CN106097026A - A kind of polymorphic type sale of electricity company coexists down sale of electricity method of bidding - Google Patents

A kind of polymorphic type sale of electricity company coexists down sale of electricity method of bidding Download PDF

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CN106097026A
CN106097026A CN201610716838.XA CN201610716838A CN106097026A CN 106097026 A CN106097026 A CN 106097026A CN 201610716838 A CN201610716838 A CN 201610716838A CN 106097026 A CN106097026 A CN 106097026A
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石帮松
张靖
何宇
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Guizhou University
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Abstract

The invention discloses a kind of polymorphic type sale of electricity company to coexist down sale of electricity method of bidding, it includes: step 1, sets up all types of sale of electricity company and bids sale of electricity model；Step 2, sale of electricity model of bidding all types of sale of electricity companies are dissolved, and ask for all types of sale of electricity companies bidding strategies；Step 3, all types of sale of electricity companies bidding strategies solved in step 2 is carried out market equilibrium analysis；Step 4, all types of sale of electricity company constantly adjust conjectural variation f in this periodiT (), finally makes all types of sale of electricity company bid equilibrium；Solving and in prior art, owing to the power supply administration of only grid company subordinate carries out sale of electricity, be formed without competition, the most existing pricing model is completely unsuitable for Duo Jia sale of electricity company and bids the technical problems such as sale of electricity.

Description

A kind of polymorphic type sale of electricity company coexists down sale of electricity method of bidding
Technical field
The invention belongs to sale of electricity pricing techniques, particularly relate to a kind of polymorphic type sale of electricity company and coexist down sale of electricity method of bidding.
Background technology
Along with deepening continuously of electric Power Reform, electricity market will break corner on the market by introduction of competition, gradually form and send out , multiclass in sales market, will necessarily be there is in this mode in electricity, transmission of electricity, distribution and the separate electricity market operation structure of sale of electricity Type sale of electricity company bids sale of electricity.In this context, how formulating and solve polymorphic type sale of electricity company sale of electricity strategy of bidding is exactly one The major issue of individual worth research, and in prior art, owing to the power supply administration of only grid company subordinate carries out sale of electricity, does not has shape Becoming competition, the most existing pricing model is completely unsuitable for Duo Jia sale of electricity company and bids the situation of sale of electricity.
Summary of the invention:
The technical problem to be solved in the present invention: provide a kind of polymorphic type sale of electricity company to coexist down sale of electricity method of bidding, to solve Certainly prior art uses the power supply administration of only grid company subordinate to carry out sale of electricity, be formed without competition, the most existing price mould Formula is completely unsuitable for Duo Jia sale of electricity company and bids the technical problems such as sale of electricity.
Technical solution of the present invention:
A kind of polymorphic type sale of electricity company coexists down sale of electricity method of bidding, and it includes:
Step 1, set up all types of sale of electricity company and bid sale of electricity model；
Step 2, sale of electricity model of bidding all types of sale of electricity companies are dissolved, and ask for all types of sale of electricity company and bid plan Slightly；
Step 3, all types of sale of electricity companies bidding strategies solved in step 2 is carried out market equilibrium analysis；
Step 4, all types of sale of electricity company constantly adjust conjectural variation f in this periodiT (), finally makes all types of selling Electricity company bids equilibrium.
The bid object function of sale of electricity model of all types of sale of electricity companies described in step 1 is:
maxπ i ( p , t ) = S i G ( p , t ) - I i G ( p , t ) - I i Y ( p , t ) - I i D ( p , t ) - I i W ( p , t ) - I i F ( p , t ) , i = 1 , 2 ... n - 1 S i G ( p , t ) - I i G ( p , t ) - I i Y ( p , t ) - I i D ( p , t ) - I i W ( p , t ) + S i H ( p , t ) + S i F ( p , t ) , i = n - - - ( 1 )
SiG(p, t)=p (t) qi(p,t) (2)
IiG(p, t)=Riwi(p,t) (3)
IiY(p, t)=diwi(p,t)+ciwi 2(p,t) (4)
IiD(p, t)=Fqi(p,t) (5)
IiW(p, t)=α wi(p,t) (6)
I i F ( p , t ) = βq i ( p , t ) , i = 1 , 2 ... n - 1 0 , i = n - - - ( 7 )
S i F ( p , t ) = 0 , i = 1 , 2 ... n - 1 Σ j = 1 n - 1 I j F , i = n - - - ( 8 )
S i H ( p , t ) = 0 , i = 1 , 2 ... n - 1 Σ j = 1 n - 1 I j D , i = n - - - ( 9 )
qi(p, t)=(1-ηi)wi(p,t) (10)
F=G* σ/(365*T*Q) (11)
D ( p , t ) = Σ i = 1 n q i ( p , t ) = μ - λ p ( t ) - - - ( 12 )
In formula: SiG(p t) is the sale of electricity income of t period sale of electricity company i；IiG(p t) is the power purchase of t period sale of electricity company i Cost；IiY(p t) is the operation cost of t period sale of electricity company i；IiD(p t) is the power grid construction cost of t period sale of electricity company i Share；IiW(p, t) be t period sale of electricity company i pay power distribution network operation and maintenance cost；IiF(p is t) that the t period is without power distribution network The sale of electricity company of the power of management pays the electric energy delivery service expense of the sale of electricity company of the power distribution network power of management；SiH(p t) is the t period There is the distribution network construction cost recovery of the sale of electricity company of the power distribution network power of management；SiF(p is t) the t period to have selling of the power distribution network power of management The electric energy delivery service income of electricity company；P (t) is t period sales market sale of electricity Settlement price；qi(p t) is t period sale of electricity Company i is to the electricity sales amount of terminal use；RiPurchase electricity price for t period sale of electricity company i；wi(p t) is t period sale of electricity company i Power purchase electricity；diAnd ciFor sale of electricity company operation cost coefficient, the management level of company will directly affect the size of its coefficient；F is Distribution network construction fixed cost sharing on unit quantity of electricity；α is power distribution network operation and maintenance cost coefficient；β is for there being distribution operation The sale of electricity company of power provides electric energy delivery service cost coefficient；ηiNetwork Loss Rate for the i electric energy conveying of sale of electricity company；G is power distribution network Building fixed cost, σ is annuity coefficient in operational period, and T is one day time hop count divided, and Q is that power distribution network passage can to user eventually The maximum sale of electricity electricity of end conveying；Formula (12) is the constraint of supply and demand electric quantity balancing, and (p t) is t period power load demand to D；Formula (11) it is distribution network construction fixed cost sharing on unit electricity sales amount.
The method asking for all types of sale of electricity companies bidding strategies described in step 2 includes:
Step 2.1, solve the optimal solution of (1) formula
∂ π i ( p , t ) ∂ p ( t ) = 0 , ( i = 1 , 2 , ... , n - 1 , n ) - - - ( 13 ) ;
Step 2.2, the optimization bid sale of electricity function curve setting up sale of electricity company k must are fulfilled for conditional expression
In formula:
Step 2.3, acquisition conjectural variation fkThe expression formula of (t)
f k ( t ) = ∂ q - k ( p , t ) ∂ p ( t ) - - - ( 15 ) ;
Step 2.4, foundation have the sale of electricity company bid sale of electricity function curve of the power distribution network power of management to meet
Conditional expression
In formula:
The method that all types of sale of electricity companies bidding strategies carries out described in step 3 market equilibrium analysis is taked for setting market Uniform price closes mechanism, is that to maximize self benefits in the t period excellent according to formula (15) without the sale of electricity company of the power distribution network power of management Change bid sale of electricity function curve to submit a tender, have the sale of electricity company of the power distribution network power of management to submit a tender according to formula (16), then draw Sales market is up to equalize as follows
Beneficial effects of the present invention:
The method using the present invention can the most fast be fixed a price, either in flexible or inelastic sale of electricity side In market, Settlement price is all different along with power load demand is different with the conjecture of each sale of electricity company and each sale of electricity corporate profit, Power load demand big then corresponding Settlement price and each sale of electricity corporate profit is the highest, on the contrary Settlement price and each sale of electricity company Profit is the lowest.Further it is found that in flexible market, adjust the electricity equilibrium of supply and demand by coefficient of elasticity, reduce electricity Amount demand, and then reduce Settlement price, the elastic demand of load makes each sale of electricity corporate profit reduce；Solve and existing skill In art, owing to the power supply administration of only grid company subordinate carries out sale of electricity, being formed without competition, the most existing pricing model is the most not It is applicable to Duo Jia sale of electricity company bid the technical problems such as sale of electricity.
Accompanying drawing illustrates:
Fig. 1 is t period nonelastic sales market Settlement price balancing procedure；
Fig. 2 is the conjectural variation balancing procedure of t period nonelastic sales market Zhong Ge sale of electricity company；
Fig. 3 is t period flexible sales market Settlement price balancing procedure；
Fig. 4 is the conjectural variation balancing procedure of t period flexible sales market Zhong Ge sale of electricity company.
Detailed description of the invention:
The present invention is directed to polymorphic type sale of electricity company bid sale of electricity problem, construct and turn to mesh with each sale of electricity corporate income maximum Target is bidded sale of electricity model.Then giving method for solving, each sale of electricity company is by constantly adjusting the sale of electricity side clearing electricity of self Valency conjectural variation, changes bidding strategy, and to reach sales market equilibrium, detailed process is as follows:
1) set up all types of sale of electricity company to bid sale of electricity model:
Have in same business district of power supply in n independent sale of electricity company, it is assumed that n-th sale of electricity company has distribution operation Power, and sale of electricity company of front n-1 family is without the power distribution network power of management.The sale of electricity company of the power of management without distribution can only be by having power distribution network warp The sale of electricity company of battalion's power carries out electric energy conveying.
Each sale of electricity company, after buying electric power, also to carry out electricity sale to user.Consider sales market sale of electricity clearing The demand response of electricity price, sale of electricity Settlement price and power load demand are mathematically in inversely prroportional relationship, if power load demand is bent Line is D=μ-λ p, and wherein D is power load demand, and p is the sale of electricity Settlement price of sales market, and μ is that power load demand is normal Number, λ is market coefficient of elasticity.
With t period sale of electricity company i (i=1,2 ..., n-1, Income Maximum n) is object function, sets up all types of sale of electricity Company bids sale of electricity model:
Object function is:
maxπ i ( p , t ) = S i G ( p , t ) - I i G ( p , t ) - I i Y ( p , t ) - I i D ( p , t ) - I i W ( p , t ) - I i F ( p , t ) , i = 1 , 2 ... n - 1 S i G ( p , t ) - I i G ( p , t ) - I i Y ( p , t ) - I i D ( p , t ) - I i W ( p , t ) + S i H ( p , t ) + S i F ( p , t ) , i = n - - - ( 1 )
SiG(p, t)=p (t) qi(p,t) (2)
IiG(p, t)=Riwi(p,t) (3)
IiY(p, t)=diwi(p,t)+ciwi 2(p,t) (4)
IiD(p, t)=Fqi(p,t) (5)
IiW(p, t)=α wi(p,t) (6)
I i F ( p , t ) = βq i ( p , t ) , i = 1 , 2 ... n - 1 0 , i = n - - - ( 7 )
S i F ( p , t ) = 0 , i = 1 , 2 ... n - 1 Σ j = 1 n - 1 I j F , i = n - - - ( 8 )
S i H ( p , t ) = 0 , i = 1 , 2 ... n - 1 Σ j = 1 n - 1 I j D , i = n - - - ( 9 )
qi(p, t)=(1-ηi)wi(p,t) (10)
In formula: SiG(p t) is the sale of electricity income of t period sale of electricity company i；IiG(p t) is the power purchase of t period sale of electricity company i Cost；IiY(p t) is the operation cost of t period sale of electricity company i；IiD(p t) is the power grid construction cost of t period sale of electricity company i Share；IiW(p, t) be t period sale of electricity company i pay power distribution network operation and maintenance cost；IiF(p is t) that the t period is without power distribution network The sale of electricity company of the power of management pays the electric energy delivery service expense of the sale of electricity company of the power distribution network power of management；SiH(p t) is the t period There is the distribution network construction cost recovery of the sale of electricity company of the power distribution network power of management；SiF(p is t) the t period to have selling of the power distribution network power of management The electric energy delivery service income of electricity company；P (t) is t period sales market sale of electricity Settlement price；qi(p t) is t period sale of electricity Company i is to the electricity sales amount of terminal use；RiPurchase electricity price for t period sale of electricity company i；wi(p t) is t period sale of electricity company i Power purchase electricity；diAnd ciFor sale of electricity company operation cost coefficient, the management level of company will directly affect the size of its coefficient；F is Distribution network construction fixed cost sharing on unit quantity of electricity；α is power distribution network operation and maintenance cost coefficient；β is for there being distribution operation The sale of electricity company of power provides electric energy delivery service cost coefficient；ηiNetwork Loss Rate for the i electric energy conveying of sale of electricity company.
The maximum sale of electricity electricity that can be carried by power distribution network passage obtains distribution network construction fixed cost on unit electricity sales amount Share for:
F=G* σ/(365*T*Q) (11)
In above formula, G is distribution network construction fixed cost, and σ is annuity coefficient in operational period, and T is one day time hop count divided, Q is that power distribution network passage can be to the maximum sale of electricity electricity of user terminal conveying.
Meanwhile, in the satisfied following constraint of t period sales market:
D ( p , t ) = Σ i = 1 n q i ( p , t ) = μ - λ p ( t ) - - - ( 12 )
Formula (12) is the constraint of supply and demand electric quantity balancing, and (p t) is t period power load demand to D.
2) single order optimal conditions is utilized by step 1) all types of sale of electricity companies that build sale of electricity model of bidding dissolves, asks Take all types of sale of electricity companies bidding strategies:
Step 1) in the optimal solution of (1) formula should meet:
∂ π i ( p , t ) ∂ p ( t ) = 0 , ( i = 1 , 2 , ... , n - 1 , n ) - - - ( 13 )
For without the power distribution network power of management sale of electricity company k (k=1,2 ..., n-1), simultaneous above equation, by formula (1) generation Enter formula (13) and derive, available formula (14).
In formula:
The optimization bid sale of electricity function curve of i.e. sale of electricity company k must is fulfilled for (14) formula relation.
(14) in formula: fkT () sale of electricity company k guesses about sales market Settlement price micro-increasing response of virtual competitor Surveying (hereinafter referred to as conjectural variation), the sale of electricity company all rivals of k are regarded as a virtual rival, it is sold Electricity isThen fkT () is represented by:
f k ( t ) = ∂ q - k ( p , t ) ∂ p ( t ) - - - ( 15 )
In like manner, the sale of electricity company bid sale of electricity function curve having the power distribution network power of management must is fulfilled for (16) formula relation.
In formula:
Analyzing according to formula (15), formula (16) and understand, if the conjectural variation of sale of electricity company is constant, then it optimizes throwing Selling tender number curve formula (15) by means of emails or letters, formula (16) are linear；If conjectural variation is with sales market Settlement price p (t) Become, then its majorized function curve is non-linear.
3) by step 2) in all types of sale of electricity companies bidding strategies that solves carry out market equilibrium analysis:
Assume that market takes uniform price to close mechanism, if without the sale of electricity company of the power distribution network power of management be the t period Bigization self benefits optimizes bid sale of electricity function curve according to formula (15) and submits a tender, have the sale of electricity company of the power distribution network power of management by Illuminated (16) is submitted a tender, and easily draws sales market to be up to as follows and equalizes:
Analyzed from above, the conjectural variation f that sale of electricity company day part usesiWhen () is constant t, formula (15) and Formula (16) is linearly, it is resolved that the parameter φ of supply function shapeiWithUnrelated with power sales Settlement price p (t).Thus formula (17) there is not many solutions, the most there is not multiple market equilibrium.If the conjectural variation f that sale of electricity company used in this periodi T () becomes with p (t), formula (15) and formula (16) are non-linear, then formula (17) there may be many solutions, i.e. there is multiple market equal Weighing apparatus.
4) the conjectural variation f that all types of sale of electricity companies constantly adjusted in this periodiT (), finally makes all types of sale of electricity Company bids equilibrium.
Concrete incorporating parametric: setting and have 3 sale of electricity companies in studied market, sale of electricity company 1, sale of electricity company 2 are without distribution The power of management, there is the distribution power of management in sale of electricity company 3.Each sale of electricity company participates in t period stock sales market and bids sale of electricity, initially Conjectural variation is [f1(t) f2(t) f3(t)]=[44 80 22], its appropriate section parameter is listed in Table 1.By one day The time hop count T=24, i.e. calculation interval that divide are 1h, and unit MW of sale of electricity electricity represents.
Table 1 sale of electricity company operation parameter
When the market of each sale of electricity company competition is nonelastic market i.e. λ=0, it is assumed that at t period power load demand D (t) For 1500MW.T period sales market Settlement price equalization iteration calculates process and sees Fig. 1, i.e. t period sales market clearing electricity Valency is 54.59 $/(MW h), and the conjectural variation iterative process of each sale of electricity company is shown in Fig. 2, each sale of electricity company equilibrium knot Fruit is shown in Table 2.
Table 2 is nonelastic sales market equilibrium result
When each sale of electricity company competition market be flexible market, it is assumed that t period power load demand curve be D (t)= 1170-3.2p(t).T period sales market Settlement price equalization iteration calculates process and sees Fig. 3, i.e. t period sales market is tied Calculating electricity price is 48.05 $/(MW h), and the conjectural variation iterative process of each sale of electricity company is shown in Fig. 4, and each sale of electricity company is equal Weighing apparatus the results are shown in Table shown in 3.
Table 3 flexible sales market equilibrium result
Fig. 1,2, table 2 and Fig. 3,4, table 3 be respectively nonelastic and flexible sales market equilibrium result.Contrast equilibrium knot Fruit it is found that either in flexible or inelastic sales market, Settlement price with, each sale of electricity company conjecture and Each sale of electricity corporate profit is all different along with power load demand is different, the big the most corresponding Settlement price of power load demand and respectively Sale of electricity corporate profit is the highest, otherwise Settlement price and each sale of electricity corporate profit are the lowest.Further it is found that in flexible city In Chang, adjust the electricity equilibrium of supply and demand by coefficient of elasticity, reduce electrical demand, and then reduce Settlement price, the bullet of load Sexual demand makes each sale of electricity corporate profit reduce.

Claims (4)

1. polymorphic type sale of electricity company coexists down a sale of electricity method of bidding, and it includes:
Step 1, set up all types of sale of electricity company and bid sale of electricity model；
Step 2, sale of electricity model of bidding all types of sale of electricity companies are dissolved, and ask for all types of sale of electricity companies bidding strategies；
Step 3, all types of sale of electricity companies bidding strategies solved in step 2 is carried out market equilibrium analysis；
Step 4, all types of sale of electricity company constantly adjust conjectural variation f in this periodiT (), finally makes all types of sale of electricity company Bid equilibrium.
A kind of polymorphic type the most according to claim 1 sale of electricity company coexists down sale of electricity method of bidding, it is characterised in that: step The bid object function of sale of electricity model of all types of sale of electricity companies described in 1 is:
maxπ i ( p , t ) = S i G ( p , t ) - I i G ( p , t ) - I i Y ( p , t ) - I i D ( p , t ) - I i W ( p , t ) - I i F ( p , t ) , i = 1 , 2 ... n - 1 S i G ( p , t ) - I i G ( p , t ) - I i Y ( p , t ) - I i D ( p , t ) - I i W ( p , t ) + S i H ( p , t ) + S i F ( p , t ) , i = n - - - ( 1 )
SiG(p, t)=p (t) qi(p,t) (2)
IiG(p, t)=Riwi(p,t) (3)
IiY(p, t)=diwi(p,t)+ciwi 2(p,t) (4)
IiD(p, t)=Fqi(p,t) (5)
IiW(p, t)=α wi(p,t) (6)
I i F ( p , t ) = βq i ( p , t ) , i = 1 , 2 ... n - 1 0 , i = n - - - ( 7 )
S i F ( p , t ) = 0 , i = 1 , 2 ... n - 1 Σ j = 1 n - 1 I j F , i = n - - - ( 8 )
S i H ( p , t ) = 0 , i = 1 , 2 ... n - 1 Σ j = 1 n - 1 I j D , i = n - - - ( 9 )
qi(p, t)=(1-ηi)wi(p,t) (10)
F=G* σ/(365*T*Q) (11)
D ( p , t ) = Σ i = 1 n q i ( p , t ) = μ - λ p ( t ) - - - ( 12 )
In formula: SiG(p t) is the sale of electricity income of t period sale of electricity company i；IiG(p t) is the purchases strategies of t period sale of electricity company i； IiY(p t) is the operation cost of t period sale of electricity company i；IiD(p t) is the power grid construction cost sharing of t period sale of electricity company i； IiW(p, t) be t period sale of electricity company i pay power distribution network operation and maintenance cost；IiF(p is t) that the t period is without the power distribution network power of management Sale of electricity company pay the electric energy delivery service expense of sale of electricity company of the power distribution network power of management；SiH(p is t) the t period to have distribution The distribution network construction cost recovery of the sale of electricity company of the net power of management；SiF(p t) is the sale of electricity company having the power distribution network power of management t period Electric energy delivery service income；P (t) is t period sales market sale of electricity Settlement price；qi(p t) is t period sale of electricity company i To the electricity sales amount of terminal use；RiPurchase electricity price for t period sale of electricity company i；wi(p t) is the power purchase of t period sale of electricity company i Electricity；diAnd ciFor sale of electricity company operation cost coefficient, the management level of company will directly affect the size of its coefficient；F is distribution Fixed cost sharing on unit quantity of electricity built by net；α is power distribution network operation and maintenance cost coefficient；β is to have the distribution power of management Sale of electricity company provides electric energy delivery service cost coefficient；ηiNetwork Loss Rate for the i electric energy conveying of sale of electricity company；G is distribution network construction Fixed cost, σ is annuity coefficient in operational period, and T is one day time hop count divided, and Q is that power distribution network passage can be defeated to user terminal The maximum sale of electricity electricity sent；Formula (12) is the constraint of supply and demand electric quantity balancing, and (p t) is t period power load demand to D；Formula (11) is Distribution network construction fixed cost sharing on unit electricity sales amount.
A kind of polymorphic type the most according to claim 1 sale of electricity company coexists down sale of electricity method of bidding, it is characterised in that: step The method asking for all types of sale of electricity companies bidding strategies described in 2 includes:
Step 2.1, solve the optimal solution of (1) formula
∂ π i ( p , t ) ∂ p ( t ) = 0 , ( i = 1 , 2 , ... , n - 1 , n ) - - - ( 13 ) ;
Step 2.2, the optimization bid sale of electricity function curve setting up sale of electricity company k must are fulfilled for conditional expression
In formula:
Step 2.3, acquisition conjectural variation fkThe expression formula of (t)
f k ( t ) = ∂ q - k ( p , t ) ∂ p ( t ) - - - ( 15 ) ;
Step 2.4, foundation have the sale of electricity company bid sale of electricity function curve of the power distribution network power of management to meet conditional expression
In formula:
A kind of polymorphic type the most according to claim 1 sale of electricity company coexists down sale of electricity method of bidding, it is characterised in that: step The method that all types of sale of electricity companies bidding strategies carries out described in 3 market equilibrium analysis takes uniform price to close for setting market Mechanism, the sale of electricity company without the power distribution network power of management is to maximize self benefits in the t period to optimize bid sale of electricity letter according to formula (15) Number curve is submitted a tender, and has the sale of electricity company of the power distribution network power of management to submit a tender according to formula (16), then show that sales market will Reach to equalize as follows
CN201610716838.XA 2016-08-25 2016-08-25 A kind of polymorphic type sale of electricity company coexists down sale of electricity method of bidding Pending CN106097026A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109543898A (en) * 2018-11-19 2019-03-29 三峡大学 A kind of more microgrid Optimization Schedulings based on two way auction
CN109993357A (en) * 2019-03-26 2019-07-09 中国电力科学研究院有限公司 A kind of sale of electricity quotient's multiple target Tender offer Tactics calculation method considering tender probability
CN110555662A (en) * 2018-05-31 2019-12-10 中国电力科学研究院有限公司 Configurable technical support system for electricity selling company

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110555662A (en) * 2018-05-31 2019-12-10 中国电力科学研究院有限公司 Configurable technical support system for electricity selling company
CN109543898A (en) * 2018-11-19 2019-03-29 三峡大学 A kind of more microgrid Optimization Schedulings based on two way auction
CN109543898B (en) * 2018-11-19 2021-04-13 三峡大学 Multi-microgrid optimal scheduling method based on two-way auction
CN109993357A (en) * 2019-03-26 2019-07-09 中国电力科学研究院有限公司 A kind of sale of electricity quotient's multiple target Tender offer Tactics calculation method considering tender probability

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