of the loads is,
is a system
tTime zone
jThe power consumed by all of the loads is,
is a platform area
jThe output power of all of the distributed power sources,
is a system
tTime zone
jThe output power of all of the distributed power sources,
numbering the transformer area;
get about
、
A set of boundary equations having
The method comprises the following steps:
wherein the content of the first and second substances,
(ii) a Will be provided with
The equation is projected on
Is a transverse axis and
on a two-dimensional coordinate system of vertical axis, the relation
And
is displayed on the display.
Moreover, the specific implementation method of the step 2.3 is as follows: for containing
The distribution network of each distribution area selects the concerned distribution area
Platform area
And platform area
Get it
The system power distribution at the moment, the fixed variable becomes constant:
wherein the content of the first and second substances,
is a platform area
The net power of the power is that of the power,
is a system
tTime zone
xThe net power of the power converter,
is a platform area
The power consumed by all of the loads is,
is a system
tTime zone
The power consumed by all of the loads is,
is a platform area
The output power of all of the distributed power sources,
is a system
tTime zone
The output power of all distributed power supplies; is obtained only about
、
And
a set of boundary equations containing
The method comprises the following steps:
wherein the content of the first and second substances,
is a platform area
iThe charging power of the electric automobile,
Is a platform area
jThe charging power of the electric automobile,
Is a platform area
kThe charging power of the electric vehicle of (1),
(ii) a Will be provided with
An equation is projected on
、
And
on a three-dimensional coordinate system of axes, the method is related to
、
And
the three-dimensional visualization image of (2).
Moreover, the specific implementation method of step 3 is as follows:
wherein the content of the first and second substances,
is hyperplane
H sVariable of (2)
The coefficient of (a) is determined,
for charging the electric automobile in the platform area 1,
is hyperplane
H sVariable of (2)
The coefficient of (a) is determined,
is a platform area
nThe charging power of the electric vehicle;
to visualize a hyperplane border in the image from the DSSR with the power of the distribution system of the area EV as a perspective,
for operating points with power of distribution system of station area EV as view angle
To
Euclidean distance of (c):
hyperplane boundary
The conditional constraints of (1) are: condition constraint 1, satisfy constraint
In a distribution room
An EV maximum dynamic chargeable power of
In that
Axial projection module
If, if
Are respectively hyperplane
Sum of normal vectors
Axial direction vector:
is derived from
The time of day begins and the time of day begins,
time zone
If the power of other areas is not changed, the area is
From
Is timed to
The variation width of EV charging power at the moment is less than or equal to
Then the power distribution system is
Meet in N-1 safety constraints at a time
Constraining;
conditional constraint 2, satisfy constraint
In a distribution room
The EV maximum static chargeable power of (a) is: working point
Edge of
Axial ray and
mode of intersection
;
Wherein, the first and the second end of the pipe are connected with each other,
to be driven from
At the beginning of the moment
Time, for any zone of the distribution system
,At the slave
Is timed to
The variation range of the EV charging power at the time is less than or equal to
Then the power distribution system is
Must meet the N-1 safety constraint at any moment
And (5) restraining.
Moreover, the power distribution internet of things cloud-edge collaborative architecture in the step 4 includes: the method comprises the steps that a distribution automation terminal DTU, a feeder automation terminal FTU, a network frame topology calculation module, a DSSR visualization module and a platform area EV chargeable margin detection evaluation module are deployed on a platform area intelligent fusion terminal TTU and a 10kV line switch;
each distribution transformer area is provided with 1 transformer area intelligent fusion terminal TTU, the plurality of transformer area intelligent fusion terminals TTUs are connected with a DSSR visualization module, a 10kV line switch is provided with a distribution automation terminal DTU and a feeder automation terminal FTU which are connected with a net rack topology calculation module, and the net rack topology calculation module is connected with a DSSR calculation module, the DSSR visualization module and a transformer area EV chargeable margin detection evaluation module in series;
the intelligent transformer substation integration system comprises a transformer area intelligent fusion terminal TTU, a 10kV line switch deployment distribution automation terminal DTU and a feeder automation terminal FTU, wherein the transformer area intelligent fusion terminal TTU is used for acquiring data of all loads, distributed power supplies and EVs in a transformer area, and the 10kV line switch deployment distribution automation terminal DTU and the feeder automation terminal FTU are used for acquiring switching value data of a 10kV power grid; the DSSR visualization module is used for calculating the power distribution of the distribution network distribution area and the charging condition of the current EV; the distribution network topology calculation module is used for calculating a distribution network topology structure, the DSSR calculation module is used for calculating a boundary equation of the DSSR, the platform area EV chargeable margin detection and evaluation module is used for calculating a platform area EV chargeable margin index based on a safety domain according to a DSSR visual image which is calculated by the DSSR visual module and takes the platform area EV power distribution system power as a visual angle, and a worker monitors the EV charging condition of the platform area according to the platform area EV chargeable margin index.
The invention has the advantages and positive effects that:
1. the invention relates to the field of safe charging of electric automobiles in a power distribution area, realizes visual monitoring of the chargeable allowance of the electric automobiles in the power distribution area by considering the N-1 safety criterion of a power distribution system and the comprehensive influence of multiple areas EV charging on a medium-voltage distribution network and based on the safety domain theory of a power system. The method can provide technical support for the power distribution network to accept safe charging of large-scale electric vehicles, can be further used for optimal scheduling aid decision in future electric vehicle-power grid interaction, and can help to achieve the double-carbon target in the traffic field.
2. The method considers the problems that the N-1 criterion of the power distribution network corresponds to complex power grid calculation and is difficult to consider in real-time and rapid evaluation, and the like, and can contain the requirement of the N-1 safety criterion in a simple boundary equation by adopting a safety domain method, so that the charging of the distribution area EV naturally meets the N-1 safety of the power distribution network. With the increase of the distribution network scale and the complexity of topology, the N-1 security is more complex, but the computed DSSR boundary form is still concise, and the advantage is more obvious.
3. The method is based on the station area EV maximum dynamic/static chargeable power index provided by the security domain, the interaction influence of charging of a plurality of station areas EV can be comprehensively considered, and the evaluated result can deal with the overall security of the distribution network.
4. The DSSR at the EV view angle has the characteristic of easy visualization, is beneficial to understanding and application of distribution network regulating and controlling personnel, and can be further displayed to EV users to help the EV users to know the influence of EV charging on a distribution network.
5. The application architecture is based on the cloud-edge architecture of the power distribution Internet of things, which is a hot point of the current power distribution network construction.
6. The invention can accurately depict the accepting capacity of the distribution area to the EV at a certain time section, after being mastered by power distribution regulating and controlling personnel, the EV charging is controlled to be close to the running boundary, the accepting capacity of the distribution network to the EV is indirectly improved, and meanwhile, because the large-scale EV and the distribution network carry out intelligent interaction in the future, the invention provides visual auxiliary decision-making indexes for intelligent interaction.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
A method for monitoring the chargeable allowance of an electric automobile in a transformer area considering N-1 safety comprises the following steps:
step 1, establishing an EV-containing power distribution system security domain model of a platform area view angle. The working point needs to completely and uniquely reflect the system state and is defined as a vector formed by net power of all unbalanced nodes when the power distribution system operates normally. In the distribution network model, a distribution transformer high-voltage incoming line of a transformer area is defined as a node, and in a radiation structure distribution network, a balance node is a feeder line head end node.
Step 1.1, constructing a state space model containing an EV power distribution system:
wherein the content of the first and second substances,
is a working point;
for the net power of the node 1 to be,
is a node
iThe net power of the power is that of the power,
is a node
Net power;
as a station area node
The load power of the access;
generating power for a distributed power supply;
charging load power for the EV power distribution system; the platform area outflow power is positive (load electricity, electric vehicle charging), and the platform area injection power is negative (DG electricity generation, electric vehicle V2G discharging). In actual operation, the power of the cell is restricted by devices such as distribution capacity and the like and is kept within a certain allowable range:
wherein the content of the first and second substances,
for distribution transformer
The capacity of (a) is set to be,
sending an upper limit coefficient for the power;
for distribution transformer
The coefficient of the heavy load is such that,
and
are all 0.8; under the N-1 operation mode, 1.0 can be taken in a short time. A bounded set of operating points within the allowed range of all node capacities, called the state space of the power distribution system, is recorded
. Since the state space is only for one time slice, the constraint problem of the residual capacity of the power battery of the EV can be not considered.
Step 1.2, constructing a normal operation constraint model of the EV power distribution system; the normal operation constraint model comprises a normal operation line capacity constraint and a normal operation main transformer capacity constraint,
wherein, the normal operation line capacity constraint is as follows:
wherein the content of the first and second substances,
as a line
The power of (a) is determined,
as a line
The set of all the nodes downstream is,
as a line
The capacity of (a) to (b),
for the set of all the lines it is,
is a node
Net power;
the capacity constraint of a normally-operated main transformer is as follows:
wherein the content of the first and second substances,
for the main change of
The power of (a) is determined,
is a main transformer
The set of all the nodes downstream is,
is a main transformer
The rated capacity of the battery pack is set,
is the collection of all main transformers.
Step 1.3, an EV power distribution system N-1 safety criterion constraint model; componentψ k Take place ofNAfter-1, in order to restore the power supply to the non-faulty area, the distribution network will be reconfigured to form a new topology, elementsψ k The associated power balance equation will change accordingly.
The N-1 safety criterion constraint modeling comprises N-1 line capacity constraint and N-1 main transformer capacity constraint,
wherein the N-1 line capacity constraint is:
wherein the content of the first and second substances,
as a line
The power of (a) is set,
is a branch
A downstream node set of (2);
is a line
The capacity of (a) is set to be,
is the set of all lines;
for on-line components, N-1 line capacity constraints indicate that the operation is to be removed
External, arbitrary line
Is not less than the absolute value of the net power of its downstream nodes;
the N-1 main transformer capacity constraint is as follows:
wherein the content of the first and second substances,
is a main transformer
The power of (a) is set,
is a main transformer
Is to be transmitted to the downstream node set of,
for the main change of
The rated capacity of the battery pack is set,
for the set of all the main transformers, N-1 main transformer capacity constraint indicates that the operation is not exited
External and arbitrary main transformer
iIs not less than the absolute value of the net power of its downstream nodes;
set the fault as
If a certain operating point
WIn the following, the first step is to put the paper into the bag,
n-1 line capacity constraint and N-1 main transformer capacity constraint are both true, then
WSatisfy the requirement of
N-1 security criteria.
Step 1.4, a Distribution System Security Region (DSSR) is defined as a set of all operating points in a state space that satisfy normal operating constraints and N-1 security criteria. The DSSR model is:
wherein the content of the first and second substances,
the method comprises an EV power distribution system state space model, equipment constraints of distribution transformer capacity and the like on station power, normal operation line capacity constraints, normal operation main transformer capacity constraints, N-1 line capacity constraints and N-1 main transformer capacity constraints. Taking the above all the constraint inequalities, all the boundary equations (with redundancy) of the DSSR can be directly written, and after invalid boundaries are simplified and removed, the final DSSR boundary equation can be obtained, where the equation is approximately expressed by a hyperplane in a state space, and its uniform expression form is:
wherein the content of the first and second substances,
is the first
In a hyperplane
The coefficient of (a).
And 2, performing DSSR visualization by taking the power of the distribution system of the transformer area EV as a viewing angle according to the security domain model established in the step 1.
And 2.1, judging the number of the concerned areas needing to be selected, if the number of the concerned areas is 2, performing the step 2.2, and if the number of the concerned areas is 3, performing the step 2.3.
And 2.2, performing DSSR two-dimensional visualization by taking the power of the distribution system of the station area EV as a viewing angle.
For containing
nThe distribution network of each distribution area selects 2 concerned distribution areas
And platform area
Get it
The system power distribution at the moment, the fixed variable becomes constant:
wherein the content of the first and second substances,
is a platform area
The net power of the power is that of the power,
system
tTime zone
The net power of the power converter,
is a platform area
iThe power of all the loads is set to be,
is a system
tTime zone
iThe power of all the loads is set to be,
is a platform area
iThe output power of all of the distributed power sources,
is a system
tTime zone
iThe output power of all of the distributed power sources,
is a platform area
jThe power consumed by all of the loads is,
is a system
tTime zone
jThe power consumed by all of the loads is,
is a platform area
jThe output power of all of the distributed power sources,
is a system
tTime zone
jThe output power of all of the distributed power sources,
numbering the transformer area; get about
、
A set of boundary equations having
The method comprises the following steps:
wherein the content of the first and second substances,
(ii) a Will be provided with
Is projected on
Is a transverse axis and
on a two-dimensional coordinate system of the vertical axis, as shown in FIG. 1, with respect to
And
is displayed on the display.
And 2.3, performing DSSR three-dimensional visualization by taking the power of the distribution system of the station area EV as a viewing angle.
For containing
The distribution network of each distribution area selects 3 concerned distribution areas
Platform area
And station area
Get it
The system power distribution at the moment, the fixed variable becomes constant:
wherein the content of the first and second substances,
is a platform area
The net power of the power is that of the power,
is a system
tTime zone
xThe net power of the power converter,
is a platform area
The power consumed by all of the loads is,
is a system of
tTime zone
The power consumed by all of the loads is,
is a platform area
The output power of all of the distributed power sources,
is a system of
tTime zone
The output power of all distributed power supplies; is obtained only about
、
And
a set of boundary equations containing
The method comprises the following steps:
wherein the content of the first and second substances,
is a platform area
iThe charging power of the electric automobile,
Is a platform area
jThe charging power of the electric automobile,
Is a platform area
kThe charging power of the electric vehicle of (1),
(ii) a Will be provided with
An equation is projected on
、
And
on a three-dimensional coordinate system of axes, the method is related to
、
And
the three-dimensional visualization image of (2).
And 3, calculating the chargeable margin index of the distribution system of the distribution area EV based on the security domain model according to the DSSR visualization in the step 2.
Wherein the content of the first and second substances,
is hyperplane
H sVariable of (2)
The coefficient of (a) is determined,
for charging the electric automobile in the platform area 1,
is hyperplane
H sVariable of (2)
The coefficient of (a) is calculated,
is a tableZone(s)
nThe charging power of the electric vehicle;
to visualize a hyperplane border in the image at the viewing angle DSSR with the power of the distribution system of the area EV,
for operating points with power of distribution system of station area EV as view angle
To
Euclidean distance of (c):
hyperplane boundary
The conditional constraints of (1) are:
condition constraint 1, satisfy constraint
In a distribution room
An EV maximum dynamic chargeable power of
In that
Axial projection module
If, if
Are respectively hyperplane
Sum of normal vectors
Axial direction vector:
is derived from
The time of day begins and the time of day begins,
time zone
If the power of other areas is not changed, the area is
From
Is timed to
The variation width of EV charging power at the moment is less than or equal to
Then the power distribution system is
Meet in N-1 safety constraints at a time
Constraining;
the maximum dynamic safe charging power of the district EV can consider the influence of power change of the related districts, and the result has conservatism and is preferentially applied to occasions with higher safety requirements.
Conditional constraint 2, satisfy constraint
In a distribution room
The EV maximum static chargeable power of (a) is: working point
Edge of
Axial ray and
mode of intersection
。
Wherein the content of the first and second substances,
to be driven from
At the beginning of the moment
Time, for any zone of the distribution system
,At the slave
Is timed to
The variation width of EV charging power at the moment is less than or equal to
Then the power distribution system is
Must meet the N-1 safety constraint at any moment
And (5) restraining.
The maximum dynamic safe charging power of the area EV cannot consider the influence of the power change of the related area, and the result may have certain intrusiveness and is preferentially applied to occasions with high economic requirements.
And 4, constructing a power distribution internet of things cloud-edge cooperative framework as shown in fig. 3, and monitoring the charging condition of the distribution area EV power distribution system according to the chargeable allowance index of the distribution area EV power distribution system calculated in the step 3.
The power distribution internet of things cloud-edge cooperative architecture comprises: the method comprises the steps that a distribution automation terminal DTU, a feeder automation terminal FTU, a network frame topology calculation module, a DSSR visualization module and a platform area EV chargeable margin detection evaluation module are deployed on a platform area intelligent fusion terminal TTU and a 10kV line switch;
each distribution transformer area is provided with 1 transformer area intelligent fusion terminal TTU, the plurality of transformer area intelligent fusion terminals TTUs are connected with a DSSR visualization module, a 10kV line switch is provided with a distribution automation terminal DTU and a feeder automation terminal FTU which are connected with a net rack topology calculation module, and the net rack topology calculation module is connected with a DSSR calculation module, the DSSR visualization module and a transformer area EV chargeable margin detection evaluation module in series;
the intelligent transformer district convergence terminal TTU is used for acquiring data of all loads, distributed power supplies and EVs in a transformer district, and the 10kV line switch deployment distribution automation terminal DTU and the feeder automation terminal FTU are used for acquiring switching value data of a 10kV power grid; the DSSR visualization module is used for calculating the power distribution of the distribution network area and the charging condition of the current EV; the distribution network topology calculation module is used for calculating a distribution network topology structure, the DSSR calculation module is used for calculating a boundary equation of the DSSR, the platform area EV chargeable margin detection and evaluation module is used for calculating a platform area EV chargeable margin index based on a safety domain according to a DSSR visual image which is calculated by the DSSR visual module and takes the platform area EV power distribution system power as a visual angle, and a worker monitors the EV charging condition of the platform area according to the platform area EV chargeable margin index.
The method comprises the following steps of constructing an operation mode of a power distribution Internet of things cloud-edge cooperative framework:
the method comprises the steps that 1 transformer area intelligent fusion terminal TTU is deployed in each power distribution transformer area, and the TTU can acquire data of all loads, distributed power supplies and EVs in the transformer areas, including charging power, voltage, current, electric quantity and the like;
the 10kV line switch is provided with a distribution automation terminal DTU and a feeder automation terminal FTU, and switching value data of a 10kV power grid can be collected;
thirdly, uploading the collected transformer area data, the DTU and the FTU, and uploading the switching value data of the 10kV line to a cloud master station of the IV area of the power distribution Internet of things by the TTU;
a DSSR calculating and visualizing module is deployed in the cloud master station in the areas IV and IV;
fifthly, according to the TTU uploaded data, the IV area cloud master station can calculate the power distribution of the distribution network area and the current EV charging condition;
sixthly, the cloud master station in the area IV can calculate a distribution network topological structure according to the data uploaded by the DTU and the FTU, and then a boundary equation of the DSSR is calculated;
according to the fourth result, the IV area cloud master station calculates a DSSR two-dimensional or three-dimensional image of the EV viewing angle and calculates a station area EV chargeable margin index based on the safety domain;
and monitoring the EV charging condition of the transformer area by a power distribution network regulation/operation personnel according to the EV chargeable allowance index of the transformer area.
According to the method for monitoring the chargeable allowance of the electric automobile in the transformer area considering the N-1 safety, the effect of the method is proved by calculating the distribution network of 10kV single-contact of a certain hand power.
As shown in fig. 4, a hand-operated single-connection 10kV distribution network is provided, the capacities of the feeders F1 and F2 are both 1.2MVA, the capacity of the distribution transformer is 0.6MVA, and the sum of the maximum powers of the EV charging designed in each distribution area is 0.3 MVA. The EV powers of the station areas 2, 4 and 5 are selected for observation, and the power distribution of each station area at a certain time is calculated as shown in table 1.
TABLE 1 calculation of Power distribution of zones at a time
Obtaining a DSSR equation according to the distribution network:
from the power distribution of the station area of Table 1, the EV view angle is obtained
The boundary expression of (1):
according to the above formula, a three-dimensional DSSR visualization image at EV viewing angle is directly available, as shown in fig. 2.
Order to
Then, dimension reduction can be performed to obtain a two-dimensional DSSR visualization image at the EV viewing angle, as shown in fig. 5.
In FIG. 5, the current working point is taken
As can be seen from fig. 5, the first,
is an important boundary of the DSSR two-dimensional image and is recorded as
,
Obtaining a working point to
Is a distance of
Comprises the following steps:
EV maximum dynamic chargeable power for
zone 2 satisfying constraint 1
Comprises the following steps:
EV maximum static chargeable power for
zone 2 satisfying constraint 1
Comprises the following steps:
the meaning in a DSSR two-dimensional image is shown in fig. 5.
It should be emphasized that the embodiments described herein are illustrative rather than restrictive, and thus the present invention is not limited to the embodiments described in the detailed description, but also includes other embodiments that can be derived from the technical solutions of the present invention by those skilled in the art.