CN107611965A - A kind of power system economy containing UPFC and static security comprehensive optimization method - Google Patents
A kind of power system economy containing UPFC and static security comprehensive optimization method Download PDFInfo
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Abstract
The present invention discloses a kind of power system economy containing UPFC and static security comprehensive optimization method.Because security of system is prior to system operation economy, optimization process in the present invention is divided into inside and outside two layers, for outer layer using system operation expense as object function, internal layer is that static system safety index is object function, object function inside and outside the form connection by increasing penalty term.The present invention considers the Static Security Constraints of system N 1, because UPFC has a variety of power flowcontrol patterns, and different control models has different responses when safety failure occurs for system, therefore the selection of UPFC control models is applied in whole optimization process by the present invention.Solved using particle cluster algorithm, internal layer target function value under UPFC difference control models is calculated every generation individual, UPFC optimal control parameters and control model are selected, result of calculation shows that this method can significantly improve system operation economy and static security.
Description
Technical field
The present invention relates to power system security and control field, more particularly to a kind of power system economy containing UPFC with
Static security comprehensive optimization method.
Background technology
With the development of FACTS (FACTS) technology, increasing power electronics transmission facility is answered
Power system is used, quietly changes the power transmission mode of conventional electric power system.THE UPFC (UPFC) is FACTS equipment
In Typical Representative, there is control circuit trend, stable busbar voltage, improve the ability of the stability of a system, it is powerful, for electricity
The operation of Force system provides new control and regulation means.Meanwhile with the continuous development of power system, the economy of power system
Property and security seem more and more important, in order to more reasonably utilize existing equipment for power transmission and distribution, while give full play to UPFC's
Control ability to the comprehensive optimization method of the economy of power system containing UPFC and safety, it is necessary to deploy research.
After UPFC power flow algorithms are established by Power-injected method, UPFC control parameter has three：Side note in parallel
Enter electric current, series side equivalent voltage amplitude and phase angle, side Injection Current in parallel is mainly for stablizing side bus voltage and string in parallel
The exchange of active power between side in parallel, the amplitude and phase angle of series side equivalent voltage source are used to be controlled Line Flow.
Therefore UPFC access not only brings new control parameter to system load flow Optimized model, while adds constraints, it will
Improve the complexity of tide optimization.
In addition, for the power system containing UPFC, when carrying out power flowcontrol, its control targe can be UPFC
Line Flow, busbar voltage and its phase angle, line impedance.According to the difference of UPFC control targes, UPFC has four kinds of different controls
Molding formula, it is respectively：Constant dc power control, phase angle adjustment control, impedance-compensated control and voltage-regulation control.In view of UPFC
There is the control characteristic of different trends under different control models, influences of the UPFC to system load flow depends on it and control mould
Formula, especially in the case where safety failure occurs in system.Therefore, UPFC control models will have an impact to the security of system,
Generally the constant dc power control pattern based on UPFC, only optimization UPFC are determining power mould for research research in terms of existing optimization containing UPFC
Control targe and control parameter under formula, and deficiency is considered to the situation of other three kinds of control models.
There is certain paradox in the economy and security of power system, rationally effective optimisation strategy seems extremely heavy
Will, this method proposes a kind of method of electric power system optimization containing UPFC for considering power system economy and security.
The content of the invention
In order to solve above-mentioned problem, the present invention provides a kind of tidal current computing method of consideration UPFC control models,
Because power system security is prior to economy, the present invention is interior using being handled by the way of two layers inside and outside optimization process is divided into
Layer optimization static system security, outer layer optimize the system operation economy, and with security constraint economy.Internal layer establishes quiet
State safety evaluation index considers the selection of tetra- kinds of control models of UPFC as object function；Outer layer uses systematic running cost
And penalty term caused by internal layer object function is as object function.Using PSO Algorithm, for up to this purpose, the present invention
A kind of power system economy containing UPFC and static security comprehensive optimization method are provided, comprised the following steps：
(1) grid data, generator output and payload related data are read；
(2) Population Size, maximum iteration and particle rapidity maximum correlation PSO algorithm essential informations are set, just
The position of each particle of beginningization and speed, the positional information of particle includes Traditional control parameter here and UPFC tri- is controlled and become
Amount, i.e. [Vgen1,…Vgen5,Pgen1,…Pgen5,T1,…T4,C1,C2,Vse,θse,Vk]；
(3) each particle of calculating corresponds to the system load flow under the method for operation, and computing system operating cost is outer layer target letter
Control targe under numerical value and each control models of UPFC, and record and whether there is overload situations；
(4) to the particle in the absence of overload situations, by Sensitivity Analysis Method, the trend after each circuit breaking is carried out
Calculate, then further Calculation Estimation index PI, is ranked up to failure.
(5) sequence concentrated according to forecast failure carries out N-1 static security verifications.Calculate respectively under four kinds of control models
Internal layer target function value after N-1 failures, until no longer there is circuit overload phenomenon in some post-fault system, take and be computed
The maximum of object function carrys out the quality of more each control model under each failure crossed；
(6) particle is evaluated according to principle of the security of system prior to economy, including particle itself and particle
Between comparison.Compare whether particle overloads in normal state first, next compares the overload feelings of the system after N-1
Condition, the equilibrium degree of system load flow distribution is compared again, finally the economic index of particle is compared, according to the above
Result of the comparison, the individual optimal pbest data of each particle are updated, and the optimal solution in pbest is replaced into global optimum
Original data in gbest, pbest and gbest include Traditional control variable, UPFC control parameters and its control model；
(7) position and the velocity vector of each particle are updated by particle cluster algorithm；
(8) whether verification reaches maximum iteration, if not up to maximum iteration, goes to step (5), otherwise goes to
Step (9)；
(9) optimum results of final UPFC control parameters and control model are exported.
Further, model optimization is in step 2；
Wherein variable is optimized for：
[Vgen1,…Vgen5,Pgen1,…Pgen5,T1,…T4,C1,C2,Vse,θse,Vk] (2)；
In formula, Vgen、PgenFor generator voltage and active power output, T is the position of OLTC taps, and C is shunt compensation
The capacity of capacitor, Vse,θse,VkIt is UPFC control variable.
Further, equality constraint is carried out to model in step 2；
For without UPFC nodes, meeting following trend balance：
In formula, i=1,2 ... N do not include the node at UPFC both ends, and k ∈ i represent the generator being connected with bus i, PG
Contributed for generated power, PLi、QLiFor the load on bus i, Gij、BijFor the conductance and susceptance on circuit i-j, θijFor circuit
I-j both ends phase angle difference, i.e. θij=θi-θj；
For the bus of UPFC installations, it is s, r that note, which is connected bus with UPFC, then bus s and r power balance equations are as follows：
In formula, Ps(upfc)、Qs(upfc)Injecting power for UPFC to bus s, Pr(upfc)、Qr(upfc)It is UPFC to bus r's
Injecting power；
Because UPFC can not produce active power in itself, so having internal constraint in itself for UPFC:
Psh+Pse=0 (5).
Further, inequality constraints is carried out to model in step 2；
Control the constraint of variable：
State variable constrains：
Restricted including load bus busbar voltage and generator reactive is contributed and restricted：
Vmin≤V≤Vmax(7)；
QGmin≤QG≤QGmax (8)。
Further, the out-of-limit circuit of system is total under the out-of-limit circuit sum of system, N-1 states under step 6 normal operation
Count with this three-level evaluation index of static system margin of safety to form static system safety evaluation function；
It is f that if circuit sum is overloaded under system health1(x) it is f that circuit sum, is overloaded under system N-1 states2(x),
Static system margin of safety f3(x), it is assumed that system has n bar circuits, and bus has k bars, and the load factor on i-th line road is λi, i-th
The voltage of bus is Vi, busbar voltage up and down be limited to Vi min, Vi maxIf generator has m platforms, the i-th generator output is Pi+jQi, on
Lower limit is Pi min+jQi min, Pi max+jQi max, system operating point Q to circuit static security limit L M distance are dline, bus electricity
The margin of safety of pressure is dbus, defining static system margin of safety is：
f3(x)=1/dline+dgen+dbus(9)；
Wherein,
Further, Operation of Electric Systems economy is weighed using Operation of Electric Systems fee forecast P (x), using increasing
Add the form and security of system of penalty term, the security of system is weighed using three-level evaluation index above, when
Exist under system health and more prescribe a time limit, then abandon this group solution, system trend occurs and more prescribed a time limit after N-1, then to economy
Index makes corresponding punishment, while in order to make static system margin of safety as high as possible, add-on system is quiet in object function
State security margin index, form following object function：
Complex optimum target：
F (x)=[N2(x)r+P(x)]f3(x) (13)；
In formula, P (x) is system operation expense, f3(x) it is the inverse of static system margin of safety, N2(x) after being system N-1
Circuit overload maximum number, r are penalty coefficient, PlossFor system losses.
Further, it is as follows using static security fault sequencing method in step 5：
The Overload for the reflection system for establishing following scalar function PI to integrate：
In formula：PiFor the active power on circuit i, PicFor transmission capacity limits on circuit i, αiTo be in parallel in circuit i
Way, ωiTo reflect the weight coefficient of circuit i importance, NL is system branch sum；
When system does not have overload,It is smaller no more than 1, PI indexs；When circuit overload in system be present,
Overload circuitMore than 1, PI indexs will become very big after square effect, therefore the index can reflect the static peace of system
Quan Xing；
After kth bar circuit disconnects, the trend being calculated by Sensitivity Analysis Method above on i-th line road is
P′i, i=1,2 ... NL and i ≠ k, this evaluation function for being are：
Then before and after circuit breaking, evaluation index variable quantity is：
ΔPIk=PI '-PI (18)；
Circuit all in system is subjected to break calculation, is ranked up to obtaining Δ PI, the order is forecast failure
Concentrate the order of each failure.
The invention discloses a kind of power system economy containing UPFC and static security comprehensive optimization method, due to system
Security is prior to system operation economy, and the optimization process in the present invention is divided into inside and outside two layers, and outer layer is with systematic running cost
With being that static system safety index is object function for object function, internal layer, mesh inside and outside the form connection by increasing penalty term
Scalar functions.The present invention considers system N-1 Static Security Constraints, because UPFC has a variety of power flowcontrol patterns, and it is different
Control model has different responses when safety failure occurs for system, therefore the present invention runs through the selection of UPFC control models
In whole optimization process.Solved using particle cluster algorithm, every generation individual is calculated under UPFC difference control models
Internal layer target function value, selects UPFC optimal control parameters and control model, and result of calculation shows that this method can be carried substantially
High system operation economy and static security.
Brief description of the drawings
Fig. 1 is UPFC power system economies and static security comprehensive optimization method flow；
Fig. 2 is test system wiring diagram；
Fig. 3 is UPFC power injection model figures；
Fig. 4 is UPFC structural representations；
Fig. 5 is iteration convergence figure；
Fig. 6 is UPFC series side equivalent circuit diagrams；
Fig. 7 is UPFC voltage mode control phasor diagrams；
Fig. 8 is UPFC Phase angle control pattern phasor diagrams；
Fig. 9 is the impedance-compensated control model phasor diagrams of UPFC；
Figure 10 is UPFC constant dc power control pattern phasor diagrams.
Embodiment
The present invention is described in further detail with embodiment below in conjunction with the accompanying drawings：
The present invention provides a kind of tidal current computing method of consideration UPFC control models, due to power system security prior to
Economy, the present invention are handled using being divided into optimization process by the way of inside and outside two layers, and internal layer optimizes static system security, outer layer
Optimize the system operation economy, and with security constraint economy.Internal layer establishes static security evaluation index as target letter
Number, while consider the selection of tetra- kinds of control models of UPFC；Outer layer is punished using caused by systematic running cost and internal layer object function
Item is penalized as object function.Using PSO Algorithm.
The present invention provides a kind of tidal current computing method of consideration UPFC control models as shown in Figure 1, comprises the following steps that：
(1) grid data, generator output and payload related data are read；
(2) Population Size, maximum iteration and particle rapidity maximum correlation PSO algorithm essential informations are set, just
The position of each particle of beginningization and speed, the positional information of particle includes Traditional control parameter here and UPFC tri- is controlled and become
Amount, i.e. [Vgen1,…Vgen5,Pgen1,…Pgen5,T1,…T4,C1,C2,Vse,θse,Vk]；
(3) each particle of calculating corresponds to the system load flow under the method for operation, computing system operating cost (outer layer object function
Value) and each control models of UPFC under control targe, and record whether there is overload situations；
(4) to the particle in the absence of overload situations, by Sensitivity Analysis Method, the trend after each circuit breaking is carried out
Calculate, then further Calculation Estimation index PI, is ranked up to failure.
(5) sequence concentrated according to forecast failure carries out N-1 static security verifications.Calculate respectively under four kinds of control models
Internal layer target function value after N-1 failures, until no longer there is circuit overload phenomenon in some post-fault system, take and be computed
The maximum of object function carrys out the quality of more each control model under each failure crossed；
(6) particle is evaluated according to principle of the security of system prior to economy, including particle itself and particle
Between comparison.Compare whether particle overloads in normal state first, next compares the overload feelings of the system after N-1
Condition, the equilibrium degree of system load flow distribution is compared again, finally the economic index of particle is compared, according to the above
Result of the comparison, individual optimal (pbest) data of each particle are updated, and the optimal solution in pbest is replaced into global optimum
(gbest) inner original data, pbest and gbest include Traditional control variable, UPFC control parameters and its control model；
(7) position and the velocity vector of each particle are updated by particle cluster algorithm；
(8) whether verification reaches maximum iteration, if not up to maximum iteration, goes to step (5), otherwise goes to
Step (9)；
(9) optimum results of final UPFC control parameters and control model are exported.
Each related detailed content is as follows：
1. Optimized model：
2. optimized variable：
[Vgen1,…Vgen5,Pgen1,…Pgen5,T1,…T4,C1,C2,Vse,θse,Vk] (2)；
In formula, Vgen、PgenFor generator voltage and active power output, T is the position of OLTC taps, C is shunt compensation
The capacity of capacitor, Vse,θse,VkIt is UPFC control variable.
3. equality constraint：
For without UPFC nodes, meeting following trend balance：
In formula, i=1,2 ... N (node for not including UPFC both ends), k ∈ i represent the generator being connected with bus i, PG
Contributed for generated power, PLi、QLiFor the load on bus i, Gij、BijFor the conductance and susceptance on circuit i-j, θijFor circuit
I-j both ends phase angle difference, i.e. θij=θi-θj。
For the bus of UPFC installations, it is s, r that note, which is connected bus with UPFC, then bus s and r power balance equations are as follows：
In formula, Ps(upfc)、Qs(upfc)Injecting power for UPFC to bus s, Pr(upfc)、Qr(upfc)It is UPFC to bus r's
Injecting power.
Because UPFC can not produce active power in itself, so having internal constraint in itself for UPFC：
Psh+Pse=0 (5)；
4. inequality constraints：
Control the constraint of variable：
State variable constrains：
Restricted including load bus busbar voltage and generator reactive is contributed and restricted：
Vmin≤V≤Vmax(7)；
QGmin≤QG≤QGmax(8)；
The present invention is with the out-of-limit circuit sum of system under the out-of-limit circuit sum of system under normal operation, N-1 states and is
System static security nargin this three-level evaluation index forms static system safety evaluation function.
It is f that if circuit sum is overloaded under system health1(x) it is f that circuit sum, is overloaded under system N-1 states2(x),
Static system margin of safety f3(x).Assuming that system has n bar circuits, bus has k bars, and the load factor on i-th line road is λi, i-th
The voltage of bus is Vi, busbar voltage up and down be limited to Vi min, Vi maxIf generator has m platforms, the i-th generator output is Pi+jQi, on
Lower limit is Pi min+jQi min, Pi max+jQi max, system operating point Q to circuit static security limit L M distance are dline, bus electricity
The margin of safety of pressure is dbus.Defining static system margin of safety is：
f3(x)=1/dline+dgen+dbus(9)；
Wherein,
In order to consider the economy of system and security, the present invention using Operation of Electric Systems fee forecast P (x) come
Weigh Operation of Electric Systems economy.In addition, form meter and security of system of the present invention using increase penalty term, using above
Three-level evaluation index the security of system weighed, more prescribe a time limit, then abandon when existing under system health
This group solution, there is trend and more prescribed a time limit in system after N-1, then corresponding punishment is made to economic indicator, while in order to make system quiet
State margin of safety is as high as possible, the add-on system static security margin index in object function, forms following object function：
Complex optimum target：
F (x)=[N2(x)r+P(x)]f3(x) (13)；
In formula, P (x) is system operation expense, f3(x) it is the inverse of static system margin of safety, N2(x) after being system N-1
Circuit overload maximum number, r are penalty coefficient, PlossFor system losses.
The present invention is as follows using static security fault sequencing method：
The Overload for the reflection system for establishing following scalar function PI to integrate：
In formula：PiFor the active power on circuit i, PicFor transmission capacity limits on circuit i, αiTo be in parallel in circuit i
Way, ωiTo reflect the weight coefficient of circuit i importance, NL is system branch sum.
When system does not have overload,It is smaller no more than 1, PI indexs；When circuit overload in system be present, mistake
Charge circuitMore than 1, PI indexs will become very big after square effect.Therefore the index can reflect the static security of system
Property.
After kth bar circuit disconnects, the trend being calculated by Sensitivity Analysis Method above on i-th line road is
P′i, i=1,2 ... NL and i ≠ k.This evaluation function for being is：
Then before and after circuit breaking, evaluation index variable quantity is：
ΔPIk=PI '-PI (18)；
Circuit all in system is subjected to break calculation, is ranked up to obtaining Δ PI, the order is forecast failure
Concentrate the order of each failure.
The present invention chooses IEEE30 bus test systems and carries out calculating analysis, and system wiring figure is as shown in Figure 2.UPFC is installed
Between circuit 4-6, addition UPFC outlets side bus 31, UPFC equivalent circuit diagram is as shown in figure 3, system reference power is
100MVA, other schematic diagrames are as shown in Figure 5-10.
PSO algorithm parameters are as follows：Inertia coeffeicent w=0.7298, accelerator coefficient c1=1.4962, c2=1.4962, population rule
Mould POP=50, maximum iteration Num=30, the system operation expense order of magnitude being calculated by chapter 2, by penalty coefficient
r2It is arranged to 10000.Iteration convergence figure is as shown in Figure 4.
The value of each control variable is as shown in table 1 after final optimization pass, and each optimizing index is as shown in table 2, is tied from calculating
Fruit can see, this group of parameter after normal condition and N-1 in system be not present overload circuit, and system possess preferably it is quiet
State margin of safety and operating cost are horizontal.
The control parameter result (p.u.) of table 1
Each index after the optimization of table 2
UPFC the preferred of control model is illustrated below.During using this group of control parameter, failure is ranked up,
Take forward 5 failures of faulty middle sequence, calculate each control models of UPFC security of system after the disconnection of following circuit
Index, as a result as shown in table 3.When UPFC uses constant dc power control pattern, system occurs without overload, and static system is abundant safely
Highest is spent, therefore selects UPFC phase angle adjustment control patterns.
Internal layer target function value of table 3 UPFC, the tetra- kinds of control models after N-1 failures
The above described is only a preferred embodiment of the present invention, it is not the limit for making any other form to the present invention
System, and any modification made according to technical spirit of the invention or equivalent variations, still fall within present invention model claimed
Enclose.
Claims (7)
1. a kind of power system economy containing UPFC and static security comprehensive optimization method, comprise the following steps, its feature exists
In：
(1) grid data, generator output and payload related data are read；
(2) Population Size, maximum iteration and particle rapidity maximum correlation PSO algorithm essential informations, initialization are set
The position of each particle and speed, the positional information of particle includes Traditional control parameter here and UPFC tri- controls variables,
That is [Vgen1,…Vgen5,Pgen1,…Pgen5,T1,…T4,C1,C2,Vse,θse,Vk]；
(3) each particle of calculating corresponds to the system load flow under the method for operation, and computing system operating cost is outer layer target function value
And the control targe under each control models of UPFC, and record and whether there is overload situations；
(4) to the particle in the absence of overload situations, by Sensitivity Analysis Method, the trend after each circuit breaking is counted
Calculate, then further Calculation Estimation index PI, is ranked up to failure.
(5) sequence concentrated according to forecast failure carries out N-1 static security verifications.The N-1 under four kinds of control models is calculated respectively
Internal layer target function value after failure, until no longer there is circuit overload phenomenon in some post-fault system, take and be computed
Each failure under the maximum of object function carry out the quality of more each control model；
(6) particle is evaluated according to principle of the security of system prior to economy, including particle itself is between particle
Comparison.Comparing whether particle overloads in normal state first, next compares the overload situations of the system after N-1,
The equilibrium degree of system load flow distribution is compared again, finally the economic index of particle is compared, according to above ratio
Compared with result, update the individual optimal pbest data of each particle, and the optimal solution in pbest is replaced into global optimum gbest
In original data, pbest and gbest include Traditional control variable, UPFC control parameters and its control model；
(7) position and the velocity vector of each particle are updated by particle cluster algorithm；
(8) whether verification reaches maximum iteration, if not up to maximum iteration, goes to step (5), otherwise goes to step
(9)；
(9) optimum results of final UPFC control parameters and control model are exported.
2. one kind power system economy containing UPFC according to claim 1 and static security comprehensive optimization method, its
It is characterised by：
Model optimization is in step 2；
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Wherein variable is optimized for：
[Vgen1,…Vgen5,Pgen1,…Pgen5,T1,…T4,C1,C2,Vse,θse,Vk] (2)；
In formula, Vgen、PgenFor generator voltage and active power output, T is the position of OLTC taps, and C is Shunt compensation capacitor
The capacity of device, Vse,θse,VkIt is UPFC control variable.
3. one kind power system economy containing UPFC according to claim 2 and static security comprehensive optimization method, its
It is characterised by：
Equality constraint is carried out to model in step 2；
For without UPFC nodes, meeting following trend balance：
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<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula, i=1,2 ... N do not include the node at UPFC both ends, and k ∈ i represent the generator being connected with bus i, PGTo generate electricity
Machine active power output, PLi、QLiFor the load on bus i, Gij、BijFor the conductance and susceptance on circuit i-j, θijFor circuit i-j two
Hold phase angle difference, i.e. θij=θi-θj；
For the bus of UPFC installations, it is s, r that note, which is connected bus with UPFC, then bus s and r power balance equations are as follows：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;P</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>&Element;</mo>
<mi>s</mi>
</mrow>
</munder>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>L</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>s</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mi>p</mi>
<mi>f</mi>
<mi>c</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;Q</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>&Element;</mo>
<mi>s</mi>
</mrow>
</munder>
<msub>
<mi>Q</mi>
<mrow>
<mi>G</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>L</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>s</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>s</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mi>p</mi>
<mi>f</mi>
<mi>c</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;P</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>&Element;</mo>
<mi>r</mi>
</mrow>
</munder>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>L</mi>
<mi>r</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>r</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>r</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mi>p</mi>
<mi>f</mi>
<mi>c</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;Q</mi>
<mi>v</mi>
</msub>
<mo>=</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>&Element;</mo>
<mi>i</mi>
</mrow>
</munder>
<msub>
<mi>Q</mi>
<mrow>
<mi>G</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>L</mi>
<mi>r</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>r</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>sin&theta;</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>cos&theta;</mi>
<mrow>
<mi>r</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>r</mi>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mi>p</mi>
<mi>f</mi>
<mi>c</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula, Ps(upfc)、Qs(upfc)Injecting power for UPFC to bus s, Pr(upfc)、Qr(upfc)For injections of the UPFC to bus r
Power；
Because UPFC can not produce active power in itself, so having internal constraint in itself for UPFC:
Psh+Pse=0 (5).
4. one kind power system economy containing UPFC according to claim 2 and static security comprehensive optimization method, its
It is characterised by：
Inequality constraints is carried out to model in step 2；
Control the constraint of variable：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>G</mi>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>&le;</mo>
<msub>
<mi>V</mi>
<mi>G</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>G</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>&le;</mo>
<msub>
<mi>P</mi>
<mi>G</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mi>min</mi>
</msub>
<mo>&le;</mo>
<mi>T</mi>
<mo>&le;</mo>
<msub>
<mi>T</mi>
<mrow>
<mi>G</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>C</mi>
<mi>min</mi>
</msub>
<mo>&le;</mo>
<mi>C</mi>
<mo>&le;</mo>
<msub>
<mi>C</mi>
<mi>max</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>&le;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&le;</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>&le;</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&le;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>i</mi>
<mrow>
<mi>q</mi>
<mi>min</mi>
</mrow>
</msub>
<mo>&le;</mo>
<msub>
<mi>i</mi>
<mi>q</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>i</mi>
<mrow>
<mi>q</mi>
<mi>max</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
State variable constrains：
Restricted including load bus busbar voltage and generator reactive is contributed and restricted：
Vmin≤V≤Vmax(7)；
QGmin≤QG≤QGmax (8)。
5. one kind power system economy containing UPFC according to claim 1 and static security comprehensive optimization method, its
It is characterised by：
The out-of-limit circuit sum of system and static system under system out-of-limit circuit sum, N-1 states under step 6 normal operation
Margin of safety this three-level evaluation index forms static system safety evaluation function；
It is f that if circuit sum is overloaded under system health1(x) it is f that circuit sum, is overloaded under system N-1 states2(x), system
Static security nargin f3(x), it is assumed that system has n bar circuits, and bus has k bars, and the load factor on i-th line road is λi, i-th bus
Voltage be Vi, busbar voltage up and down be limited to Vi min, Vi maxIf generator has m platforms, the i-th generator output is Pi+jQi, bound
ForSystem operating point Q to circuit static security limit L M distance are dline, busbar voltage
Margin of safety be dbus, defining static system margin of safety is：
f3(x)=1/dline+dgen+dbus(9)；
Wherein,
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>l</mi>
<mi>i</mi>
<mi>n</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>|</mo>
<mo>|</mo>
<mi>Q</mi>
<mo>-</mo>
<mi>L</mi>
<mi>M</mi>
<mo>|</mo>
<mo>|</mo>
<mo>=</mo>
<msqrt>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>b</mi>
<mi>u</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>=</mo>
<msqrt>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>k</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msubsup>
<mi>V</mi>
<mi>i</mi>
<mi>max</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>V</mi>
<mi>i</mi>
<mi>min</mi>
</msubsup>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>g</mi>
<mi>e</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<msqrt>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mi>min</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mi>max</mi>
</msubsup>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mfrac>
<mrow>
<msubsup>
<mi>Q</mi>
<mi>i</mi>
<mi>min</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>Q</mi>
<mi>i</mi>
<mi>max</mi>
</msubsup>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
6. one kind power system economy containing UPFC according to claim 5 and static security comprehensive optimization method, its
It is characterised by：
Operation of Electric Systems economy is weighed using Operation of Electric Systems fee forecast P (x), using the form of increase penalty term
And security of system, the security of system is weighed using three-level evaluation index above, when under system health
Exist and more prescribe a time limit, then abandon this group solution, system trend occurs and more prescribed a time limit after N-1, then economic indicator is made accordingly
Punishment, while in order to make static system margin of safety as high as possible, the add-on system static security margin index in object function,
Form following object function：
Complex optimum target：
F (x)=[N2(x)r+P(x)]f3(x) (13)；
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>N</mi>
<mi>g</mi>
</msub>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>G</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>c</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&eta;P</mi>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>s</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>s</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mi>l</mi>
</mrow>
</munderover>
<msub>
<mi>G</mi>
<mi>i</mi>
</msub>
<mo>&lsqb;</mo>
<msubsup>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<mn>2</mn>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula, P (x) is system operation expense, f3(x) it is the inverse of static system margin of safety, N2(x) circuit after being system N-1
Maximum number is overloaded, r is penalty coefficient, PlossFor system losses.
7. one kind power system economy containing UPFC according to claim 1 and static security comprehensive optimization method, its
It is characterised by：
It is as follows using static security fault sequencing method in step 5：
The Overload for the reflection system for establishing following scalar function PI to integrate：
<mrow>
<mi>P</mi>
<mi>I</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>N</mi>
<mi>L</mi>
</mrow>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>c</mi>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula：PiFor the active power on circuit i, PicFor transmission capacity limits on circuit i, αiFor way in parallel in circuit i,
ωiTo reflect the weight coefficient of circuit i importance, NL is system branch sum；
When system does not have overload,It is smaller no more than 1, PI indexs；When circuit overload in system be present, overload
CircuitMore than 1, PI indexs will become very big after square effect, therefore the index can reflect the static security of system；
After kth bar circuit disconnects, the trend being calculated by Sensitivity Analysis Method above on i-th line road is Pi', i=
1,2 ... NL and i ≠ k, this evaluation function for being are：
<mrow>
<msup>
<mi>PI</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<munderover>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
</munder>
<mrow>
<mi>i</mi>
<mo>&NotEqual;</mo>
<mi>k</mi>
</mrow>
<mrow>
<mi>N</mi>
<mi>L</mi>
</mrow>
</munderover>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mo>&prime;</mo>
</msubsup>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>c</mi>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Then before and after circuit breaking, evaluation index variable quantity is：
ΔPIk=PI '-PI (18)；
Circuit all in system is subjected to break calculation, is ranked up to obtaining Δ PI, the order is that forecast failure is concentrated
The order of each failure.
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| CN110661264A (en) * | 2019-09-03 | 2020-01-07 | 吉林大学 | Safety constraint optimal power flow calculation method based on particle swarm algorithm with inertial weight |
| CN110661265A (en) * | 2019-09-19 | 2020-01-07 | 吉林大学 | Safety constraint optimal power flow calculation method based on branch circuit breaking distribution factor |
| CN111697588A (en) * | 2020-06-08 | 2020-09-22 | 东南大学 | Prevention control method considering IPFC control mode |
| CN111697588B (en) * | 2020-06-08 | 2022-09-09 | 东南大学 | Prevention control method considering IPFC control mode |
| CN111882126A (en) * | 2020-07-24 | 2020-11-03 | 贵州电网有限责任公司 | N-1-1 static security check optimization method and system |
| CN114389270A (en) * | 2022-01-21 | 2022-04-22 | 东南大学 | Power flow optimization method for power system considering control characteristics of double-circuit IPFC |
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