CN107482651A - It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation - Google Patents

It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation Download PDF

Info

Publication number
CN107482651A
CN107482651A CN201710689404.XA CN201710689404A CN107482651A CN 107482651 A CN107482651 A CN 107482651A CN 201710689404 A CN201710689404 A CN 201710689404A CN 107482651 A CN107482651 A CN 107482651A
Authority
CN
China
Prior art keywords
mrow
msub
mfrac
msubsup
mover
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201710689404.XA
Other languages
Chinese (zh)
Inventor
葛维春
王磊
许韦华
张艳军
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
State Grid Corp of China SGCC
State Grid Liaoning Electric Power Co Ltd
Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd
Original Assignee
State Grid Corp of China SGCC
State Grid Liaoning Electric Power Co Ltd
Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by State Grid Corp of China SGCC, State Grid Liaoning Electric Power Co Ltd, Electric Power Research Institute of State Grid Liaoning Electric Power Co Ltd filed Critical State Grid Corp of China SGCC
Priority to CN201710689404.XA priority Critical patent/CN107482651A/en
Publication of CN107482651A publication Critical patent/CN107482651A/en
Pending legal-status Critical Current

Links

Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Energy or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Landscapes

  • Business, Economics & Management (AREA)
  • Engineering & Computer Science (AREA)
  • Economics (AREA)
  • Human Resources & Organizations (AREA)
  • Strategic Management (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Marketing (AREA)
  • General Physics & Mathematics (AREA)
  • General Business, Economics & Management (AREA)
  • Tourism & Hospitality (AREA)
  • Public Health (AREA)
  • General Health & Medical Sciences (AREA)
  • Primary Health Care (AREA)
  • Water Supply & Treatment (AREA)
  • Power Engineering (AREA)
  • Development Economics (AREA)
  • Game Theory and Decision Science (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Operations Research (AREA)
  • Quality & Reliability (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

The present invention is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation, proposes a kind of to be based on using WAMS (Wide Area Measurement System, WAMS) and consider the power system optimal dispatch method of primary frequency modulation.The method overcome existing prior art be only able to detect part or data transfer delay cannot get unified time point each monitoring point of system information deficiency the problem of, improve and optimizate method, using PMU and GPS WAMS can dynamically recording the whole network phasor information the characteristics of, monitoring event ex-post analysis, global and local search can be balanced well, and stability monitoring is carried out to system frequency.

Description

It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation
Technical field
The present invention relates to the operation of power system and control technology field, more particularly to a kind of lifting system optimization ability Method.Accurately to realize that Multiobjective Optimal Operation considers system primary frequency modulation characteristic.
Background technology
With expanding day by day for China's alternating current-direct current Power System Interconnection scale, the continuous growth of workload demand, novel energy it is big Amount input, power system are at the target that optimized operation state is power system optimal dispatch.
Traditional power system optimal dispatch is divided into static optimization scheduling and dynamically optimized scheduling.Dynamically optimized scheduling is examined Consider the contact between each period in dispatching cycle, can reasonably reflect the running situation of system.Traditional dispatching party Fado uses single object optimization dispatching method, i.e., is up to target to pursue total consumption of coal amount minimum or systematic economy interests, these Optimized algorithm based on mathematical theory is difficult to obtain globally optimal solution, and has the problem of algorithm is rough.Intelligent optimization Algorithm takes parallel computation mechanism, and it is convenient that algorithm is realized, and possesses stronger robustness, but being still difficult to overcome is absorbed in The problem of locally optimal solution.These problems crucial is produced when cannot be accurate unified in each monitoring point in power network Mark, also simply the data of part are effective for obtained measured value, and plus propagation time delay, target system is each when cannot unify The phasor information of individual monitoring point.And traditional algorithm do not consider fired power generating unit fire coal consumption, pollutant discharge amount etc. it is a variety of because Element.These aspects all limit the Optimized Operation of power system.
In recent years, as the strong unit commitment of the randomnesss such as wind-powered electricity generation is run, faced in terms of Power System Dynamic Optimal Dispatch The problem of new.The randomness of wind-powered electricity generation makes the predictability of power system be deteriorated, if the ratio of system apoplexy capacitance is big, is Unbalanced power phenomenon occurs in system, and now if spare capacity can not balance the fluctuation of wind power output, system can produce frequency Change, cause grid stability poor.
The primary frequency function of power system is the important means for safeguarding power grid operation, when the whole network frequency is beyond just During normal frequency range, participate in each speed regulator equipment of primary frequency modulation can automatically be increased according to the change of frequency in power network or Reduce the power of unit, while the power consumption of part also can be automatically reduced or increased in load according to the change of mains frequency, So as to reach new active balance between supply and demand.But the method for traditional measurement frequency data and do not have real-time, it is relatively coarse, Optimal Operation Model based on this data structure is also and inaccurate.With based on synchronous phasor measuring device (Phase Measurement Unit, PMU) WAMS progressively application, how accurately to realize consideration system primary frequency modulation The multi-objective optimization scheduling of characteristic is urgently to be resolved hurrily.
The Optimized Operation of current electric grid obtains because each monitoring point in power network cannot get accurate unified markers Also simply the data of part are effective for measured value, plus propagation time delay, target system each monitoring point when cannot unify Phasor information, the Multiobjective Optimal Operation for accurately accounting for system primary frequency modulation characteristic can not be realized.
The content of the invention
The purpose of the present invention is to overcome the weak point of prior art, proposes that one kind is based on using WAMS (Wide Area Measurement System, WAMS) and consider the electric power system optimization method of primary frequency modulation.This method gram The each monitoring of system that existing prior art is only able to detect part or data transfer delay cannot get unified time point is taken The problem of deficiency of the information of point, method is improved and optimizated, can dynamically recording the whole network phasor information using PMU and GPS WAMS The characteristics of, event ex-post analysis is monitored, global and local search can be balanced well, stability monitoring is carried out to system frequency. Improve traditional optimization method, constructing system primary frequency modulation method, advantageously reduce the reserved appearance of the upper and lower rotating equipment of system Amount, improve system operation economy.
Multi-objective hybrid optimization scheduling model considers fired power generating unit fire coal consumption, pollutant discharge amount, standby risk, electricity Net company purchases strategies, wind power integration etc., and make multiple optimization aims and finally occur with the situation of desired value.Consideration system one Optimization aim is initially set up during the Optimal Operation Model of secondary frequency modulation, basic constraint is added to target, before primary frequency modulation is considered Put and establish rotation condition, in the Load flow calculation of each scene, need to count and the primary frequency modulation characteristic of system；
The purpose of the present invention is realized using following technical proposals：
The present invention provide it is a kind of based on using WAMS and considering the electric power system optimization method of primary frequency modulation, It thes improvement is that methods described is based on power network wide-area monitoring systems WAMS, utilizes Fourier's phasor analysis, structure electricity The novel detection method of primary frequency modulation in Force system, this novel detection method is applied into power system optimal dispatch method In, original dispatching method is optimized, methods described comprises the steps：
Step 1：Obtain power network metrical information in real time from power network wide-area monitoring systems WAMS.
Step 2：Utilize recursion discrete fourier phasor analysis, first in improved phase quantity collection system PMU, root Power system phasor information is acquired according to the GPS data provided, fundamental phasors are obtained by the sampled point of sinusoidal signal.
Step 3：Next provides fundamental phasors recursive algorithm.
Step 4：Frequency measurement model is finally obtained by the relation of phasor phase angle and frequency input signal.Step 5：Establish The power system optimal dispatch model of consideration system primary frequency modulation.
Step 6：Mixed integer programming approach (MILP) solving model
Step 7：Contrasted, output primary frequency modulation instruction, completed with voltage x current active reactive phasor frequency sampling value System primary frequency modulation Optimized Operation
The technical scheme is that：
Step 1：Obtain power network metrical information in real time from power network wide-area monitoring systems WAMS,
Step 2：Using recursion discrete fourier phasor analysis, in improved phase quantity collection system PMU, according to GPS The data of offer are acquired to power system phasor information, and fundamental phasors are obtained by the sampled point of sinusoidal signal.
Step 2.1：Input signal is sine, and angular speed ω, voltage is represented by time domain：
ω:Angular speed；
φ:Phase shifting angle；
Y:Voltage.
Also voltage available complex phase amountRepresent：
Step 2.2：If Y (t) frequency is 50Hz, Y (t) is sampled, each cycle adopts N point, obtains discrete Sequence { Yk}：
N：Sampling number in a cycle.
Step 2.3：To obtained { YkDFT is carried out, its fundamental phasors is obtained, is represented by：
YcYs：It is defined as sequence { YkSine and cosine product and.
Step 2.4：The sinusoidal input signal complex phase amount defined by formula (1) is represented by：
Step 2.5：It can be drawn by formula (2)-(4), the complex phase amount form of sinusoidal signal was with carrying out discrete Fourier change The fundamental wave changed has following formula relation：
Voltage fundamental phasor.
Above-mentioned conclusion is all based on the sinusoidal signal of input is standard sine wave, without harmonic pollution.It is if defeated Enter and be also mingled with other frequencies in signal, the phasor in formula (6) is then filtered fundamental phasors, therefore input signal must be through Band-pass filter is crossed, to reduce error.
Step 3：Secondly fundamental phasors recursive algorithm
The sinusoidal input signal that step 3.1 is defined by formula (1) obtains sampling point sequence { Yk, k=0 ..., N-1 }, thus Sampling point sequence obtains its phasor form according to formula (6).It can obtain sampling point sequence { Y in next stepk, k=1 ..., N }, equally It can obtain its phasor form.Therebetween the radian that phasor turns over isBy formula (1), (2), (6), second group of sampled point can Do such as down conversion：
Step 3.2 can be drawn by formula (8), by v (t)=Y (t) ejθ(t)The phasor calculated, often increase a sampling Point, the radian that new phasor turns in complex plane are 2 π/N.
When obtaining the sampled point of r-th window, its fundamental phasors is calculated：
Yc (r)、Ys (r)：Sampled point is in r-th of window time series { YkSine and cosine product and.
The fundamental phasors of r-th of window.
Known by formula (10)-(12), r-th of window and the r-1 window have no direct recurrence relation, are calculating r-th Amount of calculation needs 2N multiplication, 2 (N-1) sub-additions during the phasor of window, it is contemplated that the property of DFT.Sampling The fundamental phasors that the DFT of point obtains are unrelated with the start-phase of sampled point.Phase is calculated when using recursive algorithm During amount, static phasor can be obtained in complex plane；And it is rotation in complex plane that the phasor that common Fourier transform obtains, which is, , angular speed ω.
Step 4：Frequency measurement model is finally obtained by the relation of phasor phase angle and frequency input signal.
Step 4.1：Frequency input signal, when calculating voltage phasor with formula (13), obtains to stablize 50Hz in complex plane Static phasor.
Step 4.2：If frequency input signal changes, if frequency offset (benchmark 50Hz) is Δ f, and now Sample frequency do not change, then formula (13) is changed into：
Frequency obtains initializing fundamental phasors when being 50Hz.
Δf：Frequency offset.
The rate of change of frequency input signal and its complex phase amount phase angle has direct relation.Above formula is rewritable to be：
Obtain frequency measurement model.
Step 5：Establish the power system optimal dispatch model of consideration system primary frequency modulation.
Step 5.1：The object function of the power system optimal dispatch model of consideration system primary frequency modulation：
For object function to make system operation total cost minimum, total cost includes electrical power generators cost and primary frequency modulation Standby expense, mathematic(al) representation are as follows:
Y in formulait--- unit open state, yit=1 represents to start shooting in t period units i；yit=0 represents compressor emergency shutdown；
zit--- compressor emergency shutdown state, zit=1 represents to shut down in t period units i；zit=0 represents unit start；
uit--- operating states of the units, uit=1 represents to run in t period units i；uit=0 represents unit outage；
Pit--- unit i is in t period generated energy；
--- unit i is in t period primary frequency modulation spare capacities；
--- it is respectively unit i start expense, idleness expense, operating cost and once The standby expense of frequency modulation.
The operating cost of unit can be expressed as:
In formula：ait、bit、cit--- unit consumption characteristic coefficient.
The standby expense of primary frequency modulation can be expressed as:
--- the standby cost coefficient of primary frequency modulation.
Step 5.2：The constraints of the power system optimal dispatch model of consideration system primary frequency modulation：
(1) system power Constraints of Equilibrium
The power-balance constraint for meeting system is needed after wind-electricity integration, ignores line power loss here, expression formula is:
In formula：Pwt、PLt--- t periods wind power and load.
(2) unit output constrains
In formula：--- unit minimum load constrains and EIAJ constraint.
(3) primary frequency modulation inequality constraints
(4) system frequency deviation constrains
In order to ensure system operation safety, avoid load from cutting off, need to set low-limit frequency, i.e.,:
ΔfminThe formula (24) of≤Δ f≤0
In formula, Δ fmin--- frequency departure lower limit as defined in system.
Step 6：Mixed integer programming approach (MILP) solving model
Because MILP methods belong to the category of linear programming, therefore when using MILP method Solve problems, it is necessary to first The problem of processing, is linearized.All there is non-linear letter for object function and constraints in the standby mathematical modeling of primary frequency modulation Number, needs, by a series of conversion, to introduce extra auxiliary variable, line is transformed it on the basis of required precision is met Property function, is then solved using mixed integer programming program again.
Step 6.1：The linearisation of object function
The method of nonlinear function piece-wise linearization is taken herein to handle object function.Introduce following variable:NiFor machine Total segments that group i contributes；For outputs of the unit i within the t periods on segmentation j；It is bent in its consumption function for unit i Slope in line jth section, j=1,2,3 ... Ni.By unit i output sectionIt is equally divided into NiSection, then every section Length beOutputs of the unit i on every section, can when segments is enough between 0 and segment length To be approximately considered unit i segment length of the output equal to every section, it is assumed that unit is P in period t outputit, this output can use n (n≤Ni) individual segment length represents, such as following formula:
Every section of upper corresponding slope can be calculated by consumption characteristic, therefore, the operating cost of unit can be write as segmentation Linear function sum, i.e.,
Non-linear objective function is just now completed into linearisation.
Step 6.2：The linearisation of constraints
It is most importantly a reserve frequency deviation constraint in Optimized model constraints, is needed before Solve problems Linearized, introduce binary system aid decision variable x hereit：
As system frequency excursion Δ ftBreak frequency deviation delta f less than unit iitWhen, xitTake 1；Conversely work as Δ ftIt is more than Unit i break frequency deviation delta fitWhen, xitTake 0；Then have：
It is a sufficiently large positive integer in formula, L can take here
By introducing variable xitThe standby frequency departure constraints of primary frequency modulation can be linearized：
L' is most enough big positive integer in above formula, and L' can be with value P herei max。
Notice and still have non-linear component uitDiΔft, therefore introduce variable hitAnd make hit=uitΔft, for New variables hitNeed to meet following inequality:
uitΔfmin≤hit≤ 0 formula (31)
(1-uit)Δfmin≤Δft-hit≤ 0 formula (32)
The linearisation of object function and constraints is now just completed, can be entered by mixed integer programming program The Optimization Solution of row scheme.
Step 7：Contrasted, output primary frequency modulation instruction, completed with voltage x current active reactive phasor frequency sampling value System primary frequency modulation Optimized Operation.
Brief description of the drawings：Fig. 1 is a kind of based on WAMS and to consider the electric power system optimization method flow diagram of primary frequency modulation.
Embodiment：
1 pair of this method specific implementation is described further below in conjunction with the accompanying drawings.
It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation, comprise the following steps：Step 1：From electricity Power network metrical information is obtained in net wide-area monitoring systems WAMS in real time and wind-powered electricity generation fluctuation causes frequency fluctuation Δ f
Step 2：Utilize recursion discrete fourier phasor analysis, first in improved phase quantity collection system PMU, root Power system phasor information is acquired according to the GPS data provided, fundamental phasors are obtained by the sampled point of sinusoidal signal.
Step 2.1：Input signal is sine, and angular speed ω, voltage is represented by time domain：
ω:Angular speed；
φ；Phase shifting angle；
Y:Voltage.
Also voltage available complex phase amountRepresent：
Step 2.2：If Y (t) frequency is 50Hz, Y (t) is sampled, each cycle adopts N point, obtains discrete Sequence { Yk}：
N：Sampling number in a cycle.
Step 2.3：To obtained { YkDFT is carried out, its fundamental phasors is obtained, is represented by：
YcYsIt is defined as sequence { YkSine and cosine product and.
Step 2.4：The sinusoidal input signal complex phase amount defined by formula (1) is represented by：
Step 2.5：It can be drawn by formula (2)-(4), the complex phase amount form of sinusoidal signal was with carrying out discrete Fourier change The fundamental wave changed has following formula relation：
Above-mentioned conclusion is all based on the sinusoidal signal of input is standard sine wave, without harmonic pollution.It is if defeated Enter and be also mingled with other frequencies in signal, the phasor in formula (6) is then filtered fundamental phasors, therefore input signal must be through Band-pass filter is crossed, to reduce error.
Step 3：Fundamental phasors recursive algorithm
The sinusoidal input signal that step 3.1 is defined by formula (1) obtains sampling point sequence { Yk, k=0 ..., N-1 }, thus Sampling point sequence obtains its phasor form according to formula (6).It can obtain sampling point sequence { Y in next stepk, k=1 ..., N }, equally It can obtain its phasor form.Therebetween the radian that phasor turns over isBy formula (1), (2), (6), second group of sampled point can Do such as down conversion：
Step 3.2 can be drawn by formula (8), by v (t)=Y (t) ejθ(t)The phasor calculated, often increase a sampling Point, the radian that new phasor turns in complex plane are 2 π/N.
When obtaining the sampled point of r-th window, its fundamental phasors is calculated：
Yc (r)、Ys (r)：Sampled point is in r-th of window time series { YkSine and cosine product and.
The fundamental phasors of r-th of window.
Known by formula (10)-(12), r-th of window and the r-1 window have no direct recurrence relation, are calculating r-th Amount of calculation needs 2N multiplication, 2 (N-1) sub-additions during the phasor of window, it is contemplated that the property of DFT.Sampling The fundamental phasors that the DFT of point obtains are unrelated with the start-phase of sampled point.Phase is calculated when using recursive algorithm During amount, static phasor can be obtained in complex plane；And it is rotation in complex plane that the phasor that common Fourier transform obtains, which is, , angular speed ω.
Step 4：Frequency measurement model is obtained by the relation of phasor phase angle and frequency input signal.
Step 4.1：Frequency input signal, when calculating voltage phasor with formula (13), obtains to stablize 50Hz in complex plane Static phasor.
Step 4.2：If frequency input signal changes, if frequency offset (benchmark 50Hz) is Δ f, and now Sample frequency do not change, then formula (13) is changed into：
Frequency obtains initializing fundamental phasors when being 50Hz；
Δf：Frequency offset.
The rate of change of frequency input signal and its complex phase amount phase angle has direct relation.Above formula is rewritable to be：
Obtain frequency measurement model.
Step 5：Establish the power system optimal dispatch model of consideration system primary frequency modulation.
Step 5.1：The object function of the power system optimal dispatch model of consideration system primary frequency modulation：
For object function to make system operation total cost minimum, total cost includes electrical power generators cost and primary frequency modulation Standby expense, mathematic(al) representation are as follows:
Y in formulait--- unit open state, yit=1 represents to start shooting in t period units i；yit=0 represents compressor emergency shutdown；
zit--- compressor emergency shutdown state, zit=1 represents to shut down in t period units i；zit=0 represents unit start；
uit--- operating states of the units, uit=1 represents to run in t period units i；uit=0 represents unit outage；
Pit--- unit i is in t period generated energy；
--- unit i is in t period primary frequency modulation spare capacities；
--- it is respectively unit i start expense, idleness expense, operating cost and once The standby expense of frequency modulation.
The operating cost of unit can be expressed as:
In formula：ait、bit、cit--- unit consumption characteristic coefficient.
The standby expense of primary frequency modulation can be expressed as:
--- the standby cost coefficient of primary frequency modulation.
Step 5.2：The constraints of the power system optimal dispatch model of consideration system primary frequency modulation：
(1) system power Constraints of Equilibrium
The power-balance constraint for meeting system is needed after wind-electricity integration, ignores line power loss here, expression formula is:
In formula：Pwt、PLt--- t periods wind power and load.
(2) unit output constrains
In formula：--- unit minimum load constrains and EIAJ constraint.
(3) primary frequency modulation inequality constraints
(4) system frequency deviation constrains
In order to ensure system operation safety, avoid load from cutting off, need to set low-limit frequency, i.e.,:
ΔfminThe formula (24) of≤Δ f≤0
In formula, Δ fmin--- frequency departure lower limit as defined in system.
Step 6：Mixed integer programming approach (MILP) solving model
Because MILP methods belong to the category of linear programming, therefore when using MILP method Solve problems, it is necessary to first The problem of processing, is linearized.All there is non-linear letter for object function and constraints in the standby mathematical modeling of primary frequency modulation Number, needs, by a series of conversion, to introduce extra auxiliary variable, line is transformed it on the basis of required precision is met Property function, is then solved using mixed integer programming program again.
Step 6.1：The linearisation of object function
The method of nonlinear function piece-wise linearization is taken herein to handle object function.Introduce following variable:NiFor machine Total segments that group i contributes；For outputs of the unit i within the t periods on segmentation j；It is bent in its consumption function for unit i Slope in line jth section, j=1,2,3 ... Ni.By unit i output sectionIt is equally divided into NiSection, then every section Length beOutputs of the unit i on every section, can when segments is enough between 0 and segment length To be approximately considered unit i segment length of the output equal to every section, it is assumed that unit is P in period t outputit, this output can use n (n≤Ni) individual segment length represents, such as following formula:
Every section of upper corresponding slope can be calculated by consumption characteristic, therefore, the operating cost of unit can be write as segmentation Linear function sum, i.e.,
Non-linear objective function is just now completed into linearisation.
Step 6.2：The linearisation of constraints
It is most importantly a reserve frequency deviation constraint in Optimized model constraints, is needed before Solve problems Linearized, introduce binary system aid decision variable x hereit：
As system frequency excursion Δ ftBreak frequency deviation delta f less than unit iitWhen, xitTake 1；Conversely work as Δ ftIt is more than Unit i break frequency deviation delta fitWhen, xitTake 0；Then have：
It is a sufficiently large positive integer in formula, L can take here
By introducing variable xitThe standby frequency departure constraints of primary frequency modulation can be linearized：
L' is most enough big positive integer in above formula, and L' can be with value P herei max。
Notice and still have non-linear component uitDiΔft, therefore introduce variable hitAnd make hit=uitΔft, for New variables hitNeed to meet following inequality:
uitΔfmin≤hit≤ 0 formula (31)
(1-uit)Δfmin≤Δft-hit≤ 0 formula (32)
The linearisation of object function and constraints is now just completed, can the side of progress by mixed integer programming program The Optimization Solution of case.
Step 7：Contrasted, output primary frequency modulation instruction, completed with voltage x current active reactive phasor frequency sampling value System primary frequency modulation Optimized Operation
Beneficial effect：Realize the Multi-objective hybrid optimization scheduling model of consideration system primary frequency modulation characteristic.When wind-powered electricity generation is dashed forward So during fluctuation, the imbalance of the active power of system can cause the deviation of system frequency.Within the very short time, system Primary frequency modulation acts first, the active power amount of unbalance of primary frequency modulation action meeting regulating system.If now can be inclined in frequency A part of Frequency Index is sacrificed in the allowed band of difference, then only need to be using remaining after regulating units regulation primary frequency modulation effect Unbalanced power amount, this is equivalent to alleviate standby nervous degree in peak regulation；From the perspective of from another angle, if wanting to protect Card system it is standby on certain level, it is contemplated that the primary frequency modulation characteristic of system can reduce system to a certain extent Spinning reserve reserved capacity, improve system operation economy.

Claims (11)

  1. Based on WAMS and consider the electric power system optimization method of primary frequency modulation 1. a kind of, it is characterised in that this method includes following Step：Step 1：Obtain power network metrical information in real time from power network wide-area monitoring systems WAMS；Step 2：Utilize discrete Fu of recursion In leaf phasor analysis, in improved phase quantity collection system PMU, according to GPS provide data to power system phasor information It is acquired, fundamental phasors is obtained by the sampled point of sinusoidal signal；Step 3：Provide fundamental phasors recursive algorithm；Step 4：Finally Frequency measurement model is obtained by the relation of phasor phase angle and frequency input signal；Step 5：Establish the electricity of consideration system primary frequency modulation Force system Optimal Operation Model；Step 6：Mixed integer programming approach (MILP) solving model step；7：With the active nothing of voltage x current Work(phasor frequency sampling value is contrasted, and output primary frequency modulation instruction, completes system primary frequency modulation Optimized Operation.
  2. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 2. according to claim 1 It is, frequency caused by obtaining power network metrical information and wind-powered electricity generation fluctuation in real time from power network wide-area monitoring systems WAMS in step 1 Rate fluctuation Δ f.
  3. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 3. according to claim 1 It is, recursion discrete fourier phasor analysis is utilized in step 2, in improved phase quantity collection system PMU, are carried according to GPS The data of confession are acquired to power system phasor information, and fundamental phasors are obtained by the sampled point of sinusoidal signal, sinusoidal signal Complex phase amount form has following formula relation with the fundamental wave for carrying out DFT：
    <mrow> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mi>j</mi> <mover> <msub> <mi>Y</mi> <mn>1</mn> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mrow> <mo>(</mo> <msub> <mi>Y</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>jY</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow>
  4. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 4. according to claim 1 It is, when fundamental phasors recursive algorithm is secondly provided described in step 3 obtaining the sampled point of r-th window, its base is calculated Ripple phasor：
    <mrow> <msubsup> <mi>Y</mi> <mi>c</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mrow> <mi>k</mi> <mo>+</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> </mrow>
    <mrow> <msubsup> <mi>Y</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mrow> <mi>k</mi> <mo>+</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>Y</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>jY</mi> <mi>c</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
  5. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 5. according to claim 1 It is, finally obtains frequency measurement model with entering the relation of signal frequency by phasor phase angle described in step 4, the model is：
  6. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 6. according to claim 3 It is, step 2 includes：
    Step 2.1 input signal is sine, and angular speed ω, voltage is represented by time domain：
    <mrow> <mi>Y</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mi>Y</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <mi>&amp;phi;</mi> <mo>)</mo> </mrow> </mrow>
    Also voltage available complex phase amountRepresent：
    <mrow> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <msup> <mi>Ye</mi> <mrow> <mi>j</mi> <mi>&amp;phi;</mi> </mrow> </msup> <mo>=</mo> <mi>Y</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;phi;</mi> <mo>+</mo> <mi>Y</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;phi;</mi> </mrow>
    Step 2.2：If Y (t) frequency is 50Hz, Y (t) is sampled, each cycle adopts N number of point, obtains discrete sequence {Yk}：
    <mrow> <msub> <mi>Y</mi> <mi>k</mi> </msub> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mi>Y</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> <mo>+</mo> <mi>&amp;phi;</mi> <mo>)</mo> </mrow> </mrow>
    Step 2.3：To obtained { YkDFT is carried out, its fundamental phasors is obtained, is represented by：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <msub> <mi>Y</mi> <mn>1</mn> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mi>k</mi> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mi>k</mi> </msub> <mi>cos</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> <mo>-</mo> <mi>j</mi> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mi>k</mi> </msub> <mi>sin</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>Y</mi> <mi>c</mi> </msub> <mo>-</mo> <msub> <mi>jY</mi> <mi>s</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
    YcYsIt is defined as sequence { YkSine and cosine product and.
    Step 2.4：The sinusoidal input signal complex phase amount defined by step 2.1 is represented by：
    <mrow> <msub> <mi>Y</mi> <mi>c</mi> </msub> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mi>Y</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;phi;</mi> </mrow>
    <mrow> <msub> <mi>Y</mi> <mi>s</mi> </msub> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mi>Y</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;phi;</mi> </mrow>
  7. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 7. according to claim 3 It is, the conclusion of step 2 is all based on the sinusoidal signal of input is standard sine wave, without harmonic pollution.If input Also it is mingled with other frequencies in signal, the phasor in step 2.5 is then filtered fundamental phasors, therefore input signal has to pass through Band-pass filter, to reduce error.
  8. A kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature 8. according to claim 4 It is, step 3 includes：
    The sinusoidal input signal that step 3.1 is defined by step 2.1 obtains sampling point sequence { Yk, k=0 ..., N-1 }, thus sample Point sequence obtains its phasor form according to step 2.5.It can obtain sampling point sequence { Y in next stepk, k=1 ..., N }, it can equally obtain To its phasor form.Therebetween the radian that phasor turns over isBy formula step 2.1, step 2.2, step 2.5, second group is adopted Sampling point can be done such as down conversion：
    <mrow> <mi>Y</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mi>Y</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>+</mo> <mi>&amp;phi;</mi> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mo>)</mo> </mrow> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mi>e</mi> <mi>w</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>Ye</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mi>&amp;phi;</mi> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>o</mi> <mi>l</mi> <mi>d</mi> <mo>)</mo> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mi>e</mi> <mi>w</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mi>j</mi> <msubsup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mn>1</mn> <mrow> <mo>(</mo> <mi>n</mi> <mi>e</mi> <mi>w</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mrow> <mo>(</mo> <msubsup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mi>s</mi> <mrow> <mo>(</mo> <mi>n</mi> <mi>e</mi> <mi>w</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <mi>j</mi> <msubsup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mi>c</mi> <mrow> <mo>(</mo> <mi>n</mi> <mi>e</mi> <mi>w</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Step 3.2 can be drawn by step 3.1, by v (t)=Y (t) ejθ(t)The phasor calculated, often increase a sampled point, The radian that new phasor turns in complex plane is 2 π/N.
    When obtaining the sampled point of r-th window, its fundamental phasors is calculated：
    <mrow> <msubsup> <mi>Y</mi> <mi>c</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mrow> <mi>k</mi> <mo>+</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> </mrow> 2
    <mrow> <msubsup> <mi>Y</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mn>2</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Y</mi> <mrow> <mi>k</mi> <mo>+</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>k</mi> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>Y</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>jY</mi> <mi>c</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>
  9. 9. according to claim 4, a kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature exists In, known by step 3.2, r-th of window and the r-1 window have no direct recurrence relation, calculate r-th of window phasor When amount of calculation need 2N multiplication, 2 (N-1) sub-additions, it is contemplated that the property of DFT.The discrete Fourier of sampled point The fundamental phasors that leaf transformation obtains are unrelated with the start-phase of sampled point.When calculating phasor using recursive algorithm, in complex plane It is interior to obtain static phasor；And it is to rotate in complex plane that the phasor that common Fourier transform obtains, which is, angular speed ω.
  10. 10. according to claim 5, a kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature It is, step 4 includes：
    Step 4.1：Frequency input signal, when calculating voltage phasor with formula (13), obtains static to stablize 50Hz in complex plane Phasor.
    Step 4.2：If frequency input signal changes, if frequency offset (benchmark 50Hz) is Δ f, and sampling now Frequency does not change, then step 4.1 is changed into：
    <mrow> <msubsup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>50</mn> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>f</mi> </mrow> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>Y</mi> <mo>&amp;OverBar;</mo> </mover> <mn>50</mn> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </msubsup> <mfrac> <mrow> <mi>sin</mi> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>f</mi> </mrow> <mn>50</mn> </mfrac> <mi>&amp;pi;</mi> </mrow> <mrow> <mi>N</mi> <mi>sin</mi> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>f</mi> </mrow> <mn>50</mn> </mfrac> <mfrac> <mi>&amp;pi;</mi> <mi>N</mi> </mfrac> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>f</mi> </mrow> <mn>50</mn> </mfrac> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>N</mi> </mfrac> <mi>r</mi> </mrow> </msup> </mrow>
    Frequency obtains initializing fundamental phasors when being 50Hz.
  11. 11. according to claim 1, a kind of based on WAMS and consider the electric power system optimization method of primary frequency modulation, its feature It is, step 5 includes：
    Step 5.1：The object function of the power system optimal dispatch model of consideration system primary frequency modulation：
    Object function is makes system operation total cost minimum, and total cost includes electrical power generators cost and primary frequency modulation is standby takes With mathematic(al) representation is as follows:
    <mrow> <mi>F</mi> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>&amp;lsqb;</mo> <munder> <mo>&amp;Sigma;</mo> <mi>t</mi> </munder> <munder> <mo>&amp;Sigma;</mo> <mi>i</mi> </munder> <mo>{</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>s</mi> <mi>u</mi> </mrow> </msubsup> <mo>+</mo> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>s</mi> <mi>d</mi> </mrow> </msubsup> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>}</mo> <mo>&amp;rsqb;</mo> </mrow>
    Y in formulait--- unit open state, yit=1 represents to start shooting in t period units i；yit=0 represents compressor emergency shutdown；
    zit--- compressor emergency shutdown state, zit=1 represents to shut down in t period units i；zit=0 represents unit start；
    uit--- operating states of the units, uit=1 represents to run in t period units i；uit=0 represents unit outage；
    Pit--- unit i is in t period generated energy；
    --- unit i is in t period primary frequency modulation spare capacities；
    Cit、--- respectively unit i start expense, idleness expense, operating cost and primary frequency modulation are standby Expense.
    The operating cost of unit can be expressed as:
    <mrow> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    In formula：ait、bit、cit--- unit consumption characteristic coefficient.
    The standby expense of primary frequency modulation can be expressed as:
    <mrow> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>p</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> </mrow>
    --- the standby cost coefficient of primary frequency modulation.
    Step 5.2：The constraints of the power system optimal dispatch model of consideration system primary frequency modulation：
    (1) system power Constraints of Equilibrium
    The power-balance constraint for meeting system is needed after wind-electricity integration, ignores line power loss here, expression formula is:
    <mrow> <munder> <mo>&amp;Sigma;</mo> <mi>i</mi> </munder> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mi>w</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>L</mi> <mi>t</mi> </mrow> </msub> </mrow>
    In formula：Pwt、PLt--- t periods wind power and load.
    (2) unit output constrains
    <mrow> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mi>min</mi> </msubsup> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;le;</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mi>max</mi> </msubsup> </mrow>
    In formula：--- unit minimum load constrains and EIAJ constraint.
    (3) primary frequency modulation inequality constraints
    <mrow> <mn>0</mn> <mo>&amp;le;</mo> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mo>&amp;le;</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow>
    <mrow> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mo>&amp;le;</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> <mo>-</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> </mrow>
    <mrow> <munder> <mo>&amp;Sigma;</mo> <mi>i</mi> </munder> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> </mrow> </msubsup> <mo>&amp;GreaterEqual;</mo> <msub> <mi>&amp;Delta;P</mi> <mrow> <mi>w</mi> <mi>t</mi> </mrow> </msub> </mrow>
    (4) system frequency deviation constrains
    In order to ensure system operation safety, avoid load from cutting off, need to set low-limit frequency, i.e.,:
    Δfmin≤Δf≤0
    In formula, Δ fmin--- frequency departure lower limit as defined in system.
CN201710689404.XA 2017-08-14 2017-08-14 It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation Pending CN107482651A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710689404.XA CN107482651A (en) 2017-08-14 2017-08-14 It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710689404.XA CN107482651A (en) 2017-08-14 2017-08-14 It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation

Publications (1)

Publication Number Publication Date
CN107482651A true CN107482651A (en) 2017-12-15

Family

ID=60600190

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710689404.XA Pending CN107482651A (en) 2017-08-14 2017-08-14 It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation

Country Status (1)

Country Link
CN (1) CN107482651A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108732424A (en) * 2018-04-26 2018-11-02 南京合智电力科技有限公司 Phasor backoff algorithm under fixed frequency sampling mode and compensation system
CN111146788A (en) * 2020-01-21 2020-05-12 南方电网科学研究院有限责任公司 Automatic power generation control method
CN111181173A (en) * 2019-07-05 2020-05-19 友达光电股份有限公司 Load control system and load control method
CN112531738A (en) * 2020-11-24 2021-03-19 广东电网有限责任公司佛山供电局 Device and method for multiplexing analog quantity and network communication of primary frequency modulation device

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102522775A (en) * 2011-12-22 2012-06-27 清华大学 AGG (automatic gain control) unit performance adjustment online evaluation method based on WAMS (wide area measurement system)
CN102545215A (en) * 2012-01-16 2012-07-04 河北省电力研究院 Global-positioning-system-based quantitative analysis and evaluation method for primary frequency regulation performance of regional power grid
CN103226734A (en) * 2013-03-26 2013-07-31 国家电网公司 Equivalent rescheduling determining method of wind power acceptation cost
CN103778484A (en) * 2014-02-18 2014-05-07 国家电网公司 Grid connection type micro-grid optimizing configuration method and system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102522775A (en) * 2011-12-22 2012-06-27 清华大学 AGG (automatic gain control) unit performance adjustment online evaluation method based on WAMS (wide area measurement system)
CN102545215A (en) * 2012-01-16 2012-07-04 河北省电力研究院 Global-positioning-system-based quantitative analysis and evaluation method for primary frequency regulation performance of regional power grid
CN103226734A (en) * 2013-03-26 2013-07-31 国家电网公司 Equivalent rescheduling determining method of wind power acceptation cost
CN103778484A (en) * 2014-02-18 2014-05-07 国家电网公司 Grid connection type micro-grid optimizing configuration method and system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
刘清泉: "大规模风电并网后系统调频备用优化研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 *
褚衍华: "电力系统轻型广域同步监测系统研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108732424A (en) * 2018-04-26 2018-11-02 南京合智电力科技有限公司 Phasor backoff algorithm under fixed frequency sampling mode and compensation system
CN108732424B (en) * 2018-04-26 2020-11-20 南京合智电力科技有限公司 Phasor compensation algorithm and system in fixed-frequency sampling mode
CN111181173A (en) * 2019-07-05 2020-05-19 友达光电股份有限公司 Load control system and load control method
CN111146788A (en) * 2020-01-21 2020-05-12 南方电网科学研究院有限责任公司 Automatic power generation control method
CN112531738A (en) * 2020-11-24 2021-03-19 广东电网有限责任公司佛山供电局 Device and method for multiplexing analog quantity and network communication of primary frequency modulation device
CN112531738B (en) * 2020-11-24 2022-01-21 广东电网有限责任公司佛山供电局 Device and method for multiplexing analog quantity and network communication of primary frequency modulation device

Similar Documents

Publication Publication Date Title
CN107482651A (en) It is a kind of based on WAMS and to consider the electric power system optimization method of primary frequency modulation
Jabr et al. Intermittent wind generation in optimal power flow dispatching
CN102751728B (en) Energy management method for isolated network running mode in micro network based on load interruption model
CN104835080B (en) The modeling method of micro-capacitance sensor in a few days operation plan mixed-integer programming model
CN109978362A (en) A kind of modeling of gas power grid joint multizone integrated energy system and systems organization method
CN102184475A (en) Optimizing and dispatching method for microgrid economical operation on basis of multiple time scale coordination
CN103001230A (en) Non-invasive power load monitoring and decomposing current mode matching method
CN103592528B (en) A kind of photovoltaic DC-to-AC converter model parameter identification method based on dynamic trajectory sensitivity
Silwal et al. Open-source multi-year power generation, consumption, and storage data in a microgrid
CN103066595A (en) Optimization method of extra-high voltage transient stability control
CN105871242A (en) Single-phase bidirectional converter control system
CN110400090A (en) A kind of Itellectualized uptown multiple-energy-source microgrid configuration method based on multiple target random optimization
CN107257130A (en) The low-voltage network loss computing method of decoupling is measured based on region
CN108418242B (en) Doubly-fed wind turbine dynamic equivalence method based on similarity coherence
Li et al. Economic dispatch of an integrated heat-power energy distribution system with a concentrating solar power energy hub
CN105281327A (en) Optimal power flow calculation method considering discrete and sequential decision variables for large-scale power distribution network
Ilyas et al. Optimal placement of distributed generation on radial distribution system for loss minimisation & improvement of voltage profile
CN105701609A (en) Peaking power source layout method based on comprehensive evaluation indexes
CN108258725A (en) A kind of double-fed fan motor machine Dynamic Equivalence based on the equivalent generator rotor angle people having the same aspiration and interest
Mudaheranwa et al. Estimation of Rwanda's power system inertia as input for long-term dynamic frequency response regulation planning
Kurian et al. Real time implementation of artificial neural networks‐based controller for battery storage supported wind electric generation
CN110224391A (en) A kind of mixing probability-section optimal load flow method for solving
CN102916433B (en) Reactive power task allocation method for fan group
CN103178519B (en) The method of power oscillation of power system disturbing source is located in real time based on SCADA data
Amzad Hossain et al. Output fluctuations minimization of wind integrated hybrid power system using electronic coordinated control of governor and blade

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20171215