CN106532717B - Circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method - Google Patents
Circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method Download PDFInfo
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- H—ELECTRICITY
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- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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Abstract
The invention discloses the circuit overloads based on comprehensive sensitivity analysis to join cutting load coordination optimizing method, include: node screening: establishing the node overall sensitivity index of meter and branch overload degree according to the sensitivity relation between branch current and node Injection Current, and alternative cutting load node screening is carried out by the calculating of node overall sensitivity index；Scheme search: coordinating cutting load economic cost and harmonious two targets of node cutting load, with the minimum optimization aim of weighted value of economic cost and node cutting load harmony index, establishes circuit overload connection cutting load coordination optimization Controlling model；The weighted value for setting cutting load economic cost and harmonious index calculates the circuit overload connection cutting load coordination optimization Controlling model under different weights, and optimal route overload joining-cutting load coordinates and optimizes control program, finally obtains cutting load node.The present invention substantially increases scheme search efficiency, avoids falling into dimension calamity during Optimum search.
Description
Technical field
The present invention relates to electric power network technique fields, and in particular to the circuit overload connection cutting load association based on comprehensive sensitivity analysis
Adjust optimization method.
Background technique
The continuous development of trans-regional interconnected power grid solves the inverse of energy resources and load center to a certain extent
To distribution problem, realize across big area resource distribute rationally with the economical and efficient of operation of power networks, clean and environmental protection, but simultaneously to electricity
The safe and stable operation of net brings unprecedented challenge.
In recent years, more large area blackouts show both at home and abroad: in long-distance and large-capacity power transmission system, circuit overload can
A series of cascading trip accidents can be will lead to, in turn result in large-area power-cuts.Therefore, reasonable circuit overload connection how is formulated to cut
Duty control method quickly eliminates circuit overload, is to prevent the chain power outage of large area, ensures power grid security, stabilization, economy
The key of operation.
The circuit overload connection load shedding control method used in real system at present is mainly minute wheel classification cutting load method.It should
Method refers to that different according to circuit overload degree, minute wheel grade is cut off according to each load excision round and priority ranking is preset
Load.It is rely on related personnel's experience since this method is when presetting each load excision round and priority ranking more, lack
The theoretical calculation of system, therefore often result in load in practical operation and owe to cut or cross to cut, and the priority that load is cut off in this method
Sequence is overloaded just for uniline, can not be to cutting load measure using this method when route a plurality of in system overloads simultaneously
Carry out global optimization.
In short, above-mentioned circuit overload connection cutting load method spininess solves uniline overload, lack to a plurality of line
Coordination optimization control when road is overloaded simultaneously；And in Practical Project, electric power enterprise, should when taking overload joining-cutting load measure
It pursues economic cost to minimize, considers the harmony of cutting load again, to reduce accident impact, the grading of reduction accident, and show
There is method not take in cutting load harmony.
In consideration of it, the application proposes a kind of circuit overload connection cutting load coordination optimization side based on comprehensive sensitivity analysis
Method.
Summary of the invention
To solve the shortcomings of the prior art, the invention discloses the circuit overload connection based on comprehensive sensitivity analysis to cut
Coordinated optimization method, the purpose of the present invention is: for one or more of routes after failure while overload situations, establish
The measure of node cutting load avoids the overall sensitivity index of overload route by the alternative cutting load node of index calculating sifting
Calculating falls into dimension calamity；Method constructs circuit overload connection cutting load coordination optimization Controlling model, is cut with economic cost and node
The minimum optimization aim of the weighted value of load balancing index, by the active and reactive balance of trend, node voltage, current limiter ginseng
Number is not out-of-limit to wait limitations to be included in constraint condition.The method achieve economic cost when overload joining-cutting load control is balanced with cutting load
Property coordination optimization control meet different operation of power networks requirements, guarantee quickly disappearing for circuit overload and by the way that different weights are arranged
It removes, meets Practical Project demand.
To achieve the above object, concrete scheme of the invention is as follows:
Circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method, comprising the following steps:
Node screening: forming network node admittance matrix and incidence matrix, fixed according to nodal voltage equation and incidence matrix
Justice obtains the sensitivity relation between branch current and node Injection Current；
The node of meter and branch overload degree is established according to the sensitivity relation between branch current and node Injection Current
Overall sensitivity index, and alternative cutting load node screening is carried out by the calculating of node overall sensitivity index；
Scheme search: coordinate cutting load economic cost and harmonious two targets of node cutting load, with economic cost and node
The minimum optimization aim of weighted value of cutting load harmony index establishes circuit overload connection cutting load coordination optimization Controlling model；
According to, setting cutting load economic cost and harmonious index different from harmonious requirement to cutting load economic cost
Weighted value calculates the circuit overload connection cutting load coordination optimization Controlling model under different weights, and optimal route overload connection is cut
Coordinated optimization control scheme finally obtains cutting load node.
Further, defined according to nodal voltage equation and incidence matrix, obtain branch current and node Injection Current it
Between sensitivity relation are as follows:
Wherein,For branch current column vector；Y is Nl×NlRank branch admittance matrix,For the inverse of node admittance matrix
Battle array,For node Injection Current column vector, flows into node and be positive, outflow is negative, ATFor incidence matrix transposition.
Further, cutting load measure is taken to eliminate ability definition node k to the overcurrent of all overload branches according to node k
Sensitivity index considers that branch overload degree is different, definition node overall sensitivity index:
Wherein, δjFor branch j weighted value, for indicating the overload degree of branch j；Ij、The practical electricity of respectively branch j
Flow valuve and the permission current value upper limit, NsTo overload branch total number, YjFor branch admittance battle array jth row element, the i.e. self-conductance of branch j
It receives and transadmittance, ATFor incidence matrix transposition,For the inverse matrix of node admittance matrix.
Further, calculating is normalized in node overall sensitivity index, for intuitively expressing all overload branches pair
The overall sensitivity of a certain node cutting load measure.
Further, when carrying out the screening of alternative cutting load node, node overall sensitivity value λ is takenkIt is greater than the set value
Node is included in alternative cutting load node collection.
Further, cutting load measure economic cost are as follows:
Wherein, NkFor cutting load node total number；ΔPki、ciThe i-th type load cutting load amount of respectively node k, excision i-th
Type load unit-economy cost coefficient.
Further, after calculating cutting load measure economic cost further include the steps that calculating is normalized.
Further, the cutting load harmony index definition is node cutting load rate standard deviation:
Wherein, NkFor cutting load node total number,For k node cutting load rate；For all cutting load node cutting load rates
Average value, PkiFor the i-th type load total amount of node k, Δ PkiFor the i-th type load cutting load amount of node k.
Further, the step of node cutting load rate harmony index being normalized.
Further, circuit overload connection cutting load coordinates and optimizes Controlling model are as follows:
Min f=ω1f1+ω2f2
Wherein, ω1、ω2The respectively weighted value of cutting load economic cost, node cutting load harmony index carries out normalizing
Change the cutting load measure economic cost f after calculating1, the node cutting load rate harmony index f after calculating is normalized2。
Further, the constraint condition of circuit overload connection cutting load coordination optimization Controlling model includes that trend is active and reactive
Balance, node voltage and line electricity flow valuve be not out-of-limit.
Beneficial effects of the present invention:
(1) circuit overload connection cutting load control is decomposed into node screening and searches for two steps with scheme by the present invention, passes through meter
Operator node overall sensitivity carries out alternative cutting load node screening, effectively reduces cutting load node searching range, greatly improves
Scheme search efficiency avoids falling into dimension calamity during Optimum search.
(2) previous circuit overload connection load shedding control method relies on related personnel's experience more, often results in load and owes to cut or mistake
It cuts, when a plurality of route occurs while overloading, it is difficult to coordination optimization control is carried out, for this purpose, the present invention is established with economic cost
With the circuit overload connection cutting load coordination optimization control mould of the minimum optimization aim of weighted value of node cutting load harmony index
Type, for the model by the active and reactive balance of trend, constraint condition is included in the limitations such as node voltage, line electricity flow valuve be not out-of-limit, is realized
Coordination optimization control when a plurality of route overloads simultaneously.
(3) in Practical Project, electric power enterprise should pursue economic cost minimum when taking overload joining-cutting load, again
Consider the harmony of cutting load, reduces accident impact, reduces accident grading and social influence, in the established model of the present invention, lead to
The weighted value for crossing adjust economy both cost and node cutting load harmony index, can be calculated under different weights, circuit overload
Join cutting load and coordinate and optimize control program, meets the needs of electric power enterprise in Practical Project.
Detailed description of the invention
Fig. 1 is coordination optimizing method flow chart；
Fig. 2 is somewhere Power grid structure figure.
Specific embodiment:
The present invention is described in detail with reference to the accompanying drawing:
As shown in Figure 1, a kind of circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method, including such as
Lower step:
(1) it is defined, is derived between branch current and node Injection Current according to nodal voltage equation and incidence matrix
Sensitivity relation；
(2) the node overall sensitivity index of meter and branch overload degree is established, which is able to reflect all overload branch
Road carries out alternative cutting load to the overall sensitivity of a certain node cutting load measure, and by calculate node overall sensitivity index
Node screening；
(3) coordinate cutting load economic cost and harmonious two targets of node cutting load, with economic cost and node cutting load
The minimum optimization aim of the weighted value of harmonious index establishes circuit overload connection cutting load coordination optimization Controlling model；
(4) different to cutting load economic cost and harmonious requirements according to policymaker, setting cutting load economic cost with it is equal
The weighted value of weighing apparatus property index, calculates under different weights, and optimal route overload joining-cutting load coordinates and optimizes control program.
About the sensitivity relation between branch current and node Injection Current: being built as power grid continues to develop, rack
Structure is increasingly complicated, and system interior joint is continuously increased, in carrying out circuit overload connection cutting load scheme optimization solution procedure, if
Carry out optimizing in full range of nodes, scheme may be made to fall into dimension calamity in searching process, in system it is certain electrically away from
Cutting load measure is taken to influence less on circuit overload is eliminated from node farther out, therefore, the present invention will optimize circuit overload connection and cut
Load scheme is divided into alternative cutting load node screening and scheme is searched for two steps and effectively avoided to improve Searching efficiency in side
Dimension calamity is fallen into case searching process.
By deriving sensitivity relation between computation overload branch current and node Injection Current, needle can be intuitively obtained
More sensitive node is eliminated to a certain overload branch overcurrent, provides theoretical foundation for the screening of alternative cutting load node.
Overload sensitivity relation derivation process between branch current and node Injection Current are as follows:
Wherein, formula (1) is nodal voltage equation；Formula (2) is incidence matrix definition；For node Injection Current column vector,
It flows into node to be positive, outflow is negative；YnFor Nb×NbRank node admittance matrix, wherein NbFor number of network node；For node electricity
Press column vector；For branch voltage column vector；ATFor incidence matrix transposition.
It can be derived as follows by formula (1), (2):
Sensitivity relation between branch current and node Injection Current can must be overloaded by formula (3), it may be assumed that
Node overall sensitivity index: in Practical Project, failure often results in a plurality of route while overloading, and therefore, is carrying out
When alternative cutting load node screening, the present invention proposes node overall sensitivity index, for reflecting the measure of node cutting load to institute
There is overload branch to the overall sensitivity of a certain node cutting load measure.
In Practical Project, since circuit overload degree is different, different degrees of power grid accident, social influence, warp are often resulted in
Ji influences to influence with electric power enterprise power supply quality, therefore when a plurality of route of generation overloads simultaneously, need to preferentially eliminate overload
The more serious branch of degree avoids that even more serious power grid accident occurs.Therefore, the present invention proposes that meter and branch overload degree
Node overall sensitivity index.
Certain node takes cutting load measure to eliminate ability to the overcurrent of all overload branches are as follows:
Wherein, NsTo overload branch total number；For the current variation value of branch j after node k cutting load；YjFor branch
Admittance battle array jth row element, the i.e. self-admittance of branch j and transadmittance；For its current variation value after node k cutting load.
Definition node k sensitivity are as follows:
The present invention proposes the node overall sensitivity index of meter and branch overload degree, calculation formula are as follows:
Wherein, δjFor branch j weighted value, for indicating the overload degree of branch j；Ij、The practical electricity of respectively branch j
Flow valuve and the permission current value upper limit.
Calculating is normalized in formula (7) interior joint overall sensitivity index:
Wherein, λk、λ′kRespectively the overall sensitivity normalized value of node k and actual value；λ′max、λ′minRespectively basis
Formula (7) calculates gained node overall sensitivity maxima and minima.
Calculating, which is normalized, in node overall sensitivity index can more intuitively express all overload branches to a certain
The overall sensitivity of node cutting load measure.When carrying out the screening of alternative cutting load node, it is proposed that take node overall sensitivity value
λkAlternative cutting load node collection is included in greater than 0.1 node, it is believed that λkNode less than 0.1 does not have competitiveness.
Circuit overload connection cutting load coordinates and optimizes Controlling model: circuit overload connection cutting load control belongs to complex nonlinear rule
The problem of drawing, in Practical Project, electric power enterprise will not only minimize cutting load when taking circuit overload to join cutting load measure
Amount is pursued economic cost and is minimized, and the grading of power grid accident caused by cutting load measure, social influence and electric power enterprise are also coordinated
Power supply quality influence etc., this requires to be coordinated and optimized, should be chased after from the overall situation when carrying out cutting load control
It asks cutting load economic cost to minimize, avoids the excessive unbalanced phenomena of node cutting load as far as possible again, avoid certain sensitive
It spends that high node load excision ratio is excessively high or even load complete resection phenomenon, causes major accident to grade, to give electric power enterprise
Industry and society bring adverse effect.
Circuit overload joins cutting load and coordinates and optimizes Controlling model are as follows:
Min f=ω1f1+ω2f2 (11)
Vi min≤Vi≤Vi maxI=1,2,3 ..., Nb (15)
ΔQki=σkΔPkiK=1,2,3 ..., Nk (16)
Formula (11) is the minimum optimization aim of model, including cutting load measure economic cost refers to cutting load harmony
Mark, cutting load measure economic cost and node cutting load rate harmony dimension difference are excessive, can not directly compare coordinate it is excellent
Change, therefore calculating is normalized, in formula, f1、f2Respectively cutting load measure economic cost, cutting load harmony index are returned
One change value；ω1、ω2Respectively f1、f2Weight, value is by policymaker depending on real system service requirement.NlIt is total for branch
Number；Allow the current value upper limit for branch l；Vi max、Vi minRespectively node i voltage upper and lower limit；σkIt is idle/active for node
Scale factor can have economize on electricity power factor to calculate and obtain.Pi、QiThe respectively active and reactive value of node i；Vi、VjRespectively node
I, j voltage value；θijFor node i, j phase difference of voltage；Gij、BijRespectively branch lijElectric conductivity value, susceptance value.
Two parts are directed to the active variation of node i.e. in objective function: different cutting load measures, node active power is different,
According to the definition of objective function, different target value is calculated.
Formula (12)-(16) are model constraint condition, and formula (16) indicates that node while cutting off active power, cuts off node
Corresponding reactive power after taking cutting load measure (variation of node active power), becomes according to formula (16) calculate node reactive power
Change, formula (12)-(13) are the active and reactive Constraints of Equilibrium of node, and formula (14) is the constraint of the branch current value upper limit, formula (15) is node
Voltage value constraint, wherein the parameters such as voltage, branch current of each node of network can pass through trend according to formula (12), (13)
Calculating is found out,, objective function is included in the form of penalty function carrying out model solution up-to-date style (14)-(15).
It is different from harmonious requirement to cutting load economic cost according to policymaker, be set separately in model objective function cut it is negative
The weighted value ω of lotus economic cost, node cutting load harmony index1、ω2, by calculating, provided under different weights for policymaker
Optimal route overload joining-cutting load coordinates and optimizes control program.
Cutting load measure economic cost and cutting load harmony index derivation process in model are as follows:
Define cutting load measure economic cost are as follows:
Wherein, NkFor cutting load node total number；ΔPki、ciThe i-th type load cutting load amount of respectively node k, excision i-th
Type load unit-economy cost coefficient.
Cutting load measure economic cost in formula (17) is normalized and is calculated:
Wherein, NbFor network load node total number；PkiFor the i-th type load total amount of node k.
Definition cutting load harmony index definition is node cutting load rate standard deviation:
Wherein,For k node cutting load rate；For all cutting load node cutting load rate average values.
Formula (19) interior joint cutting load rate harmony index is normalized and is calculated:
Circuit overload connection cutting load coordination optimization control is complicated multiple constraint, a nonlinear optimal problem, therefore, sheet
Inequality constraints in model is included in objective function by invention in the form of penalty function, and application is based on the adaptive of nonlinear weight
Particle swarm optimization algorithm optimizes.
Real system simulation analysis: by taking the power grid real system of somewhere as an example, validity to the mentioned method of the present invention and
Feasibility is verified.Node cutting load percentage range is set as [0,50], one, two, three load cost coefficient of this area
Respectively 1,0.4,0.1, this area's power grid total load are 5469MW.Certain planning year this area electric network composition is as shown in Figure 2.Accident
Overloading in various degree occurs in route 2-6,11-20, F-24 afterwards.
According to alternative cutting load node screening strategy, overall sensitivity calculating is carried out to nodes all in system, and by drop
The preceding N that overall sensitivity is greater than 0.1 is chosen in sequence arrangementkA node is included in alternative cutting load node collection and (thinks that overall sensitivity is small
Node in 0.1 does not have competitiveness), higher preceding 10 nodes of overall sensitivity are only listed, as shown in table 1.
The sequence of 1 node overall sensitivity of table
Using the adaptive particle swarm optimization algorithm solving model based on nonlinear weight.Taking particle length is Nk, particle
Group's scale is 30, carries out integer coding to particle in population, as shown in table 2 below.
2 particle coding structure table of table
| z1 | z2 | z3 | … | zNk |
Wherein, zkFor kth place value, arbitrary integer in [0,50] is taken.If zkArbitrary integer in [1,50] is taken, is indicated in node k
Upper excision percentage is zkLoad；If zk0 is taken, indicates that node k does not take cutting load measure.
The asynchronous optimum results of weight coefficient value are as shown in table 3 in formula (11) objective function.
Simulation result under the different design conditions of table 3
By being compared analysis to above-mentioned four kinds of schemes it is found that scheme 1 indicates only to consider when taking cutting load measure
Cutting load measure economy cost preferentially cuts off the low node of high sensitivity, economic cost, causes cutting load rate difference between node
Greatly, part economic cost lower node loss rate of load condensate is even as high as 40%, aggravates accident grading, to power grid enterprises bring compared with
High policy fine, while causing bad social influence；Scheme 2 is indicated when taking cutting load measure, is compared using node etc.
Example excision principle, simulation result show that this method causes system cutting load amount excessive, and system performance driving economy is poor, in real system
It is undesirable；Scheme 3 and scheme 4, which are all made of, coordinates economic control strategy, can both take into account cutting load economy cost with it is balanced
Property require, can effective control node cutting load rate, wherein scheme 4 more emphasizes tactful economy, when using scheme 4, system
Node maximum cutting load rate be 17%, comparison scheme 3 it is found that scheme 4 can meet node cutting load rate it is lesser under the premise of,
System cutting load amount is substantially reduced, optimal case is obtained.
Above-mentioned simulation result show scheme 3,4 using coordination optimization control strategy can be obviously improved accident grading and
To guarantee the economic feasibility of scheme.In real system, Scheme Choice should be carried out according to system service requirement.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (8)
1. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method, characterized in that the following steps are included:
Node screening: forming network node admittance matrix and incidence matrix, is defined, is obtained according to nodal voltage equation and incidence matrix
Sensitivity relation between out branch electric current and node Injection Current；
The node for establishing meter and branch overload degree according to the sensitivity relation between branch current and node Injection Current is comprehensive
Sensitivity index, and alternative cutting load node screening is carried out by the calculating of node overall sensitivity index；
Scheme search: coordinating harmonious two targets of cutting load economic cost and node cutting load, is cut with economic cost with node negative
The minimum optimization aim of weighted value of lotus harmony index establishes circuit overload connection cutting load coordination optimization Controlling model；
According to, the weight of setting cutting load economic cost and harmonious index different from harmonious requirement to cutting load economic cost
Value calculates the circuit overload connection cutting load coordination optimization Controlling model under different weights, optimal route overload joining-cutting load
Control program is coordinated and optimized, finally obtains cutting load node；
It takes cutting load measure to eliminate ability definition node k sensitivity index to the overcurrent of all overload branches according to node k, examines
It is different to consider branch overload degree, definition node overall sensitivity index:
Wherein, δjFor branch j weighted value, for indicating the overload degree of branch j；Ij、Respectively branch j actual current value
With the permission current value upper limit, NsTo overload branch total number, YjFor branch admittance battle array jth row element, i.e., the self-admittance of branch j with
Transadmittance, ATFor incidence matrix transposition,For the inverse matrix of node admittance matrix；
The cutting load harmony index definition is node cutting load rate standard deviation:
Wherein, NkFor cutting load node total number,For k node cutting load rate；It is average for all cutting load node cutting load rates
Value, PkiFor the i-th type load total amount of node k, Δ PkiFor the i-th type load cutting load amount of node k.
2. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as described in claim 1, special
Sign is defined according to nodal voltage equation and incidence matrix, show that the sensitivity between branch current and node Injection Current is closed
System are as follows:
Wherein,For branch current column vector；Y is Nl×NlRank branch admittance matrix,For the inverse matrix of node admittance matrix,
For node Injection Current column vector, flows into node and be positive, outflow is negative, ATFor incidence matrix transposition.
3. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as described in claim 1, special
Sign is that calculating is normalized in node overall sensitivity index, is cut to a certain node for intuitively expressing all overload branches negative
The overall sensitivity of lotus measure.
4. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as claimed in claim 3, special
Sign is that, when carrying out the screening of alternative cutting load node, the node for taking node overall sensitivity index value to be greater than the set value is included in standby
Select cutting load node collection.
5. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as described in claim 1, special
Sign is cutting load economic cost are as follows:
Wherein, NkFor cutting load node total number；ΔPki、ciThe i-th type load cutting load amount, the i-th class of excision of respectively node k is negative
Lotus unit-economy cost coefficient；
After calculating cutting load economic cost further include the steps that calculating is normalized.
6. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as described in claim 1, special
Sign is to further include the steps that for node cutting load rate harmony index being normalized.
7. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as described in claim 1, special
Sign is that circuit overload joins cutting load and coordinates and optimizes Controlling model are as follows:
Min f=ω1f1+ω2f2
Wherein, ω1、ω2The respectively weighted value of cutting load economic cost, node cutting load harmony index, is normalized meter
Cutting load measure economic cost f after calculation1, the node cutting load rate harmony index f after calculating is normalized2。
8. the circuit overload based on comprehensive sensitivity analysis joins cutting load coordination optimizing method as claimed in claim 7, special
Sign is that the constraint condition that circuit overload joins cutting load coordination optimization Controlling model includes the active and reactive balance of trend, node voltage
And line electricity flow valuve is not out-of-limit.
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| CN107124006B (en) * | 2017-05-05 | 2020-04-14 | 国电南瑞科技股份有限公司 | Equipment overload self-adaptive emergency control method based on measure sensitivity automatic identification |
| CN107370149B (en) * | 2017-08-25 | 2020-04-14 | 广州供电局有限公司 | Method and system for determining load reduction amount of power system |
| CN109473991B (en) * | 2018-02-12 | 2022-04-19 | 国网浙江省电力公司嘉兴供电公司 | Regional power grid optimal load control method considering regional balance |
| CN112994025B (en) * | 2021-02-05 | 2024-04-19 | 山东大学 | Power grid load removal method and system based on linear programming algorithm |
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