CN101741093B - Control method for realizing power compensation and harmonic governance - Google Patents
Control method for realizing power compensation and harmonic governance Download PDFInfo
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- CN101741093B CN101741093B CN2010101213613A CN201010121361A CN101741093B CN 101741093 B CN101741093 B CN 101741093B CN 2010101213613 A CN2010101213613 A CN 2010101213613A CN 201010121361 A CN201010121361 A CN 201010121361A CN 101741093 B CN101741093 B CN 101741093B
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract
A reactive power compensation and harmonic governance system and a control method for realizing power compensation and harmonic governance belong to the field of an electric system and solve the problems that the prior reactive power compensation technique cannot synchronously realize the full compensation for the electric network while meeting the reactive power compensation of continuous change, compensating capacity has waste and system cost is high. The system of the invention uses the structure that M groups of TSCs are connected to the electric network in parallel, the three-phase output ends of SVG are respectively connected to one end of an inductor, the other end of each of three inductors is respectively connected the three phases of the electric network. The control method of the reactive power compensation and the harmonic governance comprises: processing the collected electric current values and voltage values by a controller, obtaining the control parameters of the TSC according to a switching rule for realizing stage reactive power compensation, obtaining the control parameters of the SVG by combining with an instantaneous reactive power theory for realizing the compensation of the residual reactive power between each two stages. The invention realizes the quick and continuous reactive power compensation and the harmonic governance under the condition that load contains harmonic current, and is used for the reactive power compensation of the electric system.
Description
Technical field
The present invention relates to use the control method that reactive power compensation harmonic governing system realizes that the reactive power compensation harmonic is administered, belong to field of power.
Background technology
There are the frequent and violent equipment of many idle variations such as rolling mill, injection molding machine, asynchronous machine (soft start) and portal crane etc. in the existing distribution system; Tend to cause the problem of electric voltage dropping and low power factor; This not only makes the power distribution network line loss increase; Also the high precision equipment of some supply power voltage quality requirements is produced harm greatly simultaneously, therefore, higher to the requirement of reactive power compensator.Existing distribution network var compensation device mainly contains fixed capacitor, thyristor switchable capacitor, the fixed capacitor of passive type and the static reacance generator of thyristor-controlled reactor combination and active formula etc. of passive type.
Not enough below said apparatus exists:
1, the fixed capacitor of passive type can't compensate the idle of variation;
2, thyristor switchable capacitor can carry out grading compensation to idle, but during idle continuous variation, can not accomplish full remuneration; And when containing harmonic wave in the system,, need in the thyristor switchable capacitor capacitive branch, seal in the wave arrestment reactor in order to prevent thyristor switchable capacitor and system's generation resonance, and increased the cost of device, reduced reactive compensation capacity;
3, the combination of the fixed capacitor of passive type and thyristor-controlled reactor can be to idle realization Continuous Compensation; But thyristor-controlled reactor can produce harmonic wave; Simultaneously because thyristor-controlled reactor produces and lags behind idlely, so the capacity of the fixed capacitor of passive type and thyristor-controlled reactor capacity sum are greater than the reactive capability of the required compensation of system;
4, static reacance generator can be to the idle quick and continuous compensation of carrying out; The harmonic wave that when operation, produces is little, need not be provided with filter, does not have the possibility with system resonance; Steady-state behaviour and dynamic property all are superior to the reactive power compensator of passive type; But cost is higher at present, and most users are difficult to bear, and has therefore limited the through engineering approaches and the practicalization of static reacance generator.
Summary of the invention
The objective of the invention is when the continuous variation of satisfied compensation is idle, to realize full remuneration to network system for solving existing reactive power compensation technology; Compensation capacity exists waste and the high problem of system cost, and a kind of control method that reactive power compensation harmonic governing system realizes that the reactive power compensation harmonic is administered of using is provided.
Use reactive power compensation harmonic governing system and realize the control method that the reactive power compensation harmonic is administered; Said reactive power compensation harmonic governing system partly is made up of Passive Reactive Power Compensation part, control section and active reactive power compensation and harmonic wave control; Passive Reactive Power Compensation part and active reactive power compensation and the parallelly connected access electrical network of harmonic wave control part; Described Passive Reactive Power Compensation part is composed in parallel by M group thyristor switchable capacitor; Thyristor valve group and compensation condenser that the thyristor of two reverse parallel connections constitutes are connected into a branch road; Three groups of described branch roads adopt the triangle connected mode to connect and compose one group of thyristor switchable capacitor; Tie point is linked into respectively in the three-phase of electrical network; Wherein, M is the integer greater than 1, and described active reactive power compensation and harmonic wave control part are made up of a static reacance generator and three inductance; Static reacance generator is made up of the voltage-source type three-phase full-bridge inverter; The three-phase output end of voltage-source type three-phase full-bridge inverter connects an end of an inductance respectively, and the other end of three inductance is connected respectively in the three-phase of electrical network, and described control section is made up of controller, TSC drive circuit, SVG drive circuit, first optical coupling isolation circuit and second optical coupling isolation circuit; Controller connects the TSC drive circuit to realize the control to the TSC drive circuit through first optical coupling isolation circuit; The M of a TSC drive circuit control signal output ends links to each other with the gate pole trigger end of M group thyristor switchable capacitor respectively, and controller connects SVG drive circuit (2-3) to realize the control to the SVG drive circuit through second optical coupling isolation circuit, and 6 control signal output ends of SVG drive circuit link to each other with 6 gate pole trigger ends of static reacance generator respectively;
The process that the reactive power compensation harmonic is administered is:
The instantaneous value i of step 1, detection of grid a phase current
SaAnd the instantaneous value i of electrical network c phase current
Sc, the instantaneous value i of detection load a phase current
LaAnd the instantaneous value i of load c phase current
Lc, the instantaneous value i of a phase current of detection static reacance generator output
FaAnd the instantaneous value i of the c phase current of static reacance generator output
Fc, the instantaneous value u of detection static reacance generator DC bus-bar voltage
Dc
The instantaneous value i of the load a phase current that step 2, controller obtain according to sampling
LaAnd the instantaneous value i of load c phase current
Lc, utilize thyristor switchable capacitor switching rule to calculate the switching compound mode W of thyristor switchable capacitor, the TSC drive circuit sends TSC switching signal S
1～S
MTo accomplish above-mentioned switching compound mode;
The instantaneous value i of the electrical network a phase current that step 3, controller obtain according to sampling
SaAnd the instantaneous value i of electrical network c phase current
Sc, utilize instantaneous reactive power theory to calculate the command value i of static reacance generator offset current
* Fa
The instantaneous value i of a phase current that the static reacance generator that step 4, controller obtain according to sampling is exported
Fa, static reacance generator output the instantaneous value i of c phase current
Fc, the static reacance generator DC bus-bar voltage instantaneous value u
DcAnd the static reacance generator offset current command value i that in step 3, obtains
* Fa, adopt the Direct Current Control method to generate pwm signal, the SVG drive circuit sends SVG switching signal P
1～P
6
In step 3, the instantaneous value i of the electrical network a phase current that controller obtains according to sampling
SaAnd the instantaneous value i of electrical network c phase current
Sc, calculate reactive current and harmonic current components sum i in the power network current based on instantaneous reactive power theory
Saq, adopt i
* Fa=ki
SaqControl strategy is confirmed static reacance generator offset current command value i
* Fa, wherein, k is calculated by the SVG cancellation ratio B that hope reaches, k=B/ (1-B).
The present invention adopts the mode of Passive Reactive Power Compensation and active reactive power compensation combined reactive compensation that network system is carried out reactive power compensation; When idle the changing in the load; In described a kind of reactive power compensation harmonic governing system; Thyristor switchable capacitor is to the required idle grading compensation that carries out, static reacance generator to thyristor switchable capacitor at different levels between idle the compensating of residue.Controller of the present invention adopts full digital control method, makes described a kind of reactive power compensation harmonic governing system under the violent situation of the fluctuation of load, still have good dynamic characteristics and stable state accuracy.When containing harmonic current in the load; Static reacance generator is realized the harmonic current that contains in the load is filtered, and suppresses thyristor switchable capacitor and system's generation resonance, therefore; The wave arrestment reactor of need not connecting again in every branch road of thyristor switchable capacitor is practiced thrift system cost.The present invention combines rapidity and continuity and thyristor switchable capacitor the cost advantage when compensation big capacity idle of static reacance generator to reactive power compensation; Provide a kind of to loading on the high performance-price ratio scheme that contains the idle quick and continuous compensation of big capacity under the harmonic current environment; Have favorable social and economic benefits, be suitable in electric power system, promoting the use of.
Description of drawings
Fig. 1 is a kind of structural representation of reactive power compensation harmonic governing system; Fig. 2 uses the flow chart that a kind of reactive power compensation harmonic governing system is realized the control method that the reactive power compensation harmonic is administered; Fig. 3 is the capacity sketch map that the mode of employing TSC and SVG combined reactive compensation compensates load; Wherein, The line segment of band " △ " is the required idle capacity signal of network system; The line segment of band " * " is that thyristor switchable capacitor TSC is to the required idle capacity signal of carrying out grading compensation; The line segment of band " " be static reacance generator SVG to thyristor switchable capacitor TSC at different levels between the idle capacity signal that compensates of residue, the line segment of band " zero " is that the reactive compensation capacity that adopts TSC and SVG to carry out combined reactive compensation is illustrated; Fig. 4 is the flow chart of the switching rule of thyristor switchable capacitor TSC.
Embodiment
Embodiment one: specify this execution mode below in conjunction with Fig. 1, Fig. 2 and Fig. 3.A kind of reactive power compensation harmonic governing system is by Passive Reactive Power Compensation part 1, control section 2 and active reactive power compensation and harmonic wave control part 3; Passive Reactive Power Compensation part 1 and active reactive power compensation and harmonic wave control part 3 parallelly connected access electrical networks; Described Passive Reactive Power Compensation part 1 is composed in parallel by M group thyristor switchable capacitor TSC; Thyristor valve group and compensation condenser C that the thyristor D of two reverse parallel connections constitutes are connected into a branch road; Three groups of described branch roads adopt the triangle connected mode to connect and compose one group of thyristor switchable capacitor TSC; Tie point is linked into respectively in the three-phase of electrical network; Wherein, M is the integer greater than 1; Described active reactive power compensation and harmonic wave control part 3 are made up of a static reacance generator SVG and three inductance L, and static reacance generator SVG is made up of the voltage-source type three-phase full-bridge inverter, and the three-phase output end of voltage-source type three-phase full-bridge inverter connects an end of an inductance L respectively; The other end of three inductance L is connected respectively in the three-phase of electrical network; Described control section 2 is made up of controller 2-1, TSC drive circuit 2-2, SVG drive circuit 2-3, the first optical coupling isolation circuit 2-4 and the second optical coupling isolation circuit 2-5, and controller 2-1 connects TSC drive circuit 2-2 to realize the control to TSC drive circuit 2-2 through the first optical coupling isolation circuit 2-4, and M the control signal output ends of TSC drive circuit 2-2 links to each other with the gate pole trigger end of M group thyristor switchable capacitor TSC respectively; Controller 2-1 connects TSC drive circuit 2-3 to realize the control to SVG drive circuit 2-3 through the second optical coupling isolation circuit 2-5, and 6 control signal output ends of SVG drive circuit 2-3 link to each other with 6 gate pole trigger ends of static reacance generator SVG respectively.
Controller 2-1 described in this execution mode adopts the mode of DSP and CPLD associating to control.DSP, i.e. digital signal processor is because it has powerful data-handling capacity and the outstanding speed of service is mainly used in data acquisition and processing (DAP) in native system; CPLD, promptly CPLD is mainly used in control owing to it has good real-time observation and control ability in native system.
The present invention adopts the mode of Passive Reactive Power Compensation and active reactive power compensation combined reactive compensation that network system is carried out reactive power compensation; When idle the changing in the load; In described a kind of reactive power compensation harmonic governing system; Thyristor switchable capacitor TSC is to the required idle grading compensation that carries out, static reacance generator SVG to thyristor switchable capacitor TSC at different levels between idle the compensating of residue.Controller 2-1 of the present invention adopts full digital control method, makes described a kind of reactive power compensation harmonic governing system under the violent situation of the fluctuation of load, still have good dynamic characteristics and stable state accuracy.When containing harmonic current in the load; Static reacance generator SVG realizes the harmonic current that contains in the load is filtered; Suppress thyristor switchable capacitor TSC and system's generation resonance; Therefore, the wave arrestment reactor of need not connecting again in every branch road of thyristor switchable capacitor TSC is practiced thrift system cost.The present invention combines rapidity and continuity and thyristor switchable capacitor TSC the cost advantage when compensation big capacity idle of static reacance generator SVG to reactive power compensation, provides a kind of to loading on the high performance-price ratio scheme that contains the idle quick and continuous compensation of big capacity under the harmonic current environment.
Embodiment two: this execution mode is with the difference of embodiment one described a kind of reactive power compensation harmonic governing system:
Described M group thyristor switchable capacitor TSC, the value of building-out capacitor C is to confirm according to predefined thyristor switchable capacitor TSC compensation capacity value among the m group thyristor switchable capacitor TSC, wherein, m is the natural number from 1 to M.
This execution mode is the further supplementary notes to the capacitance of building-out capacitor C among the thyristor switchable capacitor TSC in the embodiment one; The capacitance of building-out capacitor C is to confirm according to the compensation capacity of thyristor switchable capacitor TSC, and this execution mode preestablishes M group thyristor switchable capacitor TSC respectively according to 2 of unit compensation capacity
N-1Doubly carry out capacity compensation, adopt this kind coded system compensation thyristor switchable capacitor TSC capacity, 1 times, 2 times, 4 times of the compensation capacity unit of the being respectively compensation capacity of M group thyristor switchable capacitor TSC ..., 2
N-1Doubly, wherein, n is 1 to N natural number, and N is the natural number that is not more than M.
Not on the same group among the thyristor switchable capacitor TSC capacitance of building-out capacitor C can equate therefore, among the M group thyristor switchable capacitor TSC the identical thyristor switchable capacitor TSC of compensation capacity can be arranged.
Embodiment three: specify this execution mode below in conjunction with Fig. 1, Fig. 2, Fig. 3.Use a kind of reactive power compensation harmonic governing system described in the embodiment one and realize the control method that the reactive power compensation harmonic is administered, the process that the reactive power compensation harmonic is administered is:
The instantaneous value i of step 1, detection of grid a phase current
SaAnd the instantaneous value i of electrical network c phase current
Sc, the instantaneous value i of detection load a phase current
LaAnd the instantaneous value i of load c phase current
Lc, the instantaneous value i of a phase current of detection static reacance generator SVG output
FaAnd the instantaneous value i of the c phase current of static reacance generator SVG output
Fc, the instantaneous value u of detection static reacance generator SVG DC bus-bar voltage
Dc
The instantaneous value i of the load a phase current that step 2, controller 2-1 obtain according to sampling
LaAnd the instantaneous value i of load c phase current
Lc, utilize thyristor switchable capacitor TSC switching rule to calculate the switching compound mode W of thyristor switchable capacitor TSC, TSC drive circuit 2-2 sends TSC switching signal S
1～S
MTo accomplish above-mentioned switching mode combination;
The instantaneous value i of the electrical network a phase current that step 3, controller 2-1 obtain according to sampling
SaAnd the instantaneous value i of electrical network c phase current
Sc, utilize instantaneous reactive power theory to calculate the command value i of static reacance generator SVG offset current
* Fa
The instantaneous value i of a phase current that the static reacance generator SVG that step 4, controller 2-1 obtain according to sampling exports
Fa, static reacance generator SVG output the instantaneous value i of c phase current
Fc, static reacance generator SVG DC bus-bar voltage instantaneous value u
dAnd the static reacance generator SVG offset current command value i that in step 3, obtains
* Fa, adopt the Direct Current Control method to generate pwm signal, SVG drive circuit 2-3 sends SVG switching signal P
1～P
6
The present invention adopts the mode of Passive Reactive Power Compensation and active reactive power compensation combined reactive compensation that network system is carried out reactive power compensation; When idle the changing in the load; Thyristor switchable capacitor TSC calculates the switching compound mode W of thyristor switchable capacitor TSC according to TSC switching rule, and TSC drive circuit 2-2 sends TSC switching signal S
1～S
MTo accomplish above-mentioned switching mode combination, to the required idle grading compensation that carries out, static reacance generator SVG utilizes instantaneous reactive power theory to calculate the command value i of static reacance generator offset current
* Fa, to thyristor switchable capacitor TSC at different levels between the residue idle compensating.When containing harmonic current in the load, realize filtration by static reacance generator SVG to the harmonic current that contains in the load, suppress thyristor switchable capacitor TSC and system's generation resonance.
In the three-phase three-wire system electric power system, a, b, c three-phase measuring amount sum are zero, therefore, only need to measure two phase parameters, and custom adopts a, c two are measured mutually on the engineering.Described in this execution mode electrical network a is reached calculating and the judgement that the c phase current values is done mutually, also can expand to any two phases in the electrical network three-phase.
Among Fig. 3, what ordinate was represented is compensation capacity, usually, with the inductive reactive power compensation capacity be defined as on the occasion of, the capacitive reactive power compensation capacity is defined as negative value.Q
FmaxWhat represent is thyristor switchable capacitor TSC unit compensation capacity, Q
LmaxExpression be the maximum with the required compensation capacity of network system, be that perception is idle ,-Q
LmaxThe capacitive reactive power of expression.
Embodiment four: specify this execution mode below in conjunction with Fig. 1, Fig. 4.This execution mode realizes that with a kind of reactive power compensation harmonic of execution mode three described application governing system the control method difference that the reactive power compensation harmonic is administered is: in step 2, described thyristor switchable capacitor TSC switching rule is:
Step 2 one, with M organize thyristor switchable capacitor TSC according to compensation capacity sort from small to large be the 1st group, the 2nd group ..., M group;
Step 2 two, M group thyristor switchable capacitor TSC realize that according to different switching compound modes the Passive Reactive Power Compensation capacity has the combination of 2M-1 kind, and the Passive Reactive Power Compensation capacity is Q by compiling from small to large
1, Q
2...,
Step 2 three, can obtain Passive Reactive Power Compensation capacity Q by step 2 one and step 2 two
1, Q
2...,
With thyristor switchable capacitor TSC switching compound mode W
1, W
2...,
The Q-W related table that shines upon one by one;
Step 2 four, the required reactive compensation capacity of network system are Q
L, work as Q
j＜Q
L＜Q
J+1The time, select switching compound mode W
j
This execution mode is that the switching rule of thyristor switchable capacitor TSC in the embodiment three is done further supplementary notes; M is organized thyristor switchable capacitor TSC sort from small to large according to compensation capacity, M group thyristor switchable capacitor TSC can have 2
M-1Plant switching compound mode W
1, W
2...,
, corresponding just can obtain 2
M-a kind of Passive Reactive Power Compensation capacity Q
1, Q
2...,
, Passive Reactive Power Compensation capacity Q presses sequence arrangement from small to large, processes the form that Passive Reactive Power Compensation capacity Q and thyristor switchable capacitor TSC switching compound mode W are mapped to the Q-W related table.The concrete reactive compensation capacity Q required according to electrical network
L, judge the position that it belongs in the Q-W related table, promptly work as Q
LBe positioned at (Q
j, Q
J+1) between the time, choose switching compound mode W
j, TSC drive circuit 2-2 sends M group TSC switching signal S
1～S
MThis process has realized TSC switching compound mode confirmed that thyristor switchable capacitor TSC can realize automatic switching, has accomplished thyristor switchable capacitor TSC to idle grading compensation.
Embodiment five: specify this execution mode below in conjunction with Fig. 1.This execution mode realizes that with a kind of reactive power compensation harmonic of embodiment three described application governing system the control method difference that the reactive power compensation harmonic is administered is:
In step 3, the instantaneous value i of the electrical network a phase current that controller 2-1 obtains according to sampling
SaAnd the instantaneous value i of electrical network c phase current
Sc, go out reactive current and harmonic current components sum i in the power network current based on the instantaneous reactive Theoretical Calculation
Saq, adopt i
* Fa=ki
SaqControl strategy is confirmed static reacance generator SVG offset current command value i
* Fa, wherein, k is calculated by the SVG cancellation ratio B that hope reaches, k=B/ (1-B).
This execution mode is the supplementary notes to embodiment three, and described a kind of reactive power compensation harmonic governing system obtains static reacance generator SVG offset current command value i according to said method
* Fa, be value of feedback with static reacance generator SVG output current, adopt the Direct Current Control method to generate six groups of signal P of PWM
1～P
6, the break-make of three-phase full-bridge inverter switching device among the control static reacance generator SVG after SVG drive circuit 2-3 power amplification.
Claims (1)
1. use reactive power compensation harmonic governing system and realize the control method that the reactive power compensation harmonic is administered; Said reactive power compensation harmonic governing system is made up of Passive Reactive Power Compensation part (1), control section (2) and active reactive power compensation and harmonic wave control part (3); Passive Reactive Power Compensation part (1) and active reactive power compensation and harmonic wave control part (3) parallelly connected access electrical network; Described Passive Reactive Power Compensation part (1) is composed in parallel by M group thyristor switchable capacitor (TSC); Thyristor valve group and compensation condenser C that the thyristor of two reverse parallel connections (D) constitutes are connected into a branch road; Three groups of described branch roads adopt the triangle connected mode to connect and compose one group of thyristor switchable capacitor (TSC); Tie point is linked into respectively in the three-phase of electrical network; Wherein, M is the integer greater than 1; Described active reactive power compensation and harmonic wave control part (3) are made up of a static reacance generator (SVG) and three inductance (L), and static reacance generator (SVG) is made up of the voltage-source type three-phase full-bridge inverter, and the three-phase output end of voltage-source type three-phase full-bridge inverter connects an end of an inductance (L) respectively; The other end of three inductance (L) is connected respectively in the three-phase of electrical network; Described control section (2) is made up of controller (2-1), TSC drive circuit (2-2), SVG drive circuit (2-3), first optical coupling isolation circuit (2-4) and second optical coupling isolation circuit (2-5), and controller (2-1) connects TSC drive circuit (2-2) to realize the control to TSC drive circuit (2-2) through first optical coupling isolation circuit (2-4), and M control signal output ends of TSC drive circuit (2-2) links to each other with the gate pole trigger end of M group thyristor switchable capacitor (TSC) respectively; Controller (2-1) connects SVG drive circuit (2-3) to realize the control to SVG drive circuit (2-3) through second optical coupling isolation circuit (2-5), and 6 control signal output ends of SVG drive circuit (2-3) link to each other with 6 gate pole trigger ends of static reacance generator (SVG) respectively;
The process that the reactive power compensation harmonic is administered is:
The instantaneous value i of step 1, detection of grid a phase current
SaAnd the instantaneous value i of electrical network c phase current
Sc, the instantaneous value i of detection load a phase current
LaAnd the instantaneous value i of load c phase current
Lc, the instantaneous value i of a phase current of detection static reacance generator (SVG) output
FaAnd the instantaneous value i of the c phase current of static reacance generator (SVG) output
Fc, the instantaneous value u of detection static reacance generator (SVG) DC bus-bar voltage
Dc
The instantaneous value i of the load a phase current that step 2, controller (2-1) obtain according to sampling
LaAnd the instantaneous value i of load c phase current
Lc, utilize thyristor switchable capacitor (TSC) switching rule to calculate the switching compound mode W of thyristor switchable capacitor (TSC), TSC drive circuit (2-2) sends TSC switching signal S
1～S
MTo accomplish above-mentioned switching compound mode;
The instantaneous value i of the electrical network a phase current that step 3, controller (2-1) obtain according to sampling
SaAnd the instantaneous value i of electrical network c phase current
Sc, utilize instantaneous reactive power theory to calculate the command value i of static reacance generator (SVG) offset current
* Fa
The instantaneous value i of a phase current of static reacance generator (SVG) output that step 4, controller (2-1) obtain according to sampling
Fa, static reacance generator (SVG) output the instantaneous value i of c phase current
Fc, static reacance generator (SVG) DC bus-bar voltage instantaneous value u
DcAnd static reacance generator (SVG) the offset current command value i that in step 3, obtains
* Fa, adopt the Direct Current Control method to generate pwm signal, SVG drive circuit (2-3) sends SVG switching signal P
1～P
6
It is characterized in that in step 3 the instantaneous value i of the electrical network a phase current that controller (2-1) obtains according to sampling
SaAnd the instantaneous value i of electrical network c phase current
Sc, calculate reactive current and harmonic current components sum i in the power network current based on instantaneous reactive power theory
Saq, adopt i
* Fa=ki
SaqControl strategy is confirmed static reacance generator (SVG) offset current command value i
* Fa, wherein, k is calculated by the SVG cancellation ratio B that hope reaches, k=B/ (1-B).
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