CN107404118A - Electrical interconnection system probability optimal load flow computational methods based on stochastic response surface - Google Patents

Electrical interconnection system probability optimal load flow computational methods based on stochastic response surface Download PDF

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CN107404118A
CN107404118A CN201710794144.2A CN201710794144A CN107404118A CN 107404118 A CN107404118 A CN 107404118A CN 201710794144 A CN201710794144 A CN 201710794144A CN 107404118 A CN107404118 A CN 107404118A
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mrow
msub
gas
node
msubsup
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孙永辉
张博文
张世达
王加强
翟苏巍
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Hohai University HHU
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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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • 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]
    • 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
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • 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
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses a kind of electrical interconnection system probability optimal load flow computational methods based on stochastic response surface, the present invention has initially set up power system, natural gas system model, and power system and natural gas system couple to form electrical interconnection system by gas turbine.Then with the minimum object function of the total operating cost of interacted system, consider power system and natural gas system operation constraint.The influence of the enchancement factors such as electric, gas load and wind-powered electricity generation, luminous energy is considered in optimization process, the probability statistics information of object function and its state variable is drawn by particle swarm optimization algorithm probability optimal load flow.

Description

Electrical interconnection system probability optimal load flow computational methods based on stochastic response surface
Technical field
The present invention relates to a kind of electrical interconnection system probability optimal load flow computational methods based on stochastic response surface, belong to Multiple-energy-source uncertainty analysis technical field.
Background technology
The energy is basis for the survival of mankind and important leverage, is the lifeblood of national economy, how to ensure that the energy can be held Reduced environmental pollution while continuous supply, be the emphasis that today's society is paid close attention to jointly.China is for a long time with the fossil energy such as coal, oil Energy consumption structure based on source causes huge environmental pressure.Therefore improve efficiency of energy utilization, exploitation cleaning, efficiently, Free of contamination clean energy resource turns into the certainty for solving the energy problem and environmental protection increasingly highlighted during human social development Selection.Electrical interconnection system establishes power system and the coupling of natural gas system with gas turbine, using more clear than coal Clean natural gas power, alleviate Pressure on Energy and reduce environmental pollution.
Natural gas is smaller compared to influence of other primary energy to environment, good economy performance, rich reserves and is easy to store, Available for emergency peak regulation, the coordination of regenerative resource for having randomness, indirect big can be used for；As gas turbine group is being sent out The increasingly lifting of electric side proportion, the coupling between power system and natural gas system will further be deepened, and electrical interconnection system will be into For the principal mode of following comprehensive energy net.
Optimal load flow (optimal power flow, OPF) is the important work of power system network planning and operating analysis Tool.As proportion of the gas turbine in power system gradually increases, the operation of natural gas system will necessarily influence OPF knot Fruit, but traditional OPF does not account for electric power networks and natural gas is internetwork couples.The existing research for electrical interconnection system It is based substantially under deterministic models, power system and natural gas system is probabilistic under the rare access background for new energy Research.
The content of the invention
Goal of the invention：The technical problems to be solved by the invention are that solve electrical interconnection system using stochastic response surface to exist The cost of electricity-generating under probabilistic probability optimal load flow under electricity, gas load and new energy access is minimum.
Technical scheme：A kind of electrical interconnection system probability optimal load flow computational methods based on stochastic response surface, successively Realize according to the following steps：
1) parameter information for obtaining power system carries out Steady state modeling, and its parameter information includes：Transmission line of electricity network topology Structure, the resistance of π type equivalent circuits, reactance, over the ground shunt conductance, susceptance, transformer voltage ratio and impedance, each node load and Generator exports active and reactive constraint, each node voltage constraint；
2) parameter information for obtaining natural gas network carries out Steady state modeling, and its parameter information includes：The topology of gas pipeline The parameter informations such as structure, efficiency of transmission, the topological structure of pressurizing point, each node gas load and gas source point natural gas, which are contributed, to be believed Breath, each node pressure constraint；
3) obtain and the coupling of electrical interconnection system is carried out with the parameters of gas turbine, constraints；
4) uncertainty predicted for load prediction, forecasting wind speed, illumination establishes load, wind speed, the probability letter of illumination Breath；
5) output response is expressed as on the basis of known input stochastic variable probability distribution by stochastic response surface On the chaos multinomial of known coefficient, the sampled point selected by optimal selected-point method determines the undetermined coefficient in multinomial, entered And obtain the probability distribution of estimated output response
6) according to the probability distribution of each variable, using cost as object function, the value at cost under probability optimal load flow is tried to achieve；
7) the probability statistics information of output state variable.
Brief description of the drawings
Fig. 1 is the inventive method flow chart；
Fig. 2 is the gas turbine powered pressurizing point schematic diagram of the present invention；
Fig. 3 is electrical interconnection system structure chart of the present invention；
Fig. 4 is cost of electricity-generating probability distribution graph；
Fig. 5 is No. 7 node voltage amplitude probability distribution graphs of power system；
Fig. 6 is No. 4 node pressure probability distribution graphs of natural gas system.
Embodiment
With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention The modification of form falls within the application appended claims limited range.
1 power system mesomeric state models
The active power and reactive power of each point, P can be calculated under power system rectangular coordinate system according to node voltageiFor The injection active power of PQ nodes and PV node, QiFor the injection reactive power of PQ nodes, UiFor the voltage swing of PV node.It is right In electric power networks interior joint i：
In formula：ei, fiThe respectively real and imaginary parts of node i voltage vector；Gij, BijRespectively bus admittance matrix i-th The real and imaginary parts of row jth column element.
2 natural gas system Steady state modelings
Natural gas system Steady state modeling is actual to be related to Various Components, and relevant with many factors, present invention is generally directed to day Two kinds of main elements of right feed channel and pressurizing point carry out Steady state modeling.
2.1 pipeline flow equations：
Natural gas line flow equation is relevant with many factors including pipe ends pressure, under ideal conditions for height Calm the anger and net complete turbulent flow, pipeline mn flow equations are：
Wherein：
In formula：fkmnFor pipeline flow value；πmFor node m pressure values；πnFor node n pressure Value；ε is pipeline efficiency factor；T0For normal temperature value；DkFor pipeline k internal diameter；π0For reference pressure value；G is gas phase to close Degree, air 1, natural gas 0.6；LkFor pipeline k length；TkaFor pipeline k mean gas temperature；ZaFor average gas pressure Contracting coefficient.
The energy expenditure equation of 2.2 compressors
The loss that will certainly cause natural gas due to frictional resistance in pipeline be present, in order to compensate the loss of natural gas, it is Pressurizing point rise gas pressure can be added in system.Pressurizing point raises pressure, it is necessary to consume extra energy by compressor, should Energy can both be provided by equivalent pressurizing point gas load, can also be by driven by power, and the present invention considers that equivalent gas load carries For and the load that is considered as in natural gas network.
Wherein：
In formula：fkTo pass through the gas flow of compressor；πmCompressor pressure is injected for gas；πnFor gas output squeezing Machine pressure；ZkiThe Gas Compression Factor at end is flowed into for compressor；TkiPlace's temperature is drawn for compressor natural gas；α refers to for thermal insulation Number；ηkFor pressurizing point efficiency.
Driving pressurizing point consumes the flow of natural gas：
In formula：αTk、βTk、γTkTo consume gas discharge conversion coefficient.
2.3 gas discharge equilibrium equations
Similar with power system interior joint power equation, gas discharge conservation is the flow and stream that each node flows into The flow gone out is equal, can be represented with the form of matrix：
(A+U) f+w-T τ=0
Wherein：
In formula：F is bypass flow value vector；W is the gas injection vector of each node；τ is each compressor consumed flow value Vector, matrix A are circuit-node incidence matrix, represent the contact between pipeline and node；Matrix U is that unit-node associates square Battle array, represent the contact between unit and node.T is compressor consumption and node incidence matrix, represent gas turbine and node it Between contact.
Coupling between 3 power systems and natural gas system
The natural gas input of gas turbine is considered as the gas load of natural gas system, while the electricity of gas turbine consumption natural gas Power exports the power supply for being considered as power system, and power system and natural gas system are coupled together by such gas turbine, and it, which is coupled, closes It is to be：
In formula：Hg,iCalorie value is inputted for gas turbine；PG,iIt is gas turbine to power system node i power output； αg,i、βg,i、γg,iDetermined by the heat consumption rate curve of gas turbine；The natural gas flow of gas turbine is inputted for natural gas system Amount；GHV=1015BTU/SCF, it is high heating value.
4 electrical interconnection system probability optimal load flows
According to above-mentioned model, power system is coupled with natural gas system by gas turbine, forms electrical interconnection system.With Total energy cost is object function, considers the various constraints of electric power networks, natural gas network and gas turbine, is established electrically mutual Contact system probability optimal load flow model.
4.1 object function
The present invention is used as object function using the total energy cost of system：
In formula：PGFor non-gas turbine set；ai, bi, ciFor generator cost coefficient；PiContributed for generated power, NS For source of the gas point set；giFor gas cost coefficient；wg,iFor deliverability of gas.
4.2 constraints
Equality constraint
1) power system equality constraint:
ΔPi=PG,i+PW,i-PL,i-Pi
ΔQi=QG,i-QL,i-Qi
In formula：ΔPi, Δ QiFor node i active and reactive power amount of unbalance；For the imbalance of node i voltage squared Amount；PG,i, QG,iRespectively generator i active and reactive output；PW,iFor gas turbine i active power output；PL,i, QL,iRespectively The active and reactive load of node i.
2) natural gas system equality constraint:
Δwi=wg,i-wL,i-Fi=0
In formula：ΔwiFor the amount of unbalance of each node-flow value in natural gas network；wg,iGas for gas source point to node i Body injection rate；wL,iFor the gas load of node i, FiFor the injection rate of node i.
Inequality constraints
1) power system inequality constraints：
PGmin,i≤PG,i≤PGmax,i
QGmin,i≤QG,i≤QGmax,i
In formula：PGmax,i, PGmin,iThe upper and lower bound of active power is sent by generator；QGmax,i, QGmin,iTo generate electricity Machine sends out the upper and lower bound of reactive power；For the upper and lower bound of node voltage amplitude square.
2) natural gas network inequality constraints：
wgmin,i≤wg,i≤wgmax,i
πmin,i≤πi≤πmax,i
In formula：wgmax,i, wgmin,iFor the upper and lower bound of each gas source point gas supply in natural gas network；πmax,i, πmin,iThe upper and lower bound of respectively each node pressure value；Rmax,i, Rmin,iThe respectively upper and lower bound of pressurizing point pressurization ratio.
5 uncertain factors are analyzed
In actual production, the gentle load of electric load all has randomness, likewise as connecing for the new energy such as wind-powered electricity generation, photovoltaic Enter, the randomness of its wind speed and intensity of illumination can also have an impact to system.Load, wind power plant, solar plant are passed through below Row analysis.
The randomness of 5.1 loads
The load of electrical interconnection system includes the gentle load of electric load.Largely it was verified that the probability distribution of load meets Normal distribution, i.e.,：
In formula：ELFor (electricity, gas) load power；The respectively mathematic expectaion of load power, standard deviation；f (EL) be load power probability density function.
The randomness of 5.2 output of wind electric field
Wind-driven generator output is relevant with wind speed, and the uncertainty of wind speed result in the uncertain of wind-driven generator output Property.Two-parameter Weibull curve can describe the probability density function of wind speed well, i.e.,：
In formula：vwFor wind speed variable；kwFor the form parameter of Weibull distribution；cwFor the scale parameter of Weibull distribution.
Active P is exported according to wind speed and wind-driven generatorwRelation be represented by：
Wherein：
In formula：PNFor blower fan rated power；vciTo cut wind speed；vNFor rated wind speed；vcoFor cut-out wind speed.
Practice have shown that wind speed is typically maintained in vciAnd vNBetween, therefore approximate can obtain PwAnd vwLinear function relation, so Wind-power electricity generation active power probability density is as follows：
Active power of wind power field is regarded as the Weibull distribution of three parameters, then available standards normally distributed variable represents For：
In formula：ξ represents standardized normal distribution variable.
Wind-powered electricity generation field generator is reduced to PQ node processings, it is assumed that wind power plant is controlled using constant power factor, then wind power plant is defeated Going out reactive power is：
In formula：For power-factor angle.
The randomness that 5.3 photovoltaic generations are contributed
Solar energy power generating factory output is relevant with intensity of illumination, and the randomness of intensity of illumination result in photovoltaic hair The uncertainty that power plant contributes, intensity of illumination is often distributed with Beta to be described, i.e.,：
In formula：R is intensity of illumination；rmaxFor the maximum illumination of this period；α, β are the form parameter of Beta distributions.
For solar photovoltaic generation system, the total output of solar cell array is active to be：
Pp=rA η
In formula：A is the gross area of square formation, and η is total photoelectricity transfer efficiency of square formation.
The probability density function that photovoltaic battery matrix power output can be obtained also is distributed in Beta, i.e.,：
In formula：Ppmax=rmaxA η are square formation peak power output.
Photovoltaic active power variable can be expressed as with normally distributed variable：
In formula：f-1For the inverse function of the probability density function of photovoltaic battery matrix power output.
Similar with wind power plant, photovoltaic power plant is also reduced to PQ node processings, and photovoltaic cell constant power factor is substantially constant：
In formula：For power-factor angle.
6 stochastic response surfaces
Stochastic response surface be it is known input stochastic variable probability distribution on the basis of, will output response be expressed as on The chaos multinomial of known coefficient, by sampling the undetermined coefficient determined in multinomial on a small quantity, and then obtain estimated output The probability distribution of response.Concrete operations are as follows：
(1) electrical interconnection system information is inputted, determines the number n and its probability distribution of stochastic inputs variable X in system.According to According to probability transformation principle, by all input variable standardizations, will all input variables become at random with one group of standardized normal distribution Z function representation is measured, i.e.,：
xi=Fi -1(Φ(zi))
In formula：xiFor some input variable；ziFor corresponding standardized normal distribution variable；Φ is ziProbability point Cloth function；FiFor xiProbability-distribution function.
(2) the second order chaos multinomial of corresponding output variable is built, i.e.,
In formula：Y is output variable；ξiFor n incoherent standardized normal distribution stochastic variables, corresponding n input variable； A is the polynomial each term coefficient of second order chaos.
, wherein it is desired to the coefficient number determined is
(3) parameter and standard normally distributed random variable group ξ collocation point.Hermite using higher order (i.e. 3 ranks) is multinomial The collocation point that the root combination of formula is alternatively put, there is 3nIndividual alternative point.Using optimal selected-point method, suitable collocation point C is selectedpi(i= 1,...,N).Use formula xi=Fi -1(Φ(zi)) obtain N number of collocation point and correspond to output variable sample Xpi(i=1 ..., N).
(4) by sample point XpiSubstituted into respectively in power flow equation as disturbance variable, use being determined property of particle cluster algorithm Optimal load flow calculates, and utilizes the output variable Y calculatediForm output vector Y.Use the output collocation point C selectedpiBy row structure Into Hermite coefficient matrix H, the vector for making A be chaos multinomial coefficient composition obtains system of linear equations, solves chaos multinomial Coefficient, so as to obtain the chaos multinomial of the variableI.e. with one group of n Individual standardized normal distribution stochastic variable represents the variable；
(5) probability density function and probability-distribution function of the variable are estimated using kernel density estimation method.
Sample calculation analysis
The electrical interconnection system of the present invention passes through 2 combustions by the IEEE14 node systems and the node system of natural gas 14 changed Gas-turbine is formed, and its structure is as shown in annex Fig. 3.It is assumed that 4 all gas turbine drives of pressurizing point；It is assumed that IEEE14 nodes The generator of 2,3 connections is gas turbine in system, and the node 14,12 with the node system of natural gas 14 connects respectively；IEEE14 is saved Wind power plant of the dot system in the access capacity of node 9 for 15MW, 8MW solar plant is accessed in node 14；All electricity, gas load Standard deviation be desired value 5%.Stochastic response surface is used to the electrical interconnection system, with the minimum target letter of cost of electricity-generating Number, optimal load flow calculating is carried out with particle cluster algorithm.Draw cost of electricity-generating probability curve such as Fig. 4, No. 7 node voltages of power system Amplitude probability distribution curve such as Fig. 5, No. 4 node pressure probability distribution curve such as Fig. 6 of natural gas.

Claims (6)

1. a kind of electrical interconnection system probability optimal load flow computational methods based on stochastic response surface, it is characterised in that successively Realize according to the following steps：
1) parameter information for obtaining power system carries out Steady state modeling, and its parameter information includes：Transmission line of electricity network topological structure, The resistance of π type equivalent circuits, reactance, over the ground shunt conductance, susceptance, transformer voltage ratio and impedance, each node load and generating Machine exports active and reactive constraint, each node voltage constraint；
2) parameter information for obtaining natural gas network carries out Steady state modeling, and its parameter information includes：The topological structure of gas pipeline, The parameter informations such as efficiency of transmission, the topological structure of pressurizing point, each node gas load and gas source point natural gas force information, each section Press force constraint；
3) obtain and the coupling of electrical interconnection system is carried out with the parameters of gas turbine, constraints；
4) load, wind speed, the probabilistic information of illumination are established for the uncertainty of load prediction, forecasting wind speed, illumination prediction；
5) by stochastic response surface it is known input stochastic variable probability distribution on the basis of, will output response be expressed as on The chaos multinomial of known coefficient, the sampled point selected by optimal selected-point method determines the undetermined coefficient in multinomial, and then obtains To the probability distribution of estimated output response；
6) according to the probability distribution of each variable, using cost as object function, the value at cost under probability optimal load flow is tried to achieve；
7) the probability statistics information of output state variable.
2. the electrical interconnection system probability optimal load flow computational methods based on stochastic response surface as claimed in claim 1, its It is characterised by,
Power system mesomeric state models：
For electric power networks interior joint i：
<mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>&amp;lsqb;</mo> <msub> <mi>e</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>e</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>f</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>f</mi> <mi>j</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>e</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
<mrow> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>b</mi> </munderover> <mo>&amp;lsqb;</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>e</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>f</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>e</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>f</mi> <mi>j</mi> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>e</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
<mrow> <msubsup> <mi>e</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>f</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>U</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow>
In formula：ei, fiThe respectively real and imaginary parts of node i voltage vector；Pi, QiRespectively electric power networks interior joint i wattful powers Rate and reactive power；Gij, BijThe respectively real and imaginary parts of the i-th row of bus admittance matrix jth column element；For the electricity of node i Press size.
3. the electrical interconnection system probability optimal load flow computational methods based on stochastic response surface as claimed in claim 1, its It is characterised by,
Pipeline flow equation：
For the complete turbulent flow of high pressure gas net, pipeline mn flow equations are：
<mrow> <msub> <mi>f</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>k</mi> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>M</mi> <mi>k</mi> </msub> <msub> <mi>S</mi> <mrow> <mi>m</mi> <mi>n</mi> </mrow> </msub> <msqrt> <mrow> <msub> <mi>S</mi> <mrow> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <msubsup> <mi>&amp;pi;</mi> <mi>m</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>&amp;pi;</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </msqrt> </mrow>
Wherein：
<mrow> <msub> <mi>M</mi> <mi>k</mi> </msub> <mo>=</mo> <mi>&amp;epsiv;</mi> <mfrac> <mrow> <mn>18.73</mn> <msub> <mi>T</mi> <mn>0</mn> </msub> <msubsup> <mi>D</mi> <mi>k</mi> <mrow> <mn>8</mn> <mo>/</mo> <mn>3</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;pi;</mi> <mn>0</mn> </msub> <msqrt> <mrow> <msub> <mi>GL</mi> <mi>k</mi> </msub> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mi>a</mi> </mrow> </msub> <msub> <mi>Z</mi> <mi>a</mi> </msub> </mrow> </msqrt> </mrow> </mfrac> </mrow>
In formula：fkmnFor pipeline flow value；πmFor node m pressure values；πnFor node n pressure values；ε For pipeline efficiency factor；T0For normal temperature value；DkFor pipeline k internal diameter；π0For reference pressure value；G is gas relative density, Air is 1, natural gas 0.6；LkFor pipeline k length；TkaFor pipeline k mean gas temperature；ZaCompressed for average gas Coefficient；
The energy expenditure equation of compressor：
<mrow> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>B</mi> <mi>k</mi> </msub> <msub> <mi>f</mi> <mi>k</mi> </msub> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>&amp;pi;</mi> <mi>m</mi> </msub> <msub> <mi>&amp;pi;</mi> <mi>n</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <msub> <mi>Z</mi> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;alpha;</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>&amp;alpha;</mi> </mfrac> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mn>1</mn> <mo>&amp;rsqb;</mo> </mrow>
Wherein：
<mrow> <msub> <mi>B</mi> <mi>k</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3554.58</mn> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </msub> </mrow> <msub> <mi>&amp;eta;</mi> <mi>k</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>&amp;alpha;</mi> <mrow> <mi>&amp;alpha;</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow>
In formula：fkTo pass through the gas flow of compressor；πmCompressor pressure is injected for gas；πnFor gas output squeezing machine pressure Power；ZkiThe Gas Compression Factor at end is flowed into for compressor；TkiPlace's temperature is drawn for compressor natural gas；α is adiabatic exponent；ηkFor Pressurizing point efficiency；
Driving pressurizing point consumes the flow of natural gas：
<mrow> <msub> <mi>&amp;tau;</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>T</mi> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>T</mi> <mi>k</mi> </mrow> </msub> <msub> <mi>H</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>T</mi> <mi>k</mi> </mrow> </msub> <msubsup> <mi>H</mi> <mi>k</mi> <mn>2</mn> </msubsup> </mrow>
In formula：αTk、βTk、γTkTo consume gas discharge conversion coefficient；
Gas discharge equilibrium equation：
Gas discharge conservation is that the flow that each node flows into is equal with the flow flowed out, can be represented with the form of matrix：
(A+U) f+w-T τ=0
Wherein：
In formula：F is bypass flow value vector；W is the gas injection vector of each node；τ is each compressor consumed flow value vector, Matrix A is circuit-node incidence matrix, represents the contact between pipeline and node；Matrix U is unit-node incidence matrix, table Show the contact between unit and node；T is compressor consumption and node incidence matrix, represents the connection between gas turbine and node Network.
4. the electrical interconnection system probability optimal load flow computational methods based on stochastic response surface as claimed in claim 1, its It is characterised by, the coupling between power system and natural gas system：
The natural gas input of gas turbine is considered as the gas load of natural gas system, while the electric power of gas turbine consumption natural gas is defeated Go out to be considered as the power supply of power system, power system and natural gas system are coupled together by such gas turbine, and its coupled relation is：
<mrow> <msub> <mi>H</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;beta;</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>G</mi> <mo>,</mo> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> </mrow>
<mrow> <msubsup> <mi>F</mi> <mrow> <mi>g</mi> <mi>a</mi> <mi>s</mi> </mrow> <mrow> <mi>m</mi> <mo>,</mo> <mi>i</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>/</mo> <mi>G</mi> <mi>H</mi> <mi>V</mi> </mrow> 2
In formula：Hg,iCalorie value is inputted for gas turbine；PG,iIt is gas turbine to power system node i power output；αg,i、 βg,i、γg,iDetermined by the heat consumption rate curve of gas turbine；The gas discharge of gas turbine is inputted for natural gas system； GHV=1015BTU/SCF, it is high heating value.
5. the electrical interconnection system probability optimal load flow computational methods based on stochastic response surface as claimed in claim 1, its It is characterised by, uncertain factor analysis：
A. the randomness of load
The load of electrical interconnection system includes the gentle load of electric load；Load prediction error is typically represented using normal distribution It is uncertain；
B. the randomness of output of wind electric field
Wind-driven generator output is relevant with wind speed, and the uncertainty of wind speed result in the uncertainty of wind-driven generator output； Two-parameter Weibull curve can describe the probability density function of wind speed well.
C. the randomness that photovoltaic generation is contributed
Solar energy power generating factory output is relevant with intensity of illumination, and the randomness of intensity of illumination result in solar energy power generating factory The uncertainty of output, intensity of illumination is often distributed with Beta to be described.
6. the electrical interconnection system probability optimal load flow computational methods based on stochastic response surface as claimed in claim 1, its It is characterised by, stochastic response surface is on the basis of known input stochastic variable probability distribution, and output response is expressed as closing In the chaos multinomial of known coefficient, by sampling the undetermined coefficient determined in multinomial, and then obtain estimated output and ring The probability distribution answered；
According to stochastic response surface analog result, cost probability distribution and each shape of electrical interconnection system under output probability optimal load flow The probability distribution of state amount.
CN201710794144.2A 2017-09-06 2017-09-06 Electrical interconnection system probability optimal load flow computational methods based on stochastic response surface Pending CN107404118A (en)

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