CN117060492B - Optimization method and equipment for gas-electricity coupling system considering air pressure fluctuation characteristic of pipeline - Google Patents
Optimization method and equipment for gas-electricity coupling system considering air pressure fluctuation characteristic of pipeline Download PDFInfo
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Abstract
The invention relates to a comprehensive energy system optimization technology, in particular to a method and equipment for optimizing a gas-electricity coupling system by considering the air pressure fluctuation characteristic of a pipeline. And processing the pipeline steady-state air pressure constraint by adopting a method combining Taylor series expansion and continuous linear optimization, and solving the established combined optimization model of the gas-electric coupling system. The optimization result based on the model established by the method can ensure that the air pressure of the gas-electric coupling system is kept within a safe range. The method improves the economical efficiency of the system, effectively promotes the consumption of new energy, and ensures that the air pressure of the natural gas pipeline is kept within a safe range in the dynamic process. The method also solves the problems that the piecewise linearization algorithm is difficult to simultaneously consider precision and efficiency, and no feasible solution easily appears, and the solving speed is increased.
Description
Technical Field
The invention belongs to the technical field of comprehensive energy system optimization, and particularly relates to a method and equipment for optimizing a gas-electricity coupling system by considering the air pressure fluctuation characteristic of a pipeline.
Background
As a low-carbon fossil energy source, the natural gas power generation has the characteristics of cleanness, high efficiency, wide load regulation range, quick response, strong load changing capability and the like, is complementary with the new energy power generation, and is an ideal choice for peak shaving of a power grid. In addition, with the maturity of technologies such as Power to Gas (P2G), solid oxide fuel cell (Solid Oxide Fuel Cell, SOFC) cogeneration, the extent of bi-directional coupling between Power systems and natural Gas systems is increasing: the new energy power station converts the multiple generated electric quantity into hydrogen or methane through the P2G device and the gas storage device, and the hydrogen or methane is injected into the high-pressure gas distribution network, so that the new energy consumption level is improved, the new energy power station is released in the gas consumption peak period, and the gas consumption pressure of the gas network can be relieved; meanwhile, when the power grid load is high, the user side independently generates power and supplies heat through the SOFC unit cogeneration, so that a good peak clipping effect on the power load is realized, and the power utilization safety of the user is guaranteed. In the future, the gas-electric coupling system is expected to become an important carrier for energy supply and transmission.
In order to realize safe operation of the gas-electricity coupling system, system schedulers often need to issue scheduling instructions to gas-electricity conversion equipment such as a P2G device, an SOFC unit and the like to adjust the working state of the gas-electricity conversion equipment. Because the operation main bodies and the time scales of the power system and the natural gas system are different, how to improve the new energy consumption level and the system economy on the premise of ensuring the safe and stable operation of the power system and the natural gas system becomes a concern. Therefore, the technical problems to be solved are as follows:
1) How to dynamically model the natural gas pipeline so as to describe the real-time dynamic change process of the pipeline air pressure;
2) And how to perform joint optimization on the gas-electric coupling system efficiently and quickly so as to ensure that the dynamic air pressure of the air network is always kept within a safe range.
Disclosure of Invention
The invention provides a gas-electricity coupling system joint optimization method considering the air pressure fluctuation characteristic of a pipeline, and aims to improve the new energy consumption level and the economical efficiency on the premise of ensuring the safe and stable operation of a natural gas system.
For convenience of reading, the present invention presents a variable sign beltIs a known quantity, such as the given parameter, the result of the optimization, the value of the variable to be optimized, without +.>Is an unknown quantity such as a variable to be optimized, an objective function, etc.
The invention provides a gas-electric coupling system joint optimization method considering the air pressure fluctuation characteristic of a pipeline, which comprises the steps of establishing a gas-electric coupling system joint optimization model considering the air pressure fluctuation characteristic of the pipeline, and taking 1 hour as a calculation step length and 1 day and 24 hours as a calculation time period. And (3) processing the pipeline steady-state air pressure constraint by adopting a method combining Taylor series expansion and continuous linear optimization, so as to efficiently solve the established combined optimization model of the gas-electric coupling system. A schematic diagram of the gas-electric coupling system is shown in fig. 1.
And, establish the gas-electricity coupling system joint optimization model taking the fluctuation characteristic of the pipeline air pressure into consideration and include the following steps:
step 1.1, setting an objective function, wherein the objective function is the minimum comprehensive cost:
（1.1）
（1.2）
（1.3）
（1.4）
wherein:
the unit is the civil monetary unit for the comprehensive cost, and then the unit is expressed by the unit;
the unit is the unit of the starting and running cost of the thermal power generating unit;
punishment cost is abandoned for new energy, and the unit is unit;
the natural gas purchasing cost is the unit of the natural gas purchasing cost;
is a time set; />The time is the moment;
is a thermal power unit set;
、/>、/>the consumption characteristic curve parameter is the consumption characteristic curve parameter of the thermal power generating unit i;
the unit is MW for the active output of the thermal power unit i at the moment t;
the start-stop state of the thermal power unit i at the moment t is represented by a Boolean variable;
the unit is the starting cost of the thermal power unit i;
the thermal power unit i is started at the moment t, wherein the thermal power unit i is a Boolean variable;
the method is a new energy power station set;
the unit of the electricity discarding cost of the new energy power station i is Yuan/MW.h;
the electricity rejection rate of the new energy power station i at the moment t;
the unit is MW for the maximum active output of the new energy power station i at the moment t;
is a natural gas source collection;
the unit is m for the supply flow rate of the natural gas source i at the moment t 3 /s；
The gas purchasing cost of the natural gas source i is shown as the unit of yuan/m 3 ；
Is a gas storage tank set;
the output flow rate of the air storage tank i at the moment t (air supply is performed when the output flow rate is more than 0 and air storage is performed when the output flow rate is less than 0), and the unit is m 3 /s；
The storage price of the air storage tank i at the moment t is shown as the unit of element/m 3 ；
Step 1.2, setting power system constraints, including thermal power unit output constraints, running state constraints, climbing constraints, node power balance and branch power flow constraints, wherein the description is as follows:
1) Thermal power generating unit output constraint:
（1.5）
wherein:
、/>the minimum active output and the maximum active output of the thermal power unit i are respectively shown in MW;
2) Thermal power generating unit operation state constraint:
（1.6）
（1.7）
wherein:
the thermal power unit i is stopped at the moment t, and the unit cannot be started and stopped at the same time;
3) Climbing constraint of thermal power generating unit:
（1.8）
（1.9）
wherein:
、/>the maximum value of downward climbing and upward climbing of the thermal power unit i is MW;
4) Node power balancing constraints:
（1.10）
wherein:
the incidence matrix of the thermal power generating unit and the power system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the thermal power generating units, the j column 1 of the ith row of the matrix represents that the thermal power generating unit j is positioned at the power system node i, and the j column 0 represents that the thermal power generating unit j is not positioned at the power system node i;
the matrix is a 2-dimensional matrix, and the dimension is the number of nodes +.>The number of SOFC units, the j column 1 of the ith row of the matrix represents that SOFC unit j is positioned at a power system node i, and the 0 represents that SOFC unit j is not positioned at the power system node i;
the method is characterized in that the method is an incidence matrix of nodes of a new energy power station and an electric power system, wherein the matrix is a 2-dimensional matrix, and the dimension is the number of the nodesThe number of the new energy power stations, the j column 1 of the ith row of the matrix represents that the new energy power station j is positioned at the power system node i, and the 0 represents that the new energy power station j is not positioned at the power system node i;
the matrix is a 2-dimensional matrix, and the dimension is the number of nodes +.>The number of the power lines, the j column 1 of the ith row of the matrix represents that the starting point of the power line j is positioned at the power system node i, the 1 represents that the ending point of the power line j is positioned at the power system node i, and the 0 represents that the starting point and the ending point of the power line j are not positioned at the power system node i;
the SOFC unit is assembled;
active output of the SOFC unit i at the moment t is unit MW;
is a power line set;
the input power of the P2G device i at the time t is unit MW;
active power of the line (i, j) at the moment t is unit MW;
the power system load matrix at the moment t is a 2-dimensional matrix, and the dimension is the node number +.>1, the ith row and the 1 st column of the matrix are loads at a power system node i and are in MW;
5) Branch tidal current constraint:
（1.11）
（1.12）
（1.13）
wherein:
is susceptance parameter of line (i, j), unit S;
the voltage phase angle of the power system node i at the moment t;
maximum transmission capacity value of line (i, j) at time t, unit MW;
for the voltage phase angle limitation of the power system node i, usually +.>；
Is a power system node set;
step 1.3, setting steady-state constraint of a natural gas system; the natural gas system comprises a natural gas source, a pipeline, a gas load and a pressure regulating valve (similar to a power transformer, connected with different grades of natural gas network); the steady-state constraint comprises a pressure regulating valve constraint, a gas storage tank constraint, a natural gas source constraint, a node flow balance constraint and a pipeline steady-state air pressure constraint, and is expressed as follows:
1) The air-vent valve is arranged at the joint of two-stage natural gas networks, and aims to ensure that the air pressure of the lower-stage air network is within a specified range, and the control mode is an air-vent pressure mode, as shown in fig. 2, and the air-vent valve is constrained as follows:
（1.14）
wherein:
is a pressure regulating valve set;
the outlet air pressure set for the pressure regulating valve i is unit kPa;
is a natural gas pipeline set;
the pressure is the head end air pressure of the natural gas pipeline (i, j) at the moment t, and the unit is kPa;
2) The air tank is constrained as follows:
（1.15）
（1.16）
（1.17）
wherein:
、/>respectively the minimum and maximum output flow of the air storage tank i, and the unit m 3 /s；
、/>Respectively the minimum value and the maximum value of the gas storage quantity of the gas storage tank i, and the unit m 3 ；
The air storage capacity of the air storage tank i at the moment t;
3) Because the new energy power station and the P2G device of the electric power system convert the electric quantity into natural gas and are regarded as a gas source in the natural gas system together with the gas storage tank, the supply flow of the gas source is the sum of the output flow of the gas storage tank and the output flow of the P2G device. The natural gas source constraint is as follows:
（1.18）
（1.19）
wherein:
、/>respectively the minimum value and the maximum value of the supply flow of the natural gas source i, and the unit m 3 /s；
The output flow of the P2G device i at the time t is given by the unit m 3 /s；
4) Node traffic balancing constraints:
（1.20）
wherein:
the incidence matrix of the natural gas source and the natural gas system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the natural gas sources, the j-th row and the j-th column of the matrix are 1, which means that the natural gas source j is positioned at a natural gas system node i, and 0 means that the natural gas source j is not positioned at the natural gas system node i;
the incidence matrix of the SOFC unit and the natural gas system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of SOFC units, the j column 1 of the ith row of the matrix represents that SOFC unit j is positioned at a natural gas system node i, and the 0 represents that SOFC unit j is not positioned at the natural gas system node i;
the incidence matrix of the natural gas pipeline and the natural gas system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the natural gas pipelines, the j-th row of the matrix is 1, which represents that the starting point of the natural gas pipeline j is positioned at a natural gas system node i, the 1 represents that the ending point of the natural gas pipeline j is positioned at the natural gas system node i, and the 0 represents that neither the starting point nor the ending point of the natural gas pipeline j is positioned at the natural gas system node i;
is the flow of the natural gas pipeline (i, j) at the moment t, and the unit m 3 /s；
For the input flow of the SOFC unit i at the moment t, the unit m 3 /s；
The natural gas system load matrix at the time t is a 2-dimensional matrix, and the dimension is the node number +.>1, row 1 and column 1 of the matrix are loads at a node i of the natural gas system, and the unit is m 3 /s；
5) The steady-state air pressure constraint of the pipeline adopts a Weymouth equation, and the constraint conditions are as follows:
（1.21）
（1.22）
（1.23）
wherein:
the unit kPa is the end air pressure of the natural gas pipeline (i, j) at the moment t;
、/>respectively natural gas pipeline (i)Lower and upper barometric pressure limits in kPa;
a Weymouth parameter for the natural gas pipeline (i, j);
step 1.4, constructing dynamic constraint of a natural gas system;
step 1.4.1 for each section of Natural gas pipeline (i, j), acquiring head-end air pressure in an initial state by a SCADA SystemTerminal air pressure->Length of pipe->Pipe radius->Natural gas wave velocity +.>The method comprises the steps of carrying out a first treatment on the surface of the Setting a reference value of the adjustment amountAdjusting the time reference value +.>；
Step 1.4.2 setting a calculation time intervalIs set to 0.01s, the number of time intervals N, N is a positive integer, the fluctuation of the pipeline air pressure occurs within 20 seconds, thus +.>The air pressure fluctuation amplitude threshold Th is set to 0.05kPa;
step 1.4.3 after the flow adjustment is started by calculating the parameters obtained/set in the steps 1.4.1 and 1.4.2, the air pressure at the head end of the natural gas pipeline is within 20 secondsIs a sequence of (a): p is p 0 、p 1 、p 2 、…、p N ；p i The resolvable expression for i=1, 2, …, N is as follows:
（1.24）
where H is the weaveside step function, erfc is the error complement function, defined as:
（1.25）
、/>、/>、/>、/>、/>、/>，lthe value of (2) is in the range of 1 to 10,kthe value range of (1) to (2), the process parameters introduced for the convenience of expression have no actual physical meaning, and the introduced process parameters are defined as follows:
（1.26）
（1.27）
（1.28）
（1.29）
（1.30）
（1.31）
（1.32）
（1.33）
step 1.4.4 by sequentially analyzing the sequences obtained in step 1.4.3, all sub-sequences p having a fluctuation width of not less than Th are extracted in a linear time by an on-line algorithm i ,…, p j The definition is as follows:
（1.34）
（1.35）
（1.36）
subsequence p i ,…, p j The fluctuation amplitude of (2) is:
（1.37）
extracting the starting and ending time and fluctuation amplitude of all sub-sequences, and setting the maximum value of the fluctuation amplitude as the reference value of the air pressure fluctuation amplitude；
Step 1.4.5 for natural gas pipeline (i, j), the dynamic constraints are:
（1.38）
（1.39）
（1.40）
（1.41）
wherein:
for the adjustment of the natural gas line (i, j) at time t, unit m 3 /s；
The unit s is the adjusting time of the natural gas pipeline (i, j) at the moment t;
step 1.5 sets gas-electricity coupling constraint, including P2G device operation constraint and SOFC unit operation constraint, and is specifically described as follows:
1) P2G device operation constraints:
（1.42）
wherein:
conversion efficiency for P2G device i;
for natural gas heat value, 37.62MJ/m is taken 3 ；
2) SOFC unit operation constraint:
（1.43）
wherein:
the conversion efficiency of the SOFC unit i.
And, the main purpose of adopting the method of combining Taylor series expansion and continuous linear optimization to process the pipeline steady-state air pressure constraint is to process a non-convex constraint (1.23), as shown in FIG. 3, the non-convex constraint is in a conical surface form, and is difficult to directly solve by adopting a CPLEX and other solvers. In order to enable the optimization result to meet the constraint condition as far as possible, the Newton-Laporton algorithm or the piecewise linearization method is mainly adopted for processing at present, but the Newton-Laporton algorithm is low in solving efficiency, the piecewise linearization algorithm is difficult to simultaneously consider the precision and the efficiency, and when the feasible domain range is small, the optimizer may not be capable of obtaining the feasible solution. The invention therefore proposes to process this constraint and solve the model by means of a combination of taylor series expansion and continuous linear optimization, comprising the following steps:
step 2.1, for a natural gas pipeline (i, j) at the moment t, loosening pipeline steady-state air pressure constraint type 1.23 by a Taylor series expansion method;
step 2.1.1 randomly selects 20 ternary numbers,the following constraints are satisfied:
(2.1)
(2.2)
step 2.1.2 introduction of the Boolean variable、/>Representing the flow direction of the natural gas pipeline (i, j) at the time t whenWhen the pressure is 1, the pressure at the head end of the natural pipeline (i, j) is larger than the pressure at the tail end, the flow is positive, and when the pressure is + ->When the pressure is 1, the air pressure at the tail end of the natural gas pipeline (i, j) is larger than the air pressure at the head end, and the flow is negative; formula 1.23 is rewritten as 1 constraint and 40 conditional constraints as follows:
(2.3)
(2.4)
(2.5)
step 2.2 for the natural gas pipeline (i, j) at time t, the pipeline steady-state air pressure constraint (1.23) cannot be tightened as much as possible by the relaxation of step 2.1, thus introducing non-negative auxiliary variablesAllowing equation 1.23 to overrun, and adopting an iterative algorithm to tighten the equation as much as possible;
step 2.2.1 setting the head-end air pressure, the end air pressure, and the tube obtained after the kth iterationThe flow rates are respectively、/>、/>；
In the (k+1) th iteration of step 2.2.2, the linearization of equation 1.23 is developed at the result of the (k) th iteration in the form of the following conditional constraints:
when (when)In the time-course of which the first and second contact surfaces,
(2.6)
(2.7)
when (when)In the time-course of which the first and second contact surfaces,
(2.8)
(2.9)；
step 2.2.3 introduction of penalty factor growth factorPenalty factor maximum->Penalty factor->Represents the kth iterationPenalty factors in the process, and updating rules of the penalty factors are as follows:
(2.10)
step 2.2.4 adding a penalty term to the objective function formula (1.1) to tighten the formula (1.23) as much as possible, and rewriting the objective function as follows:
(2.11)
wherein:
is the objective function at the kth iteration;
the convergence conditions for the iteration are:
(2.12)
wherein:
for the variable to be optimized after the kth iteration +.>Is a value of (2);
is a convergence threshold;
step 2.2.5 iteration procedure when Boolean variable、/>When the value of (a) is not changed any more, fixing the Boolean variable、/>The conditional constraint formula 2.4 to 2.9 is determined according to the Boolean variable +.>、/>The value of (2) is rewritten into the corresponding linear constraint, thereby accelerating the solving speed.
The implementation flow of the invention is shown in fig. 4.
The invention also provides electronic equipment, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the gas-electric coupling system joint optimization method considering the air pressure fluctuation characteristic of the pipeline when executing the program.
The invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method for joint optimization of a gas-electric coupling system taking into account the characteristics of the air pressure fluctuation of a pipeline.
The invention also provides a computer program product, which comprises a computer program, wherein the computer program is executed by a processor to realize the gas-electric coupling system joint optimization method considering the air pressure fluctuation characteristic of the pipeline.
Compared with the prior art, the invention has the beneficial effects that: 1) The method fully considers the hydrodynamic characteristics of the natural gas in the pipeline, accurately models the dynamic change process of the pipeline air pressure caused by the adjustment of the natural gas flow, and can ensure that the air pressure of the gas-electricity coupling system is kept within a safety range by establishing dynamic constraint of the natural gas system and based on the optimization result of the model;
2) In addition, the invention also provides a model solving method adopting the combination of Taylor series expansion and continuous linear optimization, which solves the problems that the piecewise linearization algorithm is difficult to simultaneously consider precision and efficiency and has no feasible solution easily, and adopts a strategy of fixed Boolean variable value in the iterative process to accelerate the solving speed;
3) Through calculation and example analysis, the invention can promote the system economy, effectively promote new energy consumption, and ensure that the natural gas pipeline air pressure is kept within a safe range in the dynamic process.
Drawings
FIG. 1 is a schematic diagram of a gas-electric coupling system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a pressure regulating valve according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of steady-state tidal current constraint of a natural gas pipeline according to an embodiment of the invention;
FIG. 4 is a flow chart of a combined optimization method of a gas-electric coupling system for pipeline air pressure fluctuation characteristics according to an embodiment of the invention;
FIG. 5 is a block diagram of an embodiment of a gas-electric coupling system according to an embodiment of the present invention;
FIG. 6 is a graph showing the pressure of the natural gas node 7 over time according to an embodiment of the present invention;
FIG. 7 is a graph of gas pressure at a gas node 12 over time according to an embodiment of the present invention;
fig. 8 is a schematic diagram of an entity structure of an electronic device according to an embodiment of the present invention; wherein: 810-processor, 820-communication interface, 830-memory, 840-communication bus.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the optimization method of the gas-electricity coupling system considering the air pressure fluctuation characteristic of the pipeline is as shown in fig. 4, and comprises the steps of constructing dynamic safety constraint of a natural gas pipe network and solving a gas-electricity coupling system joint optimization model.
Constructing dynamic safety constraint of a natural gas pipe network in two stages;
the first stage:
initializing, namely inputting fixed information such as natural gas wave speed, pipeline radius length and the like;
acquiring the information of the initial flow, the head end air pressure, the tail end air pressure and the like of the pipeline;
selecting a regulating variable reference valueAdjusting the time reference value +.>；
Based on、/>Obtaining a pipeline air pressure fluctuation amplitude reference value +.1 through the steps 1.4.1-1.4.4>；
And a second stage:
and obtaining a natural gas pipe network steady-state constraint formula 1.2.2-1.2.3 and a dynamic constraint formula 1.38-1.41 considering the air pressure fluctuation characteristic, and constructing a natural gas pipe network dynamic safety constraint considering the air pressure fluctuation characteristic.
The combined optimization model solving of the gas-electric coupling system comprises the following steps:
inputting system parameters; establishing a constraint condition formula 1.23 containing non-convex; loosening the formula 1.23 through Taylor series expansion, and introducing the flow direction of the pipeline; ensuring the tightening of formula 1.23 through continuous linear optimization; solving a model; increasing a penalty factor; judging whether the convergence conditional expression 2.10 is satisfied, if yes, ending; if not, judging whether the pipeline flow variable is not changed any more, and if not, increasing a penalty factor to solve the model; if yes, fixing the pipeline flow direction, and establishing an optimization model containing a non-convex constraint condition formula 1.23; relaxing equation 1.23 by Taylor series expansion; ensuring the tightening of formula 1.23 through continuous linear optimization; solving the model, judging whether the convergence condition formula 2.10 is satisfied again, and ending if the convergence condition formula is satisfied; and if not, increasing the penalty factor and then carrying out model solving.
Example 1
Embodiment 1 is provided as a modified IEEE39 node power system and a 16 node two-stage air network, as shown in fig. 5.
The medium-pressure natural gas network is a branched gas network formed by nodes 1 to 10, the low-pressure natural gas network is an annular gas network formed by nodes 8 and 10 to 16, the node 1 is a constant-pressure node, the pressure is controlled at 400kPa, the nodes 8 and 10 are pressure regulating devices, natural gas is input into the low-pressure gas network from the medium-pressure gas network, and the outlet pressure of the pressure regulating valve is 10kPa.
The nodes 1 and 4 are respectively connected with air sources S1 and S2, the node 7 is connected with a new energy power station (node 32 of an electric power system) with rated output of 500MW through an air storage tank and a P2G device, and is regarded as an air source S3, the electricity discarding cost of the new energy power station is 800 yuan/MW.h, the running cost of P2G is 160 yuan/MW, and the cost of the air source S3 is 0.9456/m 3 。
Nodes 3, 6, 9, 11 to 16 are connected with air charges L1 to L9, nodes 12 and 14 are connected with nodes 9 and 12 of a power system through SOFC units respectively, the cogeneration efficiency of the SOFC units is 91.2%, and the maximum air consumption is 0.006/m 3 And/s. The adjustment time of the natural gas pipelines is 1s.
The medium pressure natural gas network comprises 9 pipelines, and the upper limit of the fluctuation range of the pipeline air pressure is 20kPa. The low-pressure natural gas network comprises 7 pipelines, and the upper limit of the fluctuation range of the pipeline air pressure is 1kPa.
The improved IEEE39 node power system has 9 thermal generator sets and 46 power transmission lines, the capacity of a total assembly machine is 7142MW, and the transmission capacity of the lines connected with the node 10 and the node 32 is adjusted to be 400MW.
Optimizing the result:
the iteration number is 7, and the total time is 80.8161s.
Scene 1: the energy bidirectional coupling of the P2G device and the SOFC unit in the natural gas system and the power system is not considered, and the objective function is only the economic cost of the power system and the natural gas system.
Scene 2: considering the energy bidirectional coupling of the P2G device and the SOFC unit in a natural gas system and a power system, and omitting a dynamic constraint formula (1.38-1.41) of the natural gas system in an optimization model.
Scene 3: the energy bidirectional coupling of the P2G device and the SOFC unit in the natural gas system and the power system is considered, and the dynamic constraint formula (1.38-1.41) of the natural gas system is considered in an optimization model.
The optimization results are shown in the following table:
table 1 example optimization results under different scenarios
The new energy waste amount of the scene 1 is 393.4775MW & h, and the scenes 2 and 3 taking the energy bidirectional coupling effect of the P2G device and the SOFC unit in the natural gas system and the power system into consideration have no new energy waste amount, so that the new energy absorption capacity of the gas-electricity bidirectional coupling system can be improved by the gas-electricity conversion equipment such as the P2G device and the SOFC unit. Compared with the scene 2, the scene 3 is slightly increased in cost, because the optimization result of the scene 2 does not consider the dynamic constraint of the natural gas system, the feasible area of the optimization model is larger, and the scene 3 limits the feasible area of the optimization model to the dynamic safety range of the natural gas pipeline, so that the feasible area is reduced, and the dynamic safety of the natural gas pipeline network is ensured although the operation cost is increased.
Fig. 6 and 7 show the pressure versus time curves at nodes 7 and 12 of the natural gas system after time 23 in scenario 2 and scenario 3, respectively.
Because the dynamic constraint of the natural gas system is not considered, the air pressure fluctuation amplitude of the node 7 in the scene 2 is close to 25kPa, even reaches 45kPa in about 1s, and exceeds the limit value of 20kPa designed by an example. Under the scene 3 considering the dynamic safety constraint of the natural gas pipeline, the air pressure fluctuation amplitude of the node 7 is within 15kPa, and the constraint of the dynamic fluctuation amplitude is satisfied. Likewise, it can be observed that the amplitude of the fluctuation of node 12 in scenario 3 is also smaller than that in scenario 2.
Fig. 8 is a schematic physical structure of an electronic device, as shown in fig. 8, where the electronic device may include: processor 810, communication interface (Communications Interface) 820, memory 830, and communication bus 840, wherein processor 810, communication interface 820, memory 830 accomplish communication with each other through communication bus 840. The processor 810 may invoke logic instructions in the memory 830 to perform a method of optimizing the electro-pneumatic coupling system that accounts for the surge characteristics of the pipeline air pressure.
Further, the logic instructions in the memory 830 described above may be implemented in the form of software functional units and may be stored in a computer-readable storage medium when sold or used as a stand-alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In another aspect, the present invention also provides a computer program product, which includes a computer program, the computer program can be stored on a non-transitory computer readable storage medium, and when the computer program is executed by a processor, the computer can execute a method for optimizing a gas-electric coupling system taking into consideration the air pressure fluctuation characteristic of a pipeline provided by the above methods.
In yet another aspect, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform a method of optimizing a gas-electric coupling system taking into account the characteristics of pipe gas pressure fluctuations provided by the above methods.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. A combined optimization method of a gas-electric coupling system considering the air pressure fluctuation characteristic of a pipeline is characterized by comprising the following steps:
establishing a gas-electricity coupling system joint optimization model considering the air pressure fluctuation characteristic of the pipeline; 1 hour is used as a calculation step length, and 1 day 24 hours is used as a calculation time period; the method comprises the following specific steps:
step 1.1, setting an objective function, wherein the objective function is the minimum comprehensive cost:
（1.1）
（1.2）
（1.3）
（1.4）
wherein:
the unit is the civil monetary unit for the comprehensive cost, and the following balance is made;
the unit is the unit of the starting and running cost of the thermal power generating unit;
punishment cost is abandoned for new energy, and the unit is unit;
the natural gas purchasing cost is the unit of the natural gas purchasing cost;
is a time set; />The time is the moment;
is a thermal power unit set;
、/>、/>the consumption characteristic curve parameter is the consumption characteristic curve parameter of the thermal power generating unit i;
the unit is MW for the active output of the thermal power unit i at the moment t;
the start-stop state of the thermal power unit i at the moment t is represented by a Boolean variable;
the unit is the starting cost of the thermal power unit i;
the thermal power unit i is started at the moment t, wherein the thermal power unit i is a Boolean variable;
the method is a new energy power station set;
the unit of the electricity discarding cost of the new energy power station i is Yuan/MW.h;
the electricity rejection rate of the new energy power station i at the moment t;
the unit is MW for the maximum active output of the new energy power station i at the moment t;
is a natural gas source collection;
the unit is m for the supply flow rate of the natural gas source i at the moment t 3 /s；
The gas purchasing cost of the natural gas source i is shown as the unit of yuan/m 3 ；
Is a gas storage tank set;
the output flow rate of the air storage tank i at the moment t is greater than 0 and less than 0, and the unit is m 3 /s；
The storage price of the air storage tank i at the moment t is shown as the unit of element/m 3 ；
Step 1.2, setting power system constraints, including thermal power unit output constraints, running state constraints, climbing constraints, node power balance and branch power flow constraints, wherein the description is as follows:
1) Thermal power generating unit output constraint:
（1.5）
wherein:
、/>the minimum active output and the maximum active output of the thermal power unit i are respectively shown in MW;
2) Thermal power generating unit operation state constraint:
（1.6）
（1.7）
wherein:
the thermal power unit i is stopped at the moment t, and the unit cannot be started and stopped at the same time;
3) Climbing constraint of thermal power generating unit:
（1.8）
（1.9）
wherein:
、/>the maximum value of downward climbing and upward climbing of the thermal power unit i is MW;
4) Node power balancing constraints:
（1.10）
wherein:
the incidence matrix of the thermal power generating unit and the power system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the thermal power generating units, the j column 1 of the ith row of the matrix represents that the thermal power generating unit j is positioned at the power system node i, and the j column 0 represents that the thermal power generating unit j is not positioned at the power system node i;
the matrix is a 2-dimensional matrix, and the dimension is the number of nodes +.>The number of SOFC units, the j column 1 of the ith row of the matrix represents that SOFC unit j is positioned at a power system node i, and the 0 represents that SOFC unit j is not positioned at the power system node i;
the method is characterized in that the method is an incidence matrix of nodes of a new energy power station and an electric power system, wherein the matrix is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the new energy power stations, the j column 1 of the ith row of the matrix represents that the new energy power station j is positioned at the power system node i, and the 0 represents that the new energy power station j is not positioned at the power system node i;
the matrix is a 2-dimensional matrix, and the dimension is the number of nodes +.>The number of the power lines, the j column 1 of the ith row of the matrix represents that the starting point of the power line j is positioned at the power system node i, the 1 represents that the ending point of the power line j is positioned at the power system node i, and the 0 represents that the starting point and the ending point of the power line j are not positioned at the power system node i;
the SOFC unit is assembled;
active output of the SOFC unit i at the moment t is unit MW;
is a power line set;
the input power of the P2G device i at the time t is unit MW;
active power of the line (i, j) at the moment t is unit MW;
the power system load matrix at the moment t is a 2-dimensional matrix, and the dimension is the node number +.>1, the ith row and the 1 st column of the matrix are loads at a power system node i and are in MW;
5) Branch tidal current constraint:
（1.11）
（1.12）
（1.13）
wherein:
is susceptance parameter of line (i, j), unit S;
the voltage phase angle of the power system node i at the moment t;
maximum transmission capacity value of line (i, j) at time t, unit MW;
for the voltage phase angle limitation of the power system node i, usually +.>；
Is a power system node set;
step 1.3, setting steady-state constraint of a natural gas system; the natural gas system comprises a natural gas source, a pipeline, a gas load and a pressure regulating valve; the steady-state constraint comprises a pressure regulating valve constraint, a gas storage tank constraint, a natural gas source constraint, a node flow balance constraint and a pipeline steady-state air pressure constraint, and is expressed as follows:
1) The pressure regulating valve is arranged at the joint of the two-stage natural gas network, and is constrained as follows:
（1.14）
wherein:
is a pressure regulating valve set;
the outlet air pressure set for the pressure regulating valve i is unit kPa;
is a natural gas pipeline set;
the pressure is the head end air pressure of the natural gas pipeline (i, j) at the moment t, and the unit is kPa;
2) The air tank is constrained as follows:
（1.15）
（1.16）
（1.17）
wherein:
、/>respectively the minimum and maximum output flow of the air storage tank i, and the unit m 3 /s；
、/>Respectively the minimum value and the maximum value of the gas storage quantity of the gas storage tank i, and the unit m 3 ；
The air storage capacity of the air storage tank i at the moment t;
3) The natural gas source constraint is as follows:
（1.18）
（1.19）
wherein:
、/>respectively the minimum value and the maximum value of the supply flow of the natural gas source i, and the unit m 3 /s；
The output flow of the P2G device i at the time t is given by the unit m 3 /s；
4) Node traffic balancing constraints:
（1.20）
wherein:
the incidence matrix of the natural gas source and the natural gas system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the natural gas sources, the j-th row and the j-th column of the matrix are 1, which means that the natural gas source j is positioned at a natural gas system node i, and 0 means that the natural gas source j is not positioned at the natural gas system node i;
the incidence matrix of the SOFC unit and the natural gas system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of SOFC units, the j column 1 of the ith row of the matrix represents that SOFC unit j is positioned at a natural gas system node i, and the 0 represents that SOFC unit j is not positioned at the natural gas system node i;
the incidence matrix of the natural gas pipeline and the natural gas system nodes is a 2-dimensional matrix, and the dimension is the number of the nodes +.>The number of the natural gas pipelines, the j-th row of the matrix is 1, which represents that the starting point of the natural gas pipeline j is positioned at a natural gas system node i, the 1 represents that the ending point of the natural gas pipeline j is positioned at the natural gas system node i, and the 0 represents that neither the starting point nor the ending point of the natural gas pipeline j is positioned at the natural gas system node i;
is the flow of the natural gas pipeline (i, j) at the moment t, and the unit m 3 /s；
For the input flow of the SOFC unit i at the moment t, the unit m 3 /s；
The natural gas system load matrix at the time t is a 2-dimensional matrix, and the dimension is the node number +.>1, row 1 and column 1 of the matrix are loads at a node i of the natural gas system, and the unit is m 3 /s；
5) The steady-state air pressure constraint of the pipeline adopts a Weymouth equation, and the constraint conditions are as follows:
（1.21）
（1.22）
（1.23）
wherein:
the unit kPa is the end air pressure of the natural gas pipeline (i, j) at the moment t;
、/>the lower and upper limits of the air pressure of the natural gas pipeline (i, j) are respectively indicated as unit kPa;
a Weymouth parameter for the natural gas pipeline (i, j);
step 1.4, constructing dynamic constraint of a natural gas system;
step 1.4.1 for each section of Natural gas pipeline (i, j), acquiring head-end air pressure in an initial state by a SCADA SystemTerminal air pressure->Length of pipe->Pipe radius->Natural gas wave velocity +.>The method comprises the steps of carrying out a first treatment on the surface of the Setting a reference value of the adjustment amountAdjusting the time reference value +.>；
Step 1.4.2 setting a calculation time intervalIs set to 0.01s, the number of time intervals N, N is a positive integer, the fluctuation of the pipeline air pressure occurs within 20 seconds, thus +.>The air pressure fluctuation amplitude threshold Th is set to 0.05kPa;
step 1.4.3 the sequence of the gas pressure at the head end of the natural gas pipeline within 20 seconds after the start of the flow adjustment is calculated by the parameters acquired/set in steps 1.4.1 and 1.4.2: p is p 0 、p 1 、p 2 、…、p N ；p i The resolvable expression for i=1, 2, …, N is as follows:
（1.24）
where H is the weaveside step function, erfc is the error complement function, defined as:
（1.25）
、/>、/>、/>、/>、/>、/>，lthe value of (2) is in the range of 1 to 10,kthe value range of (2) is 1 to 2, and the introduced process parameters are defined as follows:
（1.26）
（1.27）
（1.28）
（1.29）
（1.30）
（1.31）
（1.32）
（1.33）
step 1.4.4 by sequentially analyzing the sequences obtained in step 1.4.3, all the subsequences p having a fluctuation width of not less than Th are extracted in a linear time by an on-line algorithm i ,…, p j The definition is as follows:
（1.34）
（1.35）
（1.36）
subsequence p i ,…, p j The fluctuation amplitude of (2) is:
（1.37）
extracting the starting and ending time and fluctuation amplitude of all sub-sequences, and setting the maximum value of the fluctuation amplitude as the reference value of the air pressure fluctuation amplitude；
Step 1.4.5 for natural gas pipeline (i, j), the dynamic constraints are:
（1.38）
（1.39）
（1.40）
（1.41）
wherein:
for the adjustment of the natural gas line (i, j) at time t, unit m 3 /s；
The unit s is the adjusting time of the natural gas pipeline (i, j) at the moment t;
step 1.5 sets gas-electricity coupling constraint, including P2G device operation constraint and SOFC unit operation constraint, and is specifically described as follows:
1) P2G device operation constraints:
（1.42）
wherein:
conversion efficiency for P2G device i;
for natural gas heat value, 37.62MJ/m is taken 3 ；
2) SOFC unit operation constraint:
（1.43）
wherein:
is SOFC (solid oxide Fuel cell)Conversion efficiency of the unit i;
processing the pipeline steady-state air pressure constraint by adopting a method combining Taylor series expansion and continuous linear optimization, and solving the established combined optimization model of the gas-electric coupling system; the method comprises the following steps:
2.1 For the natural gas pipeline (i, j) at the time t, relaxing the pipeline steady-state air pressure constraint type 1.23 by a Taylor series expansion method;
2.1.1 Randomly selecting 20 ternary numbers,the following constraints are satisfied:
(2.1)
(2.2)
2.1.2 Introduction of boolean variables、/>Represents the flow direction of the natural gas line (i, j) at time t, when +.>When the pressure is 1, the pressure at the head end of the natural pipeline (i, j) is larger than the pressure at the tail end, the flow is positive, and when the pressure is + ->When the pressure is 1, the air pressure at the tail end of the natural gas pipeline (i, j) is larger than the air pressure at the head end, and the flow is negative; formula 1.23 is rewritten as 1 constraint and 40 conditional constraints as follows:
(2.3)
(2.4)
(2.5)
2.2 For the natural gas pipeline (i, j) at time t, a non-negative auxiliary variable is introducedAllowing equation 1.23 to overrun, and adopting an iterative algorithm to tighten the equation as much as possible;
2.2.1 Setting the head end air pressure, the tail end air pressure and the pipeline flow rate obtained after the kth iteration as respectively、/>、；
2.2.2 In the k+1th iteration, developing linearization of equation 1.23 at the result of the k iteration in the form of the following conditional constraint:
when (when)In the time-course of which the first and second contact surfaces,
(2.6)
(2.7)
when (when)In the time-course of which the first and second contact surfaces,
(2.8)
(2.9)；
2.2.3 Introduction of penalty factor growth coefficientsPenalty factor maximum->Penalty factor->The penalty factor at the kth iteration is represented, and the update rule of the penalty factor is as follows:
(2.10)
2.2.4 Adding a penalty term to the objective function formula (1.1) to tighten the formula (1.23) as much as possible, and rewriting the objective function as follows:
(2.11)
wherein:
is the objective function at the kth iteration;
the convergence conditions for the iteration are:
(2.12)
wherein:
for the variable to be optimized after the kth iteration +.>Is a value of (2);
is a convergence threshold;
2.2.5 When Boolean variable in iterative process、/>When the value of (1) is no longer changed, the Boolean variable +.>、/>The conditional constraint formula 2.4 to 2.9 is determined according to the Boolean variable +.>、/>Is rewritten to the corresponding linear constraint.
2. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of joint optimization of a gas-electric coupling system taking into account the characteristics of the air pressure fluctuations of a pipeline as defined in claim 1 when executing the program.
3. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the gas-electric coupling system joint optimization method taking into account the piping gas pressure fluctuation characteristics as set forth in claim 1.
4. A computer program product comprising a computer program which, when executed by a processor, implements a method for joint optimization of a gas-electric coupling system taking into account the characteristics of the pressure fluctuations of a pipeline as claimed in claim 1.
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