CN107910879A - A kind of active frequency response events control strategy - Google Patents
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Abstract
The invention discloses a kind of active frequency response events control strategy, the operating status being likely to occur under off-line state according to chosen frequency stabilization correlation behavior amount to electric system carries out cluster and forms some typical scenes, the active frequency response control strategy that analysis determines to take per class scene is carried out to above-mentioned typical scene and forms control decision table, active frequency response events control strategy determines：Mains frequency fluctuation and evolution process are divided into two stages i.e. frequency decline stage and frequency retrieval stage；The event control mode of active frequency response is used in the frequency decline stage, mains frequency control is carried out using the parameter feedback controling mode of passive frequency response in the frequency retrieval stage.The control strategy that the application is proposed can effectively intercept frequency decline in the large disturbances lower frequency decline stage, avoid system low-frequency load shedding, system is recovered stable as early as possible in the frequency retrieval stage, avoid system occurrence frequency during active control from vibrating.
Description
Technical field
The present invention relates to technical field of power systems, more particularly to a kind of active frequency response events control strategy.
Background technology
Many factors cause following mains frequency to stablize situation source Wang He sides frequency that is more severe, and enriching constantly at present
Response means need preferably to coordinate, and frequency stabilization level is lifted to give full play to control performance.
The essence of frequency stabilization be after disturbance second to minute level time scale active power balance, its evolution and
The force that " attacking and defending " both ends are depended on whether stabilization contrasts." attacking " corresponds to unbalanced power quantity, " anti-" corresponding to before failure
Three principal elements such as frequency values, system inertia and frequency response ability." attacking " side, the conveying of extra-high voltage alternating current-direct current transmission line of electricity
Power quantity is increasingly lifted, and the huge thermoelectricity and nuclear power generating sets of clean and effective, which progressively instead of, pollutes poorly efficient small thermal power unit,
Power imbalances quantity is significantly increased caused by single element failure；Relatively poor environment, DC line contamination speed is fast in addition,
Cause UHV transmission line direct current monopole locking failure rate higher." anti-" side, on the one hand, what capacity accounting was constantly lifted can be again
The raw energy has tied up the power generation space of conventional fired power generating unit, causes the grid-connected quantity of conventional power unit to reduce, so as to cause system inertia
With the continuous decrease of frequency response ability；Further, the reduction of system inertia and frequency response ability, makes under normal operating condition
Frequency departure integrally increases, and causes the probability that frequency before failure is in low level to be substantially increased.
To ensure whole safe operation of electric network and riding quality, frequency response is arranged to the transregional free work(mutually supported
Energy, is the transmission of electricity assistant service of all generator unit indispensabilities, its control model is the scattered autonomous control according to local frequency difference, though
The frequency response ability of right system is the synthesis of all generating set frequency response abilities, but frequency response between each generating set
It is asynchronous, the mass action effect of frequency response can be reduced.Under large disturbances it is of greatest concern be frequency fluctuation minimum point, because of it
Whether determining the startup of low-frequency load shedding.Occur to frequency to drop to the minimum point time from disturbance it is of short duration, generally in seconds.Frequency is rung
The effect answered is to be subjected to rapid supplemental capacity missing of high-power disturbance lower frequency rapid decrease period in system, frequency is declined real
Effective interception is applied, while avoiding low-frequency load shedding from starting, the input for follow-up slowly regulating measure gains time.Due to disturbance
Frequency fast fall time is of short duration afterwards, if can improve the execution speed of frequency response during this period, can greatly change frequency wave
Dynamic transient process, avoids the generation of low-frequency load shedding.
The content of the invention
For above-mentioned problems of the prior art, the present invention provides a kind of active frequency response events control strategy,
It is a kind of after high-power miss fault occurs the purpose is to propose, it can be improved to greatest extent under existing frequency response facility
Frequency response lowest point, avoids system low-frequency load shedding, to ensure the control strategy of power system security stabilization.Concrete scheme
For：
Comprise the following steps：
S1:The fortune being likely to occur under off-line state according to chosen frequency stabilization correlation behavior amount to electric system
Row state carries out cluster and forms some typical scenes, and the active that analysis determines to take per class scene is carried out to above-mentioned typical scene
Frequency response control strategy forms control decision table；
S2:Active frequency response events control strategy determines：Mains frequency fluctuation and evolution process are divided into two stages
That is frequency decline stage and frequency retrieval stage；The event control mode of active frequency response is used in the frequency decline stage,
The frequency retrieval stage carries out mains frequency control using the parameter feedback controling mode of passive frequency response；
S3:In application on site：Current operating conditions are subjected to scene ownership identification and determine its scene ownership, according to current shape
The deviation of state and affiliated scene carries out sensitivity analysis：The control decision table for belonging to scene is modified, is currently run
Active frequency response control strategy under state；
If breaking down under current operating conditions, frequency response control is carried out according to obtained active control strategies,
If normal operation, the analysis of the electric system subsequent time method of operation is carried out, repeats the above process the control for completing mains frequency
Process processed.
Concrete mode is during the off-line analysis：
S11:Clustering processing is carried out to all operating statuses of foreseeable electric system and forms typical scene:According to power train
The parameter of Generation Side, load side and transmission system transimission power is carried out calculating analysis and contrasted, according to scene clustering rule in system
Clustering processing is carried out to all operating statuses；
S12:Divide electric power system fault urgency level：Dynamic mistake according to the generator amature equation of motion to system frequency
Cheng Jinhang is analyzed, and is divided according to the distance between frequency response minimum point in dynamic process and system low-frequency load shedding initiation culture tight
Anxious degree, i.e., distance is nearer therebetween, and urgency level higher grade；
S13:Formulate decision table：Active frequency response events control strategy is formulated for typical scene, determines control decision
Table, wherein typical scene, control strategy and control decision table are one-to-one relationship；In decision table formulation process, according to institute
The urgency level for belonging to failure under typical scene formulates decision table, carries out the startup of all kinds of units, all kinds of frequency response regulating measures
With the selection of control mode；
S14:If there is decision table same phenomenon, then it is same scene to need two kinds of typical scene clusters；If go out
Existing a certain operating status can not range any typical scene, then increase a typical scene newly.
In application on site：Scene On-line matching is carried out to current operating conditions according to source-net-lotus associated arguments, determines it
Affiliated scene type, utilizes the clear and definite frequency response situation of attacking and defending comparative analysis.
In the application on site：The control decision table of affiliated typical scene is modified using sensitivity analysis, with
Control decision table under to current operating conditions：Vector sum according to corresponding to current operating conditions amount its match typical operation
Distance is shorter between vector corresponding to scene, and the difference in the two corresponding decision table between relevant control parameter and the two institute are right
It is considered as linear relationship to answer the difference between vector, and using the difference between two vectors, typical case is run according to sensitivity analysis
Decision table corresponding to scene is modified.
Corresponding current operating conditions have a corresponding control decision table, in the event of failure, dispatcher
Using the control decision table after renewal, system is controlled, the mode of wherein active frequency response control strategy is：
Under event control, perturbing area all carries out feedforward control in the frequency decline stage with non-perturbing area using prediction frequency difference value
To make, its predicted value is determined offline by perturbing area maximum frequency difference value in passive frequency response control strategy, and in frequency retrieval rank
Two regions of section carry out feedback control according to each local frequency difference respectively：I.e. it is assumed that perturbing area frequency difference is Δ fr, reach most
Low point time is tnadir, control according to parameter be cA, non-perturbing area frequency difference be Δ fl, it is c to control according to parameterBWhen, input
A, the frequency difference of B areas governor meets
By adopting the above-described technical solution, a kind of active frequency response events control strategy provided by the invention, has
Following advantage：1st, the control strategy proposed realizes frequency response by scattered autonomous control to coordination control is concentrated, by feeding back
Feedforward control, the transformation by Corrective control to prevention and control are controlled, can be carried on the premise of frequency response facility is not increased
High system overall frequency response ability, so that the frequency stabilization resilience under lifting large disturbances.2nd, the control strategy proposed
Frequency decline can be effectively intercepted in the large disturbances lower frequency decline stage, system low-frequency load shedding is avoided, makes in the frequency retrieval stage
System recovers stable as early as possible, avoids system occurrence frequency during active control from vibrating.
Brief description of the drawings
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, below will be to embodiment or existing
There is attached drawing needed in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments described in application, for those of ordinary skill in the art, without creative efforts,
Other attached drawings can also be obtained according to these attached drawings.
Fig. 1 is the flow chart of active frequency response events control strategy of the present invention；
Fig. 2 is frequency response dynamics process schematic in the present invention；
Fig. 3 is the schematic diagram of the embodiment of active frequency response events control strategy of the present invention；
Fig. 4 is the analogous diagram of active frequency response events control strategy lower frequency change procedure in the present invention；
Embodiment
To make technical scheme and advantage clearer, with reference to the attached drawing in the embodiment of the present invention, to this
Technical solution in inventive embodiments is clearly completely described：
A kind of active frequency response events control strategy as shown in Figure 1, the parameter of control institute foundation can be trouble point
Or the operation parameters of system other nodes, also but local frequency difference.System frequency declines quickly under high-power missing, low to avoid
The generation of the events such as frequency off-load, it is desirable to which frequency response control has rapidity.And existing this continuous quantity of foundation frequency difference is in order to control
The feedback controling mode of foundation, it is poor due to needing to sample, link, the control timeliness such as comparing.Frequency under high-power missing
Response control should seize every minute and second, and therefore, according to amount of logic whether representing that event of failure occurs, can take the side of feedforward control
Formula, improves control timeliness.Obviously, only consider regional area system stable problem according to local amount control, and measured according to other places
Control can count and system frequency difference spatial and temporal distributions characteristic, can proceed from the situation as a whole to consider the frequency stabilization sex chromosome mosaicism of whole system.According to
Just start to act after disturbance causes controlled volume deviation according to the feedback control locally measured, act not in time, but its control mode is
Closed-loop control, can eliminate influence of a variety of disturbances to controlled variable；And the feedforward control according to other places amount can occur in disturbance
Deviation acts in time before occurring afterwards, can suppress controlled volume deviation as caused by disturbance, but the control has specified property compensation
Limitation, a kind of usual feedforward action can only overcome a kind of interference, and be fed back since control output will not control system,
System disturbance rejection is poor.
Frequency fluctuation and evolution process under large disturbances can be broadly divided into two benches：Frequency decline stage and frequency retrieval rank
Section.See that Fig. 2 shows, wherein Δ tACFor frequency decline stage, Δ tCBFor the frequency retrieval stage.In system operation frequency evolution process
Different phase, to frequency response control requirement also differ.In the frequency decline stage, the requirement to frequency response is quick
Property, therefore its control should use the event control mode of active frequency response；And in the frequency retrieval stage, because frequency has been blocked
Cut, the requirement to frequency response at this time is changed into accuracy by rapidity, and therefore, control mode should be changed into is rung by dynamic frequency
The parameter feedback controling mode answered.Since frequency response Active Control Mode is relative complex, cost of implementation is higher, therefore, not
Under catastrophe failure, frequency response control can respond feedforward control by active frequency and return in traditional parameter feedback controling mode.
I.e. in the case of nominal frequencies response control can decline implementation to frequency and effectively intercept, active frequency response control is not considered
System.
After a failure in the frequency decline stage, if using feed-forward control manner, if control is according to the frequency for being fault point
Difference (for by control unit, since control is according to being nonlocal frequency difference, therefore can be referred to as feed-forward control manner), then its realize compared with
To be simple, only frequency difference signal at failure need to be supplied to by related controlled unit by channel；Believe if controlling according to for failure
Number, i.e. above so-called event control, then since only control starts parameter of the parameter of institute's foundation without controlling institute's foundation,
Therefore adjustment control can not be realized.
No matter using feedforward or feedback control, it controls the parameter of institute's foundation to each depend on current operating status.Cause
Frequency response models are complicated, and frequency response process analysis procedure analysis is related to differential equation resolving, it is difficult to realize on-line analysis and control, therefore can
Solved by the way of off-line analysis, application on site.
The active frequency response events control strategy of the application comprises the following steps：
S1:The fortune being likely to occur under off-line state according to chosen frequency stabilization correlation behavior amount to electric system
Row state carries out cluster and forms some typical scenes, and the active that analysis determines to take per class scene is carried out to above-mentioned typical scene
Frequency response control strategy forms control decision table；
S2:Active frequency response events control strategy determines：Mains frequency fluctuation and evolution process are divided into two stages
That is frequency decline stage and frequency retrieval stage；The event control mode of active frequency response is used in the frequency decline stage,
The frequency retrieval stage carries out mains frequency control using the parameter feedback controling mode of passive frequency response；
S3:In application on site：Current operating conditions are subjected to scene ownership identification and determine its scene ownership, according to current shape
The deviation of state and affiliated scene carries out sensitivity analysis：The control decision table for belonging to scene is modified, is currently run
Active frequency response control strategy under state；
If breaking down under current operating conditions, frequency response control is carried out according to obtained active control strategies,
If normal operation, the analysis of the electric system subsequent time method of operation is carried out, repeats the above process the control for completing mains frequency
Process processed.
During off-line analysis, chosen frequency stabilization correlation behavior amount is first depending on to the operating status that is likely to occur
Clustered, form some typical scenes, then above-mentioned typical scene is analyzed using related analysis method, determined per class
The active frequency response control strategy that scene should be taken, forms control decision table.Control decision table is the specific reality of control strategy
Apply scheme.
In application on site, first by current operating conditions progress scene ownership identification, determine that its scene belongs to, then foundation is worked as
The deviation of preceding state and affiliated scene carries out sensitivity analysis, the control decision table for belonging to scene is modified, so as to obtain
Active frequency response control strategy under current operating conditions；If break down under current operating conditions, according to obtained
Active control strategies carry out frequency response control, if normal operation, carry out the analysis of next method of operation, repeat above-mentioned mistake
Journey.
Further, 1, during off-line analysis：Frequency response influence factor is numerous, and operation is complicated so that operating status number
It is huge, it is difficult to be analyzed one by one, and enforcement difficulty is very big.Therefore, need to be to foreseeable all operation shapes in off-line analysis
State carries out clustering processing, forms typical scene, to reduce off-line analysis workload, improves analysis efficiency.Wherein, typical scene
Formation, be that characteristic quantity can be measured to electric system " source-net-lotus " correlation, i.e., Generation Side, load side and transmission system transmission work(
The parameters such as rate are calculated, analyzed and contrasted, and then according to the comparison of " attacking ", " anti-" both ends associated arguments, according to what is formulated
Rule carries out scene clustering to all operating statuses, in order to which follow-up work simplifies operand, raising control efficiency.
After scene clustering, all operating statuses included in same typical scene can use same control plan
Slightly, it is corresponding with same control decision table, i.e., exist to correspond between typical scene, control strategy and control decision table and close
System.In decision table formulation process, decision table need to be formulated according to the urgency level of failure under affiliated typical scene, carry out all kinds of machines
Group, the startup of all kinds of frequency response regulating measures and the selection of control mode.
On the division of failure urgency level, can according to the generator amature equation of motion to the dynamic process of system frequency into
Row analysis, can be using the distance between frequency response minimum point in dynamic process and system low-frequency load shedding initiation culture as urgent journey
The foundation of division is spent, distance is nearer therebetween, and urgency level higher grade, higher to frequency response rapidity requirement.
Under same urgency level, system " source-net-lotus " state is different, may correspond to different typical scenes, its institute
Corresponding control decision table should also be different；If there is decision table same phenomenon, it is same to need two kinds of typical scene clusters
Scene；And any typical scene can not be ranged by if a certain operating status occur, then a typical scene should be increased newly.
2nd, frequency response ability is monitored on-line
The function of the part is to carry out scene On-line matching to current operating conditions according to source-net-lotus associated arguments, really
Its fixed affiliated scene type；Using attacking and defending comparative analysis, frequency response situation is specified.On the one hand the work can be that scheduling carries out phase
The prevention and control (adjustment of such as method of operation, spare capacity scheduling etc.) answered provide foundation, when on the other hand also occurring for failure
Carry out frequency response control and data basis support is provided.Available data gather with supervisor control or Wide Area Measurement System compared with
To be perfect, its data gathered, can provide hardware guarantee for the implementation of above-mentioned task.
3rd, decision table online updating
Matched although current operating conditions have been carried out typical Run-time scenario by in-service monitoring link, in general due to
Existing operating status is not identical with typical Run-time scenario, if the two difference is larger, then directly application typical case operation
Control decision table corresponding to scene is controlled, and can probably produce relatively large deviation, it is difficult to ensures system operation safety.Using spirit
Basis of sensitivity analysis is modified the control decision table of affiliated typical scene, to obtain the control decision table under current operating conditions.
Typical Run-time scenario and current operating conditions are the vectors that are made of some quantity of states to describe.Due to current operating conditions
The corresponding vector sum of amount its match vector corresponding to typical Run-time scenario between distance it is shorter, the two corresponding decision table
The difference between difference and the two corresponding vector between middle relevant control parameter can be considered as linear relationship.Therefore, Ke Yili
With the difference between two vectors, the decision table corresponding to typical Run-time scenario is modified according to sensitivity analysis.In order to protect
The rapidity applied during confirmation, controling parameter in decision table will be formed to each typical Run-time scenario by off-line analysis
Sensitivity between operating status vector deviation, prepares for further work.
4th, control strategy real-time selection
According to the work of above three step, corresponding current operating conditions have a corresponding control decision table.This
Shi Yidan breaks down, and dispatcher can apply the control decision table after renewal, and system is controlled.
For two regional power grids, interregional interconnection is represented with number line, dotted line represents communication line, and A areas are to disturb
Dynamic area, B areas are non-perturbing area, specifically as Fig. 3 shows.Wherein two Region control modes under " active frequency response events control strategy "
It is as follows：
For unit fired power generating unit, from active balance angle, unit fired power generating unit participates in mains frequency and adjusts process
Meet：
Generator-loading module meets：
In formula：PmFor mechanical frequency；PeFor electromagnetic frequency；H is generator inertia time constant；D is load damped coefficient.
Governor module meets：
In formula：R is unit difference coefficient；PspFor power increment set-point；Δf1Change input quantity for the frequency of unit；TG
For governor time constant；ΔPVFor steam flow.
Steam turbine module meets：
In formula：FHFor the power proportions produced by turbine；TRFor rethermalization time constant；KmFor power conversion efficiency；PmFor
Mechanical output.
Under event control, perturbing area all carries out feedforward control in the frequency decline stage with non-perturbing area using prediction frequency difference value
To make, its predicted value is determined offline by perturbing area maximum frequency difference value in passive frequency response control strategy, and in frequency retrieval rank
Two regions of section carry out feedback control according to each local frequency difference respectively.I.e. it is assumed that perturbing area frequency difference is Δ fr, reach most
Low point time is tnadir, control according to parameter be cA, non-perturbing area frequency difference be Δ fl, it is c to control according to parameterBWhen, input
A, the frequency difference of B areas governor meets
To the specific analogue system of Mr. Yu, it is controlled, system emulation knot using " active frequency response events control strategy "
Fruit such as Fig. 4 shows.A kind of active frequency response events control strategy disclosed by the invention was used in the system frequency rapid decrease stage
Effectively intercepted, to avoid low-frequency load shedding, the ability of strengthening system resisting risk.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art the invention discloses technical scope in, technique according to the invention scheme and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (5)
- A kind of 1. active frequency response events control strategy, it is characterised in that：Comprise the following steps：S1:The operation shape being likely to occur under off-line state according to chosen frequency stabilization correlation behavior amount to electric system State carries out cluster and forms some typical scenes, and the active frequency that analysis determines to take per class scene is carried out to above-mentioned typical scene Response control strategy forms control decision table；S2:Active frequency response events control strategy determines：Mains frequency fluctuation and evolution process are divided into two stages i.e. frequency Rate decline stage and frequency retrieval stage；The event control mode of active frequency response is used in the frequency decline stage, in frequency Restoration stage carries out mains frequency control using the parameter feedback controling mode of passive frequency response；S3:In application on site：By current operating conditions carry out scene ownership identification determine its scene ownership, according to current state with The deviation of affiliated scene carries out sensitivity analysis：The control decision table for belonging to scene is modified, obtains current operating conditions Under active frequency response control strategy；If breaking down under current operating conditions, frequency response control is carried out according to obtained active control strategies, if fortune Row is normal, then carries out the analysis of the electric system subsequent time method of operation, repeats the above process the control for completing mains frequency Journey.
- 2. a kind of active frequency response events control strategy according to claim 1, is further characterized in that：Described offline point Concrete mode is during analysis：S11:Clustering processing is carried out to all operating statuses of foreseeable electric system and forms typical scene:According in electric system The parameter of Generation Side, load side and transmission system transimission power carries out calculating analysis with contrast, according to scene clustering rule to institute There is operating status to carry out clustering processing；S12:Divide electric power system fault urgency level：According to the generator amature equation of motion to the dynamic process of system frequency into Row analysis, urgent journey is divided according to the distance between frequency response minimum point in dynamic process and system low-frequency load shedding initiation culture Degree, i.e., distance is nearer therebetween, and urgency level higher grade；S13:Formulate decision table：Active frequency response events control strategy is formulated for typical scene, determines control decision table, its Middle typical scene, control strategy and control decision table are one-to-one relationship；In decision table formulation process, according to affiliated typical case The urgency level of failure formulates decision table under scene, carries out the startup and control of all kinds of units, all kinds of frequency response regulating measures The selection of mode；S14:If there is decision table same phenomenon, then it is same scene to need two kinds of typical scene clusters；If there is certain One operating status can not range any typical scene, then increase a typical scene newly.
- 3. a kind of active frequency response events control strategy according to claim 1, is further characterized in that：Application on site In：Scene On-line matching is carried out to current operating conditions according to source-net-lotus associated arguments, its affiliated scene type is determined, utilizes The clear and definite frequency response situation of attacking and defending comparative analysis.
- 4. a kind of active frequency response events control strategy according to claim 1, is further characterized in that：It is described online In：The control decision table of affiliated typical scene is modified using sensitivity analysis, to obtain under current operating conditions Control decision table：Vector sum according to corresponding to current operating conditions amount its match vector corresponding to typical Run-time scenario Between distance it is shorter, the difference between difference in the two corresponding decision table between relevant control parameter and the two corresponding vector is recognized To be linear relationship, using the difference between two vectors, according to sensitivity analysis to the decision table corresponding to typical Run-time scenario It is modified.
- 5. a kind of active frequency response events control strategy according to claim 1, is further characterized in that：Corresponding current fortune Row state has a corresponding control decision table, and in the event of failure, dispatcher can apply the control after renewal to determine Plan table, is controlled system, and the mode of wherein active frequency response control strategy is：Under event control, perturbing area all carries out feedforward control in the frequency decline stage with non-perturbing area using prediction frequency difference value, Its predicted value determined offline by perturbing area maximum frequency difference value in passive frequency response control strategy, and in the frequency retrieval stage two Region carries out feedback control according to each local frequency difference respectively：I.e. it is assumed that perturbing area frequency difference is Δ fr, reach minimum point Time is tnadir, control according to parameter be cA, non-perturbing area frequency difference be Δ fl, it is c to control according to parameterBWhen, input A, B The frequency difference of area's governor meets<mrow> <msub> <mi>c</mi> <mi>A</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>max&Delta;f</mi> <mi>r</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo><</mo> <mi>t</mi> <mo>&le;</mo> <msub> <mi>t</mi> <mrow> <mi>n</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>r</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&Delta;f</mi> <mi>r</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>></mo> <msub> <mi>t</mi> <mrow> <mi>n</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>r</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow><mrow> <msub> <mi>c</mi> <mi>B</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>max&Delta;f</mi> <mi>r</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo><</mo> <mi>t</mi> <mo>&le;</mo> <msub> <mi>t</mi> <mrow> <mi>n</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>r</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&Delta;f</mi> <mi>l</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>></mo> <msub> <mi>t</mi> <mrow> <mi>n</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>r</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
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