CN105978046A - Precision discrete optical power flow calculation method of VSC-HVDC (voltage source converter based high voltage direct current) containing AC/DC system - Google Patents
Precision discrete optical power flow calculation method of VSC-HVDC (voltage source converter based high voltage direct current) containing AC/DC system Download PDFInfo
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Abstract
The invention relates to a precision discrete optical power flow calculation method of a VSC-HVDC (voltage source converter based high voltage direct current) containing AC/DC system. The calculation method is characterized by comprising the steps of firstly analyzing a power steady-state equation and other modified equations of the VSC-HVDC containing AC/DC system, then setting equality constraints and inequality constraints, and finally introducing a positive curvature quadratic penalty function into an interior point method. According to the calculation method, the interior point method is adopted to carry out optimization on continuous variables of the AC/DC system, the penalty function is introduced when a certain condition is reached, and discrete variables are constrained and optimized. Meanwhile, parameter values of the penalty function are continuously adjusted according to variations of the iteration quantity, and finally a purpose of optimizing the continuous variables and the discrete variables simultaneously is achieved.
Description
Technical field
The present invention relates to a kind of discrete optimal load flow computational methods Han VSC-HVDC ac and dc systems precision, belong to
Operation and control of electric power system technical field.
Background technology
High voltage dc transmission technology (voltage based on voltage source converter (VSC) and full-controlled switch device
Source converter based high voltage direct current, VSC-HVDC) be a new generation direct current defeated
Power technology, solves the many technological difficulties in conventional high-tension direct current transportation, also has plurality of advantages simultaneously, if to meritorious nothing
Merit carries out the most independent control；Quick reactive power support can be provided for AC；Trend reversal rate faster, is more easy to realize also
Connection multistage straight-flow system etc..For these reasons, VSC-HVDC and ac and dc systems not only can the more in Practical Project
Application, also becomes the study hotspot of numerous scholar simultaneously.
There is bigger difference with mathematical model and conventional high-tension direct current transportation model in the element characteristic of VSC-HVDC, original
The algorithm of the alternating current-direct current optimal load flow being applicable to conventional high-tension direct current transportation, cannot be applicable to VSC-HVDC system
Excellent Load flow calculation.By ac and dc systems OPF in article " ac and dc systems idle work optimization based on singular value decomposition and interior point method "
Model is for the calculating of optimal reactive power allocation scheme, but does not accounts for VSC-HVDC system；Article " Modeling of VSC-
Based HVDC systems for a Newton-Raphson OPF algorithm " propose based on Newton-Raphson approach
The solution of the OPF problem containing VSC-HVDC ac and dc systems, but due to the method commonly used iterative test method, by compiling
There is difficulty in Cheng Shixian.
Primal dual interior point method (abbreviation interior point method) has bigger advantage in process continuous variable optimization problem, its robust
Property strong, convergence good, but process discrete variable optimization problem time relatively difficult；Intelligent algorithm has good discrete variable
Disposal ability, document " idle work optimization mixed strategy based on genetic algorithm and interior point method " is " based on interior point method and improved genetic algorithms
The idle work optimization combined strategy of method " propose the hybrid algorithm that interior point method combines with intelligent algorithms such as genetic algorithms, process
The discrete optimization problem with continuous variable, but this type of algorithm speed of searching optimization is the slowest, the calculating time is longer, contains in calculating simultaneously
During VSC-HVDC ac and dc systems OPF problem, needing to specify hvdc control mode, this will cause intelligent algorithm to be absorbed in local optimum
Solve or make algorithm vibrate.
Summary of the invention
It is an object of the invention to the deficiency overcoming prior art to exist, and propose a kind of ac and dc systems Han VSC-HVDC
Precision discrete optimal load flow computational methods, it uses interior point method to be optimized ac and dc systems continuous variable, when reaching certain
Introduce penalty function during one condition, discrete variable is retrained and optimizes, simultaneously according to the change of iteration amount, constantly adjust and penalize letter
The parameter value of number, finally reaches continuous, the purpose of discrete variable optimizing simultaneously.
It is an object of the invention to complete by following technical solution, a kind of ac and dc systems precision Han VSC-HVDC
Discrete optimal load flow computational methods, these computational methods first analyze the power steady-state equation containing VSC-HVDC ac and dc systems and its
His update equation, then sets its equality constraint and inequality constraints, finally positive camber quadratic penalty function is introduced interior point method；Tool
Body is:
1) the described VSC-HVDC ac and dc systems that contains mainly is made up of AC system, current conversion station and DC network 3 part；
The input voltage that can make inverter isThe voltage of the exchange node injecting this node isThe power of exchange node is Psi+jQsi；The power injecting current conversion station is Pci+jQci, current conversion station converter power transformer
Equiva lent impedance be Ri+jXLi；
By above-mentioned it is assumed that can calculate and flow through the electric current of converter power transformer and be:
AC system flows into the power of current conversion station should meet relationship below:
Here δ can be madei=θsi-θci,αi=arctan (XLi/Ri), can obtain by deriving:
Herein for the relevant equation eliminating inverter so that AC system passes through equation direct correlation with straight-flow system,
The output voltage virtual value of use inverter and the relation of DC voltage:
In above formula, μdFor the utilization rate of DC voltage, generally 0 < μd< 1, modulation system is set to SPWM here, thenMiFor modulation degree, set modulation degree here as 0 < Mi<1；
The injecting power exchanging node can be obtained and exchange node, the relation of DC node relevant parameter amount:
The internal loss of inverter and transformer loss are by RiEquivalence, therefore dc power PdiWith the P injecting converter bridgeciPhase
Deng, therefore have below equation, I thereindiFor DC node electric current:
Ac and dc systems comprises exchange and DC node simultaneously, is required for being modified to different types of node, to friendship
Stream node, its update equation is consistent with tradition Load flow calculation:
For the DC node of VSC, equation is:
I, j in formula represents the numbering of node, and P, Q, U represent meritorious, idle and voltage magnitude respectively, and θ, G, B divide
Do not represent phase angle, conductance and susceptance, Pi sWithRepresent active power and the reactive power injecting node i respectively；
The update equation of straight-flow system is:
I in formula represents the numbering of VSC；
According to solving the number of variable, need to increase DC network equation:
R in formuladRepresent resistance between DC node；
2) logarithm barrier function is introduced in Newton method by interior point method, for processing the inequality in nonlinear programming problem about
Bundle, specifically can be to be described as following form:
In formula, x is unknown variable；F (x) is optimization object function；H (x), g (x) are respectively equality constraint with inequality about
Bundle；gmax、gminIt is respectively the bound of inequality constraints；
Introduce slack variable l, u, and in object function, add logarithm barrier function, it is possible to inequality constraints is changed
For equality constraint, solve the most again:
Y, z, w in formula is Lagrange multiplier, also referred to as dual variable.The essential condition that this optimization problem minimum exists
Be above formula be all 0 to the partial derivative of all of variable and multiplier, it is hereby achieved that:
Wherein μ=σ Gap/2r, Gap=lTz-uTW, Gap are referred to as duality gap, and σ is referred to as Center Parameter；L=diag
(l1,…,lr), U=diag (u1,…,ur), Z=diag (z1,…,zr), W=diag (w1,…,wr) wherein r represent
The number of formula constraint.
Use Newton-Raphson approach to solve, its linearisation can be obtained update equation group:
By above formula through k iteration, obtain the correction value of former variable and dual variable, and be updated, the side of finally obtaining
The solution of journey；
3) a positive camber quadratic penalty function being introduced interior point method, its expression formula is as follows:
In above formula, vbFor penalty factor, xb1For discrete variable xbThe centre of neighbourhood, x can be definedb1Neighborhood R (xb1) it is such as
Lower interval:
Wherein, S is its classification step-length.
By positive camber quadratic penalty functionIntroduce, can obtain:
By introducing quadratic penalty function, discrete variable can be played an effect of contraction so that it is rule during calculating
Whole to the centre of neighbourhood；The effect that the method processes discrete variable is close with the size on the opportunity and penalty factor that introduce penalty function can not
Point；
Using ac and dc systems loss minimization as object function:
In formula, PaclossFor AC system network loss, and PdclossIt is lost for the DC line in system.
As preferably: the 1st) in step, the control mode containing VSC-HVDC ac and dc systems is relatively more flexible, typically by following change
Measure as controlling target: the alternating voltage U on DC nodes, DC voltage Ud, flow into circulation transformator AC power Ps、
Qs；When carrying out Load flow calculation or optimal load flow and calculating, in system, each VSC needs to select two control variable, typically just like
Lower 4 kinds of combinations: determine Ud, determine QsControl；Determine Ud, determine UsControl；Determine Ps, determine QsControl；Determine Ps, determine UsControl；Common two ends are handed over
For straight-flow system, its control mode is combined as above-mentioned combination of two, and for multistage or multi-infeed systems, compound mode
By more diversification；
2nd), in step, AC and DC power system idle work optimization model is a nonlinear mixed-integer programming, processes idle
Compensation capacity and these discrete variables of transformer voltage ratio are the most crucial, and the virtual expense that described penalty function is added can force discrete control
Draw close in some classification of variable processed, thus former problem is converted into the nonlinear programming problem adding discrete constraint；This two
Secondary to penalize mechanism be not to be forced against by discrete variable in its most adjacent classification, and can be reduced by the expense that global optimization brings
Impact；
Quadratic penalty functionWherein abscissa xbFor discrete variable, xb0、xb1、xb2It is xbThree adjacent discrete values；
Xb1Neighborhood such as figure in R (xb1Shown in), penalty function is minimum at the centre of neighbourhood, and maximum on neighborhood border, so that discrete change
Measure and draw close to the centre of neighbourhood during optimizing.
The 3rd) in step, first, the opportunity during quadratic penalty function calculates to interior point method that introduces is most important, changes at interior point method
In generation, calculates the initial stage, and the correction value of variable is relatively big, if now introducing quadratic penalty function, can disturb global optimization, and the centre of neighbourhood is frequent
Variation, computational efficiency is low, it could even be possible to optimal solution cannot be converged to；
As Gap, < when 0.1, now neighborhood determines the most substantially, introduces quadratic penalty function and can preferably realize discrete variable to neighborhood
The function that center is drawn close；In the interior point method iteration later stage, variable correction value can be more and more less, when optimal solution is decided substantially, if
Now it is re-introduced into quadratic penalty function, then can increase iterations, reduce convergence；
Secondly, the size of penalty factor also can affect the effect of algorithm, for making penalty mechanism more flexible, and can be to different
Discrete variable chooses different penalty factors according to the size of its classification step-length, and in general, the classification step-length of capacitor is relatively
Greatly, can take penalty factor is 50；And for the no-load voltage ratio of ULTC, in general classification step-length is less, can will penalize
The factor is taken as 500 so that penalty mechanism is sensitiveer.
The present invention has a most useful technique effect:
1) stronger discrete variable disposal ability.Computational methods herein add discrete change on the basis of interior point method
The process of amount, i.e. make use of interior point method calculates the advantage quick, optimizing ability is strong, combines again the method for penalty function to discrete change
Amount is optimized so that the suitability of context of methods is more extensive；
2) speed is fast, numerical computations is stable in calculating.The method using article calculates speed, according to above-mentioned example, one
As iteration can find optimal solution for about 20 times, the time that calculates is in second level, and result of calculation numerical stability, calculates reliable receipts
Hold back；
It, based on interior point method, is transformed by the present invention by adding by the way of penalty function so that it is have process from
Dissipate the ability of variable, have studied it and applying containing the calculating in VSC-HVDC ac and dc systems, by result of calculation and with existing
Document contrasts, it was demonstrated that the present invention, in the problem processing containing VSC-HVDC ac and dc systems optimal load flow, has stronger advantage
With the ability of adaptation.
Accompanying drawing explanation
Fig. 1 is of the present invention containing VSC-HVDC ac and dc systems schematic diagram.
Fig. 2 is whole curvature quadratic penalty function figure of the present invention.
Fig. 3 is the interior point method calculation flow chart containing discretization penalty function of the present invention.
Fig. 4 is 5 nodes ac and dc systems schematic diagram Han VSC-HVDC after amendment of the present invention.
Fig. 5 is 5 node system convergence of algorithm curve charts of the present invention.
Fig. 6 is 30 nodes ac and dc systems schematic diagram Han VSC-HVDC after amendment of the present invention.
Fig. 7 is 30 node system convergence of algorithm curve charts of the present invention.
Detailed description of the invention
The present invention will be described in detail below in conjunction with the accompanying drawings and the specific embodiments: of the present invention containing VSC-HVDC
Ac and dc systems precision discrete optimal load flow computational methods, these computational methods are: first analyze containing VSC-HVDC alternating current-direct current system
The power steady-state equation of system and other update equations, then set its equality constraint and inequality constraints, finally by positive camber two
Secondary penalty function introduces interior point method；It is specifically described below as follows:
(1) schematic diagram containing VSC-HVDC ac and dc systems as it is shown in figure 1, system typically by AC system, current conversion station and
DC network 3 part forms.
The input voltage that can make inverter isThe voltage of the exchange node injecting this node isThe power of exchange node is Psi+jQsi；The power injecting current conversion station is Pci+jQci, current conversion station converter power transformer
Equiva lent impedance be Ri+jXLi。
By above-mentioned it is assumed that can calculate and flow through the electric current of converter power transformer and be:
AC system flows into the power of current conversion station should meet relationship below:
Here δ can be madei=θsi-θci,αi=arctan (XLi/Ri), can obtain by deriving:
Herein for the relevant equation eliminating inverter so that AC system passes through equation direct correlation with straight-flow system,
The output voltage virtual value of use inverter and the relation of DC voltage:
In above formula, μdFor the utilization rate of DC voltage, generally 0 < μd< 1, modulation system is set to SPWM here, thenMiFor modulation degree, set modulation degree here as 0 < Mi<1。
The injecting power exchanging node can be obtained and exchange node, the relation of DC node relevant parameter amount:
The internal loss of inverter and transformer loss are by RiEquivalence, therefore dc power PdiWith the P injecting converter bridgeciPhase
Deng, therefore have below equation, I thereindiFor DC node electric current:
Control mode containing VSC-HVDC ac and dc systems is relatively more flexible, typically using following variable as controlling target: straight
Alternating voltage U on stream nodes, DC voltage Ud, flow into circulation transformator AC power Ps、Qs.Carry out Load flow calculation or
When optimal load flow calculates, in system, each VSC needs to select two control variable, typically has following 4 kinds of combinations: determine Ud, determine QsControl
System；Determine Ud, determine UsControl；Determine Ps, determine QsControl；Determine Ps, determine UsControl；For common two ends ac and dc systems, it controls
Mode is combined as above-mentioned combination of two, and for multistage or multi-infeed systems, compound mode is by more diversification.
Ac and dc systems comprises exchange and DC node simultaneously, is required for being modified to different types of node.To friendship
Stream node, its update equation is consistent with tradition Load flow calculation:
For the DC node of VSC, equation is:
I, j in formula represents the numbering of node, and P, Q, U represent meritorious, idle and voltage magnitude respectively, and θ, G, B divide
Do not represent phase angle, conductance and susceptance, Pi sWithRepresent active power and the reactive power injecting node i respectively.
The update equation of straight-flow system is:
I in formula represents the numbering of VSC.
According to solving the number of variable, need to increase DC network equation:
R in formuladRepresent resistance between DC node
2. logarithm barrier function is introduced in Newton method by interior point method, for processing the inequality in nonlinear programming problem about
Bundle, specifically can be to be described as following form:
In formula, x is unknown variable；F (x) is optimization object function；H (x), g (x) are respectively equality constraint with inequality about
Bundle；gmax、gminIt is respectively the bound of inequality constraints.
Introduce slack variable l, u, and in object function, add logarithm barrier function, it is possible to inequality constraints is changed
For equality constraint, solve the most again:
Y, z, w in formula is Lagrange multiplier, also referred to as dual variable.The essential condition that this optimization problem minimum exists
Be above formula be all 0 to the partial derivative of all of variable and multiplier, it is hereby achieved that:
Wherein μ=σ Gap/2r, Gap=lTz-uTW, Gap are referred to as duality gap, and σ is referred to as Center Parameter；L=diag
(l1,…,lr), U=diag (u1,…,ur), Z=diag (z1,…,zr), W=diag (w1,…,wr) wherein r represent
The number of formula constraint.
Use Newton-Raphson approach to solve, its linearisation can be obtained update equation group:
By above formula through k iteration, obtain the correction value of former variable and dual variable, and be updated, the side of finally obtaining
The solution of journey, concrete steps see document " modern power systems analysis ".
AC and DC power system idle work optimization model is a nonlinear mixed-integer programming, process reactive compensation capacity and
These discrete variables of transformer voltage ratio are the most crucial, document " the new processing method of discrete controlled quentity controlled variable in newton optimal load flow algorithm "
Propose one penalty function of structure and carry out the virtual expense that analog discrete variable deviation feasible point is caused so that it is can punish that those are inclined
Variable from centrifugal pump.The virtual expense that this penalty function is added can force draws close in some classification of discrete control variable, from
And former problem is converted into the nonlinear programming problem adding discrete constraint.It is noted that this secondary penalizes mechanism not
It is discrete variable to be forced against in its most adjacent classification, and can be reduced by the expense that global optimization brings and be affected.
According to above-mentioned thinking, this paper introduces a positive camber quadratic penalty function, and its expression formula is as follows:
In above formula, vbFor penalty factor, xb1For discrete variable xbThe centre of neighbourhood, x can be definedb1Neighborhood R (xb1) it is such as
Lower interval:
Wherein, S is its classification step-length.
Fig. 2 is the quadratic penalty function of formulaWherein abscissa xbFor discrete variable, xb0、xb1、xb2It is xbThree phases
Adjacent centrifugal pump.Xb1Neighborhood such as figure in R (xb1Shown in), penalty function is minimum at the centre of neighbourhood, and maximum on neighborhood border, from
And make discrete variable draw close to the centre of neighbourhood during optimizing.
By positive camber quadratic penalty functionIntroduce, can obtain:
By introducing quadratic penalty function, discrete variable can be played an effect of contraction so that it is rule during calculating
Whole to the centre of neighbourhood.The effect that the method processes discrete variable is close with the size on the opportunity and penalty factor that introduce penalty function can not
Point.
First, the opportunity during quadratic penalty function calculates is introduced to interior point method most important.At the interior point method iterative computation initial stage,
The correction value of variable is relatively big, if now introducing quadratic penalty function, can disturb global optimization, and the centre of neighbourhood frequently changes, and calculates effect
Rate is low, it could even be possible to optimal solution cannot be converged to.As Gap, < when 0.1, now neighborhood determines the most substantially, introduces secondary and penalizes letter
Number can preferably realize the function that discrete variable is drawn close to the centre of neighbourhood.In the interior point method iteration later stage, variable correction value can be increasingly
Little, when optimal solution is decided substantially, if being now re-introduced into quadratic penalty function, then can increase iterations, reducing the receipts of algorithm
Holding back property.
Secondly, the size of penalty factor also can affect the effect of algorithm.For making penalty mechanism more flexible, can be to different
Discrete variable chooses different penalty factors according to the size of its classification step-length.In general, the classification step-length of capacitor is relatively big,
Can take penalty factor is 50；And for the no-load voltage ratio of ULTC, in general classification step-length is less, can be by penalty factor
It is taken as 500 so that penalty mechanism is sensitiveer.Additionally the function in view of penalty factor is to strengthen discrete variable to lean on to the centre of neighbourhood
The effect held together, weakens the effect to opposite direction motion, can dynamically adjust taking of penalty factor according to the direction of motion of discrete variable
Value, improves the Searching efficiency of algorithm further.
The present invention using ac and dc systems loss minimization as object function:
In formula, PaclossFor AC system network loss, and PdclossIt is lost for the DC line in system.
In sum, the calculation process of band Discrete Penalty Function interior point method can be obtained, see Fig. 3.
Embodiment: change the 3-4 branch road of 5 node example systems into direct current branch, as shown in Figure 4.The DC parameter of system
As shown in table 1:
Table 15 node system DC parameter
The range of accommodation of each parameter is made following agreement, and for continuous variable, the voltage bound of each node is set to
[0.9,1.1], the modulation degree bound of VSC-HVDC is set to [0.5,1.0], and DC voltage bound is set as [1.5,2.5],
Meritorious transmission line capability scope is [-4.0,4.0], and idle transmission line capability scope is [-1.0,1.0], and reference capacity is 100MVA；Right
In discrete variable, the no-load voltage ratio range of accommodation of ULTC is set as [0.9,1.1], and its regulation step-length is 0.0125,
The range of capacity of the reactive power compensator installed at node 1 is [0,4.0], and regulation step-length is 0.05.
The condition of convergence is set as when duality gap is less than 10-6Stopping calculating, maximum iteration time is set as 100 times；Set
When duality gap less than 0.1 and each iterative value of discrete magnitude less than the half of its step-length time, be initially added into penalty function；Penalty function
The initial value of penalty factor sets to see in Section three and illustrates, when each iterative value of discrete magnitude is less than 1/4th of its step-length and penalizes
The factor is less than 5*107Time, each iteration penalty factor increases 10 times.
The control mode of straight-flow system is set as, OPF1 is that VSC1 determines Control of Voltage and determines Reactive Power Control,
VSC2 determines active power controller and determines Reactive Power Control；OPF2 is that VSC1 determines Control of Voltage and determines reactive power control
System, VSC2 determine active power controller with surely exchange node voltage control.
The convergence curve of two kinds of control modes of 5 nodes is shown in that Fig. 5, the optimum results of each control variable and DC parameter are shown in Table
Shown in 2.
Table 2:5 node system optimum results
Before table 2 optimizes network loss represent engineered after the network loss value that obtains of 5 node ac and dc systems Load flow calculation.Logical
Crossing 5 node examples to show, the method for article can preferably calculate the optimal load flow containing VSC-HVDC ac and dc systems, calculates knot
Fruit show each variable all in limits, network loss relatively original system has greatly improved, transformator, the discrete variable of reactive-load compensation
Value all optimizes on step-length node, shows that the method is preferable to the optimum results of discrete variable, when Simultaneous Iteration number of times and calculating
Between the most ideal.
In order to the general applicability of the method is described, 30 node systems are carried out computational analysis.2-4 by 30 node systems
Branch road transform direct current branch as, as shown in Figure 6.DC parameter is as shown in table 3.
Table 3 30 node system DC parameter
Being set as of each variable, direct current transmission line capability scope of gaining merit for [-3.0,3.0], idle transmission line capability scope be [-
3.0,3.0], at node 21 and node 30, reactive power compensator, other range of variables limit values and the setting one of 5 nodes are installed
Cause.The convergence curve of two kinds of control modes of 30 nodes is shown in that Fig. 7, the optimum results of each control variable and DC parameter are shown in Table 4 institutes
Show.
Table 4 30 node system optimum results
Before table 4 optimizes network loss represent engineered after the network loss value that obtains of 30 node ac and dc systems Load flow calculation.
Equally being obtained by above-mentioned result of calculation, each state variable is in limit value, and object function network loss has had preferable improvement, from
Scattered variable optimization is on step-length node, and Simultaneous Iteration number of times and the time of calculating are the most very fast, illustrate that the method can be with efficient solution
The certainly optimal load flow of the ac and dc systems containing VSC-HVDC.
Meanwhile, the average voltage in whole system is risen to 1.0456 by original 1.0225, the voltage of whole system
Value has had lifting and more stable, and particularly from power supply point node farther out, its magnitude of voltage has had preferable lifting.
By the analysis to Fig. 2 and Fig. 4, the convergence curve of two systems be all OPF2 control mode under more smooth,
From contrast, the difference of two kinds of control modes of OPF1 Yu OPF2 is whether to carry out VSC2 node the control of reactive power
System, OPF2 does not carry out Reactive Power Control to VSC2 node so that calculates convergence more smooth, can be obtained by result of calculation
Arrive, this put reactive power is reaching the optimum method of operation on the occasion of lower system, this demonstrate this point and should be reactive power output
Point, rather than start the reactive power input point set.The sensitivity of amount that the system that the results show that is idle to DC node, simultaneously
Can obtain table 2, table 4 and OPF1, OPF2 control mode analysis, DC Variable can effectively be controlled by the method for article so that it is
It is fixed on control point, illustrates that the method can have preferable effect of contraction and optimization function to DC Variable.
The example of 5,30,57,118 nodes is revised as the ac and dc systems containing VSC-HVDC, is respectively adopted in former antithesis
Unified hybrid algorithm in the method for putting, document " the ac and dc systems optimal load flow of meter and VSC-HVDC unifies hybrid algorithm " and basis
Literary composition algorithm calculates, and control mode uses OPF2, and voltage limits is [0.9,1.1], each under Matlab programming software environment
The calculating of method is shown in Table 5 average time:
Table example more than 5 calculates the time
Can be obtained by the calculating time series analysis of method multiple to multiple examples, the calculating of interior point method is fastest, but
It is discrete variable effectively cannot to be optimized, and DC quantity is not optimized；Although unified hybrid algorithm can be to discrete
Amount and DC Variable are optimized, but its calculating time is longer, it is generally required to the optimal load flow of thousands of times calculates, and works as node
During increase, the calculating time also will be multiplied；Understand through Comprehensive Correlation, cause article owing to needs carry out process to discrete variable
Algorithm is slightly slower than the calculating of interior point method, but the required time is in an order of magnitude, so algorithm is possible not only to herein
Effectively optimizing each example, the time that simultaneously calculates is very fast, better numerical value stability, can well complete to hand over containing VSC-HVDC
The optimal power flow problems of straight-flow system.
Claims (2)
1. discrete optimal load flow computational methods Han VSC-HVDC ac and dc systems precision, it is characterised in that these computational methods
First analyze containing the power steady-state equation of VSC-HVDC ac and dc systems and other update equations, then set its equality constraint with
Inequality constraints, finally introduces interior point method by positive camber quadratic penalty function；Specifically include:
1) the described VSC-HVDC ac and dc systems that contains mainly is made up of AC system, current conversion station and DC network 3 part；
The input voltage that can make inverter isThe voltage of the exchange node injecting this node isHand over
The power of stream node is Psi+jQsi；The power injecting current conversion station is Pci+jQci, the equiva lent impedance of current conversion station converter power transformer is Ri
+jXLi；
By above-mentioned it is assumed that can calculate and flow through the electric current of converter power transformer and be:
AC system flows into the power of current conversion station should meet relationship below:
Here δ can be madei=θsi-θci,αi=arctan (XLi/Ri), can obtain by deriving:
Herein for the relevant equation eliminating inverter so that AC system and straight-flow system, by equation direct correlation, use
The output voltage virtual value of inverter and the relation of DC voltage:
In above formula, μdFor the utilization rate of DC voltage, generally 0 < μd< 1, modulation system is set to SPWM here, thenMiFor modulation degree, set modulation degree here as 0 < Mi<1；
The injecting power exchanging node can be obtained and exchange node, the relation of DC node relevant parameter amount:
The internal loss of inverter and transformer loss are by RiEquivalence, therefore dc power PdiWith the P injecting converter bridgeciIt is equal,
Therefore have below equation, I thereindiFor DC node electric current:
Ac and dc systems comprises exchange and DC node simultaneously, is required for being modified to different types of node, to exchange joint
Point, its update equation is consistent with tradition Load flow calculation:
For the DC node of VSC, equation is:
I, j in formula represents the numbering of node, and P, Q, U represent meritorious, idle and voltage magnitude, θ, G, B generation respectively respectively
Table phase angle, conductance and susceptance, Pi sWithRepresent active power and the reactive power injecting node i respectively；
The update equation of straight-flow system is:
I in formula represents the numbering of VSC；
According to solving the number of variable, need to increase DC network equation:
R in formuladRepresent resistance between DC node；
2) logarithm barrier function is introduced in Newton method by interior point method, for processing the inequality constraints in nonlinear programming problem,
Specifically can be to be described as following form:
In formula, x is unknown variable；F (x) is optimization object function；H (x), g (x) are respectively equality constraint and inequality constraints；
gmax、gminIt is respectively the bound of inequality constraints；
Introduce slack variable l, u, and in object function, add logarithm barrier function, it is possible to inequality constraints is converted to
Formula retrains, and solves the most again:
Y, z, w in formula is Lagrange multiplier, also referred to as dual variable.This optimization problem minimum exist essential condition be on
Formula is all 0 to the partial derivative of all of variable and multiplier, it is hereby achieved that:
Wherein μ=σ Gap/2r, Gap=lTz-uTW, Gap are referred to as duality gap, and σ is referred to as Center Parameter；L=diag (l1,…,
lr), U=diag (u1,…,ur), Z=diag (z1,…,zr), W=diag (w1,…,wr) wherein r represent inequality constraints
Number.
Use Newton-Raphson approach to solve, its linearisation can be obtained update equation group:
By above formula through k iteration, obtain the correction value of former variable and dual variable, and be updated, finally obtain equation
Solve；
3) a positive camber quadratic penalty function being introduced interior point method, its expression formula is as follows:
In above formula, vbFor penalty factor, xb1For discrete variable xbThe centre of neighbourhood, x can be definedb1Neighborhood R (xb1) it is following district
Between:
Wherein, S is its classification step-length.
By positive camber quadratic penalty functionIntroduce, can obtain:
By introducing quadratic penalty function, discrete variable can be played an effect of contraction during calculating so that it is regular arrive
The centre of neighbourhood；It is inseparable with the size on the opportunity introducing penalty function and penalty factor that the method processes the effect of discrete variable；
Using ac and dc systems loss minimization as object function:
In formula, PaclossFor AC system network loss, and PdclossIt is lost for the DC line in system.
2. described in a claim 1 containing VSC-HVDC ac and dc systems precision discrete optimal load flow computational methods, its feature
It is:
1st) in step, the control mode containing VSC-HVDC ac and dc systems is relatively more flexible, typically using following variable as controlling mesh
Mark: the alternating voltage U on DC nodes, DC voltage Ud, flow into circulation transformator AC power Ps、Qs；Carrying out trend
When calculating or optimal load flow calculate, in system, each VSC needs to select two control variable, typically has following 4 kinds of combinations: fixed
Ud, determine QsControl；Determine Ud, determine UsControl；Determine Ps, determine QsControl；Determine Ps, determine UsControl；To common two ends ac and dc systems
Speech, its control mode is combined as above-mentioned combination of two, and for multistage or multi-infeed systems, compound mode will be more polynary
Change；
2nd) in step, AC and DC power system idle work optimization model is a nonlinear mixed-integer programming, processes reactive-load compensation
Capacity and these discrete variables of transformer voltage ratio are the most crucial, and the virtual expense that described penalty function is added can force discrete control to become
Measure and draw close in some classification, thus former problem is converted into the nonlinear programming problem adding discrete constraint；This secondary is penalized
Mechanism is not to be forced against by discrete variable in its most adjacent classification, and the shadow that can be reduced by the expense that global optimization brings
Ring；
Quadratic penalty functionWherein abscissa xbFor discrete variable, xb0、xb1、xb2It is xbThree adjacent discrete values；Xb1's
R (x in neighborhood such as figureb1Shown in), penalty function is minimum at the centre of neighbourhood, and maximum on neighborhood border, so that discrete variable exists
Draw close to the centre of neighbourhood during optimization.
The 3rd) in step, first, introduce the opportunity during quadratic penalty function calculates to interior point method most important, at interior point method iteration meter
At the calculation initial stage, the correction value of variable is relatively big, if now introducing quadratic penalty function, can disturb global optimization, and the centre of neighbourhood frequently becomes
Dynamic, computational efficiency is low, it could even be possible to optimal solution cannot be converged to；
As Gap, < when 0.1, now neighborhood determines the most substantially, introduces quadratic penalty function and can preferably realize discrete variable to the centre of neighbourhood
The function drawn close；In the interior point method iteration later stage, variable correction value can be more and more less, when optimal solution is decided substantially, if now
It is re-introduced into quadratic penalty function, then can increase iterations, reduce convergence；
Secondly, the size of penalty factor also can affect the effect of algorithm, for making penalty mechanism more flexible, and can be to different discrete
Variable chooses different penalty factors according to the size of its classification step-length, and in general, the classification step-length of capacitor is relatively big, can
To take penalty factor for 50；And for the no-load voltage ratio of ULTC, in general classification step-length is less, penalty factor can be taken
It is 500 so that penalty mechanism is sensitiveer.
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