CN109800480A - The timing randomized optimization process of gas net and power grid coupling in multi-energy system - Google Patents
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Abstract
The present invention relates to the timing randomized optimization process that gas net in a kind of multi-energy system and power grid couple, technical characterstic is: the following steps are included: step 1, establishing the basic model that two-stage timing has compensation random optimization；Step 2, premised on the investment cost and operating cost of distribution network and natural gas network is minimum, establish the objective function of planning problem；Step 3 establishes electric power networks operation constraint, the operation constraint and natural gas network operation constraint that natural gas is coupled with distributed natural gas generator respectively；Step 4, in universal algebra modeling GAMS using extension mathematics planning framework and branch-bound algorithm problem is solved.The present invention considers the uncertainty of electricity needs, more accurate compared with existing method for solving, is more suitable for the solution of Long-term planning problem.
Description
Technical field
The invention belongs to technical field of power systems, are related to the timing random optimization of natural gas network and electric power networks coupling
Method, the timing randomized optimization process of gas net and power grid coupling in especially a kind of multi-energy system.
Background technique
Since worldwide electricity needs increases the limitation with power line transmission capacity, and reducing greenhouse gas
Under the policy guide of body discharge, the quantity of distributed power generation is in rising trend.The power of distributed generator is relatively small, capacity
Meet local electricity needs, and is connected directly with distribution network, therefore its safety and reliability that electric system can be improved, and
It cuts operating costs, diversified ancillary service is provided.Since the set-up time of distributed natural gas generator is short, generating efficiency
Height, investment is low with operation cost, can relatively well make up the defect of power supply, therefore it is very suitable for providing ancillary service, with
And alleviate the intermittent problems of renewable energy power generation.Since the operation of distributed natural gas generator depends on the confession of natural gas
It answers, therefore collaborative planning considers that the natural gas network of distributed natural gas generator and distribution network have very big necessity.
Natural gas network cooperates with optimization problem to need to consider that some uncertain parameters, such as electric power need with electric power networks
Summation Natural Gas Demand, therefore the problem is a stochastic optimization problems.Solution for the problem usually uses heuristic calculation
Method, however heuritic approach is usually best option to be chosen from total Options, therefore the precision of its solution is related with the precision of option.
If the precision of option is insufficient, the precision of solution is also poor, therefore the present invention is made on the basis of heuritic approach using analytic method
The precision of option reaches requirement, to guarantee the precision understood.
Summary of the invention
It is an object of the invention to overcome the deficiencies in the prior art, propose a kind of design rationally, safety stability it is high and
Solve the timing randomized optimization process of gas net and power grid coupling in accurate multi-energy system.
The present invention solves its realistic problem and adopts the following technical solutions to achieve:
The timing randomized optimization process of gas net and power grid coupling in a kind of multi-energy system, comprising the following steps:
Step 1 establishes the basic model that two-stage timing has compensation random optimization；
Step 2, premised on the investment cost and operating cost of distribution network and natural gas network is minimum, establish planning and ask
The objective function of topic；
Step 3 establishes electric power networks operation constraint, the operation that couples with distributed natural gas generator of natural gas about respectively
Beam and natural gas network operation constraint；
Step 4, in universal algebra modeling GAMS using extension mathematics planning framework and branch-bound algorithm to asking
Topic is solved.
Moreover, the specific steps that the two-stage timing of the step 1 has the basic model of compensation random optimization include:
(1) under the premise of not occurring with uncertain parameters, the optimization of first stage is carried out；
(2) after there are uncertain parameters, then the optimization of second stage is carried out, its calculation formula is；
S.t Ax=b
x≥0
Wherein:
Q (x, ξ)=min [q (ω)Ty(ω)]
T (ω) x+Wy (ω)=h (ω)
y(ω)≥0
In formula, c and x are n1The column vector of dimension；ΕξFor uncertain parameters；B is m1The column vector of dimension；A is m1×n1Rank square
Battle array；ω and q (ω) is n2The column vector of dimension；H (ω) is m2The column vector of dimension；T (ω) is m2×n1Rank matrix；W is compensation square
Battle array, is determining.
Moreover, the objective function of the planning problem in the step 2 includes: the cost of investment of distribution network, distribution network
Operating cost, the operating cost of the cost of investment of natural gas network and natural gas network, by above objective function can be listed:
In formula, z is totle drilling cost；Discontinuity surface number when T is；Distributed natural gas generator is added to mother for t
The year cost of investment of line b；The natural gas line year cost of investment being laid between natural gas node i and j for t；For the electricity needs of bus b；For expected electric power networks operating cost；
The function expression of formula (7) each section is as follows:
In formula, δ is annuity；For the available capacity of the distributed natural gas generator of bus b；For t bus
The cost of investment of the distributed natural gas generator of b；LijFor the duct length between node i j；yi,j,tFor binary variable, if section
There is pipeline between point i and node j, value 1, otherwise its value is 0；The cost of investment of pipeline is laid between ij for t；
Formula (10) includes probabilistic expected electric power networks operating cost for calculating；For approximation；It is corresponding
Probability；For year peak value electricity；For its cost；For the classification operating cost of distributed natural gas generator；For the generated energy of distributed natural gas generator；For short of electricity amount；For outage cod；Ir is interest rate；N is recycling
Phase.
Moreover, all kinds of operations constraint in the step 3 includes:
(1) Operation of Electric Systems constrains
-flmax≤flb,r,t≤flmax
In formula, flb,r,tThe power flowed through between t transmission line of electricity br；For the generated energy of t bus b,For
Short of electricity amount；For the distributed natural gas generator capacity upper limit；θb,tFor the voltage phase angle of bus b；Xb,r,tFor transmission line of electricity
Reactance between br；flmaxThe overpowering upper limit is flowed between transmission line of electricity br；
(2) coupling constraint of natural gas and distributed natural gas generator
In formula,For the peak value of node i t natural gas demand；For bus b t distributed natural gas
The peak value of generator power output；Ai、BiAnd CiFor conversion coefficient.
(3) the natural gas network operation constrains
Qi,j,t≤M1tBi,j,t
Bi,j,t+Bj,i,t≤yi,j,t
Bi,j,t,yi,j,t∈0,1
In formula, PPi,tFor the natural gas pressure of t node i；For the node i natural gas pressure upper limit；NGS is natural
Gas source set；WithThe node pressure bound for being t in addition to gas source；Bi,j,tFor binary variable, when
When natural gas flows to node j from node i, value 1, otherwise its value is 0；Qi,j,tFor mass flowrate；M1tIt is one very big
Number；For the natural gas demand for power supply；For the natural gas demand supplied for non-electricity；TbFor mark
Quasi- temperature, value 288K；PbFor normal pressure, value 1bar；G is natural gas gravitational constant, value 0.66；TfFor fluid standard
Temperature, value 283K；LijFor the duct length between node i j；Z is gas compressibility factor, value 0.805；F is friction factor, is taken
Value 0.0011494；ΔijFor pipe diameter；Ψi,jFor proportionality coefficient；M2It is a very big number；yi,j,tFor binary variable, if
There is pipeline between node i and node j, value 1, otherwise its value is 0.
In formula (25) into formula (29), PP2And Q2It is nonlinear, therefore by PP2It is replaced with Θ to linearize constraint condition；
Formula (28) is changed to:
Formula (29) is changed to:
The advantages of the present invention:
1, the present invention provides a kind of uncertain parameters for considering natural gas network and being cooperateed in optimization problem with electric power networks,
The optimization method that natural gas network distribution and natural gas generator addressing can be solved, on the basis of heuritic approach, using two
Stage has compensation randomized optimization process and analytic method to solve the problems, such as this, and on the basis of electricity needs uncertainty, establishes
Long-term planning model, preferably solves the problems, such as solving precision.
2, the present invention considers the uncertainty of electricity needs, more accurate compared with existing method for solving, more applicable
In the solution of Long-term planning problem.
3, the present invention can not only calculate the optimum position of distributed natural gas generator installation, moreover it is possible to calculate installation
Amount of capacity and set-up time, and be the optimal path of its supply natural gas, be conducive to the promotion and popularization of distributed power generation,
Increase the safety and stability of electric system.
Detailed description of the invention
Fig. 1 is process flow diagram of the invention；
Fig. 2 is 8 bus radial distribution measurement system diagrams of the invention；
Fig. 3 is that distributed natural gas generator of the invention installs prognostic chart.
Specific embodiment
The embodiment of the present invention is described in further detail below in conjunction with attached drawing:
The timing randomized optimization process of gas net and power grid coupling in a kind of multi-energy system of the invention, as shown in Figure 1, packet
Include following steps:
Step 1 establishes the basic model that two-stage timing has compensation random optimization；
Stochastic optimization problems be when one include uncertain parameters function minimization or maximization problems, and with electricity
In the relevant planning problem of power, electricity needs is often uncertain.Two stage optimization is the process of a multi-stage optimization, this
A process includes two steps, i.e., under the premise of not occurring with uncertain parameters, carry out the optimization of first stage；?
After there are uncertain parameters, then carry out the optimization of second stage.
The specific steps of basic model that the two-stage timing of the step 1 has compensation random optimization include:
(1) under the premise of not occurring with uncertain parameters, the optimization of first stage is carried out；
(2) after there are uncertain parameters, then the optimization of second stage is carried out, its calculation formula is；
S.t Ax=b (2)
x≥0 (3)
Wherein:
Q (x, ξ)=min [q (ω)Ty(ω)] (4)
T (ω) x+Wy (ω)=h (ω) (5)
y(ω)≥0 (6)
In formula, c and x are n1The column vector of dimension；ΕξFor uncertain parameters；B is m1The column vector of dimension；A is m1×n1Rank square
Battle array；ω and q (ω) is n2The column vector of dimension；H (ω) is m2The column vector of dimension；T (ω) is m2×n1Rank matrix；W is compensation square
Battle array, is determining.
Step 2, premised on the investment cost and operating cost of distribution network and natural gas network is minimum, establish planning and ask
The objective function of topic；
The objective function of planning problem in the step 2 includes:
Cost of investment, the operating cost of distribution network, the cost of investment and natural gas grid of natural gas network of distribution network
The operating cost of network；Since the natural gas network of the present embodiment is not directed to compressor and caisson, therefore the fortune of natural gas network
Row cost is ignored, by that can list objective function above:
In formula, z is totle drilling cost；Discontinuity surface number when T is；Distributed natural gas generator is added to mother for t
The year cost of investment of line b；The natural gas line year cost of investment being laid between natural gas node i and j for t；For the electricity needs of bus b；For expected electric power networks operating cost；
The function expression of formula (7) each section is as follows:
In formula, δ is annuity；For the available capacity of the distributed natural gas generator of bus b；For t bus
The cost of investment of the distributed natural gas generator of b；LijFor the duct length between node i j；yi,j,tFor binary variable, if section
There is pipeline between point i and node j, value 1, otherwise its value is 0；The cost of investment of pipeline is laid between ij for t；
Formula (10) includes probabilistic expected electric power networks operating cost for calculating；For approximation；It is corresponding
Probability；For year peak value electricity；For its cost；For the classification operating cost of distributed natural gas generator；For the generated energy of distributed natural gas generator；For short of electricity amount；For outage cod；Ir is interest rate；N is recycling
Phase.
Step 3 establishes electric power networks operation constraint, the operation that couples with distributed natural gas generator of natural gas about respectively
Beam and natural gas network operation constraint；
All kinds of operations in the step 3, which constrain, includes:
(1) Operation of Electric Systems constrains
-flmax≤flb,r,t≤flmax (19)
In formula, flb,r,tThe power flowed through between t transmission line of electricity br；For the generated energy of t bus b,For
Short of electricity amount；For the distributed natural gas generator capacity upper limit；θb,tFor the voltage phase angle of bus b；Xb,r,tFor transmission line of electricity
Reactance between br；flmaxThe overpowering upper limit is flowed between transmission line of electricity br；
(2) coupling constraint of natural gas and distributed natural gas generator
In formula,For the peak value of node i t natural gas demand；For bus b t distributed natural gas
The peak value of generator power output；Ai、BiAnd CiFor conversion coefficient.
(3) the natural gas network operation constrains
Qi,j,t≤M1tBi,j,t (23)
Bi,j,t+Bj,i,t≤yi,j,t (30)
Bi,j,t,yi,j,t∈0,1 (34)
In formula, PPi,tFor the natural gas pressure of t node i；For the node i natural gas pressure upper limit；NGS is natural
Gas source set；WithThe node pressure bound for being t in addition to gas source；Bi,j,tFor binary variable, when
When natural gas flows to node j from node i, value 1, otherwise its value is 0；Qi,j,tFor mass flowrate；M1tIt is one very big
Number；For the natural gas demand for power supply；For the natural gas demand supplied for non-electricity；TbFor mark
Quasi- temperature, value 288K；PbFor normal pressure, value 1bar；G is natural gas gravitational constant, value 0.66；TfFor fluid standard
Temperature, value 283K；LijFor the duct length between node i j；Z is gas compressibility factor, value 0.805；F is friction factor, is taken
Value 0.0011494；ΔijFor pipe diameter；Ψi,jFor proportionality coefficient；M2It is a very big number；yi,j,tFor binary variable, if
There is pipeline between node i and node j, value 1, otherwise its value is 0.
In formula (25) into formula (29), PP2And Q2It is nonlinear, therefore by PP2It is replaced with Θ to linearize constraint condition；
Formula (28) is changed to:
Formula (29) is changed to:
Step 4, in universal algebra modeling GAMS using extension mathematics planning framework and branch-bound algorithm to asking
Topic is solved.
The step 4 method particularly includes:
The case solved in emulation is as shown in Fig. 2, the system is the 8 bus radial distributions test system for being 20 years planning horizon
System contains 8 buses, wherein the 1st article of bus is connected with electric power networks, the 2nd article to the 8th article bus carries electric load, is used for
Extend distributed natural gas generator.In system, if the annual growth of electric load is 3%, distributed natural gas generator
Cost of investment is $ 120000/MW, and operating cost is $ 45/MWh, for estimating that the Value of lost load of Custom interruption cost is
$ 1000/MWh, the laying cost of new pipeline are 200,000/ inch/mile.Reach 3% annual growth in electricity needs
In the case of, best position, capacity and the set-up time of distributed natural gas generator are as shown in figure 3, to ensure that electric power supplies
Answer abundance.It installs concrete condition are as follows: and bus 4 is in the distributed natural gas generator that installation installed capacity in the 19th year is 2MW,
In the 20th year enlarging capacity to 4MW；Bus 5 is in the distributed natural gas generator that installation installed capacity in the 11st year is 2MW,
13rd year enlarging capacity is to 4MW；Bus 7 is in the distributed natural gas generator that installation installed capacity in the 1st year is 4MW；Bus 8
It is in the distributed natural gas generator that installation installed capacity in the 4th year is 2MW, in the 10th year enlarging capacity to 4MW.
Best position, capacity and the set-up time of distributed natural gas generator are by pipeline layout path and day
Right gas source is limited to the cost of generator transmission natural gas.
Table 1 is time and the position for being laid with pipeline, and spent totle drilling cost is $ 4,990,000.It installs concrete condition
Are as follows: natural gas line is laid with from natural gas supply point to bus 8 within the 1st year；Natural gas tube is laid with from bus 8 to bus 9 within 4th year
Road；It is laid with natural gas line from bus 8 to bus 7 within 11st year, and is laid with natural gas line from bus 7 to bus 6；19th year from
Bus 6 to bus 5 is laid with natural gas line.
Table 1
It is emphasized that embodiment of the present invention be it is illustrative, without being restrictive, therefore the present invention includes
It is not limited to embodiment described in specific embodiment, it is all to be obtained according to the technique and scheme of the present invention by those skilled in the art
Other embodiments, also belong to the scope of protection of the invention.
Claims (4)
1. the timing randomized optimization process of gas net and power grid coupling in a kind of multi-energy system, it is characterised in that: including following step
It is rapid:
Step 1 establishes the basic model that two-stage timing has compensation random optimization；
Step 2, premised on the investment cost and operating cost of distribution network and natural gas network is minimum, establish planning problem
Objective function；
Step 3, establish electric power networks operation constraint respectively, the operation that couple with distributed natural gas generator of natural gas constrains and
Natural gas network operation constraint；
Step 4, in universal algebra modeling GAMS using extension mathematics planning framework and branch-bound algorithm to problem into
Row solves.
2. the timing randomized optimization process of gas net and power grid coupling in a kind of multi-energy system, it is characterised in that: the step 1
The specific steps of basic model that two-stage timing has compensation random optimization include:
(1) under the premise of not occurring with uncertain parameters, the optimization of first stage is carried out；
(2) after there are uncertain parameters, then the optimization of second stage is carried out, its calculation formula is；
S.t Ax=b
x≥0
Wherein:
Q (x, ξ)=min [q (ω)Ty(ω)]
T (ω) x+Wy (ω)=h (ω)
y(ω)≥0
In formula, c and x are n1The column vector of dimension；ΕξFor uncertain parameters；B is m1The column vector of dimension；A is m1×n1Rank matrix；
ω and q (ω) is n2The column vector of dimension；H (ω) is m2The column vector of dimension；T (ω) is m2×n1Rank matrix；W is compensation matrix, is
Determining.
3. the timing randomized optimization process of gas net and power grid coupling in a kind of multi-energy system, it is characterised in that: in the step 2
Planning problem objective function include: the cost of investment of distribution network, the operating cost of distribution network, natural gas network throwing
The operating cost for providing cost and natural gas network, by above objective function can be listed:
In formula, z is totle drilling cost；Discontinuity surface number when T is；Distributed natural gas generator is added to bus b for t
Year cost of investment；The natural gas line year cost of investment being laid between natural gas node i and j for t；For the electricity needs of bus b；For expected electric power networks operating cost；
The function expression of formula each section is as follows:
In formula, δ is annuity；For the available capacity of the distributed natural gas generator of bus b；For point of t bus b
The cost of investment of cloth natural gas generator；LijFor the duct length between node i j；yi,j,tFor binary variable, if node i and
There is pipeline between node j, value 1, otherwise its value is 0；The cost of investment of pipeline is laid between ij for t；Formula is used
It include probabilistic expected electric power networks operating cost in calculating；For approximation；For corresponding probability；For year peak value electricity；For its cost；For the classification operating cost of distributed natural gas generator；For
The generated energy of distributed natural gas generator；For short of electricity amount；For outage cod；Ir is interest rate；N is payoff period.
4. the timing randomized optimization process of gas net and power grid coupling in a kind of multi-energy system, it is characterised in that: in the step 3
All kinds of operations constraint include:
(1) Operation of Electric Systems constrains
-flmax≤flb,r,t≤flmax
In formula, flb,r,tThe power flowed through between t transmission line of electricity br；For the generated energy of t bus b,For short of electricity
Amount；For the distributed natural gas generator capacity upper limit；θb,tFor the voltage phase angle of bus b；Xb,r,tBetween transmission line of electricity br
Reactance；flmaxThe overpowering upper limit is flowed between transmission line of electricity br；
(2) coupling constraint of natural gas and distributed natural gas generator
In formula,For the peak value of node i t natural gas demand；For the distributed natural gas power of bus b t
The peak value of machine generated energy；Ai、BiAnd CiFor conversion coefficient；
(3) the natural gas network operation constrains
Qi,j,t≤M1tBi,j,t
Bi,j,t+Bj,i,t≤yi,j,t
Bi,j,t,yi,j,t∈0,1
In formula, PPi,tFor the natural gas pressure of t node i；PPi maxFor the node i natural gas pressure upper limit；NGS is gas source
Set；WithThe node pressure bound for being t in addition to gas source；Bi,j,tFor binary variable, when natural
When gas flows to node j from node i, value 1, otherwise its value is 0；Qi,j,tFor mass flowrate；M1tIt is a very big number；For the natural gas demand for power supply；For the natural gas demand supplied for non-electricity；TbFor standard temperature
Degree, value 288K；PbFor normal pressure, value 1bar；G is natural gas gravitational constant, value 0.66；TfFor fluid standard temperature,
Value 283K；LijFor the duct length between node i j；Z is gas compressibility factor, value 0.805；F is friction factor, value
0.0011494；ΔijFor pipe diameter；Ψi,jFor proportionality coefficient；M2It is a very big number；yi,j,tFor binary variable, if section
There is pipeline between point i and node j, value 1, otherwise its value is 0；
In formula into formula, PP2And Q2It is nonlinear, therefore by PP2It is replaced with Θ to linearize constraint condition；
Formula is changed to:
Formula is changed to:
。
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