CN106786503A - Consider the direct current receiving-end system emergency load control method of voltage stability and accident integrate-cost - Google Patents
Consider the direct current receiving-end system emergency load control method of voltage stability and accident integrate-cost Download PDFInfo
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- CN106786503A CN106786503A CN201611008014.3A CN201611008014A CN106786503A CN 106786503 A CN106786503 A CN 106786503A CN 201611008014 A CN201611008014 A CN 201611008014A CN 106786503 A CN106786503 A CN 106786503A
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- 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
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- 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
- H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
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- 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]
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- 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
- H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
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- 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
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- 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
- Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]
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Abstract
The invention discloses a kind of direct current receiving-end system emergency load control method for considering voltage stability and accident integrate-cost, comprise the following steps：(1) direct current receiving-end system data are obtained；(2) calculate voltage vulnerability index and recognize some load buses of voltage weakness the most after failure；(3) set up receiving-end system emergency load control optimization problem Mathematical Modeling and approximate processing is made to accident fine curve；(4) application prim al- dual interior point m ethod solves receiving-end system emergency load control optimization problem；(5) the accident integrate-cost and voltage stability of emergency load control prioritization scheme are checked.The present invention improves the voltage stability and combination property of system on the premise of control program integrate-cost is not increased, and can be greatly enhanced calculating speed, efficiently reduces amount of calculation, is applicable to emergency load control.
Description
Technical field
The invention belongs to POWER SYSTEM EMERGENCY spatial load forecasting technical field, it is related to a kind of consideration voltage stability and accident comprehensive
Close the direct current receiving-end system emergency load control method of cost.
Background technology
In recent years, Chinese high voltage dc transmission technology quickly grows, and the scale of electric energy long-distance sand transport is increasing, and this has
Beneficial to electric cost, environmental protection is reduced, most optimum distribution of resources is realized.HVDC (high-tension current, high voltage direct
Current the structure of modern power network) is greatly changed, for receiving-end system, external transmission of electricity proportion is greatly improved,
The locking of HVDC monopoles or bipolar locking will make receiving-end system a large amount of power shortages occur, cause generator in system to slow down, frequency
Decline.Meanwhile, high-power power flow transfer will cause that some circuit delivering powers transfinite, and cause respective nodes low voltage, such as
Cannot in time process and would be possible to trigger cascading failure, or even system sectionalizing.Generator frequency modulation, region external power are supported and tight
Anxious spatial load forecasting etc. is all the effective measures for tackling DC Line Fault, and wherein emergency load control is the most commonly used.
At present, in the prior art on emergency load control, often with minimum resection or with minimum economic cost as target
Determine each load center resection, control targe is single, lack the coordination between multiple target, and to system voltage, the phase of frequency
Mutually influence concern is inadequate.For direct current receiving-end system, spread of voltage is the main of the DC Line Faults such as commutation failure, HVDC lockings
Reason, spatial load forecasting should make the system have preferable air extract, for follow-up system is recovered to provide advantage,
Therefore, the voltage level for improving key node is particularly significant.In addition, China's issuing and implementation in 2011《Electric power safety accident should
Suddenly dispose and regulations of investigating》(command of State Council the 599th) specifies, system cutting load is equal to breakdown loss load, electric power
Enterprise will not only undertake the direct economic loss that excision load is caused, in addition it is also necessary to pay penalizing for matching amount according to accident grading
Gold, therefore, the accident integrate-cost of electric power enterprise is direct economic loss and the summation of accident fine, is formulating control program
When, accident integrate-cost should be made minimum, and not only consider direct economic loss.The research of current this respect is little, Chinese patent
Application CN201510589215.6 discloses a kind of emergency load control optimization side for coordinating economy and cutting load rate fairness
Method, the weighted sum with the direct economy cost of control program and each load center cutting load rate standard deviation is solved as object function
Optimum control scheme.This method can to a certain extent reduce accident integrate-cost, but the method due to using population
Optimized algorithm, amount of calculation is larger, have impact on its application in engineering practice.
The content of the invention
It is an object of the invention to overcome the consideration target existing for prior art more single, steady to receiving-end system voltage
It is qualitative to consider not enough and computationally intensive technological deficiency, there is provided the direct current of a kind of consideration voltage stability and accident integrate-cost
Receiving-end system emergency load control method, on the premise of control program integrate-cost is not increased, improves receiving-end system as far as possible
Voltage stability.
In order to solve the problems, such as above-mentioned prior art, the present invention uses following technical scheme.
A kind of direct current receiving-end system emergency load control side for considering voltage stability and accident integrate-cost of the invention
Method, comprises the following steps：
(1) direct current receiving-end system data are obtained；
(2) calculate voltage vulnerability index and recognize some load buses of voltage weakness the most after failure；
(3) set up receiving-end system emergency load control optimization problem Mathematical Modeling and approximate place is made to accident fine curve
Reason；
(4) application prim al- dual interior point m ethod solves receiving-end system emergency load control optimization problem；
(5) the accident integrate-cost and voltage stability of emergency load control prioritization scheme are checked.
Described direct current receiving-end system data include：Each line impedance, each load center load, the controlled amounts upper limit and cost
The data such as the factor, each interconnection input power, each transformer, synchronous generator；If described direct current receiving-end system has n platforms to generate electricity
Machine, k load center, LiThe load of load center i is represented, wherein, i=1,2 ..., k；Direct current receiving-end system and external system
Between have m bar interconnections, including some HVDC power transmission lines.
In the step (2), if described calculating voltage vulnerability index and recognizing that voltage after failure is the weakest
Dry load bus, its process is：
For direct current receiving-end system, if its admittance matrix is Y, subscript G, T and L represent generator node, contact section respectively
Point and load bus, YGG、YTTAnd YLLRespectively the self-admittance submatrix of generator node, contact node and load bus, YGL、
YLGIt is generator node and the transadmittance submatrix of load bus, YTL、YLTIt is the sub- square of the transadmittance of contact node and load bus
Battle array, YGT、YTGIt is generator node and the transadmittance submatrix of contact node；U, I represent node voltage and current vector, UG、UL
It is generator node and the voltage of load bus, IG、ILIt is generator node and the Injection Current of load bus, can releases：UL
=Eopen-ZIL, in formula：
Load LiPlace node voltage ULiFor：ULi=Eopen,i-Zeq,iILi, i=1,2 ..., k, wherein, Eopen,iFor arrange to
Amount EopenI-th element,ILi、ILjRespectively flow through load LiAnd LjElectric current；According to peak power
Principle, equivalent internal resistance Zeq,iIt is smaller, load LiThe load capacity of place node is stronger, and voltage stability is better；Define load LiInstitute
In the voltage vulnerability index of node：ZL,iIt is load LiCorresponding equiva lent impedance, if load LiFor
The node voltage isThenriSmaller, then the static electric voltage stability of the node is better；Received by direct current
R maximum some nodes composition voltage weak node collection S, S can use 5-6 voltage most weak node in end system；Promptly bearing
In lotus control process, key monitoring is carried out to the voltage weak node that set S is included.
In the step (3), described sets up receiving-end system emergency load control optimization problem Mathematical Modeling and to thing
Therefore the implementation process that fine curve makees approximate processing is：
The optimization problem of described direct current receiving-end system emergency load control is described as：
Min f=f1+f2+αf3
s.t.L.F.(PG,PL,ρ,fd, U, θ)=0,
PG,min≤PG≤PG,max, Pline≤Pline,max,
|fd|≤τ,ρj≤ρj,up
Wherein,It is the direct economic loss that cutting load is caused, ciIt is excision load LiWork factor, ρi
It is load LiCutting load rate,It is load LiInitial value, i=1 ..., k；It is according to China《Electric power
Security incident response is disposed and regulations of investigating》The accident fine that should be paid, Pen (ρi) it is to impose a fine with rate of reducing load ρiBecome
The function of change；It is the quadratic sum of voltage some load bus Voltage Drop amounts the weakest,It is voltage
Higher limit, S is voltage weak node collection；α is weight coefficient, and α is bigger, and emergency load control is got over and lays particular emphasis on raising voltage weak node
Voltage level, typically can use α=20；L.F.(PG,PL,ρ,fd, U, θ) and it is the power balance equation of Load flow calculation；PG、PLAnd ρ
Respectively generated output power, load power and cutting load rate, U, θ are respectively each node voltage amplitude and phase angle；fd=(f-
fn)/fnIt is system frequency deviation, fnIt is system nominal working frequency；τ is | fd| maximum, typically can use τ=0.04；
PG,max、PG,minThe respectively bound of generator output, PlineIt is line transmission power, Pline,maxIt is circuit maximum transmitted work(
Rate； uRespectively voltage bound, typically can use 1.1,0.95；ρj,upIt is load LjThe upper limit of rate of reducing load；
China《Electric power safety accident emergency is disposed and regulations of investigating》Accident is divided into ordinary accident, compared with major issue
Therefore, major accident and special major accident classification treatment, carry out accident grading according to power network scale and rate of reducing load, and sentence phase
The fine answered, has formulated accordingly different type power networks such as province (autonomous region) People's Government location city, prefecture-level city, county-level cities
Fine rule, it is stipulated that fine and rate of reducing load between function Pen (ρ) be piecewise linearity unsmoothed curve, this to optimization
Problem solving brings difficulty, and the fine curve to different type power network can make approximate processing, using q order polynomialsCome
Fitting Pen (ρ), can use q=6, coefficient ajDetermined by least square method.
In the step (4), described application prim al- dual interior point m ethod solves the optimization of receiving-end system emergency load control and asks
The implementation process of topic is：
According to prim al- dual interior point m ethod, optimization problem is initialized first, state variable x={ ρ, f are setd, U, θ }
Initial value, wherein, ρ is each load bus cutting load rate vector, fdIt is system frequency excursion amount, U, θ is respectively each node electricity of system
Pressure amplitude value, phase angle vector, typically can use ρ=0, fd=0, U=1, θ=0, slack variable l, u and Lagrange multiplier z are set,
W, y, typically can use l=1, u=1, z=1, w=-0.5, y=0, set Center Parameter σ, general 0 ＜ σ ＜ 1, give respectively mutual
Mend the convergence precision ε of clearance G ap1, trend convergence precision ε2If, iterations initial value niter=0, maximum iteration niter_max
=150；Then, complementary clearance G ap=l is calculatedTz-uTW, judges complementation clearance G ap ＜ ε1And trend error delta L.F. ＜ ε2It is
It is no at the same set up, if so, then exporting optimal solution, otherwise continue, calculate update equation coefficient matrix, correction amount x is obtained accordingly,
Δ l, Δ u, Δ z, Δ w, Δ y, update state variable, slack variable and Lagrange multiplier；Finally, n is judgediter＞ niter_max
Whether set up, if so, then prompting " calculating does not restrain ", terminates to calculate, otherwise make niter=niter+ 1, continue to iterate to calculate.
In the step (5), the described accident integrate-cost and voltage of checking emergency load control prioritization scheme is steady
Qualitatively implementation process is：
There is locking failure in HVDC, it is urgent negative according to what is obtained when direct current receiving-end system loses high electric power from outside
Lotus control prioritization scheme quickly cuts off the load of corresponding proportion in each load center, and direct current receiving-end system dynamic response is imitated
True to calculate, the frequency response of system before and after control measure is taken in analysis, and accident integrate-cost to different control programs and receives
End system busbar voltage is fallen level and is compared, the optimality of access control scheme performance, if meeting various constraintss
It is required that, then output considers the optimum control scheme of voltage stability and accident integrate-cost, otherwise re-optimization.
Compared with prior art, the present invention has advantages below and beneficial effect：
1. the direct current receiving-end system emergency load control for considering voltage stability and accident integrate-cost proposed by the present invention
Method, the weighted sum with accident integrate-cost and the Voltage Drop amount square of voltage weak node the most as object function, comprehensively
The direct economic loss that cutting load is caused and the fine that need to be paid according to the 599th command are considered, while taking into account receiving-end system
Voltage stability, constructs the Mathematical Modeling of emergency load control optimization problem；Carried out by the fine function to piecewise linearity
Fitting of a polynomial, on the premise of degree of precision is kept, overcomes the rough solution for causing difficult；Using prim al- dual interior point m ethod
Optimum control scheme is solved, calculating speed is effectively increased；Finally, emulation has been carried out to optimization control scheme to check.The present invention
Consider the difference of the type, load work factor and controlled amounts of different load node, at the same consider frequency in control process,
Voltage is to generator, the influence of load, and the control program degree that becomes more meticulous is high, and calculating speed is fast, and feasibility is good.
2. emulation of the present invention to example shows, the control program accident synthesis generation with minimum direct economy cost as target
Valency is big, and Voltage Drop is big, therefore performance is worst；Consider that the emergent control scheme of voltage stability and accident integrate-cost can be
Substantially on the premise of not increasing accident integrate-cost, hence it is evident that improve the voltage stability of post-fault system, be conducive to system follow-up
Operation and recovery, with preferable combination property.
Brief description of the drawings
Fig. 1 is the direct current receiving-end system emergency load control side of consideration voltage stability of the invention and accident integrate-cost
Method flow chart.
Fig. 2 is direct current receiving end power system schematic diagram of the invention.
Fig. 3 is the flow chart that application prim al- dual interior point m ethod of the invention solves emergency load control optimization problem.
Fig. 4 is the node example system construction drawing of IEEE10 machines 39 containing HVDC of one embodiment of the present of invention.
Fig. 5 be one embodiment of the present of invention failure after each load bus voltage vulnerability index of direct current receiving-end system.
Fig. 6 is the accident fine and rate of reducing load that the command of State Council of the People's Republic of China the 599th of one embodiment of the present of invention specifies
Functional relation and fitting result chart, wherein solid line for regulation curve, dotted line is matched curve.
Fig. 7 is the convergence of the prim al- dual interior point m ethod solution emergency load control optimization problem of one embodiment of the present of invention
Cheng Tu.
Fig. 8 is the system frequency response curve comparison figure of one embodiment of the present of invention, when wherein solid line is for not cutting load
System frequency response curve, frequency response curve when dotted line is using emergency load control method of the invention.
Fig. 9 is the system voltage response curve comparison diagram of one embodiment of the present of invention, and wherein Fig. 9 (a) is not cutting load
When voltage response curves, voltage response curves when wherein Fig. 9 (b) is using emergency load control method of the invention.
Specific embodiment
The present invention is described in further details with reference to the accompanying drawings and examples.
A kind of direct current receiving-end system Load Emergency control for considering voltage stability and accident integrate-cost of the present invention
Method processed, Fig. 1 show the direct current receiving-end system emergency load control that the present invention considers voltage stability and accident integrate-cost
The flow chart of method, comprises the following steps：
Step one, acquisition direct current receiving-end system data.Direct current receiving-end system schematic diagram of the invention is as shown in Fig. 2 its is straight
Stream receiving-end system data include：Each branch impedance, the type of each load center load, the controlled amounts upper limit and work factor, each connection
The data such as the power that winding thread is externally exported, each transformer, synchronous generator；If described direct current receiving-end system have n platforms generator,
K load center, the load L of load center jjInitial value isWherein, j=1 ..., k；If ρjIt is cutting for load center j
Rate of load condensate, cjIt is excision load LjWork factor, j=1 ..., k；There are m bars between direct current receiving-end system and external power system
Interconnection, including some HVDC power transmission lines.
Step 2, some load buses for calculating voltage vulnerability index and recognizing voltage weakness the most after failure.
For direct current receiving-end system, if its admittance matrix is Y, subscript G, T and L represent generator node, contact section respectively
Point and load bus, YGG、YTTAnd YLLRespectively the self-admittance submatrix of generator node, contact node and load bus, YGL、
YLGIt is generator node and the transadmittance submatrix of load bus, YTL、YLTIt is the sub- square of the transadmittance of contact node and load bus
Battle array, YGT、YTGIt is generator node and the transadmittance submatrix of contact node；Node voltage, current vector, U are represented with U, IG、UL
It is generator node and the voltage of load bus, IG、ILBe generator node and the Injection Current of load bus, then load bus
Voltage vector：UL=Eopen-ZIL, in formula：
For load LiPlace node, its voltage ULiFor：ULi=Eopen,i-Zeq,iILi, i=1,2 ..., k, wherein, Eopen,i
It is column vector EopenI-th element,ILi、ILjRespectively flow through load Li、LjElectric current, according to most
High-power principle, equivalent internal resistance Zeq,iIt is smaller, then load LiThe load capacity of place node is stronger；Define load LiPlace node
Voltage vulnerability index：ZL,iIt is load LiCorresponding equiva lent impedance, if load LiForThe node
Voltage isThenriSmaller, then the static electric voltage stability of the node is better；In emergency load control
During, voltage weak node collection S is constituted by 5-6 maximum node of voltage vulnerability index r in direct current receiving-end system, by S
As key monitoring object.
Step 3, set up receiving-end system emergency load control optimization problem Mathematical Modeling and approximate is made to accident fine curve
Treatment.
The optimization problem of described direct current receiving-end system emergency load control is described as：
Min f=f1+f2+αf3
s.t.L.F.(PG,PL,ρ,fd, U, θ)=0,
PG,min≤PG≤PG,max, Pline≤Pline,max,
|fd|≤τ,ρj≤ρj,up
Wherein,It is the direct economic loss that cutting load brings, ρiIt is load LiCutting load rate, ciFor
Excision load LiWork factor,It is load LiInitial value, i=1 ..., k；It is according to China《Electricity
Power security incident response is disposed and regulations of investigating》Accident fine, Pen (ρ should be paidi) it is to impose a fine with rate of reducing load ρiBecome
The function of change；Be the quadratic sum of voltage weak node collection S median generatrix Voltage Drop amounts, Voltage Drop amount with
Upper voltage limitIt is reference；α is weight coefficient, and α is bigger, and emergency load control gets over the voltage water for laying particular emphasis on and improving voltage weak node
It is flat, typically can use α=20；L.F.(PG,PL,ρ,fd, U, θ) and it is the power balance equation of Load flow calculation；PG、PLAnd ρ is respectively hair
Output power of motor, load power and cutting load rate, U, θ are the voltage magnitude and phase angle of each node；fd=(f-fn)/fnTo be
System frequency departure, fnIt is system nominal working frequency；τ is | fd| maximum, typically can use τ=0.04；PG,max、PG,minIt is hair
The bound that motor is exerted oneself, PlineIt is line transmission power, Pline,maxIt is circuit maximum transmission power； uFor voltage is upper and lower
Limit, typically can use 1.1,0.95；ρj,upIt is load LjThe upper limit of rate of reducing load；
China《Electric power safety accident emergency is disposed and regulations of investigating》Accident is divided into ordinary accident, compared with major issue
Therefore, major accident and special major accident classification treatment, carry out accident grading according to power network scale and rate of reducing load, and sentence phase
The fine answered, has formulated accordingly different type power networks such as province (autonomous region) People's Government location city, prefecture-level city, county-level cities
Fine rule, it is stipulated that fine and rate of reducing load between function Pen (ρ) be piecewise linearity unsmoothed curve, this to optimization
Difficulty is brought, to overcome this difficult, using q order polynomialsTo be fitted Pen (ρ), approximate processing is made to curve,
Typically desirable q=6, coefficient ajDetermined by least square method.
Step 4, using prim al- dual interior point m ethod solve receiving-end system emergency load control optimization problem.
Application prim al- dual interior point m ethod of the invention solves the flow chart of emergency load control optimization problem as shown in figure 3, head
First optimization problem is initialized, state variable x={ ρ, f are setd, U, θ } initial value, wherein, ρ for each load bus cut it is negative
Lotus rate vector, fdIt is system frequency excursion amount, U, θ is respectively each node voltage amplitude of system, phase angle vector, typically desirable ρ=
0,fd=0, U=1, θ=0, slack variable l, u and Lagrange multiplier z, w, y are set, typically can use l=1, u=1, z=1, w
=-0.5, y=0, sets Center Parameter σ, general 0 ＜ σ ＜ 1, can use σ=0.7, and the convergence essence of complementation clearance G ap is given respectively
Degree ε1And trend convergence precision ε2, can use ε1=10-6, ε2=10-4If, iterations initial value niter=0, maximum iteration
niter_max=150；Then, complementary clearance G ap=l is calculatedTz-uTW, judges complementation clearance G ap ＜ ε1And trend error delta L.F.
＜ ε2Whether set up simultaneously, if so, then exporting optimal solution, otherwise continue, calculate update equation coefficient matrix, amendment is obtained accordingly
Amount Δ x, Δ l, Δ u, Δ z, Δ w, Δ y, update state variable, slack variable and Lagrange multiplier；Finally, n is judgediter＞
niter_maxWhether set up, if so, then prompting " calculating does not restrain ", terminates to calculate, otherwise make niter=niter+ 1, continue iteration meter
Calculate.
Step 5, the accident integrate-cost and voltage stability of checking emergency load control prioritization scheme.
There is locking failure in HVDC, it is urgent negative according to what is obtained when direct current receiving-end system loses high electric power from outside
Lotus control prioritization scheme quickly cuts off the load of corresponding proportion in each load center, and direct current receiving-end system dynamic response is imitated
True to calculate, the frequency response of the forward and backward system of control measure is taken in analysis, and accident integrate-cost to different control programs and receives
End system busbar voltage is fallen level and is compared, the optimality of access control scheme performance, if meeting various constraintss
It is required that, then output considers the optimum control scheme of voltage stability and accident integrate-cost, otherwise re-optimization.
Fig. 4 is the node example system construction drawing of IEEE10 machines 39 containing HVDC of one embodiment of the present of invention, this implementation
Example applies the inventive method to the node example system of IEEE10 machines 39 containing HVDC, the Load Emergency control to direct current receiving-end system
Scheme processed is optimized, and the combination property to control program is analyzed.Implementation steps are as follows：
Step 1, acquisition direct current receiving-end system data.
The node example system architecture of IEEE10 machines 39 containing HVDC of the present embodiment in IEEE10 machines 39 as shown in figure 4, save
On the basis of dot system standard example, original alternating current circuit 33-19,36-23 are replaced with into two HVDC of ± 400kV, and set
Put HVDC line parameter circuit values, Trigger Angle, blow-out angle so that before and after modification, bus 19,23 injecting powers keep constant, two HVDC
Conveying general power is 1192Mw, accounts for the 18.93% of Receiving End Load total amount；Receiving-end system includes 21 load buses altogether, if
The corresponding provincial government's urban distribution network of load bus 39, load bus { 1,9,12,31 } is utility grid at county level, and remaining is region civil power
Net, each load center controllable burden ratio ρj,upAnd work factor ciAs shown in table 1, if each node load static characteristic coefficient is identical：Its
In,It is active, load or burden without work Frequency regulation factor,AndIt is respectively active, idle negative
The proportionality coefficient of constant-impedance, constant current and invariable power part in lotus, takes generator unit power regulation KG=30.
The proportion-controllable and work factor of each load center of table 1.
Step 2, some load buses for calculating voltage vulnerability index and recognizing voltage weakness the most after failure.
Assuming that two HVDC are while the failure that is short-circuited, failure continues 0.4s, after period restarts unsuccessfully twice during 1s
HVDC bipolar lockings, now in order to keep the frequency stability and voltage stability of post-fault system, it is necessary to take Load Emergency
Control, first, calculates the trend of direct current receiving end power system after failure, draws each node voltage amplitude, phase angle, and direct current is received
The admittance matrix of power system is held, generator Node subsets G, contact node subset T and load bus subset L is determined, hair is read
The self-admittance submatrix Y of motor node, contact node and load busGG、YTTAnd YLL, generator node is mutual with load bus
Admittance submatrix YGLAnd YLG, the transadmittance submatrix Y of contact node and load busTLAnd YLT, generator node and contact node
Transadmittance submatrix YGTAnd YTG, read the voltage U of generator node and load busG、ULAnd generator node and load
The Injection Current I of nodeG、IL；Then, according to formulaAdmittance matrix Z is calculated, further according toThe voltage vulnerability index of each load bus is calculated, wherein,ILi、ILjRespectively load
The Injection Current of center i, j, ZL,iIt is load LiCorresponding equiva lent impedance, if load LiForThe node voltage isThenCalculating shows, in the present embodiment, direct current receiving end system after failure
System each load bus voltage vulnerability index as shown in figure 5,5 wherein most weak load buses be respectively bus 21,16,
24th, 15 and 20, these nodes are located near HVDC current conversion stations, maximum by accident impact, implement to answer emphasis to carry when cutting load is controlled
The voltage level of these nodes high.
Step 3, set up receiving-end system emergency load control optimization problem Mathematical Modeling and approximate is made to accident fine curve
Treatment.
The optimization problem of described direct current receiving-end system emergency load control is described as：
Min f=f1+f2+αf3
s.t.L.F.(PG,PL,ρ,fd, U, θ)=0,
PG,min≤PG≤PG,max, Pline≤Pline,max,
|fd|≤τ,ρj≤ρj,up
Wherein,It is the direct economic loss that cutting load brings, ρiIt is the cutting load rate of load center i, ci
It is excision load LiWork factor,It is load LiInitial value, i=1 ..., k；It is according to China
《Electric power safety accident emergency is disposed and regulations of investigating》Accident fine, Pen (ρ should be paidi) it is to impose a fine with rate of reducing load ρ
The function of change；It is the quadratic sum of voltage node voltage magnitude the weakest, S is weak voltage
Set of node, takes S={ 15,16,20,21,24 } in embodiment, the voltage to bus 15,16,20,21 and 24 carries out key monitoring,
Voltage Drop amount is with upper voltage limitIt is reference；Weighting factor alpha=20, L.F. (PG,PL,ρ,fd, U, θ) and it is the work(of Load flow calculation
Rate equilibrium equation, PG、PLAnd ρ is respectively generated output power, load power and cutting load rate, U, θ are the voltage amplitude of each node
Value and phase angle；fd=(f-fn)/fnIt is system frequency deviation, fnIt is system nominal working frequency；τ is | fd| maximum, take τ=
0.04；PG,max、PG,minIt is the bound of generator output, PlineIt is line transmission power, Pline,maxIt is circuit maximum transmitted work(
Rate；Voltage bound uIt is set to 1.1,0.95；ρj,upIt is load LjThe upper limit of rate of reducing load, ciAnd ρj,upIt is shown in Table 1；
《Electric power safety accident emergency is disposed and regulations of investigating》The accident fine of regulation is closed with the function of rate of reducing load
It is Pen (ρ) such as shown in solid in Fig. 6, Pen (ρ) is the unsmoothed curve of piecewise linearity, to avoid the calculating for thereby resulting in from being stranded
Difficulty, the method using fitting of a polynomial makees approximate processing, can be obtained according to least square method, to provincial government's urban distribution network, its plan
Close the desirable ρ of Pen (ρ)=- 211 ρ+5738 of function2-33687ρ3+83089ρ4-86527ρ5+32097ρ6；To region utility grid, its
Fitting function can use the ρ of Pen (ρ)=2.1 ρ+588.52-2474ρ3+4036.5ρ4-1953.1ρ5；To utility grid at county level, its fitting
Function can use Pen (ρ)=39.5833 ρ -119.7917 ρ2+260.4167ρ3-130.2083ρ4；Fig. 6 show the present embodiment
The fine that the command of State Council of the People's Republic of China the 599th specifies and accident grading functional relation and fitting result chart, wherein：Solid line is bent for regulation
Line, and matched curve is as shown in phantom in Figure 6.
Step 4, using prim al- dual interior point m ethod solve receiving-end system emergency load control optimization problem.
First, optimization problem is initialized, state variable x={ ρ, f is setd, U, θ } initial value, wherein, ρ is each
Load bus cutting load rate vector, fdIt is system frequency excursion, U, θ is respectively each node voltage amplitude of system, phase angle vector, takes
ρ=0, fd=0, U=1, θ=0, slack variable l, u and Lagrange multiplier z, w, y are set, take l=1, u=1, z=1, w=-
0.5, y=0, setting Center Parameter σ=0.7 gives the convergence precision ε of complementation clearance G ap1=10-6, the calculating of trend convergence precision
Precision ε2=10-4If, iterations initial value niter=0, maximum iteration niter_max=150；Then, complementary gap is calculated
Gap=lTz-uTW, judges complementation clearance G ap ＜ ε1And trend error delta L.F. ＜ ε2Whether set up simultaneously, if so, then exporting most
Excellent solution, otherwise continues, and calculates update equation coefficient matrix, and correction amount x, Δ l, Δ u, Δ z, Δ w, Δ y are obtained accordingly, updates
State variable, slack variable and Lagrange multiplier；Finally, n is judgediter＞ niter_maxWhether set up, if so, then prompting " meter
Not do not restrain ", terminate to calculate, otherwise make niter=niter+ 1, continue to iterate to calculate；Fig. 7 is the prim al- dual interior point m ethod of the present embodiment
The convergence process figure of emergency load control optimization problem is solved, in the present embodiment, by after 53 iteration, system is with 10-7's
Compensation gap and 10-4Trend error convergence to optimal solution, about 1 minute used time.
Step 5, the accident integrate-cost and voltage stability of checking emergency load control prioritization scheme.
There is locking failure in HVDC, when direct current receiving-end system loses high electric power from outside, A, B, C tri- has been obtained respectively
Kind of control program, wherein, option A with minimum direct economy cost as target, option b with minimum accident integrate-cost as target,
Scheme C is the coordination control of consideration voltage stability of the invention and accident integrate-cost, and 3 kinds of different control programs are corresponding each
Node cutting load rate is as shown in table 2；
The corresponding each node cutting load rate of the different control programs of 2. 3 kinds of table
A--- minimum direct economy costs；B--- minimum accident integrate-costs；C--- considers that voltage stability and accident are comprehensive
Close the coordination control of cost
For the performance of relatively more different control programs, table 3 lists direct economic loss, accident grading under different schemes
Corresponding fine and Voltage Drop amount, as shown in Table 3, under control program A, cutting load total amount and direct economic loss are minimum, but
After the accident fine for undertaking is needed according to the 599th command, its accident integrate-cost is maximum, and Voltage Drop is most tight
Weight, thus performance is worst；Option b is compared with C, and accident integrate-cost is close, but scheme C voltage magnitude is smaller, therefore scheme C has
There is optimal synthesis performance；
The Contrast on effect of the different control programs of table 3.
A--- minimum direct economy costs；B--- minimum accident integrate-costs；C--- coordinates accident integrate-cost and voltage
Stability
Response of the direct current receiving-end system after failure under emergency load control scheme C is emulated, is illustrated in figure 8
The system frequency response curve comparison figure of the present embodiment, wherein solid line be not cutting load when system frequency response curve, dotted line
Frequency response curve when being using emergency load control method of the invention；As shown in Figure 8, if not taking the inventive method institute
The measure stated, then post-fault system frequency is relatively low, and less than 0.994p.u., frequency departure passes through more than the 0.04p.u. for setting
Emergent control, system frequency rises to about 0.996p.u. according to pre-provisioning request；
Fig. 9 is the system voltage response curve comparison diagram of one embodiment of the present of invention, and wherein Fig. 9 (a) is not cutting load
When voltage response curves, voltage response curves when Fig. 9 (b) is using emergency load control method of the invention；Such as Fig. 9
Shown in (a), during quasi-steady state, the Voltage Drop most serious of bus 15 near current conversion station drop point, about 0.87p.u., less than regulation lower limit
0.9p.u.From Fig. 9 (b), after taking cutting load measure, system voltage level is obviously improved, and the voltage of bus 15 is about
0.905p.u., meets safety and stability requirement；Be can be seen that from the frequency and voltage of system, the static security stability of system is obtained
To being obviously improved.
In sum, the direct current receiving-end system Load Emergency control for considering voltage stability and accident integrate-cost of the invention
Method processed compensate for existing for prior art receiving-end system voltage stability is considered it is not enough, consider target it is more single and
The slow technological deficiency of calculating speed, will lose the direct economy cost that causes of load with according to No. 599 needs pay the penalty it is total
Be defined as accident integrate-cost, voltage weak node collection is recognized by the voltage vulnerability index of post-fault system, by node
The quadratic sum weighting of Voltage Drop value counts object function, and considers that part throttle characteristics and controlled amounts of each load center etc. are limited,
The Mathematical Modeling of emergency load control optimization problem is built, using prim al- dual interior point m ethod rapid solving prioritization scheme.With with minimum
Direct economy cost, minimum accident integrate-cost are compared for other two kinds of control programs of target, it is considered to voltage stability and thing
Therefore the direct current receiving-end system emergency load control method of integrate-cost both has relatively low accident integrate-cost, and system is improve again
Voltage stability, with preferable combination property.Compared with artificial intelligence approach, can greatly be carried using prim al- dual interior point m ethod
Calculating speed high, can preferably be applied to the on-line decision of emergency load control.
Claims (5)
1. a kind of direct current receiving-end system emergency load control method for considering voltage stability and accident integrate-cost, its feature exists
In comprising the following steps：
(1) direct current receiving-end system data are obtained；
(2) calculate voltage vulnerability index and recognize some load buses of voltage weakness the most after failure；
(3) set up receiving-end system emergency load control optimization problem Mathematical Modeling and approximate processing is made to accident fine curve；
(4) application prim al- dual interior point m ethod solves receiving-end system emergency load control optimization problem；
(5) the accident integrate-cost and voltage stability of emergency load control prioritization scheme are checked；
Described direct current receiving-end system data include：Each line impedance, each load center load, the controlled amounts upper limit and cost because
The data such as son, each interconnection input power, each transformer, synchronous generator；If described direct current receiving-end system has n platforms to generate electricity
Machine, k load center, LiThe load of load center i is represented, wherein, i=1,2 ..., k；Direct current receiving-end system and external system
Between have m bar interconnections, including some HVDC power transmission lines.
2. the direct current receiving-end system Load Emergency control for considering voltage stability and accident integrate-cost according to claim 1
Method processed, it is characterised in that described calculating voltage vulnerability index simultaneously recognizes voltage some loads the weakest after failure
Node, its process is：
For direct current receiving-end system, if its admittance matrix is Y, subscript G, T and L represent respectively generator node, contact node and
Load bus, YGG、YTTAnd YLLRespectively the self-admittance submatrix of generator node, contact node and load bus, YGL、YLGFor
The transadmittance submatrix of generator node and load bus, YTL、YLTIt is contact node and the transadmittance submatrix of load bus,
YGT、YTGIt is generator node and the transadmittance submatrix of contact node；Node voltage, current vector, U are represented with U, IG、ULFor
The voltage of generator node and load bus, IG、ILIt is generator node and the Injection Current of load bus, can releases, load
Node voltage UL=Eopen-ZIL, in formula：
Load LiPlace node voltage ULiFor：ULi=Eopen,i-Zeq,iILi, i=1,2 ..., k, wherein, Eopen,iIt is column vector
EopenI-th element,ILi、ILjRespectively load Li、LjThe electric current for flowing through；Load LiPlace node
Voltage vulnerability index be：ZL,iIt is load LiCorresponding equiva lent impedance, if load LiForThe section
Putting voltage isThenriSmaller, then the static electric voltage stability of the node is better；Cut-off stream receiving end system
Voltage vulnerability index r maximum some nodes composition voltage weak node collection S in system, it is most weak that general S can use 5-6 voltage
Node, key monitoring is carried out to the voltage weak node that set S is included.
3. the direct current receiving-end system of a kind of consideration voltage stability according to claim 1 and accident integrate-cost is promptly born
Lotus control method, it is characterised in that in the step (3), described sets up receiving-end system emergency load control optimization problem
Mathematical Modeling simultaneously makees the implementation process of approximate processing and is to accident fine curve：
For direct current receiving-end system, if its admittance matrix is Y, subscript G, T and L represent respectively generator node, contact node and
Load bus, YGG、YTTAnd YLLRespectively the self-admittance submatrix of generator node, contact node and load bus, YGL、YLGFor
The transadmittance submatrix of generator node and load bus, YTL、YLTIt is contact node and the transadmittance submatrix of load bus,
YGT、YTGIt is generator node and the transadmittance submatrix of contact node；Node voltage, current vector, U are represented with U, IG、ULFor
The voltage of generator node and load bus, IG、ILIt is generator node and the Injection Current of load bus, load bus voltage
UL=Eopen-ZIL, in formula： Load LiPlace node
Voltage ULiFor：ULi=Eopen,i-Zeq,iILi, i=1,2 ..., k, wherein, Eopen,iIt is column vector EopenI-th element,ILi、ILjRespectively load Li, LjThe electric current for flowing through；Load LiThe voltage vulnerability index of place node
For：ZL,iIt is load LiCorresponding equiva lent impedance, if load LiForThe node voltage isThenriSmaller, then the static electric voltage stability of the node is better；Voltage vulnerability in cut-off stream receiving-end system
Index r maximum some nodes composition voltage weak node collection S, general S can use the most weak node of 5-6 voltage, to set S
Comprising voltage weak node carry out key monitoring；
Described direct current receiving-end system emergency load control optimization problem is described as：
Min f=f1+f2+αf3
s.t.L.F.(PG,PL,ρ,fd, U, θ)=0,
PG,min≤PG≤PG,max, Pline≤Pline,max,
|fd|≤τ,ρj≤ρj,up
Wherein,It is the direct economic loss that cutting load brings, ρiIt is load LiCutting load rate, ciFor excision is negative
Lotus LiWork factor, PLi,0It is load LiInitial value, i=1 ..., k；It is according to China《Electric power safety
Accident emergency is disposed and regulations of investigating》Accident fine, Pen (ρ should be paidi) it is to impose a fine with rate of reducing load ρiThe letter of change
Number；It is the quadratic sum of voltage some load bus Voltage Drop amounts the weakest,It is upper voltage limit
Value, S is voltage weak node collection；α is weight coefficient, and α is bigger, and emergency load control gets over the electricity for laying particular emphasis on and improving voltage weak node
Voltage levels, typically can use α=20；L.F.(PG,PL,ρ,fd, U, θ) and it is the power balance equation of Load flow calculation；PG、PLAnd ρ difference
It is generated output power, load power and cutting load rate；U, θ are respectively the voltage magnitude and phase angle of each node；fd=(f-
fn)/fnIt is system frequency deviation, fn is system nominal working frequency；τ is | fd| maximum, typically can use τ=0.04；
PG,max、PG,minThe respectively bound of generator output, PlineIt is line transmission power, Pline,maxIt is circuit maximum transmitted work(
Rate；U is respectively voltage bound, can typically be set to 1.1,0.95；ρj,upIt is load LjThe upper limit of rate of reducing load；
According to China《Electric power safety accident emergency is disposed and regulations of investigating》Accident is divided into ordinary accident, compared with major issue
Therefore, the classification treatment of major accident and special major accident, carry out accident grading according to power network scale and rate of reducing load, and sentence
Corresponding fine, formulates the different types of power network such as province or autonomous district people's government location city, prefecture-level city, county-level city
Corresponding fine rule, the function Pen (ρ) between the fine and rate of reducing load of defined is the unsmoothed curve of piecewise linearity, is
The difficulty in its calculating is solved, the fine curve to different type power network can use multinomialTo be fitted the side of Pen (ρ)
Method makees approximate processing, can use q=6, coefficient ajDetermined by least square method.
4. the direct current receiving-end system of a kind of consideration voltage stability according to claim 1 and accident integrate-cost is promptly born
Lotus control method, it is characterised in that in the step (4), it is urgent that described application prim al- dual interior point m ethod solves receiving-end system
The implementation process of spatial load forecasting optimization problem is：
For direct current receiving-end system, if its admittance matrix is Y, subscript G, T and L represent respectively generator node, contact node and
Load bus, YGG、YTTAnd YLLRespectively the self-admittance submatrix of generator node, contact node and load bus, YGL、YLGFor
The transadmittance submatrix of generator node and load bus, YTL、YLTIt is contact node and the transadmittance submatrix of load bus,
YGT、YTGIt is generator node and the transadmittance submatrix of contact node；Node voltage, current vector, U are represented with U, IG、ULFor
The voltage of generator node and load bus, IG、ILIt is generator node and the Injection Current of load bus, load bus voltage
UL=Eopen-ZIL, in formula： Load LiPlace node
Voltage ULiFor：ULi=Eopen,i-Zeq,iILi, i=1,2 ..., k, wherein, Eopen,iIt is column vector EopenI-th element,ILi、ILjRespectively load Li, LjThe electric current for flowing through；Load LiThe voltage vulnerability index of place node
For：ZL,iIt is load LiCorresponding equiva lent impedance, if load LiForThe node voltage isThenriSmaller, then the static electric voltage stability of the node is better；R maximums is some in cut-off stream receiving-end system
Node composition voltage weak node collection S, general S can use the most weak node of 5-6 voltage, and the voltage included to set S is weak
Node carries out key monitoring；
The optimization problem of described direct current receiving-end system emergency load control is described as：
Min f=f1+f2+αf3
s.t.L.F.(PG,PL,ρ,fd, U, θ)=0,
PG,min≤PG≤PG,max, Pline≤Pline,max,
|fd|≤τ,ρj≤ρj,up
Wherein,It is the direct economic loss that cutting load brings, ρiIt is load LiCutting load rate, ciFor excision is negative
Lotus LiWork factor,It is load LiInitial value, i=1 ..., k；It is according to China《Electric power safety
Accident emergency is disposed and regulations of investigating》Accident fine, Pen (ρ should be paidi) it is to impose a fine with rate of reducing load ρiThe letter of change
Number；It is the quadratic sum of voltage some load bus Voltage Drop amounts the weakest,It is upper voltage limit
Value, S is voltage weak node collection；α is weight coefficient, and α is bigger, and emergency load control gets over the electricity for laying particular emphasis on and improving voltage weak node
Voltage levels, typically can use α=20；L.F.(PG,PL,ρ,fd, U, θ) and it is the power balance equation of Load flow calculation；PG、PLAnd ρ difference
It is generated output power, load power and cutting load rate；U, θ are respectively the voltage magnitude and phase angle of each node；fd=(f-
fn)/fnIt is system frequency deviation, fnIt is system nominal working frequency；τ is | fd| maximum, typically can use τ=0.04；
PG,max、PG,minThe respectively bound of generator output, PlineIt is line transmission power, Pline,maxIt is circuit maximum transmitted work(
Rate；U is respectively voltage bound, can typically be set to 1.1,0.95；ρj,upIt is load LjThe upper limit of rate of reducing load；
Receiving-end system emergency load control optimization problem is solved using prim al- dual interior point m ethod, first, is initialized, state is set
Variable x={ ρ, fd, U, θ } initial value, wherein, ρ be each load bus cutting load rate vector, fdIt is system frequency excursion, U, θ point
Wei not each node voltage amplitude of system, phase angle vector, desirable ρ=0, fd=0, U=1, θ=0, slack variable l, u and drawing are set
Ge Lang multiplier z, w, y, can use l=1, u=1, z=1, w=-0.5, y=0, setting Center Parameter σ=0.7, between giving complementation
The convergence precision ε of gap Gap1=10-6And trend convergence precision ε2=10-4If, iterations initial value niter=0, greatest iteration time
Number niter_max=150；Then, complementary clearance G ap=l is calculatedTz-uTW, judges complementation clearance G ap ＜ ε1And trend error delta
L.F. ＜ ε2Whether set up simultaneously, if so, then exporting optimal solution, otherwise continue, calculate update equation coefficient matrix, obtain accordingly
Correction amount x, Δ l, Δ u, Δ z, Δ w, Δ y, update state variable, slack variable and Lagrange multiplier；Finally, judge
niter＞ niter_maxWhether set up, if so, then prompting " calculating does not restrain ", terminates to calculate, otherwise make niter=niter+ 1, continue
Iterative calculation.
5. the direct current receiving-end system of a kind of consideration voltage stability according to claim 1 and accident integrate-cost is promptly born
Lotus control method, it is characterised in that in the step (5), the accident of described check emergency load control prioritization scheme is comprehensive
The implementation process for closing cost and voltage stability is：
There is locking failure in HVDC, when direct current receiving-end system loses high electric power from outside, according to the Load Emergency control obtained
Scheme processed quickly cuts off the load of corresponding proportion in each load center, and simulation calculation is carried out to direct current receiving-end system dynamic response,
The frequency response of system before and after control measure is taken in analysis, and female to the accident integrate-cost and receiving-end system of different control programs
Line voltage is fallen level and is compared, and verifies the performance of control program of the present invention, defeated if meeting the requirement of various constraintss
It has the optimum control scheme for considering voltage stability and accident integrate-cost, otherwise re-optimization.
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