CN115481883A - Electrical coupling system safety analysis method based on improved iterative jacobian matrix - Google Patents
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Abstract
The invention discloses an electric coupling system safety analysis method based on an improved iterative jacobian matrix, which comprises the following steps: establishing steady-state models of a natural gas system and a power system; establishing an expected running state set of each gas source; extracting an expected running state of a natural gas source, and calculating a corresponding natural gas network steady-state load flow; evaluating and sequencing all the obtained steady-state tide results by using a static safety index of the gas network; determining dangerous working conditions, and carrying out the next static safety evaluation; extracting expected accidents of the power grid for simulation, and calculating the steady-state power flow of the power grid after the accidents occur; evaluating all power grid steady-state use power grid static safety indexes after expected accidents and sequencing according to the size of the indexes; generating an expected accident sequencing table of the electric-gas coupling system; it is determined whether the system passes security checks. According to the invention, different expected accident sets and static safety evaluation index systems are set according to the operation difference of the power system and the natural gas system, so that static safety evaluation can be effectively carried out on the electricity-gas coupling system.
Description
Technical Field
The method relates to electric safety analysis, in particular to an electric coupling system safety analysis method based on an improved iteration Jacobian matrix.
Background
The continuous development and application popularization of the gas power generation technology and the gradual maturity of the power-to-gas (P2G) technology make the connection between the gas system and the power system increasingly tight. The gas turbine set is an adjusting power supply which is flexible in operation and high in power generation efficiency, redundant electric energy can be converted into hydrogen or methane by an electricity-to-gas technology for storage and utilization, energy conversion of the gas power generation and electricity-to-gas technology and space-time translation characteristics of the storage in the gas network provide a new way for absorbing renewable energy and stabilizing the peak-valley difference of the power grid, a mode of fusion development of natural gas power generation and new energy power generation is more and more important, and energy interconnection gradually becomes a future development trend of China along with technical progress and market development.
The safety of the power system or the gas system is directly related to the development of social economy and the stability of national life, and the electric-gas coupling system has the complex characteristics of the gas system and the power system, so that accidents are more various, and the operation safety of the electric-gas coupling system is more necessary to be paid attention to. In the past, an electric power system and a natural gas system are two mutually independent energy systems, but as the coupling degree between the two is continuously improved, an electric-gas coupling system comprising the electric power system, the natural gas system and the like is gradually the leading edge of research. The static safety analysis is carried out on the electric-gas coupling system, and the capability of the system for continuously providing service after the system suffers from sudden accident disturbance to cause element failure can be obtained.
The electric-gas coupling network safety analysis method firstly needs to perform steady-state modeling on an electric power system and a natural gas system, analyzes various element accident characteristics of the electric-gas coupling network in different operation scenes on the basis of the model, evaluates the safety degree of the system through a static safety index, and performs sequencing according to the severity of accident consequences to form a predicted accident sequencing table so as to play a role in guiding power grid operation and planning personnel.
For a coupling system composed of a power system and a natural gas system, the number of methods for carrying out static safety analysis on the coupling system is small at present, and a method close to the actual situation is urgently needed for evaluating the coupling system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an electric coupling system safety analysis method based on an improved iterative jacobian matrix, sets different expected accident sets and static safety evaluation index systems aiming at the operation difference of an electric system and a natural gas system, performs static safety analysis on the electric-gas coupling system based on the improved iterative jacobian matrix, and can effectively perform static safety evaluation on the electric-gas coupling system.
The purpose of the invention is realized by the following technical scheme: an electric coupling system safety analysis method based on an improved iteration jacobian matrix comprises the following steps:
step S1: establishing steady-state models of a natural gas system and a power system;
step S2: establishing an expected running state set of each gas source by considering the characteristics and technical conditions of a natural gas system pipe network;
and step S3: extracting an expected running state of a natural gas source, and calculating a corresponding natural gas network steady-state flow;
and step S4: evaluating all obtained steady-state tide results by using a static safety index of the air network, and sequencing according to the size of the index;
step S5: taking the expected running states of the first 60% of the sequences in the natural gas system as dangerous working conditions, and substituting the running states of the coupling elements under each steady-state trend into the power system to carry out the next static safety evaluation;
step S6: the method comprises the steps of simulating an expected accident of a power grid extracted by a power system substituted into different coupling element states, and calculating a steady-state power flow of the power grid after the accident occurs;
step S7: evaluating all power grid steady-state used power grid static safety indexes after the expected accident and sequencing according to the size of the indexes;
step S8: generating an expected accident sequencing list of the electric-gas coupling system according to the accident sequencing;
step S9: and analyzing the anticipated accidents with the front rank by using a precision trend algorithm to determine whether the tested system passes the safety check.
The beneficial effects of the invention are: (1) Considering that the Weymouth equation has absolute values and sign functions, the iterative format is difficult to derive by directly using the cow-pulling method, and the pipeline flow direction can be obtained only by judging the air pressure difference during programming, which is not beneficial to programming. The invention replaces the sign function and the absolute value by adopting an equivalent format, deduces the derivation process by using a Newton method on the format, and has simple iterative Jacobian matrix element calculation formula and easy programming after the derivation.
(2) Compared with an N-1 accident set of an electric power system, the N-1 accident set of a gas network pipeline is established, and in practice, for a large part of a network system of a natural gas network, the topological structure is relatively simple and is a special case of a branched network, the consequence caused by disconnection of topological branches is serious, and the fault is avoided to the utmost extent. In the selection of the expected accident set at the gas network side, the invention establishes an applicable expected accident set according to the characteristics of the natural gas system, rather than moving the power system mode. And accordingly, static safety check of the electric-gas coupling system is completed.
(3) And respectively establishing indexes on the air network side and the power network side according to the operation characteristics of the system. The gas network side index meter can comprehensively evaluate accidents according to the state of the gas turbine unit, the node gas pressure and the residual gas supply capacity of the system.
Drawings
FIG. 1 is a flow chart of the generation of an expected incident ranking table according to the present invention;
FIG. 2 is a schematic diagram of interval division for calculating an air pressure up/down shift indicator;
FIG. 3 is a static safety index system diagram of the gas-electric coupling system.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
The invention sets different expected accident sets and static safety evaluation index systems aiming at the operation difference of an electric power system and a natural gas system, provides an electric-gas coupling system static safety analysis method considering the improved iteration Jacobian matrix, can effectively perform static safety evaluation on the electric-gas coupling system, removes sign functions and absolute values in an equation, and changes the equation into a form more beneficial to derivation. And a method for solving the air network trend by using the Newton method is deduced. Meanwhile, an applicable expected accident set is established according to the characteristics of the natural gas system, but not according to the mode of the power system. And thus completing static security check of the electric-gas coupling system, specifically:
as shown in fig. 1, the method for analyzing the safety of the electrical coupling system based on the improved iterative jacobian matrix is characterized in that: the method comprises the following steps:
step S1: establishing steady-state models of a natural gas system and a power system;
step S2: establishing an expected running state set of each gas source by considering the characteristics and technical conditions of a natural gas system pipe network;
and step S3: extracting an expected running state of a natural gas source, and calculating a corresponding natural gas network steady-state load flow;
and step S4: evaluating all obtained steady-state tide results by using a static safety index of the air network, and sequencing according to the size of the index;
step S5: the method comprises the following steps of (1) regarding the expected running states of the first 60% of the sequences in the natural gas system as dangerous working conditions, and substituting the running states of coupling elements (P2G stations and gas turbine units) under each steady-state tide into the power system to carry out the next static safety evaluation;
step S6: the method comprises the following steps of simulating an expected accident of the power grid extracted by the power system with different coupling element states substituted, and calculating the steady-state power flow of the power grid after the accident occurs;
step S7: evaluating all power grid steady-state used power grid static safety indexes after the expected accident and sequencing according to the size of the indexes;
step S8: generating an expected accident sequencing table of the electric-gas coupling system according to the accident sequencing;
step S9: and analyzing the anticipated accidents with the front rank by using a precision trend algorithm to determine whether the tested system passes the safety check.
Further, the specific method of step 1 is: in a steady-state model of a natural gas system, natural gas common pipe flow is expressed by using a Weymouth equation, and the method performs equivalent expression on a symbolic function in the Weymouth equation, so that the pipe flow direction does not need to be considered during programming, the generation of a jacobian matrix in each iteration of a Newton-Raphson method is simplified, and the compressor pipe flow is expressed by using a pressurization equation; the power system is modeled using a conventional ac steady state model. Two system steady state modeling methods are represented as follows:
steady state models for natural gas systems include normal pipe flow models and compressor models:
wherein, the establishment process of the common pipe flow model comprises the following steps:
a1, regarding a starting point, a collection point, an end point of natural gas flow in a natural gas system and connection points of different pipelines as gas network nodes, and expressing each node i as:
in the formula: n is the number of nodes connected with the node i; q ij Is the flow from i node to j node, if this value is negative, then the direction is opposite to the assumed direction; d i And S i Demand and air supply at node i, respectively;
the flow rate Q of the pipeline is calculated by the Weymouth equation ij Expressed as:
p i and p j Respectively the air pressure of the first node and the last node; sgn (p) i ,p j ) Is a symbolic function when p i Greater than p j The value is 1 when the current value is larger than the value, and is-1 when the current value is smaller than the value; c ij For the pipeline constants, the calculation is as follows:
in the formula: d ij Is the inner diameter of the pipeline, and the unit is mm; t is the natural gas temperature in K; epsilon is the absolute roughness of the pipeline, and the unit is mm; delta is the ratio of the density of the gas in the pipeline to the density of the air; z is the gas compressibility;
a2, sign-pair function sgn (p) i ,p j ) Equivalent substitution is carried out, and the process of generating the Jacobian matrix is deduced:
the sign function equivalent is expressed as:
then the pipe flow Q between node i and node j ij The formula is deformed as:
and (3) deriving a generation method of the Jacobian matrix:
the node flow equation is expressed in general form:
Q SP ＝Q(p) (7)
wherein Q is SP Injecting a natural gas flow into the node; q is Q SP A functional expression between the corresponding physical quantity and the node voltage; p is the node air pressure, the above equation is written as the flow deviation:
f(p)＝Q SP -Q(p)＝0 (8)
solving based on a Newton-Raphson method: at a given initial value of p (0) The first order Taylor expansion of equation (8) is performed:
definition of
Jacobian matrix, J, being the gas network flow equation 0 Is J at p (0) The values of (b) are then:
correction of p by Δ p (0) Obtaining new value of p, expressing iteration times by k, writing general expression including
Node-arranged natural gas injection flow Q SP The positive direction is that the inflow node is positive, namely the left side of the equation is the injection flow of each node, the right side is the flow relation with other nodes, the sum of each row on the right side of the equation is the outflow flow of each node, and the pipeline flow Q is used ij Expressed as:
Q i injection flow for node i, Q ij For the pipe flow Q between the node i and the node j ij
The above equation is expressed in terms of flow deviation as:
due to Q SP For a constant column vector, deriving f (p) from p is equivalent to deriving-Q (p) in equation (13), then the jacobian matrix is:
and also
The iteration format is then:
and A3, further deducing the calculation of elements in the Jacobian matrix:
according to the branch flow formula, node Q i Expressed as:
then
Due to the right side elements of the formulas (18) and (19)
And
the method for generating all elements of the Jacobian matrix can be obtained only by deducing the calculation formulas of the two, and the specific process is as follows:
A31、
derivation of
The branch flow formula is as follows:
is provided with
Then
This gives:
and then
Let t = p i -p j And δ t = δ p i Then, there are:
when p is i ＞p j Time-piece
When p is i ＜p j Time of flight
Will find out
And
are respectively substituted into
When p is i ＞p j Time-piece
When p is i ＜p j Time-piece
A32、
Of (2)
Is provided with
Then
This gives:
and then
Let t = p j -p i And δ t = δ p j Then, there are:
when t > 0, i.e. p j ＞p i Time of flight
When t < 0, i.e. p j ＜p i Time of flight
Finishing to obtain:
when p is j ＞p i Time of flight
When p is j ＜p i Time of flight
Will find out
And
are respectively substituted into
To obtain
When p is j ＞p i Time of flight
When p is j ＜p i Time of flight
And (4) finishing the results:
from the symmetry:
in the embodiments of the present application, the correctness of the above derivation result has been verified by using a full derivative method, which is not described herein again.
In summary, the general pipe flow model iteration format
The jacobian matrix J of (a) is:
diagonal elements in jacobian matrix
And off-diagonal elements
The calculation formula is as follows:
the establishment process of the compressor model comprises the following steps:
determining the gas loss equation and the gas pressure relation entering the compressor as follows:
in the formula: q in And p in Respectively, total natural gas flow into the compressor; q com And p com Respectively the natural gas flow and the gas pressure of the natural gas flowing out of the compressor after being pressurized; q cp Natural gas flow consumed for the compressor; k is the air pressure transformation ratio。
Expressing natural gas flow Q consumed by a compressor using a compressor boost equation cp ：
In the formula: k is the air pressure transformation ratio; q in Is the natural gas flow entering the compressor; the energy source driving the compressor is natural gas flowing through the compressor; t is gas Is the natural gas temperature; h gas Is the heat value of natural gas; alpha is a polytropic exponent;
due to Q removal cp And Q in The other indices are constants in addition to the two variables, and for simplicity of representation, the above equation is written as:
Q cp ＝M·Q in (49)
the gas loss equation and gas pressure relationship for the compressor becomes a more concise form as follows:
the above equation is written in the form of a bias equation:
f(Q)＝Q com -(1-M)·Q in
f(p)＝p com -k·p in (52)
the iteration format of the newton-raphson method is:
further, in step S1, when the steady-state model of the system is established, a traditional alternating-current steady-state model in a polar coordinate system is used for modeling:
wherein, P i Injecting active power, Q, for a node i Injecting reactive power, U, for the node i Is the voltage amplitude of node i, G ij And B ij Respectively the conductance and susceptance of the branch between node i and node j.
The specific method of the step 2 comprises the following steps: the expected accidents of the natural gas system are fluctuation and supply interruption of the gas source, and the gas source is divided into two types according to the operating characteristics. For a large part of network systems of a natural gas pipe network, the topological structure is relatively simple and is a special case of a dendritic pipe network, the consequence caused by disconnection of topological branches is serious, such faults are avoided to the utmost extent, and with the improvement of gas transmission technology, a standby pipeline is put into use when a main pipeline is disconnected, so that the topological structure is not changed after the pipeline is disconnected, in addition, patrol staff use equipment to monitor gas leakage along the pipeline, and the possibility of the change of the topological structure of the natural gas network caused by the pipeline fault is very little. At present, the accident of the natural gas system is mainly that the gas supply of an upstream branch transmission station is reduced or cut off due to program misoperation, and the fault lasts for about several minutes to more than ten minutes. China is a country lacking 'gas' as a whole, and compared with industrial gas and power generation gas, natural gas is prior to supply to people. For example, when the gas consumption in Beijing city is short, a Huaneng gas unit is shut down and a thermal power unit is started to ensure the life of gas consumption of people. The operation of the gas turbine is easily affected when the natural gas source fluctuates or the gas supply is stopped. It is therefore meaningful and practical to establish a set of anticipated incidents of a natural gas system.
Two modes are considered for different gas source types, one mode is an external gas source conveyed through a pipeline, and the gas supply range has a lower limit and an upper limit; the other type of gas source is a gas storage tank type gas source, which is commonly found in an LNG (liquefied natural gas) gasification station, a P2G station and a natural gas storage and distribution station, and the lower gas supply limit of the gas storage tank type gas source is considered to be 0, namely the gas supply range is a complete interval from 0 to the upper gas supply limit. 10 operating states can be selected at equal intervals within the air supply range of the two air sources for analysis. The set of expected operating states is the natural gas flow rate supplied by each natural gas source in unit time after an expected accident occurs. The selection of the operation state is envisioned as a specific step of the specific step 2.
In the embodiment of the application, 2A-type gas sources are assumed as examples, the gas supply intervals are 4.6-10 scm/day and 3.5-8 scm/day respectively, the 3B-type gas sources are provided, and the upper gas supply limits are 3.6, 2.7 and 2.34scm/day respectively. The gas supply condition of the gas source of the natural gas system is expected to be:
table 1 gas source forecast supply status example for natural gas system
In the step S3, the selected operation state of each gas source is extracted first, and the gas network steady-state model established in the step S1 is used to perform load flow calculation.
The step S4 includes: calculating static safety indexes of the operation conditions of each natural gas system and sequencing the danger degrees according to the static safety indexes, wherein the static safety evaluation index system and the calculation method of the natural gas system comprise the following steps:
s401, calculating the percentage of gas supply reduction in gas power generation
The gas power plant is a coupling element for connecting a gas network and a power grid, the gas network fault can influence the operation of the power grid through a gas unit, the gas supply of the gas power plant is reduced, the generated energy and the theoretical upper limit of power generation can be reduced, the gas unit is taken as a typical frequency modulation unit and represents the adjusting capacity of the power grid, and the index is used for describing the existing adjusting capacity of the power grid:
in the formula: ng is the number of gas units; delta Q Gas,n The gas supply reduction amount of the gas unit n caused by the gas network fault is reduced;
the upper limit of the gas supply requirement of the gas unit n;
s402, calculating air pressure up/down deviation indicator
As shown in fig. 2, for node air pressure in normal operation
Respectively to the upper limit of the air pressure
And lower limit of
The interval of (2) is divided, the interval within plus or minus 40% of the deviation of the normal air pressure distance upper and lower limits is a safety interval, the interval within plus or minus 40% of the deviation is an alarm interval, and air pressure data in the alarm interval is recorded into an air pressure deviation index:
in the formula: npr and npd are the number of air network nodes of which the air pressure is shifted upwards and downwards to enter the alarm region after the fault respectively; p is a radical of i The air pressure of the node i after the fault occurs;
and
alarming air pressure for the fault of the node i;
and
the upper limit and the lower limit of the air pressure operation of the node i are set;
s403, calculating flexible adjustment capability index of system
The gas storage tank is a container for storing gas in urban gas supply engineering, is commonly used in an LNG (liquefied natural gas) gasification station, a P2G (plant gas) station and a natural gas storage and distribution station, is an important element for realizing emergency peak regulation of natural gas, is used as a gas source capable of flexibly supplying gas in a gas supply interval, and the gas supply quantity of the gas storage tank represents the regulation capacity in an emergency state of a gas network. The gas network is used as a fluid network, natural gas can be stored in the gas transmission pipeline network, and in the steady-state modeling, the natural gas flow conservation flowing into and out of the gas network is considered, so that the gas storage capacity of the natural gas pipeline is not calculated into the regulation capacity index. The index physical meaning is that when the gas supply reduction occurs in the gas source, the percentage of the gas supply reduction which can be counteracted theoretically only by the self-regulating capacity of the natural gas is as follows:
in the formula: nf is the number of the gas storage tanks which can be operated after the natural gas system fails;
the maximum air supply quantity of the ith air storage tank; q h.i The current air supply quantity of the ith air storage tank; q c The gas supply amount of a natural gas system is reduced due to failure.
S404, the method for calculating the comprehensive static safety index of the natural gas system comprises the following steps:
PI gas ＝λ s PI s +λ pr PI pr +λ pd PI pd -λ f PI f (60)
in the formula, λ s 、λ pr 、λ pd And λ f Respectively, the weight coefficients of the indexes. Gas-electric couplingThe system static security index system diagram is shown in fig. 3.
The specific method of the step 5 comprises the following steps: and according to the size of the comprehensive static safety index of the natural gas system, considering the expected running state of 60 percent of the natural gas system in the first sequence as a dangerous working condition. The P2G station and the gas unit are used as a coupling element for connecting a natural gas system and a gas load and a power system. According to the steady-state tidal current result of the natural gas, the running states of the coupling elements (the P2G station and the gas turbine set) under all dangerous working conditions are substituted into the power system to carry out the next static safety evaluation.
In the step S6, an expected accident of the power system is extracted to analyze the power grid side in the coupling state, a one-time iterative solution of the steady-state power flow of the power grid after the accident is calculated, and the expected accident of the power system considers the on-off simulation of the line and the on-off simulation of the generator.
The step S7 includes:
calculating the static safety index of the power system after each expected accident and sequencing the danger degree according to the static safety index: in order to overcome the shielding phenomenon, the power grid index adopts a behavior index, PI, only containing out-of-limit information P Active power behavior index, PI, for measuring the degree of line active power overload V In order to measure the voltage behavior index of the voltage overload degree, the calculation method comprises the following steps:
in the formula, PI P,l Is an active power behavior index of the line l, and represents the severity of line tidal current out-of-limit under various cut-off conditions, omega l Is the weight of the line l, nl is the total number of lines in the current running state of the system, P l For the active power flow of line l, P l,max Is the active power limit of line l;
in the formula, PI V,i Is an index of the voltage amplitude behavior of node i, ω i Is the weight of node i, nb is the total number of nodes in the system, U i Is the voltage amplitude of node i, U i,max 、U i,min Respectively are the upper and lower limit values of the voltage amplitude of the node i;
the method for calculating the comprehensive static safety index of the power system comprises the following steps:
PI power ＝λ P PI P +λ V PI V (65)
in the formula of lambda P And λ V The weight coefficients are the active power behavior index and the voltage behavior index respectively.
In the step S8, an expected accident ranking table of the electric-pneumatic coupling system is generated according to the accident ranking obtained in the step S7, and each accident corresponds to one air network operation state and one power network disconnection accident.
The step S8 includes: and analyzing expected accidents ranked in the front by using a precise power flow algorithm, determining whether the tested electric-gas coupling system passes safety check, and in order to ensure the rapidity of screening the expected accidents, adopting an iterative solution instead of an accurate solution as a steady-state power flow result of the power system in the step S6, wherein the result is obtained by calculating according to the maximum load, each load peak value has distribution time in practice, so that the result has greater safety redundancy, the screened dangerous accidents need to be checked by using the precise algorithm, and an operator analyzes whether the electric-gas coupling system passes static safety analysis according to the checked result.
While the foregoing description shows and describes a preferred embodiment of the invention, it is to be understood, as noted above, that the invention is not limited to the form disclosed herein, but is not intended to be exhaustive or to exclude other embodiments and may be used in various other combinations, modifications, and environments and may be modified within the scope of the inventive concept described herein by the above teachings or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. The electrical coupling system safety analysis method based on the improved iterative jacobian matrix is characterized by comprising the following steps: the method comprises the following steps:
step S1: establishing steady-state models of a natural gas system and a power system;
step S2: establishing an expected running state set of each gas source by considering the characteristics and technical conditions of a natural gas system pipe network;
and step S3: extracting an expected running state of a natural gas source, and calculating a corresponding natural gas network steady-state load flow;
and step S4: evaluating all obtained steady-state tide results by using a static safety index of the air network, and sequencing according to the size of the index;
step S5: taking the expected running states of the first 60% of the sequences in the natural gas system as dangerous working conditions, and substituting the running states of the coupling elements under each steady-state trend into the power system to carry out the next static safety evaluation;
step S6: the method comprises the following steps of simulating an expected accident of the power grid extracted by the power system with different coupling element states substituted, and calculating the steady-state power flow of the power grid after the accident occurs;
step S7: evaluating all power grid steady-state use power grid static safety indexes after expected accidents and sequencing according to the size of the indexes;
step S8: generating an expected accident sequencing table of the electric-gas coupling system according to the accident sequencing;
step S9: and analyzing the expected accidents with the top rank by using a precision trend algorithm to determine whether the tested system passes the security check.
2. The improved iterative jacobian matrix-based safety analysis method for the electric coupling system according to claim 1, wherein: the coupling element under the steady state tide comprises a P2G station and a gas turbine set; the top ranked forecast accidents refer to the top 30% ranked forecast accidents.
3. The improved iterative jacobian matrix-based electrical coupling system safety analysis method of claim 1, wherein: in the step S1, the steady-state model of the natural gas system includes a common pipe flow model and a compressor model:
wherein, the establishment process of the common pipe flow model comprises the following steps:
a1, regarding a starting point, a collection point and a terminal point of natural gas flow in a natural gas system and connection points of different pipelines as gas network nodes, and according to a node mass conservation equation, expressing each node i as:
in the formula: n is the number of nodes connected with the node i; q ij Is the flow from node i to node j, if this value is negative, the opposite direction is assumed; d i And S i Demand and air supply at node i, respectively;
the flow rate Q of the pipeline is calculated by the Weymouth equation ij Expressed as:
p i and p j Respectively the air pressure of the first node and the last node; sgn (p) i ,p j ) Is a sign function when p i Greater than p j The value is 1 when the current value is larger than the value, and is-1 when the current value is smaller than the value; c ij For the pipeline constants, the calculation is as follows:
in the formula: d ij Is the inner diameter of the pipeline, and the unit is mm; t is the natural gas temperature in K; epsilon is the absolute roughness of the pipeline, and the unit is mm; delta is the ratio of the gas density in the pipeline to the air density; z is the gas compressibility;
a2, sign-pair function sgn (p) i ,p j ) Equivalent substitution is carried out, and the process of generating the Jacobian matrix is deduced:
the sign function equivalent is expressed as:
then the pipe flow Q between node i and node j ij The formula is modified as follows:
a generation method of a derived Jacobian matrix comprises the following steps:
the node flow equation is expressed in general form:
Q SP ＝Q(p) (7)
wherein Q is SP Injecting a natural gas flow into the node; q is Q SP A functional expression between the corresponding physical quantity and the node voltage; p is the node air pressure, writing the above equation as a form of flow deviation:
f(p)＝Q SP -Q(p)＝0 (8)
solving based on a Newton-Raphson method: at a given initial value of p (0) The first order Taylor expansion of equation (8) is performed:
definition of
Jacobian matrix, J, being the gas network flow equation 0 Is J at p (0) The values of (b) are then:
correction of p by Δ p (0) Obtaining new value of p, expressing iteration times by k, writing general expression including
Natural gas flow Q injected by node SP The positive direction is that the inflow node is positive, namely the left side of the equation is the injection flow of each node, the right side is the flow relation with other nodes, the sum of each row on the right side of the equation is the outflow flow of each node, and the pipeline flow Q is used ij Expressed as:
Q i injection flow for node i, Q ij For the pipe flow Q between the node i and the node j ij
The above equation is expressed in terms of flow deviation as:
due to Q SP For a constant column vector, the derivation of f (p) with respect to p is equivalent to the derivation of-Q (p) with respect to p in equation (13), then the jacobian matrix is:
diagonal elements in jacobi matrix
And off diagonal elements
The calculation formulas are formulas (15) and (16):
the process of establishing the compressor model comprises the following steps:
determining the gas loss equation and the gas pressure relation entering the compressor as follows:
in the formula: q in And p in Respectively, total natural gas flow into the compressor; q com And p com Respectively the natural gas flow and the gas pressure of the natural gas flowing out of the compressor after being pressurized; q cp Natural gas flow consumed for the compressor; k is the air pressure variation ratio.
Method for expressing natural gas flow Q consumed by compressor by using compressor supercharging equation cp ：
In the formula: k is the air pressure transformation ratio; q in Is the natural gas flow entering the compressor; the energy source driving the compressor is natural gas flowing through the compressor; t is gas Is the natural gas temperature; h gas Is the heat value of natural gas; alpha is a polytropic exponent;
due to Q removal cp And Q in For simplicity, the above equation is written as:
Q cp ＝M·Q in (19)
the gas loss equation and gas pressure relationship for the compressor becomes a more compact form as follows:
the above equation is written in the form of a deviation equation:
the iteration format of the newton-raphson method is:
4. the improved iterative jacobian matrix-based electrical coupling system safety analysis method of claim 1, wherein: in step S1, when the steady-state model of the system is established, a traditional alternating-current steady-state model under a polar coordinate system is used for modeling:
wherein, P i Injecting active power, Q, for a node i Injecting reactive power, U, for the node i Is the voltage amplitude of node i, G ij And B ij Respectively, the conductance and susceptance of the branch between the node i and the node j.
5. The improved iterative jacobian matrix-based safety analysis method for the electric coupling system according to claim 1, wherein: in the step S2, the expected accidents of the natural gas system are set as the fluctuation and the supply interruption of the gas source, and the gas source is divided into two types according to the operation characteristics:
one is an external gas source delivered through a pipeline, and the gas supply range has a lower limit and an upper limit; the other is a gas storage tank type gas source, the lower gas supply limit is considered to be 0, namely the gas supply range is a complete interval from 0 to the upper gas supply limit, and 10 operation states are selected at equal intervals in the gas supply ranges of the two gas sources for analysis;
the set of the expected operation states is the natural gas flow supplied by each natural gas source in unit time after an expected accident occurs.
6. The improved iterative jacobian matrix-based safety analysis method for the electric coupling system according to claim 1, wherein: in the step S3, firstly, the selected operation state of each gas source is extracted, and the gas network steady-state model established in the step S1 is used for load flow calculation: namely, a steady-state model is established based on the formulas (6) and (17), the model is solved by using a bovine-derived-method, and the calculation modes of Jacobian matrixes in the bovine-derived-method are respectively the formulas (14) and (23).
7. The improved iterative jacobian matrix-based safety analysis method for the electric coupling system according to claim 1, wherein: and S4, calculating static safety indexes of the operation conditions of all the natural gas systems and sequencing danger degrees according to the static safety indexes, wherein the static safety evaluation index system and the calculation method of the natural gas systems comprise:
s401, calculating the percentage of gas supply reduction in gas power generation
The gas power plant is a coupling element for connecting a gas network and a power grid, the gas network fault can influence the operation of the power grid through a gas unit, the gas supply of the gas power plant is reduced, the generated energy and the theoretical upper limit of power generation can be reduced, the gas unit is taken as a typical frequency modulation unit and represents the adjusting capacity of the power grid, and the index is used for describing the existing adjusting capacity of the power grid:
in the formula: ng is the number of gas turbine units; delta Q Gas,n The gas supply reduction amount of the gas unit n caused by the gas network fault is reduced;
is the upper limit of the gas supply requirement of the gas unit n;
s402, calculating an air pressure up/down deviation indicator
For node air pressure in normal operation
Respectively to the upper limit of the air pressure
And lower limit
The interval of (2) is divided, the interval within plus or minus 40% of the deviation of the upper and lower limits of the normal air pressure distance is a safety interval, the deviation within plus or minus 40% is an alarm interval, and the air pressure data in the alarm interval is counted into an air pressure deviation index:
in the formula: npr and npd are the number of air network nodes of which the air pressure is shifted upwards and downwards to enter the alarm region after the fault respectively; p is a radical of i The air pressure of the node i after the fault occurs;
and
alarming the air pressure for the fault of the node i;
and
the upper limit and the lower limit of the air pressure operation of the node i are set;
s403, calculating flexible adjustment capability index of system
The index physical meaning is that when the gas supply reduction of the gas source occurs, the percentage of the gas supply reduction which can be offset theoretically only by the self-regulating capacity of the natural gas is as follows:
in the formula: nf is the number of the gas storage tanks which can be operated after the natural gas system fails;
the maximum air supply quantity of the ith air storage tank; q h.i The current air supply quantity of the ith air storage tank; q c Is a natural gas system reasonThe amount of air supplied is reduced by a failure.
S404, the method for calculating the comprehensive static safety index of the natural gas system comprises the following steps:
PI gas ＝λ s PI s +λ pr PI pr +λ pd PI pd -λ f PI f (30)
in the formula, λ s 、λ pr 、λ pd And λ f Respectively, the weight coefficients of the indexes.
8. The improved iterative jacobian matrix-based safety analysis method for the electric coupling system according to claim 1, wherein: in the step S6, an expected accident of the power system is extracted to analyze the power grid side in the coupling state, a one-time iterative solution of the steady-state power flow of the power grid after the accident is calculated, and the expected accident of the power system considers the on-off simulation of the line and the on-off simulation of the generator.
9. The improved iterative jacobian matrix-based electrical coupling system safety analysis method of claim 1, wherein: the step S7 includes:
calculating the static safety index of the power system after each expected accident and sequencing the danger degree according to the static safety index: in order to overcome the shielding phenomenon, the power grid index adopts a behavior index, PI, only containing out-of-limit information P Active power behavior index, PI, for measuring the degree of line active power overload V In order to measure the voltage behavior index of the voltage overload degree, the calculation method comprises the following steps:
in the formula, PI P,l Is an index of the active power behavior of the line l,characterizing the severity of line tidal current overrun, ω, under various cut-off conditions l Is the weight of the line l, nl is the total number of lines in the current running state of the system, P l For the active power flow of line l, P l,max Is the active power limit of line l;
in the formula, PI V,i Is the voltage amplitude behavior index of node i, ω i Is the weight of node i, nb is the total number of nodes in the system, U i Is the voltage amplitude of node i, U i,max 、U i,min Respectively are the upper and lower limit values of the voltage amplitude of the node i;
the method for calculating the comprehensive static safety index of the power system comprises the following steps:
PI power ＝λ P PI P +λ V PI V (35)
in the formula, λ P And λ V The weight coefficients are the active power behavior index and the voltage behavior index respectively.
In the step S8, an expected accident sequence table of the electric-pneumatic coupling system is generated according to the accident sequence obtained in the step S7, and each accident corresponds to one air network operation state and one power network disconnection accident.
10. The improved iterative jacobian matrix-based electrical coupling system safety analysis method of claim 1, wherein: the step S8 includes: the expected accidents ranked in the front are analyzed by using a precise power flow algorithm, whether the tested electric-gas coupling system passes safety check is determined, in order to ensure the rapidity of screening of the expected accidents, an iterative solution is adopted in the steady-state power flow result of the power system in the step S6, the iterative solution is not an accurate solution, the result is obtained by calculating according to the maximum load, the distribution time of each load peak value is in practice, the result has large safety redundancy, the screened dangerous accidents need to be checked by using the precise algorithm, and an operator analyzes whether the electric-gas coupling system passes static safety analysis according to the checked result.
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| CN117713251A (en) * | 2024-02-05 | 2024-03-15 | 华北电力大学 | Steady-state multi-energy flow calculation method and system of electro-hydro-carbon multi-energy system |
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| CN117713251A (en) * | 2024-02-05 | 2024-03-15 | 华北电力大学 | Steady-state multi-energy flow calculation method and system of electro-hydro-carbon multi-energy system |
| CN117713251B (en) * | 2024-02-05 | 2024-04-26 | 华北电力大学 | Steady-state multi-energy flow calculation method and system of electro-hydro-carbon multi-energy system |
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