CN117875161B - Source network load collaborative elastic lifting method and system considering multi-fault uncertainty - Google Patents
Source network load collaborative elastic lifting method and system considering multi-fault uncertainty Download PDFInfo
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Abstract
The invention relates to a source network load collaborative elastic lifting method and a system considering multi-fault uncertainty, wherein the method comprises the following steps: acquiring power transmission network information and constructing a multi-type fault probability distribution uncertainty set under typhoon disasters; based on a distribution robust optimization idea, constructing a source network load collaborative elastic lifting model considering the multi-type fault probability distribution uncertainty set; based on the Benders decomposition and column and constraint generation ideas, solving the source network load collaborative elastic lifting model by adopting an original-dual parallel decomposition algorithm to obtain a source network load collaborative planning strategy. Compared with the prior art, the invention has the advantages of reducing line investment and power failure loss of the most serious fault scene under typhoon disasters to different degrees, further coordinating the economical efficiency of the power system and the elastic lifting target and the like.
Description
Technical Field
The invention relates to the field of elastic lifting of power transmission networks, in particular to a source network load collaborative elastic lifting method and system considering multi-fault uncertainty under typhoon disasters.
Background
The small probability, high loss (HIGH IMPACT AND low probability, HILP) extreme weather events, represented by typhoons, present a significant challenge to the safe and economical power supply of power systems. The elasticity of the power system refers to the prevention, resistance, response and recovery capability of HILP events, and the elastic power system has four performance characteristics: based on the perception, the adaptability, the resistance and the restoring force, long-term planning optimization measures are adopted from various links of a power system source, a network and a load, so that the degree of system performance degradation, the performance degradation speed, the duration of an elastic process and the restoring speed of the system performance are reduced under HILP events, and the elasticity of the power system is improved.
In the prior art, modeling research aiming at element fault states and uncertainty of fault rate under disasters is insufficient, and elastic lifting of a power transmission network cannot be effectively realized. In order to meet the requirement of elastic lifting of the power system under the new situation, the existing modeling method of the element fault state and the uncertainty of the fault rate under the typhoon disaster is required to be further researched and developed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide the source network load collaborative elastic lifting method and system which can reduce line investment and power failure loss of the most serious fault scene under typhoon disasters to different degrees, and further coordinate the economical efficiency of a power system and consider multi-fault uncertainty under typhoon disasters of an elastic lifting target.
The aim of the invention can be achieved by the following technical scheme:
a source network load collaborative elastic lifting method considering multi-fault uncertainty comprises the following steps:
acquiring power transmission network information and constructing a multi-type fault probability distribution uncertainty set under typhoon disasters;
Based on a distribution robust optimization idea, constructing a source network load collaborative elastic lifting model considering the multi-type fault probability distribution uncertainty set;
Based on the Benders decomposition and column and constraint generation ideas, solving the source network load collaborative elastic lifting model by adopting an original-dual parallel decomposition algorithm to obtain a source network load collaborative planning strategy.
Further, the grid information includes grid structure data, cost data, and the like.
Further, the multiple types of faults include a most severe fault, a most probable fault, and a cascading fault.
Further, the multiple types of fault probability distribution uncertainty sets are constructed based on probability models of the types of faults.
Further, the multi-type fault probability distribution uncertainty set is expressed as:
wherein, Is a multi-type fault probability distribution uncertainty set; p s(Zn) is the actual probability of the nth fault scene Z n, and p 0(Zn) is the relative theoretical probability of the nth fault scene after normalizing the probability of the N c fault scenes; ψ is the total deviation of the probability distribution of the actual and theoretical fault scenarios; is the upper and lower limits of the fluctuation range; n c is the total number of multi-type fault scenarios.
Further, the source network load collaborative elastic lifting model aims at minimizing running cost expectations under the worst multi-type fault probability distribution scene under line investment and typhoon disasters, and adopted constraint conditions comprise line total investment constraint, preventive unit combination and power generation scheduling constraint, power transmission line switch operation constraint and node power balance and differential load shedding constraint.
Further, the objective function of the source network load collaborative elastic lifting model is expressed as:
Wherein, C l is annual line investment cost, L c is a line set to be selected, x and v are line construction and line switch state variables, u st、udt、uot is a starting-up, shutdown and unit operation state variable, 1 is taken to represent a starting-up state, otherwise 0 is taken, To start up and shut down the cost, p gt,Is the power generation capacity and the important and normal load shedding load quantity of each node, G is a generator set, T represents a scheduling period,For the feasible domain to which each state variable belongs,Is the cost of generator fuel, the important and conventional load cut-off cost of each node, the three are converted into annual cost through annual extreme disaster duration, P (Z) is the probability distribution of multi-type fault scenes, E p is the expectation,Is a feasible domain, and B is a set of all nodes.
Further, when the original-dual parallel decomposition algorithm is adopted to solve the source network load cooperative elastic lifting model, the objective function of the source network load cooperative elastic lifting model is converted into a matrix objective function comprising upper, middle and lower three layers of problems.
Further, the specific steps of solving the source network load collaborative elastic lifting model by adopting an original-dual parallel decomposition algorithm include:
step 1: initializing parameters, defining an upper bound UB, a lower bound LB, a maximum iteration number and an upper and lower bound gap threshold v, and setting a render cut set phi b and an original cut set phi a as empty sets;
Step 2: in each iteration, the solution builds a master problem based on the upper-layer problem, expressed as follows:
Benders pair cut set: phi (phi) b
Original cutset: phi (phi) a
Wherein y 1 is all 0/1 decision variables, c 1 is a cost vector corresponding to y 1, and p is the actual fault probability; τ and α are the pairs of middle layer problems, A is the coefficient matrix corresponding to y 1, B is the constant vector corresponding to y 1, L c is the set of lines to be selected, G is the set of generators, B is all node sets, and L e is the set of existing lines;
Recording the optimal solutions of the main problems as y 1 (m) and alpha (m), wherein the optimal values are as follows UpdatingM is the current iteration number;
Step 3: taking y 1 (m) as input, solving a sub-problem formed by performing dual transformation on the middle-lower layer problem, wherein the sub-problem is expressed as follows:
BTβ≤c2
β≥0
Wherein: beta is a dual vector of constraint By 2+C(y1) not less than d, y 2 is a lower-layer problem decision vector formed By all continuous decision variables, B is a coefficient matrix corresponding to y 2, C (y 1)、C(y1 (m)) is a vector related to y 1、y1 (m), d is a constant vector corresponding to y 2, and C 2 is a cost vector corresponding to y 2;
Recording the optimal value of the sub-problem corresponding to each fault scene Z n And beta (m);
Step 4: judging whether a convergence condition is met, wherein the convergence condition is UB-LB is less than or equal to v, if yes, ending, and if not, entering the next step;
Step 5: and (3) generating a Benders dual cut by beta (m), adding phi b, generating an original cut by a sub-problem objective function and a feasible domain, adding phi a, and returning to the step (2).
Further, the source network load collaborative planning strategy comprises a long-term and short-term elastic measure scheme under the worst multi-type fault probability distribution scene.
The present invention also provides a source network load collaborative elastic lifting system that accounts for multiple failure uncertainties, comprising one or more processors, memory, and one or more programs stored in the memory, the one or more programs comprising instructions for performing a source network load collaborative elastic lifting method that accounts for multiple failure uncertainties as described above.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, by considering the component fault uncertainty set of the uncertainty of the multi-type fault probability distribution under the typhoon disaster, the three typical fault probability distribution uncertainties of the worst, most probable and cascading faults under the typhoon disaster are described, so that the elasticity and economy of the model are balanced better.
(2) According to the invention, by coordinating with the load elastic lifting measures of the power grid, the line investment and the power failure loss of the most serious fault scene under typhoon disasters can be reduced to different degrees, so that the economical efficiency and the elastic lifting target of the power system are coordinated.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a comparison of multiple types of fault theory and worst probability distribution;
FIG. 3 shows the number of starts and the most severe fault down load rate expectations for different power supply regulation capabilities.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
Example 1
The embodiment provides a source network load collaborative elastic lifting method considering multi-type fault uncertainty under typhoon disasters, as shown in fig. 1, the method comprises the following steps:
s1, constructing a multi-type fault probability distribution uncertainty set to characterize probability distribution uncertainties of three typical faults, namely the most serious, the most probable and the cascading faults under typhoon disasters.
In this embodiment, the construction of the multi-type fault probability distribution uncertainty set includes three steps:
(1) The theoretical failure rate of the component is calculated. The classical typhoon simulation model Batts is adopted to simulate typhoons, which damage elements such as an overhead line and a pole tower, and in the embodiment, the overhead line is taken as a typical damaged element under typhoon disasters, and the line theoretical fault rate is calculated by using a line vulnerability curve under typhoon disasters.
(2) Searching for multiple types of fault scenes under typhoon disasters.
The present embodiment considers three fault types under typhoon disasters: the most serious faults, the most probable faults and cascading faults, and each fault type can account for the faults of the N-K loop line.
1) Modeling of most severe faults
The most serious N-K faults are searched by adopting an attack-defense-attack (defense-attack-defense, DAD) model based on robust optimization, and the load elasticity improving measures of the additional source network are not considered, such as formulas (1) - (2).
Where p gt is the output of generator g at time t, p lt is the transmission power of line l at time t, Δd bt is the load shedding at time t at node b,The method is an operation constraint such as a decision variable feasible domain before and during the disaster, namely a line tide constraint, a generator output constraint, a load shedding constraint and the like. The objective function f is the power generation and load shedding costs, z l is the fault state variable for element l, z l =1/0 represents normal/fault state, Ω is the element fault state constraint set, N L is the total number of elements, and K max is the upper limit of the actual number of faulty elements. N 1 most serious N-K fault scenes can be calculated by the model according to the cutting load from large to small, and the probability calculation of each fault scene is divided into three steps. First, batts typhoons were constructed as shown in equation (3).
Wherein R max is the distance from the typhoon center to the maximum wind speed zone, namely the maximum wind speed radius of typhoon; Δp is the difference between the peripheral air pressure and the typhoon center; w gx is the air flow rate caused by the air pressure gradient; f is the earth rotation coriolis force coefficient; θ is an empirical coefficient, typically taken to be 6.72; w Rmax is the wind speed of R max at the maximum wind speed radius, i.e., the maximum wind speed; w T is typhoon moving speed; w rin,Wrout is the wind speed of each position inside and outside the maximum wind speed radius; r is the distance from the target position to the typhoon center; x is typhoon radial intensity attenuation parameter; ΔP 0 is the pressure difference between the peripheral air pressure and the typhoon center when typhoon logs in; phi is the included angle between the typhoon path and the coastline.
Then, constructing a line theoretical fault rate model based on a vulnerability curve, as shown in formulas (4) to (5):
wherein, For the failure rate of the element l at the moment t in typhoon weather, w t is the typhoon wind speed suffered by the line at the moment t, and w r is the line design wind speed. Lambada l represents the theoretical failure rate of element l during typhoons (beginning at t 0 and ending at t e).
Finally, constructing single-element and multi-element fault scene probability calculation models, taking single-element and double-element as examples, wherein the probability calculation formula is shown as formula (6):
Wherein Z 1 is the failure scene of only element l, p (Z 1) is the probability thereof, Z 2 is the failure scene of only element l, i, p (Z 2) is the probability thereof, v li represents the probability of simultaneous failure of element l, i, and v lij represents the probability of simultaneous failure of element l, i, j. v lijh denotes the probability of simultaneous failure of elements i, j, h.
2) Most likely fault modeling
And the most probable N-K faults are combined into N 2 fault scenes with the fault rate from large to small according to the N-K requirements.
3) Cascading failure modeling
The construction of the cascading failure set is divided into two steps. Firstly, selecting a line with N 3 loops, which is required to be paid attention to in engineering experience, or has higher fault probability as an initial fault line set for cascading faults. Then, disconnecting the primary fault line, and calculating the cascading N-K fault propagation links according to the formula (7).
In the method, in the process of the invention,For the line rating and maximum transmission capacity,The fault rate of the line before and after the cascading failure is obtained. After searching for the initial line fault, the equation (7) leads to the line overload and even overload caused by the power flow transfer and further leads to the line cascading failure until reaching the N-K cascading failure.
(3) And constructing a multi-type fault probability distribution uncertainty set.
The typhoon and the ageing state of the element cannot be accurately predicted, so that the theoretical fault rate and the actual fault rate of the line deviate, and therefore, the actual probability of each fault scene is uncertain, and the line is characterized by adopting a formula (8).
Wherein,Is a multi-type fault probability distribution uncertainty set, and the mathematical essence is a fuzzy set for describing fault probability distribution. p s(Zn) is the actual probability of the nth fault scenario Z n, p 0(Zn) is the relative theoretical probability of the nth fault scenario after normalizing the N c fault scenario probabilities, using relative values instead of absolute values, mathematically essentially because the sum of the probability distributions of all fault scenarios should be equal to 1, physically essentially the set is assumed hereinAll fault scenes to be dealt with by elastic lifting measures are contained, and ψ is the total deviation of probability distribution of actual and theoretical fault scenes, the mathematical meaning of the total deviation is the distance between the two probability distributions, and for the case that the data size of a probability distribution sample is large, the empirical formula can be used for calculating ψ, and for the HILP event scene lacking data, the total deviation is more suitable for selection according to engineering experience. Considering that the actual probability of the fault scene should fluctuate within the limited range of the theoretical probability, introducingThe range of fluctuation is limited and,The conservation degree of the model can be adjusted by selecting the psi. N c is the total number of the three fault scenes, N c＝N1+N2+N3 and the essence of the formula (8) is that the probability distribution uncertainty of the three fault scenes of the most serious fault, the most probable fault and the cascading failure is marked by adopting 1 norm. P s(Zn)-p0(Zn) is represented by p k(Zn), and the set is assembledThe absolute value expression of (2) is converted to equation (9) for subsequent model solving.
S2, based on a distribution robust optimization idea, a long-period combination and source network load cooperative distribution robust elastic lifting model is provided.
On the basis of the uncertainty set of the multi-type fault probability distribution obtained based on the steps, a source network load collaborative elastic lifting model considering multi-type fault uncertainty under typhoon disasters is constructed: in the aspect of long-term measures, the redundancy of the power transmission network frame is increased through power transmission network expansion planning, and typhoon disasters are prevented. In terms of short-term measures, a power supply side considers preventive unit combinations of units with different regulation performances and rescheduling in disaster; on the power grid side, the optimal switching operation of the line which can be disconnected is considered, and the source network cooperatively plays a role in flexible adjustment of the power generation and transmission system; on the load side, the importance of different nodes and the importance difference of access loads thereof are considered, important loads are preferentially reserved, and the elasticity and economical targets are coordinated to the greatest extent in a differential load cutting mode. Based on a distribution robust optimization idea, with the aim of minimizing line investment and running cost expectations under the worst multi-type fault probability distribution scene under typhoon disasters, a three-layer optimization model is provided, and a long-period elastic measure scheme capable of resisting the worst fault probability distribution searched by the middle layer is determined by using the upper layer and lower layer problems, wherein the model targets are shown in formulas (10) - (11).
Wherein, C l is annual line investment cost, L c is a line set to be selected, x and v are line construction and line switch state variables, u st、udt、uot is a starting-up, shutdown and unit operation state variable, 1 is taken to represent a starting-up state, otherwise 0 is taken,To start up and shut down the cost, p gt,Is the power generation capacity and the important and normal load shedding capacity of each node, G is a generator set, T represents a scheduling period, the embodiment takes 24 hours,Is a feasible domain to which each state variable belongs.Is the cost of generator fuel, the important and conventional load cut-off cost of each node, the three are converted into annual cost through annual extreme disaster duration, P (Z) is the probability distribution of multi-type fault scenes, E p is the expectation,Is a feasible domain of the long-short period optimization problem in the disaster, and B is a set of all nodes.
Constraint conditions of the source network load collaborative elastic lifting model in the embodiment comprise line total investment constraint, preventive unit combination and power generation scheduling constraint, power transmission line switch operation constraint and node power balance and differential load shedding constraint.
(1) Line total investment constraint
xl∈{0,1}(13)
Wherein: and II, L is the total investment budget of the line, x l is 1 to represent the line to be built, and otherwise 0 is taken.
(2) Preventive unit combination and power generation scheduling constraints
Wherein: For the minimum continuous on-time and off-time of the unit g, And (5) climbing up and down the slope for each generator.
(3) Power transmission line switch operation constraints
-(2-zlt-vlt)M≤plt-Bl(θs(l)t-θe(l)t)≤(2-zlt-vlt)M (23)
Wherein: v l takes 0 as the disconnected line, otherwise takes 1, N v as the total number of the disconnected lines, L e as the existing line set, M as a sufficiently large positive number for linearization of line flow constraint, and θ s(l)t,θe(l)t as the phase angle of the start and end nodes of line L.
(4) Node power balance and differentiated load shedding constraint
Wherein: d bt is the load of each node, L +(b),L- (b) is the set of lines from node b into which power flows,Is the important and normal load proportion of each node.
S3, combining mathematical structural features of the model, and designing an original-dual parallel decomposition algorithm to complete model solving based on the ideas of Benders decomposition and column and constraint generation.
Writing the provided source network load elastic lifting measure model into a matrix form, wherein the objective function is as follows:
Wherein y 1 is an upper-layer problem decision vector composed of all 0/1 decision variables (including line construction, unit combination and structure optimization), and c 1 is a cost vector corresponding to y 1. y 2 is the lower problem decision vector of all continuous decision variables, and c 2 is the corresponding cost vector of y 2.
Upper layer problem feasible regionComprising about (12) - (18), (21) - (22), can be expressed as:
Wherein A is a coefficient matrix corresponding to y 1; b is a constant vector corresponding to y 1.
Middle layer problem feasible domains, i.e. collectionsThe expression can be as follows:
Ep≤f (35)
wherein p consists of p s,pk.
Underlying problem feasible regionContaining the remaining constraints, for each failure scenario Z n, the underlying problem can be expressed as:
By2+C(y1)≥d (36)
Wherein B is a coefficient matrix corresponding to y 2; d is a constant vector corresponding to y 2.
Wherein: c (y 1) is a vector related to y 1, and y 1 is solved for the upper-layer problem, so C (y 1) is a constant value.
With reference to the ideas of column and constraint generation and Benders decomposition, an original-dual parallel decomposition algorithm is designed to complete model solving, and the steps are as follows:
Step 1: initializing parameters, an Upper Bound (UB), a Lower Bound (LB), a maximum iteration number M e, an upper and lower bound gap threshold v, an iteration number m=1, a binder cut set Original cutting set
Step2: for m=1..m e, solve the following main problem:
benders pair cut set: phi b (39)
Original cutset: phi a (40)
Wherein p is the actual failure probability; τ and α are the pairs of middle layer problems, respectively.
Recording the optimal solutions of the main problems as y 1 (m) and alpha (m), wherein the optimal values are as followsUpdating
Step 3: and solving a sub-problem formed by performing dual conversion on the middle-lower layer problem. With y 1 (m) as input, for each fault scene Z n, the lower-layer problem is a large-scale linear programming problem with more constraints, and the dual problem is solved:
BTβ≤c2 (42)
β≥0
Wherein: beta is the dual vector of constraint By 2+C(y1) not less than d, and recording the optimal value of the sub-problem corresponding to each fault scene Z n And beta (m).
Step 4: and judging convergence conditions. If UB-LB is less than or equal to v, the algorithm converges, otherwise, the next step is carried out.
Step 5: benders pair cuts are generated from the original cuts. The Benders pair cut was generated from β (m) and Φ b was added.
α≥(d-C(y1))Tβ(m) (43)
Generating an original cut by the objective function of the sub-problem and the feasible domain, adding phi a, and entering the step 2, wherein m=m+1.
By2 (m+1)+C(y1)≥d (45)
The main problem of the proposed model is a mixed integer linear programming problem, which can be solved directly by a commercial solver.
To verify the validity of the above method, the present embodiment uses IEEE 30 node as an example for example analysis, and the system includes 8 generators, 41 back to existing lines, and 41 back to selected lines. The relevant programming parameters are set as follows:
In the theoretical vulnerability curve parameters, w r takes 20m/s, 20% of each node is an important load, the maximum line can be disconnected for 6 times, the conventional load shedding penalty cost is 5 yuan/kWh, the important load shedding cost is 25 yuan/kWh, the typhoon occurrence frequency is considered to be 20 days each year on average, the line investment cost is 25 years according to 10%, and the annual investment is about 100 ten thousand yuan/time.
The economic index adopted by the embodiment is annual average line investment and annual average typhoon disaster period power generation cost; the technical index, namely the elasticity evaluation index, is the expected cost (WELC) of the power outage of the worst fault probability distribution scene under typhoon disasters, and the formula is as follows:
wherein, Is an important and conventional cut load under the worst fault probability distribution of each section.
4 Sets of calculation examples C1-C4 are set to embody the advantages of the fault uncertainty set. And C1, C2 and C4 comprise 5 most serious, most probable and cascading failures, namely 15 failure scenes in total, different types of failure superposition situations can occur in actual calculation, the superposition failures are reserved in one type, and the unreserved failure types continue to search for the next failure scene. Another advantage of the proposed model is that multiple N-k faults of different levels can be considered simultaneously, according to the N-3 and N-4 fault levels of C1 and C2-C3, for this purpose, the calculation example C4 is designed, each fault type contains 2N-3 and 3N-4 scenes, and 15 fault scenes are total. And C3, adopting a classical DAD model, wherein in the element fault uncertain set, the actual and theoretical probability fluctuation of a single fault scene is +/-20%, and the total deviation of the probability distribution of the fault scene is 0.15.
Taking C2 as an example, three types of 15 faults are searched out, wherein the theoretical probability distribution and the calculated actual worst probability distribution are shown in the table 1, and the comparison of the calculated results of C1 to C4 are shown in the table 2. As can be seen in fig. 2, the most severe fault probability distribution scenario has the following features: the actual probability of the fault scene 6-10 (namely the most serious fault) is increased by more than 15% compared with the theoretical probability, and the actual probability of the fault scene 4-5 and 13-15 is obviously reduced in the most probable and cascading fault scenes, and the system load shedding loss is smaller in the scenes, so that the probability of occurrence is smaller. Table 2 shows that the failure level is increased from N-3 to N-4, a new line 2 is added, and WELC is increased, i.e., the conservation of the elastic lifting model is increased, and the total investment of the N-3 and N-4 integrated failure set (C4) is between N-3 and N-4 considered alone. In addition, compared with the DAD model (C3), the number of newly added lines of the proposed model is reduced by 4 times, WELC is reduced by nearly 1000 ten thousand, which shows that the proposed multi-type fault uncertainty set simultaneously improves the elasticity and the economy compared with the traditional N-K uncertainty set.
TABLE 1 comparison of Multi-type fault theory and worst probability distribution
TABLE 2 comparison of model results under different element fault uncertainty sets
Under the N-4 fault level, 3 groups of calculation examples C5-C7 are set to be compared with a C2 source network load cooperative model, and the results are shown in Table 3.
C5: the source network cooperates, and differential load shedding is not considered, namely, the load shedding cost of each node is the same, and the important load proportion is 0.
C6: source-load collaboration, and no extension planning and structural optimization.
C7: network load cooperation is carried out, preventive unit combination is not considered, and a conventional unit starting mode is kept before disaster.
Table 3 shows that the elastic lifting effect of the source load synergy is the worst for the system, because the system is installed and load-tightly balanced, and the typhoon route is seriously damaged on network weak links (the large-capacity generator and the large-load node island are caused, such as 16 and 23 nodes), so that the elastic lifting measures at the network side, especially the long-term expansion planning measures, have the greatest significance on the elastic lifting of the system. The second difference of the elastic lifting effect of the source network cooperation is that the line investment is basically unchanged compared with C2, but the source network cooperation cuts off part of important load due to neglecting the load difference, and the load cutting cost is approximately 700 ten thousand higher than that of the source network load cooperation. The network load cooperative elastic lifting effect is inferior to the source network load cooperative elastic lifting effect, WELC is not different, but the economical efficiency is poor, and two circuits are required to be invested, so that the normal starting mode can be guaranteed to better support loads under disasters.
Table 3 comparison of different source network load synergistic scenario results
TABLE 4 planning results of elastic Power Transmission network under different set parameters
On the power supply side, in order to take the elastic lifting effect of units with different adjustment capacities into account, the minimum output level of the units and the minimum continuous on/off time of the units are changed, 2 groups of calculation examples C8-C9 are set: the minimum output was 40% of the installed, the minimum output was 25% of the installed (same as C2) but the minimum sustained on/off time for all slow-running machines was increased by 1 hour; on the power grid side, keeping the planning constraint of the power grid unchanged, observing the structure optimization effect, and setting 2 groups of calculation examples C10-C11: the planning scheme of maximum break 0, 3-loop line is compared with the C2 planning scheme (maximum break 6-loop); on the load side, 10% of the important load of each node of the example C12 is set in consideration of the calculated non-differential cut load scene. The results of C8-C12 are shown in Table 4, and are as follows:
1) The increase in minimum start-up time/minimum output level of the unit results in an increase in investment costs and WELC, i.e., poor system economy and flexibility, and further, as can be seen in fig. 3, the system cut load is expected to be greater at 1-3 hours and 20-22 hours. The former is caused by the restriction of flexible regulation capability of the unit, because the system load is rapidly reduced in 1-4 hours, the starting number of the unit is limited, but the load is rapidly increased in 4-6 hours, at the moment, the lower limit of the output of the unit is higher, or the starting time is longer, and the load is difficult to be timely ensured; the power supply notch is caused by serious faults in peak load time periods, and the load is obviously cut off in 3 groups of calculation examples.
2) As the maximum number of openable lines increases, the newly added line investment decreases. Compared with a maximum cut-off 3 loop, the WELC of the maximum cut-off 6 loop is increased by 80 ten thousand yuan, the line investment is reduced by 2800 ten thousand yuan, and the line width is reduced by 20%, so that the elasticity is improved through structural optimization, and the input-output ratio is better.
3) For differential load shedding measures, each node of the system has 10% or 20% of important load, the cooperative elastic lifting result of the source network load is not affected, the load shedding amount of each node is below 80% due to failure after differential load shedding is mainly considered, and the important load is not cut off no matter the load shedding amount is 10%/20%.
Example 2
The invention also provides a source network load collaborative bullet lifting model and a system for considering multi-type fault uncertainty under typhoon disasters, comprising one or more processors, a memory and one or more programs stored in the memory, wherein the one or more programs comprise instructions for executing the source network load collaborative bullet lifting model for considering multi-type fault uncertainty under typhoon disasters as described in the embodiment 1.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The scheme in the embodiment of the invention can be realized by adopting various computer languages, such as object-oriented programming language Java, an transliteration script language JavaScript and the like.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (5)
1. The source network load collaborative elastic lifting method considering multi-fault uncertainty is characterized by comprising the following steps of:
acquiring power transmission network information and constructing a multi-type fault probability distribution uncertainty set under typhoon disasters;
Based on a distribution robust optimization idea, constructing a source network load collaborative elastic lifting model considering the multi-type fault probability distribution uncertainty set;
based on the Benders decomposition and column and constraint generation ideas, solving the source network load collaborative elastic lifting model by adopting an original-dual parallel decomposition algorithm to obtain a source network load collaborative planning strategy;
The set of multi-type fault probability distribution uncertainties is expressed as:
wherein, Is a multi-type fault probability distribution uncertainty set; p s(Zn) is the actual probability of the nth fault scene Z n, and p 0(Zn) is the relative theoretical probability of the nth fault scene after normalizing the probability of the N c fault scenes; ψ is the total deviation of the probability distribution of the actual and theoretical fault scenarios; Is the upper and lower limits of the fluctuation range; n c is the total number of multi-type fault scenarios;
The source network load collaborative elastic lifting model aims at minimizing running cost expectations under the worst multi-type fault probability distribution scene under line investment and typhoon disasters, and adopted constraint conditions comprise line total investment constraint, preventive unit combination and power generation scheduling constraint, power transmission line switch operation constraint and node power balance and differential load shedding constraint;
The objective function of the source network load collaborative elastic lifting model is expressed as:
Wherein, C l is annual line investment cost, L c is a line set to be selected, x and v are line construction and line switch state variables, u st、udt、uot is a starting-up, shutdown and unit operation state variable, 1 is taken to represent a starting-up state, otherwise 0 is taken, To start up and shut down the cost, p gt,Is the power generation capacity and the important and normal load shedding load quantity of each node, G is a generator set, T represents a scheduling period,For the feasible domain to which each state variable belongs,Is the cost of generator fuel, the important and conventional load cut-off cost of each node, the three are converted into annual cost through annual extreme disaster duration, P (Z) is the probability distribution of multi-type fault scenes, E p is the expectation,Is a feasible domain, B is a set of all nodes;
When an original-dual parallel decomposition algorithm is adopted to solve the source network load collaborative elastic lifting model, converting an objective function of the source network load collaborative elastic lifting model into a matrix-form objective function comprising an upper problem, a middle problem and a lower problem;
The specific steps for solving the source network load collaborative elastic lifting model by adopting an original-dual parallel decomposition algorithm include:
step 1: initializing parameters, defining an upper bound UB, a lower bound LB, a maximum iteration number and an upper and lower bound gap threshold v, and setting a render cut set phi b and an original cut set phi a as empty sets;
Step 2: in each iteration, the solution builds a master problem based on the upper-layer problem, expressed as follows:
Benders pair cut set: phi (phi) b
Original cutset: phi (phi) a
Wherein y 1 is all 0/1 decision variables, c 1 is a cost vector corresponding to y 1, and p is the actual fault probability; τ and α are the pairs of middle layer problems, A is the coefficient matrix corresponding to y 1, B is the constant vector corresponding to y 1, L c is the set of lines to be selected, G is the set of generators, B is all node sets, and L e is the set of existing lines;
Recording the optimal solutions of the main problems as y 1 (m) and alpha (m), wherein the optimal values are as follows UpdatingM is the current iteration number;
Step 3: taking y 1 (m) as input, solving a sub-problem formed by performing dual transformation on the middle-lower layer problem, wherein the sub-problem is expressed as follows:
BTβ≤c2
β≥0
Wherein: beta is a dual vector of constraint By 2+C(y1) not less than d, y 2 is a lower-layer problem decision vector formed By all continuous decision variables, B is a coefficient matrix corresponding to y 2, C (y 1)、C(y1 (m)) is a vector related to y 1、y1 (m), d is a constant vector corresponding to y 2, and C 2 is a cost vector corresponding to y 2;
Recording the optimal value of the sub-problem corresponding to each fault scene Z n And beta (m);
Step 4: judging whether a convergence condition is met, wherein the convergence condition is UB-LB is less than or equal to v, if yes, ending, and if not, entering the next step;
Step 5: and (3) generating a Benders dual cut by beta (m), adding phi b, generating an original cut by a sub-problem objective function and a feasible domain, adding phi a, and returning to the step (2).
2. The source network load collaborative resilient lifting method considering multi-fault uncertainty according to claim 1, wherein the multi-type faults include most severe faults, most probable faults, and cascading faults.
3. The source network load collaborative elastic lifting method considering multi-fault uncertainty according to claim 1, wherein the multi-type fault probability distribution uncertainty set is constructed based on probability models of each type of fault.
4. The method for improving the source network load collaborative elasticity considering multi-fault uncertainty according to claim 1, wherein the source network load collaborative planning strategy comprises a long-term elastic measure scheme under the worst multi-type fault probability distribution scene.
5. A source network load co-elastic lifting system that accounts for multiple fault uncertainties, comprising one or more processors, memory, and one or more programs stored in the memory, the one or more programs comprising instructions for performing the source network load co-elastic lifting method that accounts for multiple fault uncertainties as recited in any one of claims 1-4.
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