CN110263387A - The integrated energy system optimal operation model and its linear processing methods that power distribution network, natural gas grid based on energy hub are established - Google Patents
The integrated energy system optimal operation model and its linear processing methods that power distribution network, natural gas grid based on energy hub are established Download PDFInfo
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Abstract
The integrated energy system optimal operation model and its linear processing methods established the present invention relates to a kind of power distribution network based on energy hub, natural gas grid, it can be by energy hub model that power distribution network, natural gas grid couple, the lowest cost is purchased as optimization aim using the energy, the safe operation constraint of power distribution network, natural gas grid and energy hub, including the constraint of power distribution network Branch Power Flow, node voltage constraint, branch power constraint are considered simultaneously；The constraint of natural gas line air balance, the constraint of gas source gas output, the constraint of node air pressure size constraint, natural gas line Weymouth steady-state load flow, pressurizer boosting relation constraint；The heating power balance of energy hub constrains and the operation power constraint of each energy conversion apparatus, to realize the optimization operation of integrated energy system.Before solving model, linearization process is carried out to initial model, finally to solve integrated energy system optimal operation model by CPLEX.
Description
Technical field
The present invention relates to field of power electronics, especially a kind of power distribution network based on energy hub, natural gas grid are established
Integrated energy system optimal operation model and its linear processing methods.
Background technique
Environment worsening and the energy are petered out the problem of having become global concern, how to make full use of clean energy resource and
Guarantee that the mankind's uses energy demand simultaneously again, it has also become the common focus of attention of countries in the world today.For the association for realizing various energy resources
It adjusts management and makes full use of the complementarity of different energy sources, integrated energy system comes into being.Integrated energy system refers to certain
Coordinated planning, the optimization operation between the various energy resources subsystems such as coal, petroleum, natural gas, electric energy, thermal energy are realized in region.
Therefore, while meeting diversification energy demand in system, it is necessary to effectively promote efficiency of energy utilization, promote the energy can
Sustainable development.
It by power grid, the combined operating of gas net, runs while firepower unit can be reduced, and then alleviates the further of fossil energy
The further deterioration of consumption and environmental pollution.Power grid can not only realize that the energy is complementary with the joint of gas net, and high efficiency may be used also
Sufficiently meeting using for user side can demand.Accordingly, it is considered to the integrated energy system optimization of new generation in combination of power distribution network, natural gas grid
Operation, the operating mechanism of comprehensive study energy resource system also help it is following set up a unified market value measurement standard,
So that the conversion and complementation of the energy fully demonstrate economy and society value, enable electric power promote to more cleaning, it is more green
The energy transformation, and will for future bring a more efficient, economic, renewable, reliable, sustainable and stable synthesis
Energy resource system brings long-term and positive height interests.
Summary of the invention
In view of this, the purpose of the present invention is to propose to a kind of power distribution network based on energy hub, natural gas grids to establish
Integrated energy system optimal operation model and its linear processing methods can consider the mutual shadow of power network, natural gas grid simultaneously
It rings, under the premise of meeting electricity, air and heat workload demand, integrated energy system is more economically and safely run.
The present invention is realized using following scheme: the synthesis that a kind of power distribution network based on energy hub, natural gas grid are established
Energy resource system optimal operation model, comprising the following steps:
Step S1: providing one can be by energy hub model that power distribution network, natural gas grid couple；
Step S2: objective function is established, and about according to the safe operation of power distribution network, natural gas grid and energy hub
Beam completes the modeling of integrated energy system optimal operation model.
Further, objective function described in step S2 is shown below for energy acquisition cost, including purchases strategiesWith purchase gas costTo make integrated energy system in dry run
Total cost during scheduling is minimum；
In formula, TR indicates the set of substation's injecting power node in power distribution network；GS indicates gas source node in natural gas grid
Set；Unit price of power, gas price in distribution expression period t；Function injects in substation in respectively period t
The purchase of electricity of rate node j；For the purchase tolerance of the gas source node j in period t.
Further, the safe operation of power distribution network described in step S2 constraint includes: node power Constraints of Equilibrium, node voltage
Filters with Magnitude Constraints, the constraint of distribution line maximum carrying capacity and substation's power constraint；
The node power Constraints of Equilibrium are as follows:
In formula, rij、xijThe respectively resistance of branch ij, reactance；δ (j) is indicated using j as the end of the branch of headend node
The set of node, π (j) are indicated using j as the set of the headend node of the branch of endpoint node；Pij,t、Qij,tRespectively branch ij's
Active power and reactive power；Respectively indicate major network power output and electric load active power；Respectively indicate use
The active power output of P2G device electric conversion in Hub；Indicate Hub in CHP device injection power distribution network etc.
Imitate active power；Respectively indicate the reactive power value of major network power output, electric load；
The node voltage amplitude constraint are as follows:
Umin≤Uj,t≤Umax
In formula, Uj,t、UminAnd UmaxRespectively node voltage amplitude and its lower and upper limit；
The distribution line maximum carrying capacity constraint are as follows:
0≤Iij,t≤Imax
In formula, Iij,t、ImaxRespectively branch current magnitudes and its upper limit；
Substation's power constraint are as follows:
Further, the particular content natural gas network constrained in step S2 are as follows:
The constraint of node air balance:
In formula, σ (jk) is indicated using j as the pipeline set of headend node；μ (ij) respectively indicates the pipe using j as endpoint node
Road set；fp,t/fl,tFor the flow of pipeline p/l；The respectively gentle source node gas output of gas load；Respectively indicate the amount of natural gas for GF, CHP energy conversion in (comprehensive energy unit) Hub；P2G device electricity is converted into the equivalent natural gas injection rate of gas in expression Hub；
The constraint of gas source gas output:
The natural gas being produced from gas well needs the purification by refinery, due to by gas at place capacity and gas well
The limitation of pressure, gas source gas output should meet following constraint in the unit time:
In formula,For the output amount of natural gas of gas source j,Respectively gas source j exports amount of natural gas
Bound；
Node air pressure constraint:
The air pressure of each node of natural gas network must be maintained in safe, reasonable range of operation, and mathematic(al) representation is such as
Under:
In formula,Respectively represent air pressure upper lower limit value at node i；
The constraint of natural gas line Weymouth steady-state load flow:
The relationship of gas flow and both ends air pressure, expression are portrayed using Weymouth steady-state load flow model
Are as follows:
Wherein,
In addition pipeline flow also should ensure that within safe and reasonable range of operation:
In formula, fp,tRepresent the natural gas flow that pipeline p flows through；πi,tAnd πj,tRespectively indicate pipeline p both ends air pressure size；φp
Indicate the air stream transportation parameter of pipeline p；sgnpIndicate the air flow direction of pipeline p；Indicate maximum pipeline transmission capacity.
Pressurizer boosting relation constraint:
πj,t=Γcπi,t
In formula, fc,tIndicate the delivery air of pressurizer c；πi,tAnd πj,tRespectively represent pressurizer c inlet end and outlet side
Air pressure；Γc、The respectively boosting ratio and maximum transfer capacity of pressurizer c.
Further, the operation constraint of energy hub described in step S2 are as follows:
The constraint of the energy hub thermal power equilibrium of supply and demand:
The unidirectional constraint of energy hub energy conversion:
Further, the present invention also provides a kind of power distribution network based on energy hub, natural gas grid establish it is comprehensive
Close the linear processing methods of energy resource system optimal operation model, comprising the following steps:
Step S3: linearization process is carried out to the model established in step S2；
Step S4: using CPLEX solver, to linearisation in step S3, treated that model solves.
Further, the particular content of the step S3 are as follows: will using second order cone relaxation and increment piecewise-linear techniques
Model conversation carries out linearization process；Due to containing nonlinear terms in node power Constraints of Equilibrium, using second order cone relaxation method
Abbreviation is carried out to constraint, new variables is introduced and eliminates voltage and current quadratic term, be shown below:
Node power Constraints of Equilibrium can eliminate the nonlinear quadratic item of voltage and current, as follows:
Voltage, current amplitude constraint modification as a result, are as follows:
The third formula of node power constraint is further converted to second order tapered by relaxation；Concrete form is as follows:
Line is carried out to the pipeline Weymouth steady-state load flow constraint in natural gas network using increment piecewise-linear techniques
Property, it is non-linear by the quadratic term bring for being introduced into air pressure in new variable cancellation pipeline Weymouth steady-state load flow constraint,
Shown in specific as follows:
1、
Therefore, pipeline Weymouth steady-state load flow constraint can tentatively rewrite are as follows:
Due to sgnp(πi,t,πj,t) it is a sign function, work as πi,tGreater than πj,tWhen take 1, otherwise take -1；Therefore, formula
The left side write as absolute value expression, even Yp,t=fp,t|fp,t|；That is Yp,t=fp,t|fp,t| it can also be expressed as f (x)=x | x
| non-linearization formula, the step of increment piece-wise linearization is as follows:
Step SA: number of segment n is averagely segmented according to model built setting；
Step SB: carrying out n equal part for the value interval of x, and this makes it possible to obtain n+1 discrete points, i.e. x0,x1...xn；
Step SC: discrete point x is calculated0,x1...xnCorresponding f (x) functional value；
Step SD: introducing new auxiliary variable, and guarantees to meet following constraint:
In conjunction with the above method, the constraint of pipeline Weymouth steady-state load flow is finally described as:
Compared with prior art, the invention has the following beneficial effects:
The present invention considers that power network, natural gas grid interact simultaneously, in the premise for meeting electricity, air and heat workload demand
Under, integrated energy system is more economically and safely run.Plan model has fully considered the characteristic flexibly converted between electricity, gas,
On the basis of meeting safe operation constraint, totle drilling cost is purchased as optimization aim using the energy of integrated energy system, promotes synthesis
Economy in energy system operation level.
Detailed description of the invention
Fig. 1 is the energy hub schematic diagram of the embodiment of the present invention.
Fig. 2 is the natural gas network rough schematic of the embodiment of the present invention.
Fig. 3 is the temporal characteristics figure of the electricity of the embodiment of the present invention, air and heat load.
Fig. 4 is the IEEE-14 node power distribution net topology of the embodiment of the present invention.
Fig. 5 is 20 node natural gas network topologies of the embodiment of the present invention.
Fig. 6 is purchase of electricity after the electricity price of the embodiment of the present invention, gas price curve and optimization, purchase tolerance curve.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
Present embodiments provide a kind of power distribution network based on energy hub, integrated energy system that natural gas grid is established it is excellent
Change moving model, comprising the following steps:
Step S1: establish it is a kind of can by energy hub that power distribution network, natural gas grid couple (energy hub,
EH) model completes integrated energy system modeling；
Step S2: considering the safe operation constraint of power distribution network, natural gas grid and energy hub, establish optimization aim,
Complete integrated energy system modeling.
The following are the specific implementation processes of the present embodiment.
(1) as shown in Fig. 1, establish it is a kind of can be by energy hub model that power distribution network, natural gas grid couple.
(2) using energy the lowest cost as target, the objective function of Optimized model is established.
(3) comprehensively consider power distribution network safe operation constraint.
(4) natural gas network reduction models and considers that natural gas Cybersecurity Operation constrains.
(5) comprehensively consider the safe operation constraint of energy hub.
In the present embodiment, terminal comprehensive energy model of element is established, step S1's is implemented as follows:
The energy demand of the forms such as electricity, heat, gas load is existed simultaneously in integrated energy system.To meet load need as far as possible
Ask, establish it is a kind of can be by energy hub (energy hub, EH) model that power distribution network and natural gas grid couple.The energy
Hub mainly by cogeneration of heat and power (combined heat and power, CHP), gas fired-boiler (gas furnace, GF) and
P2G (power to gas, P2G) device composition, based on the energy hub that this is established, not only between achievable electricity, gas
Mutually conversion, also can be supplied to thermic load.
In the present embodiment, step S2 is implemented as follows:
2, the objective function of Optimized model is established
The main target of the Optimized model of proposition is the total cost for making integrated energy system during dry run scheduling
It is minimum, therefore objective function mainly considers energy acquisition cost, including purchases strategies and purchase gas cost.
In formula, TR indicates the set of substation's injecting power node in power distribution network；GS indicates gas source node in natural gas grid
Set；Unit price of power, gas price in distribution expression period t；Function injects in substation in respectively period t
The purchase of electricity of rate node j；For the purchase tolerance of the gas source node j in period t.
3, consider power distribution network operation constraint:
Node power Constraints of Equilibrium
In formula, rij、xijThe respectively resistance of branch ij, reactance；δ (j) is indicated using j as the end of the branch of headend node
The set of node, π (j) are indicated using j as the set of the headend node of the branch of endpoint node；Pij,t、Qij,tRespectively branch ij's
Active power and reactive power；Major network power output and electric load active power are respectively indicated,It respectively indicates
Active power output for P2G device electric conversion in Hub；Indicate CHP device injection power distribution network in Hub
Equivalent active power,Respectively indicate the reactive power value of major network power output, electric load.
Node voltage amplitude constraint
Umin≤Uj,t≤Umax
In formula, Uj,t、UminAnd UmaxRespectively node voltage amplitude and its lower and upper limit.
The constraint of distribution line maximum carrying capacity
0≤Iij,t≤Imax
In formula, Iij,t、ImaxRespectively branch current magnitudes and its upper limit
Substation's power constraint
4, natural gas network model is established, and considers natural gas grid operation constraint
As shown in Fig. 2, natural gas network is mainly made of gas source, natural gas line, pressurizer and natural gas load.
Always mainly frictional dissipation inevitably occurs for gas flow in the flow process from exploitation to transport, by certain
After conveying distance (generally 80~160km), air pressure can be gradually decreased.To avoid excessive frictional dissipation, guarantee natural gas energy
It is transported to enough high-quality and high-efficiencies load side, the installation pressurizer on certain pipelines is generally required in natural gas system and is boosted,
To maintain node air pressure safety operation level.It can thus be seen that the effect of pressurizer is analogous in fact in natural gas network
Transformer in electric system.Natural gas grid network is constrained below:
The constraint of node air balance
In formula, σ (jk) indicates to respectively indicate the pipe using j as endpoint node by the pipeline set of headend node, μ (ij) of j
Road set；fp,t/fl,tFor the flow of pipeline p/l；The respectively gentle source node gas output of gas load,Respectively indicate the amount of natural gas for GF, CHP energy conversion in comprehensive energy unit (Hub)；P2G device electricity is converted into the equivalent natural gas injection rate of gas in expression Hub.
The constraint of gas source gas output
The natural gas being produced from gas well needs the purification by refinery.Due to by gas at place capacity and gas well
The limitation of pressure, gas source gas output should meet following constraint in the unit time:
In formula,For the output amount of natural gas of gas source j,Respectively gas source j exports amount of natural gas
Bound.
Node air pressure constraint
The air pressure of each node of natural gas network must be maintained in safe, reasonable range of operation, and mathematic(al) representation is such as
Under:
In formula,Respectively represent air pressure upper lower limit value at node i.
The constraint of natural gas line Weymouth steady-state load flow
This project portrays the relationship of gas flow and both ends air pressure, specific table using Weymouth steady-state load flow model
Up to formula are as follows:
Wherein,
In addition pipeline flow also should ensure that within safe and reasonable range of operation:
In formula, fp,tRepresent the natural gas flow that pipeline p flows through；πi,tAnd πj,tRespectively indicate pipeline p both ends air pressure size；φp
Indicate the air stream transportation parameter of pipeline p；sgnpIndicate the air flow direction of pipeline p；Indicate maximum pipeline transmission capacity.
Pressurizer boosting relation constraint
Pressurizer model is simplified herein, has ignored the energy consumed when its operation, and only retains the air inlet of pressurizer
The transmission capacity constraint of boosting ratio relationship and pressurizer between mouth and gas outlet.
πj,t=Γcπi,t
In formula, fc,tIndicate the delivery air of pressurizer c；πi,tAnd πj,tRespectively represent pressurizer c inlet end and outlet side
Air pressure；Γc、The respectively boosting ratio and maximum transfer capacity of pressurizer c.
5, energy hub operation constraint
The constraint of the energy hub thermal power equilibrium of supply and demand
The unidirectional constraint of energy hub energy conversion
Preferably, the synthesis energy that the present embodiment also provides a kind of power distribution network based on energy hub, natural gas grid is established
The linear processing methods of source system optimized operation model, comprising the following steps:
Step S3: carrying out linearization process to built Optimized model, to solve integrated energy system optimization by CPLEX
Moving model.
Step S4: integrated energy system optimal operation model is solved by CPLEX.
I.e. are as follows: (6) linearization process is carried out to built Optimized model.
(7) integrated energy system optimal operation model is solved by CPLEX.
Step S3's is implemented as follows:
The model that step S2 is proposed is a comprehensive non-convex problem.In order to solve this problem, before solving model,
First linear problem is converted by master mould with increment piecewise-linear techniques using second order cone is loose.
6, model linearization
1) second order cone relaxing techniques
Due to containing nonlinear terms in node power Constraints of Equilibrium, in order to solve this problem, using second order cone relaxing techniques
Abbreviation is carried out to constraint.It introduces new variables and eliminates voltage and current quadratic term, be shown below:
Node power Constraints of Equilibrium can eliminate the nonlinear quadratic item of voltage and current, as follows:
Voltage, current amplitude constraint can also be modified as a result, are as follows:
The third formula of node power constraint can be further converted to second order tapered by relaxation.The following institute of concrete form
Show:
2) increment piecewise-linear techniques
Pipeline Weymouth steady-state load flow constraint in natural gas network is a more intractable Nonlinear Nonconvex expression
Formula, it is difficult to which therefore direct solution also needs to linearize it.
It is possible, firstly, to pass through the quadratic term band for being introduced into air pressure in new variable cancellation pipeline Weymouth steady-state load flow constraint
That comes is non-linear, specific as follows shown:
Therefore, pipeline Weymouth steady-state load flow constraint can tentatively rewrite are as follows:
Due to sgnp(πi,t,πj,t) it is a sign function, work as πi,tGreater than πj,tWhen take 1, otherwise take -1.It therefore, can be
Absolute value expression is write as in the left side of formula, even Yp,t=fp,t|fp,t|。
Such as f (x)=x | x | this kind of non-linearization formula, the step of increment piece-wise linearization approximately as:
Step1: the characteristics of according to model built, suitable segmentation number of segment n is set；
Step2: carrying out n equal part for the value interval of x, and this makes it possible to obtain n+1 discrete points, i.e. x0,x1...xn；
Step3: discrete point x is calculated0,x1...xnCorresponding f (x) functional value；
Step4: introducing new auxiliary variable, and guarantees to meet following constraint:
In conjunction with the above method, the constraint of pipeline Weymouth steady-state load flow can finally be described as:
So far, all nonlinear terms in model are converted into linear term, can directly be asked by CPLEX solver
Solution.
CPlEX is that one kind can be to the tool that Optimized model effectively solves.First according to required majorization of solutions model,
Program is write under MATLAB environment, must define decision variable, objective function and linear constraint condition, i.e. root respectively in program
The model content solved according to foregoing description；The CPLEX being then based in the tool box this routine call YALMIP is had
Effect solves.
First by matlab environment, program is write based on the tool box yalmip, solution procedure passes through yalmip work
Having case calls CPLEX optimization solver to model solution.
It is illustrated below by specific example:
The present embodiment uses a comprehensive energy system being coupled to form by 14 node power distribution nets and 20 node natural gas networks
System carries out simulation analysis.Power distribution network has 1 power transformation tiny node, 7 electric load nodes, 8 nodes and 16 lines coupled
Road.Natural gas network has 2 gas source nodes, 10 gas load bus and 8 switching nodes and 25 pipelines.It is worth noting
, it can be also its supply thermal power that 8 switching nodes, which can not only meet electricity, gas workload demand,.The present embodiment passes through simulation one
The operation of 24 hours in it, with the minimum target of day operation expense, to obtain economic scheduling scheme.
Electric (Fig. 3 a), gas (Fig. 3 b), thermic load (Fig. 3 c) timing curve as shown in figure 3, related example topological diagram such as Fig. 4
With shown in Fig. 5, Hub node coupling information is as shown in table 1.
Each Hub cell node corresponding relationship of table 1 and load parameter
In conjunction with the corresponding example of the present embodiment, in power distribution network, node voltage amplitude (pu) bound is respectively 1.05 Hes
0.95.In natural gas grid, pipeline air pressure bound is respectively 60 and 50bar.Simultaneously, it is assumed that each each energy conversion apparatus of Hub
Efficiency it is identical, P2G 75%, cogeneration efficiency of fuel cell generation is 37%, heat production 37%, and boiler heat production efficiency is 96%, gas
The conversion coefficient for turning electricity is 0.0096MW/m3。
Purchase of electricity, purchase tolerance curve after the electricity price of the embodiment of the present invention, gas price curve and optimization is as shown in Figure 6.It can
See, the integrated energy system optimization of the power distribution network based on energy hub, natural gas grid foundation that are proposed according to the present embodiment
Moving model and linear processing methods, the electricity price shown in Fig. 6 (a), gas price change under influence, which will
It rationally responds, with decision reasonably purchase of electricity and purchase tolerance (such as Fig. 6 (b) shown in), minimizes energy purchase to realize
Cost.
The foregoing is merely presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with
Modification, is all covered by the present invention.
Claims (7)
1. the integrated energy system optimal operation model that a kind of power distribution network based on energy hub, natural gas grid are established, special
Sign is: the following steps are included:
Step S1: providing one can be by energy hub model that power distribution network, natural gas grid couple；
Step S2: establishing objective function, and constrained according to the safe operation of power distribution network, natural gas grid and energy hub, complete
At the modeling of integrated energy system optimal operation model.
2. the comprehensive energy system that a kind of power distribution network based on energy hub according to claim 1, natural gas grid are established
System optimal operation model, it is characterised in that: objective function described in step S2 is that energy acquisition cost is shown below, including purchases
Electric costWith purchase gas costSimulating integrated energy system
Total cost during traffic control is minimum；
In formula, TR indicates the set of substation's injecting power node in power distribution network；GS indicates the collection of gas source node in natural gas grid
It closes；Unit price of power, gas price in distribution expression period t；Substation's injecting power section in respectively period t
The purchase of electricity of point j；For the purchase tolerance of the gas source node j in period t.
3. a kind of power distribution network based on energy hub according to claim 1, the integrated energy system of natural gas grid are excellent
Change moving model, it is characterised in that: the safe operation constraint of power distribution network described in step S2 includes: node power Constraints of Equilibrium, section
The constraint of point voltage magnitude, the constraint of distribution line maximum carrying capacity and substation's power constraint；
The node power Constraints of Equilibrium are as follows:
In formula, rij、xijThe respectively resistance of branch ij, reactance；δ (j) is indicated using j as the endpoint node of the branch of headend node
Set, π (j) are indicated using j as the set of the headend node of the branch of endpoint node；Pij,t、Qij,tThe respectively wattful power of branch ij
Rate and reactive power；Respectively indicate major network power output and electric load active power；It respectively indicates in Hub
The active power of P2G device electric conversion exports；Indicate the equivalent wattful power of CHP device injection power distribution network in Hub
Rate；Respectively indicate the reactive power value of major network power output, electric load；
The node voltage amplitude constraint are as follows:
Umin≤Uj,t≤Umax
In formula, Uj,t、UminAnd UmaxRespectively node voltage amplitude and its lower and upper limit；
The distribution line maximum carrying capacity constraint are as follows:
0≤Iij,t≤Imax
In formula, Iij,t、ImaxRespectively branch current magnitudes and its upper limit；
Substation's power constraint are as follows:
4. a kind of power distribution network based on energy hub according to claim 1, the integrated energy system of natural gas grid are excellent
Change moving model, it is characterised in that: the particular content constrained in step S2 the natural gas network are as follows:
The constraint of node air balance:
In formula, σ (jk) is indicated using j as the pipeline set of headend node；μ (ij) respectively indicates the pipeline collection using j as endpoint node
It closes；fp,t/fl,tFor the flow of pipeline p/l；The respectively gentle source node gas output of gas load；
Respectively indicate the amount of natural gas converted for GF, CHP energy in Hub；Indicate P2G device electricity conversion in Hub
At the equivalent natural gas injection rate of gas；
The constraint of gas source gas output:
The natural gas being produced from gas well needs the purification by refinery, due to by air pressure at place capacity and gas well
Limitation, gas source gas output should meet following constraint in the unit time:
In formula,For the output amount of natural gas of gas source j,Above and below respectively gas source j output amount of natural gas
Limit；
Node air pressure constraint:
The air pressure of each node of natural gas network must be maintained in safe, reasonable range of operation, and mathematic(al) representation is as follows:
In formula,Respectively represent air pressure upper lower limit value at node i；
The constraint of natural gas line Weymouth steady-state load flow:
The relationship of gas flow and both ends air pressure, expression are portrayed using Weymouth steady-state load flow model are as follows:
Wherein,
In addition pipeline flow also should ensure that within safe and reasonable range of operation:
In formula, fp,tRepresent the natural gas flow that pipeline p flows through；πi,tAnd πj,tRespectively indicate pipeline p both ends air pressure size；φpIt indicates
The air stream transportation parameter of pipeline p；sgnpIndicate the air flow direction of pipeline p；Indicate maximum pipeline transmission capacity.
Pressurizer boosting relation constraint:
πj,t=Γcπi,t
In formula, fc,tIndicate the delivery air of pressurizer c；πi,tAnd πj,tRespectively represent the gas of pressurizer c inlet end and outlet side
Pressure；Γc、The respectively boosting ratio and maximum transfer capacity of pressurizer c.
5. a kind of power distribution network based on energy hub according to claim 1, the integrated energy system of natural gas grid are excellent
Change moving model, it is characterised in that: the operation of energy hub described in step S2 constrains are as follows:
The constraint of the energy hub thermal power equilibrium of supply and demand:
The unidirectional constraint of energy hub energy conversion:
6. a kind of a kind of power distribution network based on energy hub according to any one of claims 1 to 5, natural gas grid are established
Integrated energy system optimal operation model linear processing methods, which comprises the following steps:
Step S3: linearization process is carried out to the model established in step S2；
Step S4: using CPLEX solver, to linearisation in step S3, treated that model solves.
7. the comprehensive energy system that a kind of power distribution network based on energy hub according to claim 6, natural gas grid are established
The linear processing methods of system optimal operation model, it is characterised in that: the particular content of the step S3 are as follows: using second order cone relaxation
Model conversation is subjected to linearization process with increment piecewise-linear techniques；
Due to containing nonlinear terms in node power Constraints of Equilibrium, abbreviation is carried out to constraint using second order cone relaxation method, is introduced
New variables eliminates voltage and current quadratic term, is shown below:
Node power Constraints of Equilibrium can eliminate the nonlinear quadratic item of voltage and current, as follows:
Voltage, current amplitude constraint modification as a result, are as follows:
The third formula of node power constraint is further converted to second order tapered by relaxation；Concrete form is as follows:
The pipeline Weymouth steady-state load flow constraint in natural gas network is linearized using increment piecewise-linear techniques,
It is non-linear by the quadratic term bring for being introduced into air pressure in new variable cancellation pipeline Weymouth steady-state load flow constraint, specifically such as
Shown in lower:
Therefore, pipeline Weymouth steady-state load flow constraint can tentatively rewrite are as follows:
Due to sgnp(πi,t,πj,t) it is a sign function, work as πi,tGreater than πj,tWhen take 1, otherwise take -1；Therefore, the left side of formula
Write as absolute value expression, even Yp,t=fp,t|fp,t|；That is Yp,t=fp,t|fp,t| can also be expressed as f (x)=x | x | it is non-
The step of linearisation formula, increment piece-wise linearization, is as follows:
Step SA: number of segment n is averagely segmented according to model built setting；
Step SB: carrying out n equal part for the value interval of x, and this makes it possible to obtain n+1 discrete points, i.e. x0,x1...xn；
Step SC: discrete point x is calculated0,x1...xnCorresponding f (x) functional value；
Step SD: introducing new auxiliary variable, and guarantees to meet following constraint:
In conjunction with the above method, the constraint of pipeline Weymouth steady-state load flow is finally described as:
。
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