CN110263387B - Energy system operation device based on power distribution network and natural gas network - Google Patents
Energy system operation device based on power distribution network and natural gas network Download PDFInfo
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Abstract
The invention relates to a comprehensive energy system optimization operation model established by a power distribution network and a natural gas network based on an energy hub and a linear processing method thereof, wherein the energy hub model for coupling the power distribution network and the natural gas network takes the total cost of energy purchasing as the lowest optimization target, and simultaneously considers the safety operation constraints of the power distribution network, the natural gas network and the energy hub, including the branch power flow constraint, the node voltage constraint and the branch power constraint of the power distribution network; the method comprises the following steps of natural gas pipeline gas flow balance constraint, gas source gas output constraint, node gas pressure size constraint, natural gas pipeline Weymouth steady-state flow constraint and pressurizer boosting relationship constraint; and the thermal power balance of the energy concentrator is constrained and the operating power of each energy conversion device is constrained, so that the optimal operation of the comprehensive energy system is realized. Before solving the model, the initial model is subjected to linearization so as to finally solve the optimization operation model of the comprehensive energy system by means of CPLEX.
Description
Technical Field
The invention relates to the field of power electronics, in particular to an energy hub-based comprehensive energy system optimization operation model established by a power distribution network and a natural gas network and a linear processing method thereof.
Background
The environmental deterioration and the gradual energy depletion have become global concerns, and how to fully utilize clean energy and guarantee the energy demand of human beings has become the focus of the common concern of all countries in the world today. In order to realize the coordinated management of various energy sources and fully utilize the complementarity of different energy sources, a comprehensive energy source system is developed. The comprehensive energy system is used for realizing coordinated planning and optimized operation among various energy subsystems such as coal, petroleum, natural gas, electric energy, heat energy and the like in a certain area. Therefore, while meeting the diversified energy demand in the system, it is necessary to effectively improve the energy utilization efficiency and promote the sustainable development of energy.
Through the combined operation of the power grid and the gas grid, the operation of a thermal power unit can be reduced, and further consumption of fossil energy and further deterioration of environmental pollution are relieved. The combination of the power grid and the air grid can realize energy source complementation, and the high efficiency can fully meet the energy utilization requirement of a user side. Therefore, considering the optimized operation of a new generation of integrated energy system combining a power distribution network and a natural gas network, the research on the operation mechanism of the integrated energy system is also beneficial to establishing a uniform market value measurement standard in the future, so that the economic and social values are fully embodied by the energy conversion and complementation, the electric power can be promoted to be converted into cleaner and greener energy, and a long-term and highly active benefit is brought to the future by the integrated energy system which is more efficient, economic, renewable, reliable, sustainable and stable.
Disclosure of Invention
In view of the above, the present invention provides an energy hub-based optimal operation model of an integrated energy system established in a power distribution network and a natural gas network, and a linear processing method thereof, which can consider the mutual influence of the power network and the natural gas network, and enable the integrated energy system to operate more economically and safely on the premise of meeting the demand of electricity, gas and heat loads.
The invention is realized by adopting the following scheme: an energy hub-based comprehensive energy system optimization operation model established by a power distribution network and a natural gas network comprises the following steps:
step S1: providing an energy hub model capable of coupling a power distribution network and a natural gas network;
step S2: and establishing an objective function, and completing modeling of an optimized operation model of the comprehensive energy system according to the safe operation constraints of the power distribution network, the natural gas network and the energy concentrator.
Further, the objective function in step S2 is the energy purchase cost as shown in the following formula, including the electricity purchase cost
And the cost of purchasing air>
To minimize the total cost of the integrated energy system during the simulated operation schedule;
in the formula, TR represents a set of injection power nodes of a substation in a power distribution network; GS represents the set of source nodes in the natural gas network;
the distribution represents unit electricity price and gas price in the time t; />
Respectively injecting the electricity purchasing quantity of the power node j into the transformer substation in the time period t; />
The gas purchasing quantity of the gas source node j in the time period t.
Further, the power distribution network safe operation constraint in step S2 includes: node power balance constraint, node voltage amplitude constraint, distribution line maximum current-carrying capacity constraint and transformer substation power constraint;
the node power balance constraint is:
in the formula, r ij 、x ij The resistance and reactance of the branch ij are respectively; δ (j) represents a set of end nodes of a branch with j as a head node, and π (j) represents a set of head nodes of a branch with j as a head node; p is ij,t 、Q ij,t The active power and the reactive power of the branch ij are respectively;
respectively representing the main network output power and the power load active power; />
Respectively, the active power output for electrical conversion of the P2G device in Hub; />
Representing the equivalent active power injected into the distribution network by the CHP device in Hub; />
Respectively representing the reactive power values of the main network output and the power load;
the node voltage amplitude constraint is:
U min ≤U j,t ≤U max
in the formula of U j,t 、U min And U max The node voltage amplitude and the lower limit and the upper limit thereof are respectively;
the maximum ampacity constraint of the distribution line is as follows:
0≤I ij,t ≤I max
in the formula I ij,t 、I max The branch current amplitude and the upper limit thereof are respectively;
the power constraint of the transformer substation is as follows:
further, the specific content of restricting the natural gas network in step S2 is as follows:
node airflow balance constraint:
in the formula, σ (jk) represents a pipeline set with j as a head end node; mu (ij) respectively represents a pipeline set taking j as an end node; f. of p,t /f l,t The flow rate is p/l of the pipeline;
respectively the gas load and the gas source node gas output;
respectively representing the natural gas amount used for GF and CHP energy conversion in the (integrated energy unit) Hub;
representing the equivalent natural gas injection amount for electrically converting the P2G device in the Hub into gas;
and (3) natural gas source gas output restraint:
natural gas produced from a gas well needs to be refined by a refinery, and due to the limitations of equipment capacity and gas pressure at the gas well, the gas output of a natural gas source per unit time should meet the following constraints:
in the formula (I), the compound is shown in the specification,
is the output natural gas quantity of the gas source j>
Respectively outputting the upper limit and the lower limit of the natural gas quantity for a gas source j;
node air pressure constraint:
the gas pressure of each node of the natural gas network must be maintained within a safe and reasonable operation range, and the mathematical expression is as follows:
in the formula (I), the compound is shown in the specification,
respectively representing the upper and lower limit values of the air pressure at the node i;
and (3) carrying out steady-state flow constraint on a natural gas pipeline Weymouth:
a Weymouth steady-state trend model is adopted to depict the relation between natural gas flow and air pressure at two ends, and the specific expression is as follows:
wherein the content of the first and second substances,
in addition, the flow of the pipeline is ensured to be within a safe and reasonable operation range:
in the formula (f) p,t Representing the natural gas stream flowing through line p; pi i,t And pi j,t Respectively representing the air pressure at two ends of the pipeline p; phi is a unit of p Representing the gas flow transmission parameter of the pipeline p; sgn p Indicating the flow direction of the gas flow in the pipeline p;
indicating the maximum pipe transport capacity.
Pressurizer boost relationship constraints:
π j,t ＝Γ c π i,t
in the formula (f) c,t The delivery air flow representing the pressurizer c; pi i,t And pi j,t Respectively representing the air pressure of the air inlet end and the air outlet end of the pressurizer c; gamma-shaped c 、
Respectively, the boosting ratio and the maximum transmission capacity of the pressurizer c.
Further, the operation constraints of the energy hub in step S2 are:
the thermal power supply and demand balance constraint of the energy concentrator is as follows:
energy conversion unidirectional constraint of the energy concentrator:
further, the invention also provides a linear processing method of the comprehensive energy system optimization operation model established by the power distribution network and the natural gas network based on the energy concentrator, which comprises the following steps:
and step S3: carrying out linearization processing on the model established in the step S2;
and step S4: and (4) solving the model after linearization processing in the step (S3) by using a CPLEX solver.
Further, the specific content of step S3 is: converting the model by adopting a second-order cone relaxation and incremental piecewise linearization method to carry out linearization treatment; because the node power balance constraint contains a nonlinear term, the constraint is simplified by adopting a second-order cone relaxation method, and a new variable is introduced to eliminate a voltage and current square term, which is shown as the following formula:
the node power balance constraint may cancel the non-linear quadratic terms of voltage and current as follows:
thus, the voltage, current amplitude constraint is modified to:
the third formula of the node power constraint is further converted into a second-order conical formula through relaxation; the specific form is as follows:
the method is characterized in that the pipeline Weymouth steady-state power flow constraint in the natural gas network is linearized by adopting an incremental piecewise linearization method, and nonlinearity caused by a square term of air pressure in the pipeline Weymouth steady-state power flow constraint is eliminated by introducing a new variable, and the method is specifically as follows:
1、
therefore, the pipeline Weymouth steady state power flow constraint can be initially rewritten as:
since sgn p (π i,t ,π j,t ) Is a sign function when i,t Greater than pi j,t Taking 1 when the current value is zero, or taking-1 when the current value is zero; thus, writing the left side of the expression as an absolute value expression, i.e. let Y be p,t ＝f p,t |f p,t L, |; i.e. Y p,t ＝f p,t |f p,t I can also be expressed as a non-linearized expression of f (x) = x | x | the steps of incremental piecewise linearization are as follows:
step SA, setting average subsection number n according to the established model;
step SB, the value interval of x is equally divided by n, thus n +1 discrete points, namely x, can be obtained 0 ,x 1 ...x n ；
Step SC, calculating discrete point x 0 ,x 1 ...x n The corresponding function value of f (x);
step SD, introducing a new auxiliary variable and ensuring that the following constraints are met:
in conjunction with the above method, the pipeline Weymouth steady state power flow constraint is ultimately described as:
compared with the prior art, the invention has the following beneficial effects:
the invention simultaneously considers the mutual influence of the power grid and the natural gas grid, and the comprehensive energy system operates more economically and safely on the premise of meeting the requirements of electricity, gas and heat loads. The planning model fully considers the characteristic of flexible conversion between electricity and gas, and improves the economy of the comprehensive energy system in the operation aspect by taking the total energy purchasing cost of the comprehensive energy system as an optimization target on the basis of meeting the safe operation constraint.
Drawings
Fig. 1 is a schematic diagram of an energy hub according to an embodiment of the invention.
Fig. 2 is a simple schematic diagram of a natural gas network according to an embodiment of the present invention.
FIG. 3 (a) is a diagram illustrating electrical timing characteristics according to an embodiment of the present invention.
FIG. 3 (b) is a time-series characteristic diagram of the gas according to the embodiment of the present invention.
Fig. 3 (c) is a timing characteristic diagram of the thermal load according to the embodiment of the present invention.
Fig. 4 is an IEEE-14 node power distribution network topology according to an embodiment of the present invention.
Fig. 5 is a 20-node natural gas network topology of an embodiment of the present invention.
Fig. 6 (a) is a power rate/gas rate curve according to an embodiment of the present invention.
Fig. 6 (b) is a graph of the optimized power purchase amount and gas purchase amount according to the embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
The embodiment provides an energy hub-based comprehensive energy system optimization operation model established for a power distribution network and a natural gas network, which comprises the following steps:
step S1: establishing an Energy Hub (EH) model capable of coupling a power distribution network and a natural gas network to complete the modeling of a comprehensive energy system;
step S2: and (4) considering the safe operation constraints of the power distribution network, the natural gas network and the energy concentrator, establishing an optimization target, and completing the modeling of the comprehensive energy system.
The following is a specific implementation procedure of the present embodiment.
(1) As shown in fig. 1, an energy concentrator model capable of coupling a power distribution network and a natural gas network is established.
(2) And establishing an objective function of the optimization model by taking the lowest total energy cost as an objective.
(3) And comprehensively considering the safe operation constraint of the power distribution network.
(4) The natural gas network simplifies modeling and takes into account natural gas network safe operating constraints.
(5) And comprehensively considering the safe operation constraint of the energy concentrator.
In this embodiment, a terminal integrated energy unit model is established, and the specific implementation of step S1 is as follows: energy requirements in the forms of electricity, heat, gas load and the like exist in the comprehensive energy system at the same time. In order to meet the load requirement as much as possible, an Energy Hub (EH) model capable of coupling a power distribution network and a natural gas network is established. The energy hub is mainly composed of Combined Heat and Power (CHP), gas boiler (GF) and P2G (power to gas, P2G) devices, and the energy hub established based on the energy hub not only can complete the interconversion between electricity and gas, but also can supply heat load.
In this embodiment, the step S2 is implemented as follows:
2. establishing an objective function of an optimization model
The main objective of the proposed optimization model is to minimize the total cost of the integrated energy system during the simulated operation schedule, so the objective function mainly considers the energy acquisition costs, including the electricity purchase cost and the gas purchase cost.
In the formula, TR represents a set of injection power nodes of a substation in a power distribution network; GS represents the set of source nodes in the natural gas network;
the distribution represents unit electricity price and gas price in the time t; />
Respectively injecting the purchased electric quantity of the power node j into the transformer substation in the time interval t；/>
The gas purchasing quantity of the gas source node j in the time period t.
3. Considering the operation constraint of the power distribution network:
node power balance constraints
In the formula, r ij 、x ij The resistance and reactance of the branch ij are respectively; δ (j) represents a set of end nodes of a branch with j as a head node, and π (j) represents a set of head nodes of a branch with j as a head node; p is ij,t 、Q ij,t The active power and the reactive power of the branch ij are respectively;
respectively represents the main network output and the active power of the electrical load>
Respectively representing the active power output for electrical conversion of the P2G device in Hub; />
Represents the equivalent active power injected into the distribution grid by the CHP device in Hub, and>
respectively representing the reactive power values of the main network output and the power load.
Node voltage amplitude constraints
U min ≤U j,t ≤U max
In the formula of U j,t 、U min And U max The node voltage amplitude and its lower and upper limits, respectively.
Maximum ampacity constraint for distribution line
0≤I ij,t ≤I max
In the formula I ij,t 、I max Branch current amplitude and its upper limit, respectively
Power constraint of transformer substation
4. Establishing a natural gas network model and taking into account natural gas network operating constraints
As shown in fig. 2, the natural gas network is primarily comprised of a natural gas source, natural gas pipelines, pressurizers, and natural gas loads. The natural gas flow always inevitably generates friction loss in the flowing process from mining to transportation, and the gas pressure is gradually reduced after a certain transportation distance (generally 80-160 km). In order to avoid excessive friction loss and ensure that the natural gas can be delivered to the load side with high quality and high efficiency, some pipelines in the natural gas system are generally required to be provided with pressurizers for boosting pressure so as to maintain the safe operation level of the node air pressure. It can be seen that the role of the booster in the natural gas network is essentially similar to that of a transformer in an electrical power system. The natural gas network is constrained as follows:
nodal airflow balance constraints
In the formula, σ (jk) represents a pipeline set taking j as a head end node, and μ (ij) represents a pipeline set taking j as a tail end node; f. of p,t /f l,t The flow rate is p/l of the pipeline;
respectively the air load and the air source node air output,
respectively representing the natural gas amount used for GF and CHP energy conversion in an integrated energy unit (Hub);
represents the equivalent natural gas injection amount for electrically converting the P2G device in Hub to gas.
Natural gas source air output restriction
Natural gas produced from gas wells requires refinery purification. Due to the limitation of the capacity of equipment and the air pressure at a gas well, the gas output of a natural gas source in unit time meets the following constraint:
in the formula (I), the compound is shown in the specification,
is the output natural gas quantity of the gas source j>
Respectively outputting the upper limit and the lower limit of the natural gas quantity for the gas source j.
Nodal point air pressure constraint
The gas pressure of each node of the natural gas network must be maintained within a safe and reasonable operation range, and the mathematical expression is as follows:
in the formula (I), the compound is shown in the specification,
respectively represent the upper and lower limit values of the air pressure at the node i.
Natural gas line Weymouth steady state flow constraint
The relation between natural gas flow and air pressure at two ends is described by a Weymouth steady-state trend model, and the specific expression is as follows:
wherein the content of the first and second substances,
in addition, the flow of the pipeline is ensured within a safe and reasonable operation range:
in the formula (f) p,t Representing the natural gas stream flowing through line p; pi i,t And pi j,t Respectively representing the air pressure at two ends of the pipeline p; phi is a p Representing the gas flow transmission parameter of the pipeline p; sgn p Represents the airflow direction of the pipeline p;
indicating the maximum pipe transport capacity.
Pressurizer boost relationship constraints
The pressurizer model is simplified, energy consumed during operation of the pressurizer is ignored, and only the boosting proportional relation between the air inlet and the air outlet of the pressurizer and the transmission capacity constraint of the pressurizer are reserved.
π j,t ＝Γ c π i,t
In the formula (f) c,t Represents the delivery flow of the pressurizer c; pi i,t And pi j,t Respectively representing the air pressure of the air inlet end and the air outlet end of the pressurizer c; gamma-shaped c 、
Respectively, the boosting ratio and the maximum transmission capacity of the pressurizer c.
5. Energy hub operation constraints
Thermal power supply and demand balance constraint of energy concentrator
Energy concentrator energy conversion unidirectional constraint
Preferably, the embodiment further provides a linear processing method of an integrated energy system optimized operation model established on the basis of the power distribution network and the natural gas network of the energy hub, which includes the following steps:
and step S3: and carrying out linearization treatment on the established optimization model so as to solve the optimization operation model of the comprehensive energy system by means of CPLEX.
And step S4: and solving an optimized operation model of the comprehensive energy system by means of CPLEX.
Namely: and (6) carrying out linearization processing on the established optimization model.
(7) And solving an optimized operation model of the comprehensive energy system by means of CPLEX.
The specific implementation of step S3 is as follows:
the model proposed in step S2 is a comprehensive non-convex problem. In order to solve the problem, before solving the model, a second-order cone relaxation and incremental piecewise linearization method is adopted to convert the original model into a linear problem.
6. Model linearization
1) Second order cone relaxation technique
Because the node power balance constraint contains a nonlinear term, in order to solve the problem, a second-order cone relaxation technology is adopted to simplify the constraint. Introducing a new variable to cancel the voltage-current squared term as shown in the following equation:
the node power balance constraint may eliminate the non-linear quadratic terms of voltage and current as follows:
thus, the voltage and current amplitude constraints can also be modified as:
the third equation for the node power constraint may be further converted to a second order cone equation by relaxation. The specific form is as follows:
2) Incremental piecewise linearization method
The Weymouth steady-state power flow constraint of the pipeline in the natural gas network is a relatively troublesome nonlinear non-convex expression which is difficult to directly solve, and therefore linearization needs to be carried out on the constraint.
First, the nonlinearity due to the squared term of the air pressure in the Weymouth steady-state flow constraint of the pipeline can be eliminated by introducing a new variable, as shown below:
therefore, the pipeline Weymouth steady state power flow constraint can be initially rewritten as:
since sgn p (π i,t ,π j,t ) Is a sign function when i,t Greater than pi j,t If so, 1 is taken, otherwise, 1 is taken. Thus, the left side of the expression can be written as an absolute value expression, i.e. let Y be p,t ＝f p,t |f p,t |。
A non-linearized expression such as f (x) = x | x | the step of incremental piecewise linearization is roughly as follows:
step1, setting a proper number n of segmentation segments according to the characteristics of the built model;
step2, equally dividing the value interval of x by n, thereby obtaining n +1 discrete points, namely x 0 ,x 1 ...x n ；
Step3, calculating a discrete point x 0 ,x 1 ...x n The corresponding function value of f (x);
step4, introducing new auxiliary variables and ensuring that the following constraints are met:
in conjunction with the above approach, the pipeline Weymouth steady state power flow constraint can be ultimately described as:
so far, all the nonlinear terms in the model are converted into linear terms, and the linear terms can be directly solved by a CPLEX solver.
CPlEX is a tool that can efficiently solve the optimization model. Firstly, writing a program in an MATLAB environment according to an optimization model to be solved, wherein a decision variable, an objective function and a linear constraint condition are respectively defined in the program, namely the content of the model which is solved according to the description; then based on this procedure, CPLEX in the YALMIP toolbox is called for efficient resolution.
Firstly, a program is written on the basis of a yalmould tool box through a matlab environment, and a CPLEX optimization solver is called through the yalmould tool box in the solving process to solve the model.
The following is illustrated by specific examples:
the embodiment adopts a comprehensive energy system formed by coupling a 14-node power distribution network and a 20-node natural gas network for simulation analysis. The distribution network has 1 substation node, 7 power load nodes, 8 coupled nodes and 16 lines. The natural gas network has 2 gas source nodes, 10 gas load nodes, 8 coupling nodes and 25 pipelines. It is worth noting that the 8 coupling nodes can not only meet the electrical and gas load requirements, but also supply thermal power. The present embodiment obtains an economic scheduling scheme by simulating 24 hours of operation in a day, targeting the minimum daily operating cost.
The electrical (fig. 3 a), gas (fig. 3 b) and thermal load (fig. 3 c) time sequence curves are shown in fig. 3, the topological graphs of the related examples are shown in fig. 4 and fig. 5, and the Hub node coupling information is shown in table 1.
TABLE 1 correspondence of each Hub unit node and load parameter
Corresponding calculations in connection with the present embodimentFor example, in a power distribution network, the upper and lower limits of the node voltage amplitude (pu) are 1.05 and 0.95, respectively. In the natural gas network, the upper and lower limits of the pipeline gas pressure are 60 and 50bar respectively. Meanwhile, assuming that the efficiency of each energy conversion device of each Hub is the same, the P2G is 75%, the power generation efficiency of the cogeneration is 37%, the heat generation efficiency of the boiler is 96%, and the conversion coefficient of gas to electricity is 0.0096MW/m 3 。
The electricity price and gas price curves and the optimized electricity purchasing quantity and gas purchasing quantity curves of the embodiment of the invention are shown in fig. 6. It can be seen that according to the comprehensive energy system optimization operation model and the linear processing method established by the power distribution network and the natural gas network based on the energy hub provided by the embodiment, under the influence of the change of the electricity price and the gas price shown in fig. 6 (a), the comprehensive energy system can reasonably respond to decide to reasonably purchase the electricity quantity and the gas quantity (as shown in fig. 6 (b)), so that the energy purchase cost can be minimized.
The above description is only a preferred embodiment of the present invention, and all the equivalent changes and modifications made according to the claims of the present invention should be covered by the present invention.
Claims (3)
1. Energy system operation device based on distribution network, natural gas net, its characterized in that: the method comprises the following steps:
step S1: providing an energy hub model capable of coupling a power distribution network and a natural gas network;
step S2: establishing an objective function, and completing modeling of an optimized operation model of the comprehensive energy system according to the safe operation constraints of the power distribution network, the natural gas network and the energy concentrator;
the objective function in step S2 is the energy acquisition cost, which includes the electricity acquisition cost, as shown in the following formula
And the cost of purchasing air>
Total charge for the integrated energy system during the simulated operation scheduleThe lowest use rate is used;
in the formula, TR represents a set of injection power nodes of a substation in a power distribution network; GS represents the set of source nodes in the natural gas network;
respectively representing unit electricity price and gas price in a time period t; />
Injecting the purchase electric quantity of the power node j into the transformer substation in the time period t; />
The gas purchasing quantity of the gas source node j in the time period t is shown;
in the step S2, the power distribution network safe operation constraint comprises the following steps: node power balance constraint, node voltage amplitude constraint, distribution line maximum current-carrying capacity constraint and transformer substation power constraint;
the node power balance constraint is:
in the formula, r ij 、x ij The resistance and reactance of the branch ij are respectively; δ (j) represents a set of end nodes of a branch having j as a head node, and π (j) represents a set of end nodes having j as a head nodeA set of head-end nodes of a branch of the end node; p ij,t 、Q ij,t The active power and the reactive power of the branch ij are respectively;
representing the active power of the electrical load; />
Respectively representing the active power output for electrical conversion of the P2G device in Hub; />
Representing the equivalent active power injected into the distribution network by the CHP device in Hub; />
Respectively representing the reactive power values of main network output and power load;
the node voltage amplitude constraint is:
U min ≤U j,t ≤U max
in the formula of U j,t 、U min And U max The node voltage amplitude and the lower limit and the upper limit thereof are respectively;
the maximum ampacity constraint of the distribution line is as follows:
0≤I ij,t ≤I max
in the formula I ij,t 、I max The branch current amplitude and the upper limit thereof are respectively;
the power constraint of the transformer substation is as follows:
the specific content of restricting the natural gas network in the step S2 is as follows:
node airflow balance constraint:
in the formula, σ (jk) represents a pipeline set with j as a head end node; mu (ij) respectively represents a pipeline set taking j as an end node; f. of p,t 、f l,t The flow rates of the pipelines p and l are shown;
respectively the gas load and the gas source node gas output; />
Respectively representing the natural gas amount used for GF and CHP energy conversion in Hub; />
Representing the equivalent natural gas injection amount for electrically converting the P2G device in the Hub into gas;
and (3) gas output restriction of a natural gas source:
natural gas produced from a gas well needs to be refined by a refinery, and due to the limitations of equipment capacity and gas pressure at the gas well, the gas output of a natural gas source per unit time should meet the following constraints:
in the formula (I), the compound is shown in the specification,
respectively outputting the upper limit and the lower limit of the natural gas quantity for the gas source j;
and (3) node air pressure constraint:
the gas pressure of each node of the natural gas network must be maintained within a safe and reasonable operation range, and the mathematical expression is as follows:
in the formula (I), the compound is shown in the specification,
respectively representing the upper and lower limit values of the air pressure at the node i;
and (3) steady-state flow constraint of a natural gas pipeline Weymouth:
a Weymouth steady-state trend model is adopted to depict the relation between natural gas flow and air pressure at two ends, and the specific expression is as follows:
wherein the content of the first and second substances,
in addition, the flow of the pipeline is ensured to be within a safe and reasonable operation range:
in the formula (f) p,t Represents the natural gas stream flowing through the pipeline p; pi i,t And pi j,t Respectively indicating the air pressure at two ends of the pipeline p; phi is a p Representing the gas flow transmission parameter of the pipeline p; sgn p Indicating the flow direction of the gas flow in the pipeline p;
represents the maximum pipe transmission capacity;
pressurizer boost relationship constraints:
π′ j,t ＝Γ c π′ i,t
in the formula (f) c,t Showing pressurizers cA transport gas stream; pi' i,t And pi' j,t Respectively representing the air pressure of the air inlet end and the air outlet end of the pressurizer c; gamma-shaped c 、
The boosting ratio and the maximum transmission capacity of the pressurizer c are respectively;
the operation constraint of the energy hub in the step S2 is as follows:
the thermal power supply and demand balance constraint of the energy concentrator is as follows:
energy conversion unidirectional constraint of the energy concentrator:
2. the power distribution network, natural gas network based energy system operation apparatus of claim 1, comprising the steps of:
and step S3: carrying out linearization processing on the model established in the step S2;
and step S4: and (4) solving the model after linearization processing in the step (S3) by using a CPLEX solver.
3. The power distribution network, natural gas network-based energy system operation device of claim 2, wherein: the specific content of the step S3 is as follows: converting the model by adopting a second-order cone relaxation and incremental piecewise linearization method to carry out linearization treatment;
because the node power balance constraint contains a nonlinear term, the constraint is simplified by adopting a second-order cone relaxation method, and a new variable is introduced to eliminate a voltage and current square term, which is shown as the following formula:
the node power balance constraint may cancel the non-linear quadratic terms of voltage and current as follows:
thus, the voltage, current amplitude constraint is modified to:
the third formula of the node power constraint is further converted into a second-order conical form through relaxation; the specific form is as follows:
linearization is carried out on the Weymouth steady-state flow constraint of the pipeline in the natural gas network by adopting an increment piecewise linearization method, nonlinearity caused by a square term of air pressure in the Weymouth steady-state flow constraint of the pipeline is eliminated by introducing a new variable, and the method is specifically shown as follows:
therefore, the pipeline Weymouth steady state power flow constraint can be initially rewritten as:
due to sgn p (π i,t ,π j,t ) Is a symbolic function when i,t Greater than pi j,t Taking 1 when the current value is zero, or taking-1 when the current value is zero; thus, writing the left side of the expression as an absolute value expression, i.e. let Y be p,t ＝f p,t |f p,t L; i.e. Y p,t ＝f p,t |f p,t I can also be expressed as a non-linearized expression of f (x) = x | x | the steps of incremental piecewise linearization are as follows:
step SA, setting average subsection number n according to the established model;
step SB, equally dividing the value interval of x into n, thereby obtaining n +1 discrete points, namely x 0 ,x 1 ...x n ；
Step SC, calculating discrete point x 0 ,x 1 ...x n The corresponding function value of f (x);
step SD, introducing a new auxiliary variable and ensuring that the following constraints are met:
in conjunction with the above method, the pipeline Weymouth steady state power flow constraint is ultimately described as:
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