CN110796295B - Energy Internet air network transmission optimization method - Google Patents
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Abstract
The invention discloses an energy internet air network transmission optimization method, which belongs to the field of energy internet system operation, and comprises the steps of establishing a convex optimization model of an air flow network considering an absolute boosting type air compressor, solving and converting an air flow nonlinear equation problem into an optimized solution of the convex optimization model, converting the convex optimization model by a high-dimensional energy potential function non-integer piecewise dimension reduction method and adopting an approximate processing method, solving the converted convex optimization model to enable an energy potential function to reach a minimum operation point, namely the solution of a nonlinear air flow equation set, solving by adopting the convex optimization model, essentially overcoming the difficulty in initial value selection, reducing the solving difficulty of the model and improving the solving efficiency by a high-dimensional energy potential function non-integer piecewise dimension reduction method, obtaining the dimension reduction optimization problem easy to solve, and greatly reducing the calculation complexity to be smaller than a piecewise linearization method containing integers, so that the energy internet air network transmission efficiency is improved, and the energy internet air network transmission operation difficulty is reduced.
Description
Technical Field
The invention belongs to the field of operation of energy Internet systems, and particularly relates to an energy Internet air network transmission optimization method.
Background
With the rapid development of the economic society, the demand of human beings on energy is continuously increased, and the problems of resource exhaustion, environmental pollution and the like caused by the large-scale exploitation of traditional fossil energy are increasingly serious. Under the background, an energy utilization mode is changed, and an integrated energy system with mutually coupled multi-energy systems based on an energy internet is imperative. The energy internet uses the intercoupling of various energy sources as a core, aims to improve the consumption capacity of an energy system to renewable energy sources, improve the utilization efficiency of the energy sources, reduces the emission of carbon dioxide, and is a bridge for the transition of a system energy structure from traditional fossil energy sources to renewable energy sources. Therefore, the operation of the energy Internet is a research hotspot problem of scholars at home and abroad.
The energy internet realizes the high-efficiency utilization of energy and the improvement of the consumption of renewable energy through multi-energy complementation and coordinated optimization, and has important economic and environmental protection significance. Natural gas, hydrogen and the like which are important elements of the energy Internet can be transmitted through a pipe network, and the transmission process of the natural gas and the hydrogen needs to meet certain nonlinear physical equation limitations. Different from a traditional power network, a certain nonlinear airflow equation needs to be met in the transmission process of natural gas, hydrogen and the like through pipelines in a gas network, and great challenges are brought to calculation. The traditional optimization model of the gas-containing network is usually solved by adopting a piecewise linearization method, but because the gas flow equation is nonlinear equation constraint, the feasible domain of the optimization model is non-convex, integer variables are required to be introduced for directly performing piecewise linearization on the nonlinear equation constraint, the obtained optimization model is an NP-hard problem, the number of the introduced integer variables is also increased in proportion along with the increase of the number of segments, thus the complexity of the solution is greatly increased, and under the most serious condition, the calculation time of the solution is exponential order of the number of the integer variables.
Disclosure of Invention
The invention aims to provide an energy internet air network transmission optimization method to solve the problems of high calculation difficulty and low efficiency of the existing method.
In order to achieve the purpose, the invention adopts the following technical scheme:
an energy Internet air network transmission optimization method comprises the following steps:
step 1), establishing a convex optimization model of an airflow network considering an absolute boost type compressor, wherein the KKT condition of the convex optimization model is the same as the mathematical structure of an airflow equation of the airflow network;
and 2) converting the convex optimization model by a high-dimensional energy potential function non-integer piecewise dimension reduction method by adopting an approximate processing method to obtain a converted convex optimization model, and solving an operating point, namely a solution of a nonlinear air flow equation set, of the converted convex optimization model to enable the energy potential function to reach the minimum so as to complete energy internet air network transmission optimization.
Further, in step 1), the convex optimization model of the airflow network includes an airflow pipeline model, an absolute boost compressor model and a network node airflow balance equation model.
Further, the airflow pipeline model is as follows:
in the formula:
is a collection of gas flow conduits without a compressor; m and n are respectively a starting node and a terminal node of the airflow pipeline mn; f. of mn The flow rate of the gas flowing through the gas flow pipeline mn; y is a constant less than 1, α =1/y; c mn Is the gas flow transmission constant, pi, of the gas flow duct mn m And pi n Respectively are the square values of the air pressure of the node m and the node n; f. of mn The condition that the air flow flows from the m node to the n node is pi when the value is more than 0 m ＞π n ；f mn < 0 indicates that the air flow flows from n node to m node, i.e. pi m ＜π n 。
Further, the absolute boost compressor model is:
in the formula:
is a collection of airflow pipelines containing a compressor; pi m And pi n The air pressure square values of the inlet end and the outlet end of the air compressor are respectively; delta nm Loss of the pressure drop square value of the compressor mn; delta. For the preparation of a coating nm Absolute boost square value for a given compressor; tau. nm The absolute pressure rise square value of the compressor after considering the pressure drop loss is given.
Further, the network node airflow balance equation model is as follows:
in the formula, GF is an airflow pipeline set taking an m node as an initial node; GT is an airflow pipeline set which takes n nodes as terminal nodes; g m And D m The airflow injection amount and the airflow load of the node m are respectively;
is the set of all nodes of the air flow network.
Furthermore, each node comprises an air source node, an air flow load node and a communication node, and each node in the air flow network meets an air flow balance equation.
Further, establishing a convex optimization model considering the airflow network of the absolute boost compressor comprises:
let g MN ＝|f MN | α+1 /(α+1)C MN ，k MN ＝τ MN f MN ，g MN And k MN Are all non-negative, and the objective function second derivative is also non-negative, i.e.:
furthermore, a high-dimensional energy potential function set dimensionality reduction optimization solving method is adopted to carry out dimensionality reduction processing on the high-order part of the convex optimization model objective function, and therefore an approximate numerical value solution of the convex optimization model is obtained.
Further, the convex optimization model after the dimension reduction processing is as follows:
η i taking value in the range of 0 to 1, and obtaining an approximate optimization solution by solving a convex optimization model after dimension reduction treatment
I.e., a solution to the nonlinear system of gas flow equations.
Further, in the section of the air flow pipeline
Set up N mn 1 number of segments, the number of segments satisfying the following condition:
epsilon is the error of the function and,
compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to an energy Internet gas network transmission optimization method, which comprises the steps of establishing a convex optimization model considering an air flow network of an absolute boost compressor, converting KKT conditions of the convex optimization model into optimized solution problems of the convex optimization model, converting the solving of an air flow nonlinear equation problem into the convex optimization model by a high-dimensional energy potential function non-integer piecewise dimension reduction method through an approximate processing method to obtain the converted convex optimization model, solving the operating point of the converted convex optimization model, namely the solution of a nonlinear air flow equation set, so that the energy Internet gas network transmission optimization is completed, solving by the convex optimization model, essentially overcoming the difficulty in initial value selection, reducing the solving difficulty of the model and improving the solving efficiency by the high-dimensional energy potential function non-integer piecewise dimension reduction method, and obtaining the energy Internet gas network transmission optimization problem easy to solve by the high-dimensional energy potential function non-integer piecewise dimension reduction method without introducing integer variables, wherein the calculating complexity is far smaller than that of the energy Internet transmission efficiency is reduced, and the energy transmission efficiency of the Internet is reduced.
Furthermore, a convex optimization model considering the airflow network of the absolute boost type compressor is established, and the transmission power of the compressor is reduced because the transmission of the compressor has directionality; because the transmission of the pipeline is bidirectional, the pipeline part is in a monotone increasing model, and the transmission power of the pipeline is reduced.
Drawings
FIG. 1 is a schematic view of an airflow network node;
FIG. 2 is a diagram of high-dimensional function non-integer piecewise dimensionality reduction;
FIG. 3 is a diagram showing the pressure values of the nodes under three pipeline airflow models;
FIG. 4 is a maximum error scatter diagram of the high-dimensional energy potential function non-integer piecewise dimensionality reduction optimization solution;
FIG. 5 is a maximum error distribution histogram of a high-dimensional energy potential function non-integer piecewise dimensionality reduction optimization solution;
FIG. 6 is a 11 node air network architecture diagram;
FIG. 7 is a diagram of a 135 node air network architecture
And (5) judging the node air pressure optimization value and feasibility under different working modes of the air compressor in the graph 8.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the energy internet realizes the high-efficiency utilization of energy and the improvement of the consumption of renewable energy through multi-energy complementation and coordinated optimization, and has important economic and environmental protection significance. Natural gas, hydrogen and the like which are important elements of the energy Internet can be transmitted through a pipe network, and the transmission process of the natural gas and the hydrogen can meet certain nonlinear physical equation limits (Weymouth equation, panhandle A equation and Panhandle B equation). However, the nonlinear gas flow equation presents certain challenges to the solution computation of the multi-energy flow. The invention considers a convex optimization model of an absolute boost type compressor aiming at the problem of difficult transmission and operation of an air network in an energy internet, wherein the KKT (Karush-Kuhn-Tucker) condition of the model and the pipeline air flow equation have the same mathematical structure, so that the problem of solving the air flow nonlinear equation is converted into the optimal solution problem of the convex optimization model. And the high-dimensional energy potential function non-integer segmentation dimension reduction method is used for carrying out approximate processing, the convex optimization model is converted into a model easy to solve, and the operation point enabling the energy potential function to reach the minimum is obtained, so that the calculation difficulty of the air network in the energy internet is reduced, and the transmission efficiency is improved.
1. First, modeling and analyzing an airflow network
Gas flow networks (e.g., natural gas, hydrogen, and carbon dioxide) are primarily composed of gas sources, pipelines, pressurizing stations, and loads. The gas is injected from a gas source point and is conveyed to a load end through a pipeline. In long-distance transportation, the air pressure of the pipeline is reduced due to the friction of the pipeline wall, so that the node air pressure of the airflow network is lower than the lower limit of a normal working range, and the compressor in the pressurizing station is used for improving the node air pressure of the airflow network and compensating energy loss in the long-distance transportation process.
1.1 gas flow duct
The size of the airflow in the airflow pipeline is determined by the node air pressure at two sides of the pipeline, and the direction of the airflow flows from the high-pressure side to the low-pressure side. At present, three steady-state airflow models are mainly used for describing the relationship between airflow in an airflow pipeline and air pressure on two sides, namely a Weymouth model, a Panhandle A model and a Panhandle B model, and can be uniformly expressed as follows:
in the formula:
is a collection of gas flow conduits without a compressor; m and n are respectively a starting node and a terminal node of the airflow pipeline mn; f. of mn The flow of air flowing through the air flow pipeline mn; p is a radical of formula m And p n Air pressures of the node m and the node n respectively; y is a constant less than 1, y =0.5 in the Weymouth model, y =0.5392 in the panhandle a model, y =0.51 in the panhandle B model; c mn Is the air flow transmission constant of the air flow pipe mn in each model.
Taking into account the direction of the gas flow in the pipe and introducing the variable pi = p 2 Eliminating the square term in the gas flow equation yields:
where sign (. Cndot.) is a sign function, defined as follows
Wherein α =1/y; pi m And pi n Respectively are the square values of the air pressure of the node m and the node n; f. of mn The condition that the air flow flows from the m node to the n node is pi when the value is more than 0 m ＞π n ；f mn < 0 indicates that the air flow flows from n node to m node, i.e. pi m ＜π n 。
1.2 gas compressor
The relationship of the pressures on both sides of the compressor can be specified in a number of ways, e.g. by giving the pressureStep-up ratio of machine pi n /π m Or given the absolute boost of the compressor π n -π m . The method for calculating the absolute boost ratio of the booster compressor is characterized in that the boost ratio is adopted to ignore the air pressure loss inside the booster, the boost ratio is a simple and rough estimation and is generally used in a planning model, and the absolute boost of the given compressor can accurately reflect the relation between nodes and can account for the air pressure loss. The invention adopts the absolute boosting mode of a given compressor to describe the air pressure relation of two ends of the compressor, namely:
in the formula,
is a collection of airflow pipelines containing a compressor; pi m And pi n The air pressure square values of the inlet end and the outlet end of the air compressor are respectively; delta of nm Loss of the pressure drop square value of the compressor mn; delta. For the preparation of a coating nm The absolute boost square value for a given compressor is given. Thereby simplifying and obtaining
In the formula: tau is nm The absolute pressure rise square value of the compressor after considering the pressure drop loss is given.
1.3 network node airflow balance equation
As shown in fig. 1, for any airflow network, each node includes an air source node, an airflow load node, and a communication node. Each node in the system should satisfy the airflow balance equation, namely:
in the formula, GF is an airflow pipeline set taking an m node as an initial node; GT is an airflow pipeline set which takes n nodes as terminal nodes; g m And D m The airflow injection amount and the airflow load of the node m are respectively;
is the set of all nodes of the air flow network.
And solving an air flow equation, namely, giving the air flow injection quantity of each node and waiting to obtain the node air pressure of each node. Because the equations (8) and (11) only give the squared difference value of the two-node air pressure, namely pi m -π n Therefore, the absolute air pressure values of all the nodes cannot be obtained only from (8) and (11). Therefore, a balance node with known node air pressure needs to be given, the air pressure of the balance node is used as reference air pressure to calculate the air pressure values of all nodes, and an air source is generally selected as the balance node:
π o ＝const (17)
in the formula: o is a given balancing node.
Finally, the system of air flow equations that satisfy the physical constraints of the air flow network can be described as a system of nonlinear equations (14). It has been found that even though only the gas flow duct equation of the first formula (14) in the system of nonlinear equations is nonlinear, the overall solution is very challenging. In particular, how to select the initial value is the key to solve the nonlinear equation system.
2. Convex optimization model of airflow network
In order to overcome the problem of directly solving the complex nonlinear equation set, the invention firstly constructs the following convex optimization model:
let g be mn ＝|f mn | α+1 /(α+1)C mn ，k mn ＝τ mn f mn G, since 0 < y < 1 in all three steady state flow models, then α =1/y > 1 mn And k mn Are all non-negative, and the objective function second derivative is also non-negative, i.e.:
therefore, the objective function in the formula (15) is a convex function, and the constraint condition is a linear equation constraint, so that the constructed optimization model (15) is a convex optimization model.
The KKT condition of the convex optimization model equation (15) is isomorphic with the nonlinear equation set (14) as will be demonstrated below; this illustrates that the convex optimization model (15) is identical to the solution of the non-linear system of equations (14).
The Lagrangian function of the convex optimization model (15) is:
wherein λ is m The corresponding multiplier for the mth equation constraint (i.e., the flow balance equation for the mth node). The optimal solution of the optimization model can be obtained according to the KKT condition
And lagrange multiplier corresponding to constraint condition (15)
The finishing formula (18) gives:
comparing the KKT condition (19) of the convex optimization model with the nonlinear equation set (14) can find that the KKT condition and the nonlinear equation set have the same mathematical structure. This indicates thatThe system of flow network nonlinear equations (14) can be transformed into an optimized solution to the convex optimization model (15)
And lagrange multiplier
It should be noted that the equilibrium node air pressure obtained from the convex optimization model satisfies the condition (14), and therefore:
wherein,
representing the collection of branches in the air network (including the piping and air compressor branches). The physical meaning of equation (20) is to shift the convex optimized multiplier such that the balanced node multiplier is exactly equal to the balanced node multiplier
Thus, the multipliers of the other nodes are the air pressure square value pi of the node * . Further, each node pi obtained by the formula (20) * The air pressure p of each node of the natural gas network can be obtained by evolution * 。
3. High-dimensional energy potential function group integer-free segmented dimensionality reduction optimization solution
The model (15) is a convex optimization model that is relatively easy to solve for initial value selection. For example, solving by the interior point method, only any point satisfying the equation constraint needs to be selected. However, since the objective function is a high-order nonlinear function, solving the convex optimization directly is complex and time-consuming. In order to reduce the solving difficulty of the model and improve the solving efficiency, the invention adopts a high-dimensional energy potential function group dimension reduction optimization solving method to carry out the high-order part of the objective function of the convex optimization model
And performing dimensionality reduction treatment to obtain an approximate numerical solution of the convex optimization model.
The airflow of the airflow duct always satisfies certain physical constraints, i.e.
Thus in the interval
Setting up a reasonable number of segments, e.g. N mn 1, then there is N mn A segmentation point
As shown in FIG. 2, g (f) corresponding to each segment point is obtained mn ) Is composed of
Introducing a new variable eta i and satisfying:
where η i ranges from 0 to 1, reflecting the distribution among the segments. The physical meaning of equation (21) is to treat the segmentation points as some poles of the convex optimization feasible domain, and to obtain the variable f by using the expression theorem mn And the pole.
The original optimization model can be optimized by converting into the following optimization models:
by solving the convex optimization model (22), an approximate optimal solution for the model (14) can be obtained
Further, the following equation (20) can be obtained
Since the approximation function always causes a certain error, the optimal solution obtained by the approximated convex optimization model (22)
Solution to a precise non-linear set of gas flow equations
There is a certain error. The error can be controlled by the number of segments. In other words, if the number of segments is increased, the accuracy of the calculation result can be improved, as demonstrated below.
Let the energy potential function be expressed as
Due to primitive function g mn ＝|f mn | α+1 /(α+1)C mn Is a continuous function, and therefore, with the number of segments N mn Increase of (a), h mn Will approach the coincidence to g mn Given a functional error epsilon, the number of segments satisfies the following condition:
for the optimal solution
And approximate optimal solution
Can obtain
Wherein,
and
to approximate to an optimal solution
Carry-in function h mn And g mn The results obtained were. Further, it can be seen that,
further, in the present invention,
it is readily apparent that the following inequality holds
On the one hand, as can be seen from equation (28), the error of the optimal solution can be strictly controlled by epsilon, that is, the optimal solution can be strictly controlled by the error, so that the optimization model is a global optimal solution under the control of epsilon error. On the other hand, if the error of the desired optimal solution is η, the error can be controlled
The number of segments can then be determined from ε according to (23).
4. Discussion of the proposed method and some applications
4.1 physical meanings of the optimization models mentioned
Viewed directly, the objective function of the model (15) comprises two parts of a pipeline and a compressor: the compressor part is a linear model, and as the transmission of the compressor is directional, the objective function of the part is used for reducing the transmission power of the compressor; since the transmission of the pipe is bidirectional, the pipe portion is | f mn A monotonically increasing model of | the part of the objective function is to reduce the transmission power of the pipe. In practice, the objective function has some specificity, which is the integral to the left of the first two equations of the nonlinear equation for gas flow (14). Through equivalence to obtain
It can be seen that the objective function z is a non-negative function, and (π) m -π n )f mn Is a measure of energy. Therefore, the physical meaning of the objective function z is the total energy potential function of the duct airflow. Furthermore, the convex optimization model (15) is used for searching the operating point with the minimum energy potential function, and the operating point is just the solution of the model (14). Therefore, solving the solution of the air flow network equation set can construct a convex energy potential function and find the operating point which makes the energy potential function reach the minimum.
4.2 physical meanings of the optimization models
The traditional optimization model of the gas-containing network is usually solved by adopting a piecewise linearization method, but because the gas flow equation is nonlinear equation constraint, the feasible domain of the optimization model is non-convex, integer variables are required to be introduced for directly performing piecewise linearization on the nonlinear equation constraint, the obtained optimization model is an NP-hard problem, the number of the introduced integer variables is also increased in proportion along with the increase of the number of segments, thus the complexity of the solution is greatly increased, and under the most serious condition, the calculation time of the solution is exponential order of the number of the integer variables.
The optimization model provided by the invention is a convex optimization model, and the method of adopting a high-dimensional energy potential function non-integer segmentation does not need to introduce integer variables, so that a dimension reduction optimization problem which is easy to solve is obtained, the problem is essentially a polynomial time algorithm problem, and the algorithm complexity is far less than that of a piecewise linearization method containing integers. Meanwhile, as the number of the segments increases, the degree of increase of the calculation time is not obvious because an integer variable does not need to be introduced.
4.3 economic dispatch model feasibility determination and initial feasible solution determination of the airflow equation
For the economic dispatching model of the air network, the objective function can be any function related to the optimization variable, and the constraint condition needs to satisfy the following inequality constraint besides the equality constraint corresponding to the air flow in the air flow pipeline and the node air pressure formula (14):
wherein,
the upper limit of the air flow in the pipeline;
and
the squares of the upper and lower node air pressure limits, respectively. Meanwhile, for the air supply nodes in the air flow network, there are upper and lower limits on the air flow supply amount of each air supply, as follows:
in the formula:
is a set of gas source nodes;
and
the minimum value and the maximum value of the supply quantity of the air source node are respectively.
Secondly, the control variable G in the economic dispatch model m Some other linear equality and inequality constraints may also need to be satisfied, as follows:
wherein X is the convex feasible region of the state variable.
Solving an economic dispatch model containing airflow equation constraints first requires a fast judgment of the feasibility of the model. And the feasibility of the optimization model only depends on the feasible domain formed by the constraint conditions and is not related to the objective function.
Further, the optimization model feasibility judgment can construct a linear optimization model.
Optimized solution of the solution model (33)
Constructing a convex optimization model (34) according to the optimal solution, wherein if the convex optimization model is feasible, the original economic dispatching model has a feasible solution; otherwise, there is no feasible solution.
A convex optimization model (34) is solved according to the feasibility determinations, and if the model is feasible, a feasible solution is available. The convex optimization model (34) is further solved to obtain an optimal solution of the convex optimization model, and the optimal solution can be used as an initial feasible solution of the optimization model.
Example (b):
1.20 node natural gas network example
The improved 20-node high-calorific-value natural gas system is adopted in the embodiment and comprises 6 gas source nodes, 9 load nodes, 5 contact nodes, 23 natural gas pipelines and 3 pressurizing stations, and the structure of the system is that two natural gas pipelines are arranged between the two nodes.
Selecting a node I as a balance node, and setting the air pressure of the balance node to be p 1 =55bar, then
The present example sets the following 3 scenarios for calculation and analysis:
1) Scene one: the number of segments of the dimension reduction is 100, the natural gas loads are all given expected values, the three test groups are set according to the type of the pipeline airflow equation, and the difference between the pipeline airflow and the calculated value of the node air pressure under the three airflow models is compared.
Case A: all pipes were modeled using the Weymouth model.
Case B: all pipelines adopt Panhandle A model.
Case C: all pipelines adopt Panhandle B model.
2) Scene two: the number of segments of the dimension reduction is different, the natural gas load is a given expected value, the pipeline gas flow equation adopts a Weymouth model, and the error of the piecewise linearization under the condition of different number of segments and the solving efficiency of the LP model are obtained.
3) Scene three: the number of segments of the dimension reduction is 100, the natural gas load fluctuates around a given expected value according to normal distribution, and the error of the LP model under the condition of fluctuating load is obtained by adopting a Weymouth model in a pipeline gas flow equation.
1.1 scenarios
The number of segments of the dimension reduction and the natural gas load are given values, and meanwhile, a Weymouth model, a Panhandle A model and a Panhandle B model are respectively adopted for calculating an air flow equation of a natural gas pipeline. According to the model provided by the invention, the gas flow of each pipeline of the natural gas network is shown in table 3, and the optimization results of the natural gas supply quantity, the natural gas load and the gas pressure of each node are shown in table 4 and fig. 3.
TABLE 3 gas flow rate of natural gas pipeline
TABLE 4 optimized values for natural gas supply, load and node voltage
It can be known from table 4 that the gas flow rate results obtained by solving the three pipeline gas flow equations are the same because the system is a radial network structure, and the solution of the pipeline gas flow is unique under the condition that the natural gas supply amount and the load value of each node are known. However, the node air pressures calculated by adopting the three pipeline air flow equations are different, and it is seen from table 4 and fig. 3 that the node air pressures of the nodes 1 to 18 are approximately equal in three cases, and the node air pressures of the nodes 19 to 20 have larger differences and are all lower than those of other nodes. The actual condition analysis of the system shows that the distance between the node 18 and the node 19 is long, the pipeline distance is long, and the pipeline air pressure is greatly reduced due to much energy consumed by friction of the pipe wall of natural gas in the transmission process, so that a pressurizing station is arranged between the nodes 17 and 18, the air pressure level of the node 18 can be improved, and the air pressure of the nodes 19 and 20 is ensured not to fall below the lower limit of the air pressure. Meanwhile, the calculation example shows that the difference of the Weymouth model, the Panhandle A model and the Panhandle B model in the calculation of the long-distance pipeline is large, so that how to select the proper model needs to be determined according to the field test result.
1.2 scene two
The error of the model (29) for reducing the dimension of the objective function is obtained by the formula (23) under the condition of different segment numbers, and the relative error can be obtained:
and then get the scoreMaximum value err of relative error max As follows
Table 5 shows the solution accuracy of the computation time for different numbers of segments. It can be seen from table 5 that the more the number of the selected segments is, the higher the solving accuracy of the convex optimization model is, and when the number of the segments is 50, the maximum value err of the relative error is obtained max Is less than 5 percent, and when the number of segments is 100, the maximum value of the relative error is less than 0.1 percent. Meanwhile, with the increase of the number of the segments, the increasing degree of the model solving time is not obvious because an integer variable is not required to be introduced, and when the number of the segments is increased to 500, the solving time is still less than 0.1s. This shows that the model can improve the solution accuracy by increasing the number of segments, while still maintaining high solution efficiency.
TABLE 5 solving accuracy and efficiency of models at different fractional numbers
1.3 scenarios three
Since the solution of the gas flow equation is obtained under the condition of the boundary of a given section. However, in an actual natural gas system, both the natural gas load and supply are changing, and thus the boundary conditions are also changing. For example, the correctness of the method of the present invention is verified under different boundary conditions, assuming that the fluctuation of the natural gas load satisfies normal distribution near its expected value, the probability distribution function is:
in the formula, μ is an expected value of the load of each node, and σ =3%.
Aiming at the uncertainty of the natural gas load, a Monte Carlo method is adopted to carry out modeling solution, and for each load node of the natural gas network, 1000 groups of random load waves are generated by using simulation softwareDynamic data, corresponding to a given load fluctuation probability distribution (37). Through 1000 Monte Carlo simulations, the maximum error err of each solution can be obtained max Fig. 4, the corresponding probability density distribution map is shown in fig. 5. As can be seen from fig. 4 and 5, the error is mainly distributed at 3.5 × 10 in 1000 load simulations -4 To 5.5X 10 -4 And the maximum value is 6.3 multiplied by 10 < -4 >, which shows that the solutions can better meet the nonlinear constraint of the pipeline airflow under the load fluctuation scene, and the correctness of the method is verified.
2.11 node Hydrogen network example
The 11-node hydrogen gas network is shown in figure 6, which contains 3 gas source nodes, 3 load nodes, 5 communication nodes, 11 gas flow lines and 2 pressurizing stations. Suppose that the steady-state airflow models of the airflow pipelines in this example all adopt Weymouth model, and the node No. 1 is selected as the balance node, and the air pressure of the balance node is set as p 1 ＝p 0 =50bar, i.e.
Two groups of data A and B with different hydrogen supply amounts and load values are selected for calculation, the air pressure value of each node is obtained by adopting the proposed linear programming according to corresponding boundary conditions, and the feasibility verification of the model calculation result is completed according to the method of 2.3.3 sections. A. The hydrogen supply amount and load values, the gas pressure values, and the judgment results on the gas pressure feasibility at each node of the two groups B are shown in Table 6. It can be seen from Table 6 that in the data of group A and group B, the air pressure values of group A are all within the given air pressure range, so the results of group A are feasible; the air pressure values of the load nodes 4 and 6 in the group B are too low to be lower than the given air pressure lower limit value, so the group B results are not feasible. Meanwhile, the calculation shows that in the actual operation of the air network, the air pressure of part of the nodes of the air network is too low due to the fluctuation of the part of the load nodes (for example, the loads of the node 4 and the node 6 in the group B are increased on the basis of the group A), which requires that feasibility verification must be carried out on the premise of carrying out optimization calculation on the air network, and if the optimization solution of the model is not feasible, the operation mode of the air network needs to be changed, for example, the pressure boost value of the air compressor needs to be changed, so that the air pressure of each node is in a normal range.
TABLE 6 judgment of node air pressure value and feasibility
3.135 node natural gas network example
The improved 135-node natural gas network test system is adopted in the embodiment, and the structure of the system is shown in figure 7. The system comprises 6 air source nodes, 99 load nodes, 30 communication nodes, 141 airflow pipelines and 2 pressurizing stations.
All airflow pipelines in the embodiment adopt a Weymouth model, a node 103 (air source node) is selected as a balance node, and the reference air pressure of the balance node is set to be p 103 ＝p 0 =80bar, i.e.
And setting two groups of scenes A and B with the same air flow supply and load value of each node but different compressor working modes for calculation. And the air flow supply quantity, the load value and the pressure boosting value of the air compressor of each air source node in the same group are the same, and the specific data are shown in a table 7. A. The air pressure values of the two groups B are shown in figure 8. It can be seen from fig. 8 that the air pressure value of the partial node in scenario a is lower than the lower air pressure limit of the system by 30bar, so that the solution is not feasible, and the air pressures of all nodes in scenario B are within the normal range, which satisfies the verification of feasibility. Meanwhile, the working mode of the gas compressor also influences the air pressure value of each node, and when the air pressure of part of the nodes is too low, the pressure boosting value of the gas compressor can be increased until the air pressure of all the nodes is in a normal range.
TABLE 7 data for scenarios A and B
Claims (2)
1. An energy internet air network transmission optimization method is characterized by comprising the following steps:
step 1), establishing a convex optimization model of an airflow network considering an absolute boost type compressor, wherein the Carlo-Cohen-Tak condition of the convex optimization model is the same as the mathematical structure of the airflow equation of the airflow network;
the convex optimization model of the airflow network comprises an airflow pipeline model, an absolute boosting type compressor model and a network node airflow balance equation model;
wherein the airflow pipeline model is as follows:
in the formula:
is a collection of gas flow conduits without a compressor; m and n are respectively an initial node and a terminal node of the airflow pipeline mn; f. of mn The flow rate of the gas flowing from the starting node m to the terminal node n in the gas flow pipeline mn is shown; y is a constant less than 1, α =1/y; c mn Is the gas flow transmission constant, pi, of the gas flow duct mn m And pi n Respectively are the square values of the air pressure of the starting node m and the terminal node n; f. of mn A value > 0 indicates that the air flow flows from the m node to the n node, namely pi m ＞π n ；f mn < 0 indicates that the air flow flows from n node to m node, i.e. pi m ＜π n ；
The absolute boost compressor model comprises the following components:
in the formula:
is composed ofA set of gas flow conduits of the compressor; pi M And pi N The air pressure square values of the inlet end and the outlet end of the air compressor are respectively; delta of NM Loss of the pressure drop square value of the compressor; delta. For the preparation of a coating NM Absolute boost square value for a given compressor; tau is NM Setting an absolute boost square value of the compressor considering the pressure drop loss;
the network node airflow balance equation model is as follows:
in the formula, GF is an airflow pipeline set taking an m node as an initial node; GT is an airflow pipeline set which takes n nodes as terminal nodes; g m And D m The airflow injection amount and the airflow load of the node m are respectively;
is the set of all nodes of the air flow network;
establishing a convex optimization model considering the airflow network of the absolute boost type compressor as follows:
let g MN ＝|f MN | α+1 /(α+1)C MN ，k MN ＝τ NM f MN ，g MN And k MN Are all non-negative, and the objective function second derivative is also non-negative, i.e.:
step 2), performing dimensionality reduction treatment on the high-order part of the convex optimization model objective function by adopting a high-dimensional energy potential function set dimensionality reduction optimization solving method to obtain an approximate numerical solution of the transformed convex optimization model, and solving an operating point, namely a solution of a nonlinear airflow equation set, of the transformed convex optimization model, wherein the energy potential function reaches the minimum so as to complete energy internet air network transmission optimization;
the convex optimization model after the dimensionality reduction treatment is as follows:
wherein eta i Taking values in the range of 0 to 1, and obtaining an approximate optimal solution by solving a convex optimization model after dimension reduction treatment
I.e. the solution of the nonlinear gas flow equation set;
in the region of the gas flow ducts
Set up T mn -1 number of segments, the number of segments satisfying the condition:
epsilon is the error of the function and,
2. the method as claimed in claim 1, wherein each node comprises an air source node, an air flow load node and a communication node, and each node in the air flow network satisfies an air flow balance equation.
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