CN104852383A - Emergency control method for offshore oilfield cluster power grid - Google Patents

Abstract

The invention provides an emergency control method for an offshore oilfield cluster power grid, comprising operation parameter collection, control strategy table generation, and execution control. Operation parameter collection comprises the steps of collecting current operation parameters of a power grid and determining the current mode of operation and mode of wiring and the overall structure of a system, and operation parameter collection is periodic. Control strategy table generation comprises the steps of analyzing possible types of faults of the system, scanning and calculating different types of faults, finding corresponding optimal strategies, generating a strategy table corresponding to the current operation parameters, judging whether the collected operation parameters are refreshed, and regenerating a strategy table when a data refreshing signal is detected. Execution control comprises the steps of judging current accident disturbance of the power grid and searching a matching control strategy in the strategy table according to the type of accident disturbance to guide operation of the system. The amount of calculation is reduced, the flexibility is increased, and safe and stable operation of the system is further guaranteed.

Description

A kind of emergency control method of offshore oilfield cluster power grid

Technical field

The present invention relates to offshore oilfield cluster power grid technical field, specifically a kind of emergency control method of offshore oilfield cluster power grid.

Background technology

Emergency control refers to that system is disturbed and enters state that is urgent or extreme emergency, by the measure of series, prevents the stability of a system from destroying or to the development of more severe situation, avoids causing serious situation about having a power failure.In emergency control, the measure of emergency control mainly comprises excision generator, excision load, steam turbine fast valve porthole, generator automatic exciter, parallel connection or series compensation, high voltage direct current are modulated, off-the-line system.

Offshore oilfield cluster power grid has an accident after disturbance and System recover can be made to stablize by corresponding load shedding measure.Due to the quick adjustment characteristic of gas turbine set, after system loading changes, unit can regulate rapidly and exert oneself, with the balance of satisfied generating and load.Therefore the dynamic stability such as transient state, voltage can not be considered separately at the emergency control system for current offshore oilfield cluster power grid, and these dynamic effects are included in stability margin to a certain extent, main consideration break down after the load of system and the balance of generated output, the major measure of corresponding emergency control system is cutting load, is also called preferential tripping system.Thus, the core of offshore oilfield cluster power grid emergency control policy can be converted into and comprise trend and constrain in interior multiple constraint Emergency Control Strategy optimization problem.

The preferential tripping system of southwest, current Wei Oilfield Group electrical network, is enumerate out by security and stability control strategy CASE corresponding for all faults when off-line, by Trouble Match after breaking down, finds out corresponding control strategy.The core constraint that safety control strategy is formulated is the total power generating capacity of system and mating of system total load.

Along with the increase of electrical network complexity, foundation is enumerated all CASE and can be brought amount of calculation in large scale, and in original control strategy, only meets total generated output and total load, but other security constraints are not all considered.

The emergency control policy of land electrical network is a very complicated process, comprises Transient Stability Control, step-out and premature beats, frequency stabilization controls, Voltage Stability Control etc.And it is known by analysis above, the preferential tripping system of offshore oilfield group net does not consider concrete failure mode (as single failure, multiple faults etc.), but when mainly consideration system occurs that generator off-grid or system line disconnect, the cutting load measure that system is concrete.

Current preferential tripping system mainly comprises the function of two aspects:

Unit off-grid:

Main calculating is when system one or several online units are forced to off-grid, and system needs the corresponding load cut away.

Its principle calculated is: the nargin of exerting oneself of computing system, namely under typical condition, the maximum output of online unit cuts at specific electric load, and then cuts the unit maximum output of off-grid and deduct correction value.Be expressed as with formula:

$\mathrm{\ΔP}=\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\Σ}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_D}{\mathrm{\Σ}}}{P}_{\mathrm{Di}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\Σ}}}{P}_{\mathrm{gi}\max }-\mathrm{\ϵ}$ Formula 20

Wherein, P _gimaxrepresent the maximum output of generator i, P _direpresent the current loads of node i, ε represents correction value (nargin of exerting oneself), N _gonrepresent online generator unit number, N _gtriprepresent the generator unit number of off-grid, N _dthe nodes of expression system.

If Δ P>0, then, after representing unit off-grid, system still can keep stable, therefore without the need to cutting load; If Δ P<0, then according to priority from low to high each load is not rejected, and mark disallowable load, until Δ P>0, therefore, not disallowable load is exactly the peak load that system can bear after cutting away unit, and the load be labeled is exactly the load needing to cut away, once the order of unit off-grid (TRIP CASE) triggers, the load marked will be laid down.

Circuit disconnects:

Main calculating when circuit disconnect after, the load that system should be cut away.

Its principle calculated is that, after system circuit disconnects, system may form two or more electrical network, carries out calculating respectively to exert oneself nargin for each electrical network.

$\mathrm{\&Delta;P}=\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}-\mathrm{\&epsiv;}$ Formula 21

Wherein, P _gimaxrepresent the maximum output of generator i, P _direpresent the current loads of node i, ε represents correction value (nargin of exerting oneself), N _gonrepresent online generator unit number, N _dthe nodes of expression system.

If Δ P>0, then represent that the system after circuit disconnection still can keep stable, therefore without the need to cutting load; If Δ P<0, then according to priority from low to high each load is not rejected, and mark disallowable load, until Δ P>0, therefore, not disallowable load is exactly the peak load that system can bear after cutting away unit, and the load be labeled is exactly the load needing to cut away, once the command triggers that circuit disconnects, the load marked will be laid down.

Adopt the method for exhaustion, the situation likely affecting power network safety operation is calculated, form different CASE, the result of all CASE being gathered is stored in Microsoft Excel, and carry out precomputation in real time, and by operation result in the upper friendly display in real time of HMI (Human Machine Interface, man-machine interface); Traffic control personnel, by HMI blending equipment priority level, find balance point in production importance and electric network security.

Southwest, current Wei Oilfield Group net, communicated by the fiber optic network of High performance industrial level Ethernet switch composition, about muzzle velocity 100ms, effectively can ensure the speed unloaded.At present in the simple situation of systematic comparison, the preferential tripping system of off-line decision-making can most of fault of effective answering system appearance.

But along with the expansion of oil platform and the networking of different oil platform, and the networking of in the future wider regional platform, the complexity of electrical network can progressively increase, the shortcoming of off-line decision-making will progressively display, data scale increases considerably, control strategy lacks flexibility and comprehensive etc., therefore needs to improve current emergency control policy.

Summary of the invention

Present applicant proposes a kind of emergency control method of offshore oilfield cluster power grid, the preferential tripping system of off-line decision-making will be changed into the preferential tripping system of on-line pre-decision system, by the operational factor of system from former emergency control policy CESE show exhaustive independent, adopt the mode of periodic collection current operating parameter, reduce amount of calculation, increase flexibility, in the process of Modling model, add multiple constraints, thus the safe and stable operation of further guarantee system.

For solving the problems of the technologies described above, this application provides a kind of emergency control method of offshore oilfield cluster power grid, comprise the collection of operational factor, control scheme list generation, perform control;

Described operational factor is collected to comprise and is collected the current operational factor of electrical network, determine the overall structure of current operational mode, the mode of connection, certainty annuity, operational factor is collected to adopt and is periodically collected, under the prerequisite that power system operating mode is not undergone mutation, carry out parameter collection at set intervals, more new data;

The generation of described control scheme list comprises the following steps: the fault type that the system of analyzing may exist, and namely N-1, N-2 or multimachine cut machine and different system splitting faults; Carry out scanning to dissimilar fault to calculate, search out corresponding optimal policy, generate the Policy Table that current operating parameter is corresponding; And judge whether the operational factor of collecting has refreshing, when after signal Refresh Data being detected, regenerates Policy Table;

Described execution controls to comprise the following steps: the accident disturbance of current electric grid judges; According to the accident disturbance type of current electric grid, in Policy Table, search for the control strategy of coupling, the operation of guidance system.

When after the signal receiving operational factor refreshing, generation strategy table comprises following two large divisions's content:

(1) unit off-grid fault scanning

Unit off-grid fault scanning and computing system N-1, N-2 ... optimal control policy corresponding under N-Nmin fault, and the Policy Table of generation is stored.

(2) circuit disconnects scanning

The optimal control policy that circuit is corresponding under disconnecting scanning and the contingent various circuit open failure of computing system, and the Policy Table of generation is stored.

The Policy Table that above-mentioned two parts calculate is combined and obtains final control scheme list.

The Mathematical Modeling of described optimal control policy is:

min f(u,x)

$s.t.\left\{\begin{array}{c}h(u,x)=0\\ g(u,x)\&le;0\\ u_{\min }\&le;u\&le;u_{\max }\\ x_{\min }\&le;x\&le;x_{\max }\end{array}\right.$ Formula 1

Wherein, u is control variables, and x is state variable, and f (u, x) is target function, and h (u, x)=0 is equality constraint, and g (u, x)≤0 is inequality constraints, u _min, u _maxfor control variables m bound, x _min, x _maxfor state variable u bound;

Wherein, m _ifor i-th measure taked, N _mfor the number of control measure, x comprises each class variable representing system running state, is defined as wherein e _iand f _irepresent the horizontal component of node i and vertical component respectively, N _dfor system node number;

Wherein, target function is the restricted driving combination of the different weights of all load operation, is expressed as

$f=\underset{i=1}{\overset{N_m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{Ci}}{M}_i$ Formula 2

ω _cithe cost paid needed for i for taking measures;

Wherein, constraints specifically comprises:

A) power-balance constraint

Power-balance constraint refers to that intrasystem generated output should reach balance with load power and line loss, is specially:

A-1) unit off-grid

$\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-{\mathrm{\&epsiv;}}_P\&GreaterEqual;0$ Formula 3

Wherein, P _gimaxrepresent that the maximum meritorious of generator i is exerted oneself, P _direpresent the current loads active power of node i, ε _prepresent correction value (meritorious nargin of exerting oneself), N _gongenerator unit number online before representing the non-off-grid of unit, N _gtriprepresent the generator unit number of off-grid, N _dthe nodes of expression system;

A-2) circuit disconnects

$\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}-{\mathrm{\&epsiv;}}_P\&GreaterEqual;0$ Formula 4

B) trend constraint

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Di}}-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)+e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\end{array}\right.$ Formula 5

Wherein, P _gifor the generating active power that node i is injected, P _difor the load active power of node i, Q _gifor the generating reactive power that node i is injected, Q _difor the load reactive power of node i, G _ijfor node i and the direct transconductance of node j, B _ijfor node i and node j directly mutual susceptance;

C) voltage constraint

$V_{i\min }^2\&le;e_i^2+f_i^2\&le;V_{i\max }^2,i=1,...,N_D$ Formula 6

Wherein V _imin, V _imaxrepresent lower limit and the upper limit of node i voltage magnitude respectively;

D) branch road transmission power constraint

$(G_{\mathrm{ij}}^2+B_{\mathrm{ij}}^2)[{(e_i{e}_j+f_i{f}_j-e_i^2-f_i^2)}^2+{(f_i{e}_j-e_i{f}_j)}^2]\&le;S_{\mathrm{ij}\max }^2,i=1,...,N_L$ Formula 7

Wherein, N _lfor system branch number, S _ijmaxfor node i and node j directly exchange the maximum of power;

E) control variables constraint

For every control measure, the restriction of its correspondence

M _iMIN≤ M _i≤ M _iMAXi=1 ..., N _mformula 8

M _iMIN, M _iMAXbe respectively control measure M _iminimum value and maximum.

The Mathematical Modeling simplification of described optimal control policy comprises the following steps:

The first step, under judging current loads, can system be stablized

When after system generation unit off-grid, do not excising load if judge, can system reach stable, namely when not excising load, whether can meet following constraints:

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Di}}-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)+e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\\ (G_{\mathrm{ij}}^2+B_{\mathrm{ij}}^2)[{(e_i{e}_j+f_i{f}_j-e_i^2-f_i^2)}^2+{(f_i{e}_j-e_i{f}_j)}^2]\&le;S_{\mathrm{ij}\max }^2,i=1,...,N_L\\ V_{i\min }^2\&le;e_i^2+f_i^2\&le;V_{i\max }^2,i=1,...,N_D\end{array}\right.$ Formula 9

If unit exert oneself and load can meet this constraint equation, then represent system can reach stable, do not need the measure of cutting load; If this constraint equation is without solution, then represent current unit possible exert oneself and current loads situation there is serious imbalance, need the calculating carrying out next step;

Second step, calculates the restriction of cutting load amount

Consider that unit off-grid and circuit disconnect two kinds of situations respectively:

Unit off-grid

Calculating formula 3, can obtain thus,

$\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&le;\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-{\mathrm{\&epsiv;}}_P$ Formula 10

Wherein, after expression cutting load, total burden with power of system, can obtain thus,

$\mathrm{\&Delta;}{P}_D=P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&GreaterEqual;P_{\mathrm{\&Sigma;Load}}-(\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max })+{\mathrm{\&epsiv;}}_P$ Formula 11

Wherein, P _{Σ Load}total burden with power of representative system before cutting load measure, Δ P _dthe load of cutting away needed for expression;

In addition, define all can cutting load and corresponding cost thereof, cutting load cost can not can be set to infinity, removing can not cutting load, if can the total amount of cutting load be P _{∑ Dmax}, then the constraints that cutting load amount should meet is:

$P_{\mathrm{\&Sigma;Load}}-(\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max })+{\mathrm{\&epsiv;}}_P\&le;\mathrm{\&Delta;}{P}_D\&le;P_{\mathrm{\&Sigma;}D\max }$ Formula 12

Circuit disconnects

Calculating formula 4, can obtain thus,

$\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&le;\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-{\mathrm{\&epsiv;}}_P$ Formula 13

Wherein, total burden with power of system after expression cutting load.Can obtain thus,

${\mathrm{\&Delta;P}}_D=P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&GreaterEqual;P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P$ Formula 14

Wherein, P _{Σ Load}total burden with power of representative system before cutting load measure, Δ P _dthe load of cutting away needed for expression;

In addition, define all can cutting load and corresponding cost thereof, cutting load cost can not can be set to infinity, removing can not cutting load, if can the total amount of cutting load be P _{∑ Dmax}.The constraints that then cutting load amount should meet is:

$P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P\&le;\mathrm{\&Delta;}{P}_D\&le;P_{\mathrm{\&Sigma;}D\max }$ Formula 15

Namely tried to achieve the constraints of required cutting load amount by above calculating, be specially:

3rd step, finds possible control strategy

The cutting load quantitative limitation drawn by previous step, find the combination of possible cutting load, before finding possible cutting load combination, user is needed to provide descriptor to each load level, namely the cost that load brings is cut away, if cost is infinitely great, then this load should in the scope of cutting load, and obtaining thus can the scope of cutting load;

Solve the minimum cost combination meeting cutting load amount constraints, the cutting load combination of the minimum cost of cutting load amount constraint can be met thus, this combination may be a kind of, also may be multiple, in addition, the load of trying to achieve not necessarily meets the constraints of formula 9, therefore needs to provide multiple possible combination:

Obtain optimal cost f _minand the cutting load combination of correspondence;

Calculation cost is f _minthe Δ P of all cutting loads combination _d, find out maximum Δ P wherein _dmax;

If find out all cutting load combinations meeting following constraints:

$P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P\&le;\mathrm{\&Delta;}{P}_D\&le;{\mathrm{\&Delta;P}}_{D\max }$ Formula 17

If ${\mathrm{\&Delta;P}}_{D\max }=P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P,$ Directly go to the 4th step;

Can obtain the combination that n1 kind meets cutting load amount constraints thus, all combinations be sorted according to cost is ascending, wherein Least-cost is f _min, result is supplied to next step and calculates;

No matter off-line generates load meter, still generate load meter online, if one or more combinations finally can be obtained, then put the mark flag=1 of load meter, if do not excise any cutting load combination meeting cutting load amount constraints, then put the mark flag=0 of load meter;

4th step, search optimal control policy

Before further calculating, first the result that the 3rd step is tried to achieve is judged, if flag=0, then represent do not exist make System recover stable can cutting load combination, need user's output alarm information; If flag=1, then proceed to calculate;

No matter be that off-line generates load meter, still load meter is generated online, the combination of the cutting load amount that the meets constrained obtained by the 3rd step is sorted from low to high according to the size of cost, these combination not necessarily can to satisfy equation 9 constraints, therefore need to verify, the combination of multiple cutting load may be there is under same cost, therefore need the control strategy therefrom choosing a kind of optimum;

According to the cutting load combination obtained, from the one combination that cost is minimum, call flow optimization procedure, if there is optimal solution in program, then represent this kind cut machine combination can to satisfy equation 9 constraints, and cost is minimum, and therefore the compound mode of this kind of cutting load is exactly optimum control strategy; If there is not optimal solution in program, represent this kind cut machine compound mode can not to satisfy equation 9 constraints, then the lower a kind of cutting load combination of checking, until search optimal solution; Cutting load for same cost combines, and calls flow optimization procedure, compares both target function values, using combination little for target function value as optimal control policy;

If the cutting load of previous step being tried to achieve combines whole checking and obtains optimal solution not yet, then judging whether in addition can cutting load, namely judges following formula,

Δ P _dmax+ P _dmin≤ P _{∑ Dmax}formula 18

Wherein, P _dminfor can the minimum value of cutting load;

If this formula is false, then there are not other in expression system can cutting load, allly at present can the combination of cutting load System recover all cannot be made to stablize, and needs user's output alarm information;

If this formula is set up, then put cutting load amount and be constrained to:

Δ P _dmax+ P _dmin≤ Δ P _d≤ P _{∑ Dmax}formula 19

Return to the 3rd step, find possible cutting load combination table.

Beneficial effect

The application at least has following technique effect or advantage:

The preferential tripping system of off-line decision-making will be changed into the preferential tripping system of on-line pre-decision system, by the operational factor of system from former emergency control policy CESE show exhaustive independent, adopt the mode of periodic collection current operating parameter, reduce amount of calculation, increase flexibility, in the process of Modling model, add multiple constraints, thus the safe and stable operation of further guarantee system.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is the overall control flow chart of the embodiment of the present application;

Fig. 2 is Policy Table's product process figure of the embodiment of the present application;

Fig. 3 be the optimal control policy of the embodiment of the present application solve flow chart.

Embodiment

In order to better understand technique scheme, below in conjunction with Figure of description and concrete execution mode, technique scheme is described in detail.

As shown in Figure 1, the invention provides a kind of emergency control method of offshore oilfield cluster power grid, comprise the collection of operational factor, control scheme list generation, perform control,

Described operational factor is collected to comprise and is collected the current operational factor of electrical network, determine the overall structure of current operational mode, the mode of connection, certainty annuity, operational factor is collected to adopt and is periodically collected, under the prerequisite that power system operating mode is not undergone mutation, carry out parameter collection at set intervals, more new data;

As shown in Figure 2, the generation of described control scheme list comprises the following steps: the fault type that the system of analyzing may exist, and namely N-1, N-2 or multimachine cut machine and different system splitting faults; Carry out scanning to dissimilar fault to calculate, search out corresponding optimal policy, generate the Policy Table that current operating parameter is corresponding; And judge whether the operational factor of collecting has refreshing, when after signal Refresh Data being detected, regenerates Policy Table;

Described execution controls to comprise the following steps: the accident disturbance of current electric grid judges; According to the accident disturbance type of current electric grid, in Policy Table, search for the control strategy of coupling, the operation of guidance system.

Wherein, in the present embodiment, when after the signal receiving operational factor refreshing, generation strategy table comprises following two large divisions's content:

(1) unit off-grid fault scanning

Unit off-grid fault scanning and computing system N-1, N-2 ... optimal control policy corresponding under N-Nmin fault, and the Policy Table of generation is stored.

(2) circuit disconnects scanning

The optimal control policy that circuit is corresponding under disconnecting scanning and the contingent various circuit open failure of computing system, and the Policy Table of generation is stored.

The Policy Table that above-mentioned two parts calculate is combined and obtains final control scheme list.

Wherein, in the present embodiment, the Mathematical Modeling of described optimal control policy is

min f(u,x)

$s.t.\left\{\begin{array}{c}h(u,x)=0\\ g(u,x)\&le;0\\ u_{\min }\&le;u\&le;u_{\max }\\ x_{\min }\&le;x\&le;x_{\max }\end{array}\right.$ Formula 1

Wherein, u is control variables, and x is state variable, and f (u, x) is target function, and h (u, x)=0 is equality constraint, and g (u, x)≤0 is inequality constraints, u _min, u _maxfor control variables m bound, x _min, x _maxfor state variable u bound;

Wherein, m _ifor i-th measure taked, N _mfor the number of control measure, x comprises each class variable representing system running state, is defined as wherein e _iand f _irepresent the horizontal component of node i and vertical component respectively, N _dfor system node number;

Wherein, target function is the restricted driving combination of the different weights of all load operation, is expressed as

$f=\underset{i=1}{\overset{N_m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{Ci}}{M}_i$ Formula 2

ω _cithe cost paid needed for i for taking measures;

Wherein, constraints specifically comprises:

A) power-balance constraint

Power-balance constraint refers to that intrasystem generated output should reach balance with load power and line loss, is specially:

A-1) unit off-grid

$\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-{\mathrm{\&epsiv;}}_P\&GreaterEqual;0$ Formula 3

Wherein, P _gimaxrepresent that the maximum meritorious of generator i is exerted oneself, P _direpresent the current loads active power of node i, ε _prepresent correction value (meritorious nargin of exerting oneself), N _gongenerator unit number online before representing the non-off-grid of unit, N _gtriprepresent the generator unit number of off-grid, N _dthe nodes of expression system;

A-2) circuit disconnects

$\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}-{\mathrm{\&epsiv;}}_P\&GreaterEqual;0$ Formula 4

B) trend constraint

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Di}}-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)+e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\end{array}\right.$ Formula 5

Wherein, P _gifor the generating active power that node i is injected, P _difor the load active power of node i, Q _gifor the generating reactive power that node i is injected, Q _difor the load reactive power of node i, G _ijfor node i and the direct transconductance of node j, B _ijfor node i and node j directly mutual susceptance;

C) voltage constraint

$V_{i\min }^2\&le;e_i^2+f_i^2\&le;V_{i\max }^2,i=1,...,N_D$ Formula 6

Wherein V _imin, V _imaxrepresent lower limit and the upper limit of node i voltage magnitude respectively;

D) branch road transmission power constraint

$(G_{\mathrm{ij}}^2+B_{\mathrm{ij}}^2)[{(e_i{e}_j+f_i{f}_j-e_i^2-f_i^2)}^2+{(f_i{e}_j-e_i{f}_j)}^2]\&le;S_{\mathrm{ij}\max }^2,i=1,...,N_L$ Formula 7

Wherein, N _lfor system branch number, S _ijmaxfor node i and node j directly exchange the maximum of power;

E) control variables constraint

For every control measure, the restriction of its correspondence

M _iMIN≤ M _i≤ M _iMAXi=1 ..., N _mformula 8

M _iMIN, M _iMAXbe respectively control measure M _iminimum value and maximum.

As shown in Figure 3, wherein, in the present embodiment, the Mathematical Modeling simplification of described optimal control policy comprises the following steps:

The first step, under judging current loads, can system be stablized

When after system generation unit off-grid, do not excising load if judge, can system reach stable, namely when not excising load, whether can meet following constraints:

$\left\{\begin{array}{c}{P}_{\mathrm{Gi}}-P_{\mathrm{Di}}-e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Di}}-f_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{e}_j-B_{\mathrm{ij}}{f}_j)+e_i\underset{j=1}{\overset{N_D}{\mathrm{\&Sigma;}}}(G_{\mathrm{ij}}{f}_j+B_{\mathrm{ij}}{e}_j)=0,i=1,...,N_D\\ (G_{\mathrm{ij}}^2+B_{\mathrm{ij}}^2)[{(e_i{e}_j+f_i{f}_j-e_i^2-f_i^2)}^2+{(f_i{e}_j-e_i{f}_j)}^2]\&le;S_{\mathrm{ij}\max }^2,i=1,...,N_L\\ V_{i\min }^2\&le;e_i^2+f_i^2\&le;V_{i\max }^2,i=1,...,N_D\end{array}\right.$ Formula 9

If unit exert oneself and load can meet this constraint equation, then represent system can reach stable, do not need the measure of cutting load; If this constraint equation is without solution, then represent current unit possible exert oneself and current loads situation there is serious imbalance, need the calculating carrying out next step;

Second step, calculates the restriction of cutting load amount

Consider that unit off-grid and circuit disconnect two kinds of situations respectively:

Unit off-grid

Calculating formula 3, can obtain thus,

$\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&le;\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-{\mathrm{\&epsiv;}}_P$ Formula 10

Wherein, after expression cutting load, total burden with power of system, can obtain thus,

$\mathrm{\&Delta;}{P}_D=P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&GreaterEqual;P_{\mathrm{\&Sigma;Load}}-(\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max })+{\mathrm{\&epsiv;}}_P$ Formula 11

Wherein, P _{Σ Load}total burden with power of representative system before cutting load measure, Δ P _dthe load of cutting away needed for expression;

In addition, define all can cutting load and corresponding cost thereof, cutting load cost can not can be set to infinity, removing can not cutting load, if can the total amount of cutting load be P _{∑ Dmax}, then the constraints that cutting load amount should meet is:

$P_{\mathrm{\&Sigma;Load}}-(\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-\underset{i=1}{\overset{N_{\mathrm{Gtrip}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max })+{\mathrm{\&epsiv;}}_P\&le;\mathrm{\&Delta;}{P}_D\&le;P_{\mathrm{\&Sigma;}D\max }$ Formula 12

Circuit disconnects

Calculating formula 4, can obtain thus,

$\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&le;\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }-{\mathrm{\&epsiv;}}_P$ Formula 13

Wherein, total burden with power of system after expression cutting load.Can obtain thus,

${\mathrm{\&Delta;P}}_D=P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_D}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Di}}\&GreaterEqual;P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P$ Formula 14

Wherein, P _{Σ Load}total burden with power of representative system before cutting load measure, Δ P _dthe load of cutting away needed for expression;

In addition, define all can cutting load and corresponding cost thereof, cutting load cost can not can be set to infinity, removing can not cutting load, if can the total amount of cutting load be P _{∑ Dmax}.The constraints that then cutting load amount should meet is:

$P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P\&le;\mathrm{\&Delta;}{P}_D\&le;P_{\mathrm{\&Sigma;}D\max }$ Formula 15

Namely tried to achieve the constraints of required cutting load amount by above calculating, be specially:

formula 16

3rd step, finds possible control strategy

The cutting load quantitative limitation drawn by previous step, find the combination of possible cutting load, before finding possible cutting load combination, user is needed to provide descriptor to each load level, namely the cost that load brings is cut away, if cost is infinitely great, then this load should in the scope of cutting load, and obtaining thus can the scope of cutting load;

Solve the minimum cost combination meeting cutting load amount constraints, the cutting load combination of the minimum cost of cutting load amount constraint can be met thus, this combination may be a kind of, also may be multiple, in addition, the load of trying to achieve not necessarily meets the constraints of formula 9, therefore needs to provide multiple possible combination:

Obtain optimal cost f _minand the cutting load combination of correspondence;

Calculation cost is f _minthe Δ P of all cutting loads combination _d, find out maximum Δ P wherein _dmax;

If find out all cutting load combinations meeting following constraints:

$P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P\&le;\mathrm{\&Delta;}{P}_D\&le;{\mathrm{\&Delta;P}}_{D\max }$ Formula 17

If ${\mathrm{\&Delta;P}}_{D\max }=P_{\mathrm{\&Sigma;Load}}-\underset{i=1}{\overset{N_{\mathrm{Gon}}}{\mathrm{\&Sigma;}}}{P}_{\mathrm{gi}\max }+{\mathrm{\&epsiv;}}_P,$ Directly go to the 4th step;

Can obtain the combination that n1 kind meets cutting load amount constraints thus, all combinations be sorted according to cost is ascending, wherein Least-cost is f _min, result is supplied to next step and calculates;

No matter off-line generates load meter, still generate load meter online, if one or more combinations finally can be obtained, then put the mark flag=1 of load meter, if do not excise any cutting load combination meeting cutting load amount constraints, then put the mark flag=0 of load meter;

4th step, search optimal control policy

Before further calculating, first the result that the 3rd step is tried to achieve is judged, if flag=0, then represent do not exist make System recover stable can cutting load combination, need user's output alarm information; If flag=1, then proceed to calculate;

No matter be that off-line generates load meter, still load meter is generated online, the combination of the cutting load amount that the meets constrained obtained by the 3rd step is sorted from low to high according to the size of cost, these combination not necessarily can to satisfy equation 9 constraints, therefore need to verify, the combination of multiple cutting load may be there is under same cost, therefore need the control strategy therefrom choosing a kind of optimum;

According to the cutting load combination obtained, from the one combination that cost is minimum, call flow optimization procedure, if there is optimal solution in program, then represent this kind cut machine combination can to satisfy equation 9 constraints, and cost is minimum, and therefore the compound mode of this kind of cutting load is exactly optimum control strategy; If there is not optimal solution in program, represent this kind cut machine compound mode can not to satisfy equation 9 constraints, then the lower a kind of cutting load combination of checking, until search optimal solution; Cutting load for same cost combines, and calls flow optimization procedure, compares both target function values, using combination little for target function value as optimal control policy;

If the cutting load of previous step being tried to achieve combines whole checking and obtains optimal solution not yet, then judging whether in addition can cutting load, namely judges following formula,

Δ P _dmax+ P _dmin≤ P _{∑ Dmax}formula 18

Wherein, P _dminfor can the minimum value of cutting load;

If this formula is false, then there are not other in expression system can cutting load, allly at present can the combination of cutting load System recover all cannot be made to stablize, and needs user's output alarm information;

If this formula is set up, then put cutting load amount and be constrained to:

Δ P _dmax+ P _dmin≤ Δ P _d≤ P _{∑ Dmax}formula 19

Return to the 3rd step, find possible cutting load combination table.

The above, it is only preferred embodiment of the present invention, not any pro forma restriction is done to the present invention, although the present invention with preferred embodiment demonstration as above, but and be not used to limit the present invention, any those skilled in the art, do not departing within the scope of technical solution of the present invention, make a little change when the technology contents of above-mentioned announcement can be utilized or be modified to the Equivalent embodiments of equivalent variations, in every case be the content not departing from technical solution of the present invention, according to any simple modification that technical spirit of the present invention is done above embodiment, equivalent variations and modification, all still belong in the scope of technical solution of the present invention.

Claims (4)

1. an emergency control method for offshore oilfield cluster power grid, is characterized in that: comprise the collection of operational factor, control scheme list generation, perform control;

Described operational factor is collected to comprise and is collected the current operational factor of electrical network, determine the overall structure of current operational mode, the mode of connection, certainty annuity, operational factor is collected to adopt and is periodically collected, under the prerequisite that power system operating mode is not undergone mutation, carry out parameter collection at set intervals, more new data;

The generation of described control scheme list comprises: the fault type that the system of analyzing may exist, and namely N-1, N-2 or multimachine cut machine and different system splitting faults; Carry out scanning to dissimilar fault to calculate, search out corresponding optimal policy, generate the Policy Table that current operating parameter is corresponding; And judge whether the operational factor of collecting has refreshing, when after signal Refresh Data being detected, regenerates Policy Table;

Described execution controls to comprise: the accident disturbance of current electric grid judges; According to the accident disturbance type of current electric grid, in Policy Table, search for the control strategy of coupling, the operation of guidance system.

2. the emergency control method of a kind of offshore oilfield cluster power grid according to claim 1, is characterized in that, when after the signal receiving operational factor refreshing, generation strategy table comprises following two large divisions's content:

(1) unit off-grid fault scanning

Unit off-grid fault scanning and computing system N-1, N-2 ... optimal control policy corresponding under N-Nmin fault, and the Policy Table of generation is stored;

(2) circuit disconnects scanning

The optimal control policy that circuit is corresponding under disconnecting scanning and the contingent various circuit open failure of computing system, and the Policy Table of generation is stored;

The Policy Table that above-mentioned two parts calculate is combined and obtains final control scheme list.

3. the emergency control method of a kind of offshore oilfield cluster power grid according to claim 2, is characterized in that, the Mathematical Modeling of described optimal control policy is

minf(u，x)

formula 1

Wherein, u is control variables, and x is state variable, and f (u, x) is target function, and h (u, x)=0 is equality constraint, and g (u, x)≤0 is inequality constraints, u _min, u _maxfor control variables m bound, x _min, x _maxfor state variable u bound;

Wherein, m _ifor i-th measure taked, N _mfor the number of control measure, x comprises each class variable representing system running state, is defined as wherein e _iand f _irepresent the horizontal component of node i and vertical component respectively, N _dfor system node number;

Wherein, target function is the restricted driving combination of the different weights of all load operation, is expressed as

formula 2

ω _cithe cost paid needed for i for taking measures;

Wherein, constraints specifically comprises:

A) power-balance constraint

Power-balance constraint refers to that intrasystem generated output should reach balance with load power and line loss, is specially:

A-1) unit off-grid

formula 3

Wherein, P _gimaxrepresent that the maximum meritorious of generator i is exerted oneself, P _direpresent the current loads active power of node i, ε _prepresent correction value (meritorious nargin of exerting oneself), N _gongenerator unit number online before representing the non-off-grid of unit, N _gtriprepresent the generator unit number of off-grid, N _dthe nodes of expression system;

A-2) circuit disconnects

formula 4

B) trend constraint

formula 5

Wherein, P _gifor the generating active power that node i is injected, P _difor the load active power of node i, Q _gifor the generating reactive power that node i is injected, Q _difor the load reactive power of node i, G _ijfor node i and the direct transconductance of node j, B _ijfor node i and node j directly mutual susceptance;

C) voltage constraint

formula 6

Wherein V _imin, V _imaxrepresent lower limit and the upper limit of node i voltage magnitude respectively;

D) branch road transmission power constraint

Formula 7

Wherein, N _lfor system branch number, S _ijmaxfor node i and node j directly exchange the maximum of power;

E) control variables constraint

For every control measure, the restriction of its correspondence

M _iMIN≤ M _i≤ M _iMAXi=1 ..., N _mformula 8

M _iMIN, M _iMAXbe respectively control measure M _iminimum value and maximum.

4. the emergency control method of a kind of offshore oilfield cluster power grid according to claim 3, is characterized in that, the Mathematical Modeling simplification of described optimal control policy comprises the following steps:

The first step, under judging current loads, can system be stablized

When after system generation unit off-grid, do not excising load if judge, can system reach stable, namely when not excising load, whether can meet following constraints:

formula 9

If unit exert oneself and load can meet this constraint equation, then represent system can reach stable, do not need the measure of cutting load; If this constraint equation is without solution, then represent current unit possible exert oneself and current loads situation there is serious imbalance, need the calculating carrying out next step;

Second step, calculates the restriction of cutting load amount

Consider that unit off-grid and circuit disconnect two kinds of situations respectively:

Unit off-grid

Calculating formula 3, can obtain thus,

formula 10

Wherein, after expression cutting load, total burden with power of system, can obtain thus,

formula 11

Wherein, P _{Σ Load}total burden with power of representative system before cutting load measure, Δ P _dthe load of cutting away needed for expression;

In addition, define all can cutting load and corresponding cost thereof, cutting load cost can not can be set to infinity, removing can not cutting load, if can the total amount of cutting load be P _{∑ Dmax}, then the constraints that cutting load amount should meet is:

formula 12

Circuit disconnects

Calculating formula 4, can obtain thus,

formula 13

Wherein, total burden with power of system after expression cutting load.Can obtain thus,

formula 14

Wherein, P _{Σ Load}total burden with power of representative system before cutting load measure, Δ P _dthe load of cutting away needed for expression;

In addition, define all can cutting load and corresponding cost thereof, cutting load cost can not can be set to infinity, removing can not cutting load, if can the total amount of cutting load be P _{∑ Dmax}, then the constraints that cutting load amount should meet is:

formula 15

Namely tried to achieve the constraints of required cutting load amount by above calculating, be specially:

formula 16

3rd step, finds possible control strategy

The cutting load quantitative limitation drawn by previous step, find the combination of possible cutting load, before finding possible cutting load combination, user is needed to provide descriptor to each load level, namely the cost that load brings is cut away, if cost is infinitely great, then this load should in the scope of cutting load, and obtaining thus can the scope of cutting load;

Solve the minimum cost combination meeting cutting load amount constraints, the cutting load combination of the minimum cost of cutting load amount constraint can be met thus, this combination may be a kind of, also may be multiple, in addition, the load of trying to achieve not necessarily meets the constraints of formula 9, therefore needs to provide multiple possible combination:

Obtain optimal cost f _minand the cutting load combination of correspondence;

Calculation cost is f _minthe Δ P of all cutting loads combination _d, find out maximum Δ P wherein _dmax;

If find out all cutting load combinations meeting following constraints:

formula 17

If directly go to the 4th step;

Can obtain the combination that n1 kind meets cutting load amount constraints thus, all combinations be sorted according to cost is ascending, wherein Least-cost is f _min, result is supplied to next step and calculates;

No matter off-line generates load meter, still generate load meter online, if one or more combinations finally can be obtained, then put the mark flag=1 of load meter, if do not excise any cutting load combination meeting cutting load amount constraints, then put the mark flag=0 of load meter;

4th step, search optimal control policy

Before further calculating, first the result that the 3rd step is tried to achieve is judged, if flag=0, then represent do not exist make System recover stable can cutting load combination, need user's output alarm information; If flag=1, then proceed to calculate;

No matter be that off-line generates load meter, still load meter is generated online, the combination of the cutting load amount that the meets constrained obtained by the 3rd step is sorted from low to high according to the size of cost, these combination not necessarily can to satisfy equation 9 constraints, therefore need to verify, the combination of multiple cutting load may be there is under same cost, therefore need the control strategy therefrom choosing a kind of optimum;

According to the cutting load combination obtained, from the one combination that cost is minimum, call flow optimization procedure, if there is optimal solution in program, then represent this kind cut machine combination can to satisfy equation 9 constraints, and cost is minimum, and therefore the compound mode of this kind of cutting load is exactly optimum control strategy; If there is not optimal solution in program, represent this kind cut machine compound mode can not to satisfy equation 9 constraints, then the lower a kind of cutting load combination of checking, until search optimal solution; Cutting load for same cost combines, and calls flow optimization procedure, compares both target function values, using combination little for target function value as optimal control policy;

If the cutting load of previous step being tried to achieve combines whole checking and obtains optimal solution not yet, then judging whether in addition can cutting load, namely judges following formula,

Δ P _dmax+ P _dmin≤ P _{Σ Dmax}formula 18

Wherein, P _dminfor can the minimum value of cutting load;

If this formula is false, then there are not other in expression system can cutting load, allly at present can the combination of cutting load System recover all cannot be made to stablize, and needs user's output alarm information;

If this formula is set up, then put cutting load amount and be constrained to:

Δ P _dmax+ P _dmin≤ Δ P _d≤ P _{Σ Dmax}formula 19

Return to the 3rd step, find possible cutting load combination table.