CN109166036B - V2G energy trading method based on block chain and contract theory - Google Patents

V2G energy trading method based on block chain and contract theory Download PDF

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CN109166036B
CN109166036B CN201810793834.0A CN201810793834A CN109166036B CN 109166036 B CN109166036 B CN 109166036B CN 201810793834 A CN201810793834 A CN 201810793834A CN 109166036 B CN109166036 B CN 109166036B
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周振宇
谭露
廖斌
郭宇飞
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North China Electric Power University
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Abstract

The invention designs a safe and efficient V2G energy transaction mechanism in a network physical system by using block chains, edge calculation and contract theory. In this context, we propose a safe and efficient V2G energy trading framework by exploring block chains, contract theory and edge calculation. First, we developed a federation blockchain-based secure energy transaction mechanism for V2G. Then, an effective incentive mechanism based on contract theory is provided by considering the information asymmetric scene. The social welfare optimization problem belongs to the category of differences in convex (DC) planning and is solved by an iterative convex-concave process (CCP) algorithm. Next, edge calculations have been incorporated to improve the probability of success of block creation. The computational resource allocation problem is modeled as a two-stage Steinberg game, with the optimal strategy being obtained by using a backward induction method.

Description

V2G energy trading method based on block chain and contract theory
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to a V2G energy trading method based on a block chain and contract theory in a physical network system, so as to realize the safety and high efficiency of energy trading and maximize social benefits. The energy transaction mechanism based on the block chain can meet the safety performance to a great extent, and the edge calculation is applied to ensure the high efficiency of the transaction; a trading mechanism based on a contract theory can better stimulate an Electric Vehicle (EV) to participate in energy trading under the condition of asymmetric information, so that social benefits are maximized.
Background
As network computing technology advances, the capabilities of computing and communication are deeply embedded into the design of physical systems. The close integration of physical systems and these advanced computing technologies has led to a new generation of engineering systems, namely Cyber Physical Systems (CPS). A typical application of CPS in the energy field is the smart grid, which employs the latest information communication and control techniques to optimize the management and operation of the grid.
However, the large-scale popularity of intermittent distributed renewable energy sources and Electric Vehicles (EVs) has resulted in significant power fluctuations. To maintain reliable and safe operation of the smart grid, a large number of centralized generators and energy storage devices must be deployed, resulting in substantial capital and operational expenditures. Another option is to utilize the two-way energy trading capability of electric vehicles. In particular, it is possible to coordinate the absorption of excess energy by a large number of electric vehicles during off-peak hours and the return of energy to the grid during peak hours, which is a promising solution. Peak loads are eliminated and the level of demand imbalance is reduced without deploying additional generators and storage devices. This new energy transaction model is referred to as vehicle-to-grid (V2G), which is critical to establishing a safer and more sustainable CPS in the energy domain. Despite these advantages of V2G, challenges such as lack of distributed security mechanisms and efficient incentive mechanisms still exist.
In the present invention, to address the above challenges, we have developed a new V2G framework for CPS that utilizes block chaining, contract theory and edge calculations to achieve safe and efficient energy trading. The blockchain is a specific distributed shared database that allows each transaction to be recorded in a verifiable and permanent manner, which is critical to creating a distributed, transparent, and secure energy trading environment. The computing resources in the edge computing are distributed at the edge of the network, so that the difficulty of work certification in the block chain of the alliance is solved, a distributed account book in the block chain is created, audits are published, and the distributed account book is shared by a plurality of authorization nodes, and the cost is moderate. The contract theory provides a powerful tool for solving the problem of information asymmetric excitation and has been applied to a plurality of fields.
Disclosure of Invention
The invention firstly provides a safe energy transaction mechanism based on an alliance block chain, then provides a V2G energy transaction incentive mechanism based on a contract theory, and finally provides calculation task unloading based on edge calculation. The specific implementation process is as follows:
one, as shown in fig. 1, fig. 2 shows a federation blockchain-based V2G secure energy transaction consisting of three major entities: electric vehicles, Local Energy Aggregators (LEAGs), and edge computing service providers (ESPs). The specific capabilities and functions of each entity are elaborated as follows:
electric automobile: electric vehicles with bidirectional energy trading capabilities may play different roles. On the one hand, electric vehicles may act as energy producers during peak hours by releasing battery power. On the other hand, it can also act as an energy consumer by charging the battery with cheaper electricity, while helping to absorb excess energy during off-peak hours. Through a well-designed incentive scheme, each electric vehicle can actively adjust its charging and discharging behavior to maximize its personal benefits. The detailed excitation mechanism design is described below.
Local energy aggregator: the local energy aggregator provides a range of energy transaction services including information collection, condition monitoring and charge/discharge coordination. For example, during peak hours, a local energy aggregator may use a bank of discharged electric vehicles to generate energy in response to local peak load demands. Meanwhile, the electric vehicle participating in the energy transaction obtains special payment for paying the local supply and demand balance. In this context, an energy coin of a digital cryptocurrency is used as payment for an energy transaction. There are three main components in a local energy aggregator: a memory server, an account server and a transaction server. All transaction records in the federation blockchain are stored in the memory server. The energy coin digital assets for each electric vehicle are stored in a digital wallet. To protect privacy, the real address of the wallet is replaced by a set of public keys, such as random pseudonyms. Each electric vehicle also has a transaction account, which stores all transaction records, and a mapping relationship between the random wallet address and the corresponding transaction account is maintained in the account server. The transaction server is responsible for implementing the incentive mechanism and coordinating the charging and discharging activities.
An edge computing service provider that unifies control of integrated computing, communication, and storage resources provides edge computing services for a local energy aggregator. The edge computing service provider issues a price for its services, and each local energy aggregator determines the demand for the services to be purchased based on the price. The compute-intensive workload verification puzzle can then be offloaded from the local energy aggregator to its neighboring edge computing nodes, rather than processed locally or by remote cloud nodes. Detailed information on how to model the interaction between the edge computing service provider and the local energy aggregator and how to design the optimal service price and service requirements will be explained below
Details of the operation of the federation blockchain-based secure energy transaction are explained below. The existing cryptographic algorithms are adopted, including elliptic curve digital signature, Boneh-Boyen short signature and SHA-256. Initially, each electric vehicle must register with a legitimate authority to obtain its public, private and certificate. The public or private key may be generated and distributed by an authority. The certificate represents the unique identity of the electric vehicle by binding its registration information. Each electric car has a set of wallet addresses issued by the organization. During initialization, the electric car will look up the wallet address used by the nearest LEAG and verify the integrity of the wallet. Then, it downloads the corresponding data from the memory server.
LEAG devised a contract that specifies performance, i.e., the relationship between the energy required to discharge the EV and the reward, i.e., the discharge EV payout in terms of the source coin. In a contract, each distinct performance benefit association is defined as a contract term, and a contract typically contains a variety of contract terms. The LEAG then broadcasts the contract, and each EV selects its desired contract terms to maximize its return. After the energy transaction, the discharging EV will receive a designated reward if the corresponding contract terms have been successfully completed. The energy coin is transferred from the LEAG to the wallet address of the EV. The authenticity of the payment can be verified by checking the last block of the federation blockchain. The LEAG creates a new transaction record that must first be verified and digitally signed by the electric vehicle, then uploaded and audited publicly.
All transaction records collected by the LEAG over a period of time will be encrypted, digitally signed, and then organized into blocks. Invalid transactions (e.g., fake transactions) will be discarded. Each new chunk is linked to the previous chunk in the federation blockchain by a cryptographic hash. Then, similar to the proof of work process in bitcoin, each authorized LEAG in the federation blockchain competes for creating blocks by finding valid proof of work, i.e., hash values that meet certain difficulty requirements. A hash value is calculated based on the random nonce α and a data set Φ that includes the hash value of the previous block, the timestamp, and other necessary data. Effective α must satisfy Hash (α + Φ) < β, where β represents the difficulty level.
If the LEAG has limited computational power, it can purchase edge computing services from the ESP. The compute-intensive workload verification process is then handled by nearby edge compute nodes with powerful computational power, and the probability of success of block creation will increase significantly. First the LEAGs that find valid proof of operation broadcast the created block to all authorized LEAGs in the network. Next, each LEAG reviews and validates the transaction records in the received block and chooses whether to accept the new block. If a new tile is accepted by all LEAGs, i.e. a consensus is reached, it will be appended at the end of the current federation chain of tiles, and the LEAGs that created this tile will be awarded a certain number of energy coins.
Second, V2G energy trading incentive mechanism based on contract
1. Electric vehicle type modeling
We use the electric car type to quantify the electric car's preference for discharge, and this type information is known only to the electric car itself. Higher-grade electric vehicles are more willing to participate in the V2G energy trade and release more power for higher return, while electric vehicles with higher types may also be more favored by LEAG. For simplicity, we assume that the set of electric car types belongs to a discrete and limited space. The EV type is defined as follows:
definition 1: considering a parking lot with K discharged EVs, these EVs may be sorted and classified into K types in ascending order according to their preference. If the set of electric vehicle types is expressed as: theta ═ theta1，…，θk，…，θKThen we get
θ1＜…＜θk＜…＜θK，k＝1，…，K.
Next, we will derive a specific expression of the type of electric vehicle. Consider type as thetakElectric vehicle of (1), leftThe calculation formula of the residual capacity is as follows:
Figure GDA0002949744490000041
wherein
Figure GDA0002949744490000042
Indicating the current available charge, Ek，maxIs the battery capacity. After discharging, the remaining SOC should meet the minimum electric demand for driving:
Figure GDA0002949744490000051
wherein L iskIs the amount of electricity required, dkIs the distance, χ (d), that must be traveled before the next chargek) Indicating the distance d traveledkThe minimum amount of power required, which is dkIs a monotonically increasing function of. By combining the above two formulas, we can solve the type as thetakThe discharge capacity of the electric vehicle of (1), which is expressed as:
Figure GDA0002949744490000052
further, the type θkCan be defined as:
Figure GDA0002949744490000053
note 1: as can be seen from the above equation, θkAnd
Figure GDA0002949744490000054
and Ek，maxProportional to x (d)k) In inverse proportion. For example, a larger electric vehicle type indicates that the electric vehicle has more available energy or will not travel a long distance in the near future.
In the case of asymmetric information, the LEAG does not know the specifics of each EVTypes, but only the probability distribution of each type is known. Let us assume that LEAG knows there are K types of discharging cars and that one discharging car belongs to type θkProbability P ofkThen, then
Figure GDA0002949744490000055
2. Contract construction
The contract composed of K contract items is not provided with the same contract for different types of EVs, but different contract items are designed for K discharge EV types. E.g. specific to type thetakThe designed contract item is expressed as (L)k，Rk) Wherein L iskRepresents the required power, RkIndicating the resulting specific reward. The contract is expressed as:
Figure GDA0002949744490000056
which is composed of
Figure GDA0002949744490000057
Considering this K type of discharging car, the expected utility of the LEAG is calculated as follows:
Figure GDA0002949744490000058
wherein gamma isLIs the unit electricity price of LEAG.
Note 2: contract item (L)k＝0，Rk0) is represented by type θkThe electric vehicle of (2) is not intended to participate in the discharge. On the other hand, if and only if γLLk-RkLEAG will benefit from EV discharge only when the value is more than or equal to 0, otherwise LEAG will not adopt the type thetakThe electric vehicle of (2) discharges.
Accepting contract item (L)k，Rk) Type theta ofkThe utility function of the electric vehicle is expressed as:
Figure GDA0002949744490000061
where gamma is the unit price of the cell discharge, thetakm(Rk) Is of type thetakR of (A) to (B)kThe value of (A) is obtained. Function m (R)k) Is RkWhere m (0) is 0, m' (R)k) > 0 and m' (R)k) Is less than 0. Without loss of generality, m (R)k) Can be defined as a quadratic function:
Figure GDA0002949744490000062
where a and b are assumed to be constant and must satisfy m' (R)k) > 0 and m' (R)k) Is less than 0. Nevertheless, the proposed solution can also be extended to other forms.
The expected social benefit is the sum of the total utility of LEAG and K EVs:
Figure GDA0002949744490000063
the social welfare maximization problem under asymmetric information is described as follows:
Figure GDA0002949744490000064
s.t.C1：θkm(Rk)-γLk≥0，(IR)
C2：θkm(Rk)-γLk≥θkm(Rk′)-γLk′，(IC)
C3：0≤R1…＜Rk＜…＜RK
C4：Lk≤θk
Figure GDA0002949744490000065
where C1, C2 and C3 represent IR, IC and monotonicity constraints, respectively. C4 represents LkThe upper limit of (3).
Definition 2: the IR, IC and monotonicity constraints are defined as follows:
personal rational constraints (IR constraints): for collections
Figure GDA0002949744490000066
Is any one of the types thetakIf it selects the contract item (L)k，Rk) Then it will get a positive reward.
Incentive compatibility constraints (IC constraints): IC constraints ensure the self-revealing nature of contracts. For collections
Figure GDA0002949744490000071
Is any one of the types thetakIf and only if it selects a contract item (L) designed for its own typek，Rk) The maximum return is obtained.
Monotonicity constraint: for collections
Figure GDA0002949744490000073
Is any one of the types thetakOf the type θk-1Is high, but has a specific type of thetak+1EV of (2) is low.
Based on IR, IC and monotonicity constraints, the following properties can be derived.
Introduction 1: for collections
Figure GDA0002949744490000074
Is any one of the types thetakIf θ is equal tok＞θk′Then Rk＞Rk′. If and only if thetak＝θk′When R isk＝Rk′。
2, leading: for L in set Ck，RkThe following inequalities are satisfied:
0≤R1＜…＜Rk＜…＜RK
0≤L1＜…＜Lk＜…＜LK
Figure GDA0002949744490000072
3. design of optimal contract theory under information asymmetric situation
1) Contract feasibility: first, we define the sufficient requirements for contract feasibility
Theorem 1: contract feasibility: any one contract (L) in the set C when and only when the following conditions are satisfiedk，Rk) It is feasible:
a：0≤R1＜…＜Rk＜…＜RKand 0. ltoreq.L1＜…＜Lk＜…＜LK
b：θ1m(R1)-γL1≥0
c: for K e {2, …, K }, there is γ Lk-1+θk-1[m(Rk)-m(Rk-1)]≤γLk≤γLk-1+θk[m(Rk)-m(Rk-1)]
2) Problem transformation: the social welfare maximization problem involves K IR constraints and K (K-1) IC constraints, and in order to make the problem easy to solve, we perform the following steps to simplify:
step 1: eliminating IR constraints
For collections
Figure GDA0002949744490000075
Is any one of the types thetakWe can derive:
θkm(Rk)-γLk≥θkm(R1)-γL1≥θ1m(R1)-γL1≥0
the first inequality is due to IC constraints and the second inequality is due to θk＞θ1The third inequality is due to the IR constraint. Therefore, if the guaranteed type isθ1The IR constraint of an EV of higher type is then automatically satisfied.
Step 2: removing IC constraints
We define type θkAnd thetak′The IC constraint of (k' ∈ {1, …, k-1}) is the downward excitation constraint (DICs). Likewise, type θkAnd thetak′The IC constraint of (K' ∈ { K +1, …, K }) is the upward excitation constraint (UICs). We will next demonstrate that DICs and UICs can both be reduced.
We consider three adjacent EV types, θk-1＜θk＜θk+1They satisfy:
θk+1m(Rk+1)-γLk+1≥θk+1m(Rk)-γLk
θkm(Rk)-γLk≥θkm(Rk-1)-γLk-1
wherein the first expression represents the type θk+1And thetakDIC therebetween, the second expression representing the type θkAnd thetak-1DIC in between.
Reunion of Rk+1≥Rk≥Rk-1We can get:
θk+1m(Rk+1)-γLk+1≥θk+1m(Rk-1)-γLk-1
therefore, if the type θk+1And thetakDIC in between, then type θk+1And thetak-1DIC in between also holds. DIC constraints may be derived from type θk-1Down to type theta1Given by:
θk+1m(Rk+1)-γLk+1≥θk+1m(Rk-1)-γLk-1
≥…
≥θk+1m(R1)-γL1
therefore, we demonstrate that if a DIC between adjacent types is established, all DIC will be automatically retained. Also, we can prove that if UICs between adjacent types hold, then all UICs will automatically be retained.
Based on the above analysis, the K IR constraints and K (K-1) IC constraints are reduced to 1 and K-1, respectively, so the social welfare maximization problem under asymmetric information can be transformed:
Figure GDA0002949744490000081
s.t.C1：θ1m(R1)-γL1≥0，(IR)
C2：θkm(Rk-1)-γLk-1≥θkm(Rk)-γLk，(IC)
C3，C4，k＝2，…，K
and step 3: reducing optimal contracts under constraints
We can prove by examining the Hessian matrix that the goal of the social welfare maximization problem is a concave function. However, convex programming cannot be applied directly here, since constraint C2 relates to the difference of two concave functions, i.e., θkm(Rk-1)-γLk-1And thetakm(Rk)-γLk. Therefore, we use the CCP algorithm to solve, which is summarized in algorithm 1.
Denotes fk(Rk)＝θkm(Rk). Due to fk(Rk) With respect to RkIs differentiable, so fk(Rk) Can be expanded by using its first order taylor series as:
Figure GDA0002949744490000091
wherein R isk，o[τ]Representing the initial point of the iteration tau.
Thus, constraint C2, having a difference of two concave functions, is converted to a difference of a concave function and an affine function, written as
Figure GDA0002949744490000092
By using
Figure GDA0002949744490000093
Instead of C2, social welfare maximization is translated into a convex programming problem and can be easily solved by using the Karush-Kuhn-tucker (kkt) condition. At each iteration τ, a locally optimal solution is obtained by solving the transformed convex problem
Figure GDA0002949744490000094
And
Figure GDA0002949744490000095
then, the initial point of the Taylor series expansion at the iteration of τ +1 is defined as
Figure GDA0002949744490000096
Next, the above iteration is repeated to find a new locally optimal solution.
The iterative process terminates until a predefined stopping criterion is met. For example, the improvement in social welfare is less than or equal to some positive value threshold e, i.e.:
Figure GDA0002949744490000097
theorem 2: convergence property: at any iteration τ, obtained
Figure GDA0002949744490000098
And
Figure GDA0002949744490000099
is feasible. In addition to this, the present invention is,
Figure GDA00029497444900000910
is non-regressive and will converge to the maximum social benefit, i.e.:
Figure GDA00029497444900000911
4. contract design without information asymmetry
If there is a selfish LEAG, it can accurately know the type of each EV, and it can further increase profit as long as each EV accepts only contract terms designed for its own type. In this case, the LEAG must ensure that the revenue for each EV is non-negative. Otherwise, the electric vehicle does not have power to accept the contract item. To this end, the contractual terms must comply with the IR constraints. In addition, the contract terms must satisfy the following characteristics:
and 3, introduction: in contract design without information asymmetry, contract items (L) in any set Ck，Rk) All should satisfy thetakm(Rk)＝γLk. That is, the yield of any EV is 0.
And (3) proving that: lemma 3 can be demonstrated with contradictions. Giving an optimal contract term (L)k，Rk) If theta is greater than thetakm(Rk)-γL k0, then LEAG can be increased by increasing LkUp to thetakm(Rk)-γL k0. This is in combination with (L)k，Rk) The assumption of being optimal contradicts.
Thus, by forcing the benefit of each EV to be 0, the social benefit is equivalent to the benefit of the LEAG, and the corresponding optimization problem is expressed as:
Figure GDA0002949744490000101
s.t.C1：θkm(Rk)-γLk＝0
C2：0≤R1＜…＜Rk＜…＜RK
Figure GDA0002949744490000102
to solve this problem, we must find the solution of K quadratic equations, i.e.
Figure GDA0002949744490000103
Let R bek1And Rk2Are two solutions to the kth quadratic, the optimal solution is given by:
Figure GDA0002949744490000104
and (4) introduction: in contract design when there is no information asymmetry, θ is calculated for any one EV typek，RkAre all fixed, with thetakIs irrelevant.
And (3) proving that: will thetakm(Rk)-γLkSubstituting 0 into the formula
Figure GDA0002949744490000105
Can prove the social welfare SW follow
Figure GDA0002949744490000106
Monotonically increasing, so the LEAG may increase LkUp to Lk＝θk. Next, L is addedk＝θkSubstitution of thetakm(Rk)-γL k0, m (R) can be obtainedk)＝γLThis proves that RkIs fixed with respect to thetakIs irrelevant.
Third, computing task unloading based on edge computing
1. Establishment of layered game
To win the blockchain mining competition, the LEAG may purchase edge computation services from the ESP to expand its computational power. We assume that there are N LEAGs, and the group of LEAGs is represented as
Figure GDA0002949744490000107
The service requirement of the nth LEAG is denoted as sn. For the nth LEAG, the probability of success P of block creationnI.e. depends on two factors: its relative hash capability Pn，hAnd its block isolation probability Pn，oIt is explained as follows:
the relative hash capability of the nth LEAG is defined as the ratio of its computational power to the total computational power, i.e.:
Figure GDA0002949744490000111
wherein P isn，hIs greater than 0 and
Figure GDA0002949744490000112
after finding a valid proof of operation, the nth LEAG must broadcast the created block to other LEAGs to achieve consensus. If the nth LEAG happens to select a large block that propagates slowly due to the data size, the block is more likely to be dropped due to high transmission delay. Therefore, the chance that the nth LEAG wins the block mining competition will be reduced. This phenomenon is called islanding. By assuming that the block propagation times follow a poisson distribution, the block isolation probability is expressed as:
Figure GDA0002949744490000113
where T represents the expected inter-block time and the bitcoin is 10 minutes. Δ t (D)n) Is expressed as size DnIs defined as the relative propagation time of the block of (a):
Δt(Dn)＝t(Dn)-t(0)
wherein, t (D)n) For propagation of a signal of size DnT (0) represents the delay of the communication channel, i.e. the time required to transmit the block header. t (0) is defined by the constraint t (0) ≧ dcC is a boundary where dcRepresenting the transmission distance, c represents the speed of the light.
Found by investigation that t (D)n) Can be prepared by using the same at DnThe first order taylor series expansion near 0 is approximated as:
Figure GDA0002949744490000114
the second term of the above equation is related in part to the carrying capacity of the communication channel and can be written as Shannon-Hartley's theorem
Figure GDA0002949744490000118
Wherein G is1And G2Respectively, channel capacity and coding gain. Therefore, by at (D)n)＝t(Dn) -t (0) is taken
Figure GDA0002949744490000115
And
Figure GDA0002949744490000116
Δt(Dn) Is written as:
Δt(Dn)＝t(Dn)-t(0)≈Dn/(G1 G2)
probability of success P of block creationnGiven by:
Figure GDA0002949744490000117
once the consensus process is successful, the nth LEAG will receive revenue, which consists of two parts: reward contribution Q to creation of a blocknAnd a transaction fee Mn. The net revenue for the nth LEAG can be calculated as the expected profit minus the cost of service:
Un，b(sn)＝(Qn+Mn)Pn(sn)-pcsn
wherein p iscIs the unit price of the edge computing service.
The utility of an ESP is defined as the total revenue gained by providing the service minus the operating cost, i.e.:
Figure GDA0002949744490000121
wherein gamma iscIs the unit cost of service provisioning.
Because ESP is dominant compared to LEAGs, the competitive interaction between ESP and LEAG can be modeled as a two-stage stainberg leader follower game. In the first phase, ESP is the leader that decides the price per service pc and obtains revenue from the LEAG for resolving the offloaded workload verification problem. In the second phase, the LEAG acts as a follower and determines the need for service to be purchased. The two-stage stainberg leads the formulation of the follower game as follows:
step 1: service price optimization problem:
Figure GDA0002949744490000122
s.t.C5：pc，min＜pc＜pc，max
wherein p isc，minAnd pc，maxRespectively representing the minimum and maximum ranges of service unit prices.
Step 2: service demand optimization problem
Figure GDA0002949744490000123
s.t.C6：sn，min＜sn＜sn，max
Wherein s isn，minIs the minimum computational resource (hashing capability) required by the nth LEAG, sn，maxRepresenting the maximum resource that the ESP can provide.
2. Equilibrium analysis
Optimal price and optimal service demand can be achieved by using backward induction.
1) Second stage optimization problem resolutionThe scheme is as follows: first, a service price p is givencThe second phase service requirement optimization problem is solved for each LEAG. During service demand optimization, each LEAG competes with each other to maximize its own relative hashing capability, and thus its likelihood of successfully creating a chunk. From formulas
Figure GDA0002949744490000131
It can be seen that the relative hashing capability of the nth LEAG depends not only on its policy sn but also on the policies of other LEAGs, e.g.
Figure GDA0002949744490000132
Thus, competition between the N LEAGs may be modeled as an N-player non-cooperative game, with the optimal strategy for the nth LEAG being expressed as
Figure GDA0002949744490000133
And order
Figure GDA0002949744490000134
Representation collection
Figure GDA0002949744490000135
Of other LEAGs than the nth LEAG. We have the following attributes:
theorem 3: nash equilibrium: the set of best service requirement policies, i.e.
Figure GDA0002949744490000136
Forming nash equilibrium of the second stage N-player non-cooperative game.
And (3) proving that: for collections
Figure GDA0002949744490000137
Any feasible policy sn we can get:
Figure GDA0002949744490000138
therefore, the temperature of the molten metal is controlled,
Figure GDA0002949744490000139
constituting nash equilibrium.
Theorem 4: presence of nash equilibrium: nash equilibrium exists in the second stage N-person non-cooperative game.
And (3) proving that: by investigation, nash equilibrium exists if the following two conditions are met:
a.
Figure GDA00029497444900001310
is a non-empty compact convex set of Euclidean space
b.Un，b(sn) For snContinuous and quasi-concave.
First, for a collection
Figure GDA00029497444900001313
Any n in (1), policy space [ s ]n，min，sn，max]Is a convex, continuous, compact and non-empty subset of euclidean space, which satisfies the first condition.
Second, formula Un，b(sn)＝(Qn+Mn)Pn(sn)-pcsnOfnThe second derivative of (d) is given by:
Figure GDA00029497444900001311
wherein
Figure GDA00029497444900001312
This proves Un，b(sn) For snIs concave and therefore nash equilibrium exists in the N-player non-cooperative game in the second stage.
Theorem 5: optimal response: in view of
Figure GDA00029497444900001414
Best response function of nth LEAG
Figure GDA0002949744490000141
As given below.
And (3) proving that: due to Un，b(sn) For snIs concave, C6Is affine, so the service requirement optimization problem is a convex optimization problem by applying the formula Un，b(sn)＝(Qn+Mn)Pn(sn)-pcsnIs set to 0, i.e.
Figure GDA0002949744490000142
We can get:
Figure GDA0002949744490000143
the optimal solution can be obtained
Figure GDA0002949744490000144
Theorem 6: uniqueness of nash equilibrium: if the condition is
Figure GDA0002949744490000145
If so, then the nash balance of the second stage N-player non-cooperative game is unique.
And (3) proving that: if the optimal response function of any LEAG is as
Figure GDA0002949744490000146
Nash equalization is unique if it is a standard function. After the investigation of the relevant documents, the inventor has found that,
Figure GDA0002949744490000147
is a standard function if the following conditions are satisfied:
positive value:
Figure GDA0002949744490000148
monotonicity: if it is not
Figure GDA0002949744490000149
Then
Figure GDA00029497444900001410
Expansibility: for all psi > 1,
Figure GDA00029497444900001411
first, to demonstrate the first condition we must demonstrate
Figure GDA00029497444900001412
By making
Figure GDA00029497444900001413
We can get:
Figure GDA0002949744490000151
sum of all miners for the above two passes
Figure GDA0002949744490000152
We have:
Figure GDA0002949744490000153
can also be written as:
Figure GDA0002949744490000154
in addition to that, the slave
Figure GDA0002949744490000155
We can get
Figure GDA0002949744490000156
The expression of (a) is:
Figure GDA0002949744490000157
by means of a handle
Figure GDA0002949744490000158
Substituting into the above formula, and then using the conditions
Figure GDA0002949744490000159
We can get:
Figure GDA00029497444900001510
will be provided with
Figure GDA00029497444900001511
Taking the square, then multiplying both sides by pc at the same time, we can get the expression:
Figure GDA0002949744490000161
substituting the above formula into
Figure GDA0002949744490000162
In the above step, the following results are obtained:
Figure GDA0002949744490000163
multiplying both ends of the above formula simultaneously
Figure GDA0002949744490000164
Then, taking the square root, we can get:
Figure GDA0002949744490000165
the first condition to satisfy a positive value can be proven:
Figure GDA0002949744490000166
next we demonstrate the corresponding function BnIs monotonic.
If it is not
Figure GDA0002949744490000167
Figure GDA0002949744490000168
The expression of (a) is given by:
Figure GDA0002949744490000171
if the above equation is positive, then the two functions g on the right hand side1And g2Should also be positive. Due to the fact that
Figure GDA0002949744490000172
We can easily prove g1> 0, using g1＞0，g2Can be written as:
Figure GDA0002949744490000173
by in the formula
Figure GDA0002949744490000174
Open square root on both sides, we have:
Figure GDA0002949744490000175
therefore, we have
Figure GDA0002949744490000176
This completes the proof of monotonicity.
Finally, we demonstrate that
Figure GDA0002949744490000177
The monotonicity of (c) is as follows:
Figure GDA0002949744490000181
therefore, the best response function of any LEAG is a standard function, and nash equalization is unique.
2) Solution of first stage optimization problem
Based on the optimal service demand strategy of all the LEAGs obtained in the second stage, the problem of optimizing the service price in the first stage can be solved. By substituting nash equilibrium of the second stage N-player non-cooperative game
Figure GDA0002949744490000182
ESP UEThe utility of (a) can be written as:
Figure GDA0002949744490000183
then we can get the following properties:
theorem 7: the concavity is as follows: the service price optimization problem is a standard convex optimization problem.
And (3) proving that: we can prove that the second derivative of the above equation is negative, i.e.
Figure GDA0002949744490000184
The certification is complete.
Since the service price optimization problem is a standard convex optimization problem, the optimal solution is obtained
Figure GDA0002949744490000185
Can be obtained simply by using KKT conditions, and has the following properties:
theorem 8: stenberg equilibrium: second stageNash equilibrium for segment N non-cooperative game
Figure GDA0002949744490000186
And first phase service price optimization problem optimal solution
Figure GDA0002949744490000187
Constituting a steinberg equilibrium.
And (3) proving that: for collections
Figure GDA00029497444900001810
Of any feasible strategy snWe have:
Figure GDA0002949744490000188
further, it is possible to obtain:
Figure GDA0002949744490000189
the certification is complete.
Drawings
FIG. 1 is a block chain alliance-based V2G security energy transaction architecture diagram
Fig. 2 is a flow chart of the CCP algorithm.
FIG. 3 shows the discharge capacity LkTheta with respect to EV typekIs shown in the variation trend chart
FIG. 4 is a prize RkTheta with respect to EV typekIs shown in the variation trend chart
FIG. 5 is a trend graph of benefit of an EV versus contract item type
FIG. 6 is the utility U of the LEAGLType theta with EVkIs shown in the variation trend chart
FIG. 7 shows the effectiveness of an EV
Figure GDA0002949744490000191
Type theta with EVkIs shown in the variation trend chart
FIG. 8 is a graph of social benefit SW vs. EV type θkIs shown in the variation trend chart
Fig. 9 is a graph of the convergence performance of the proposed CCP based solution.
FIG. 10 is a graph of the success probability of the proposed edge-based approach as a function of the purchased service demand.
FIG. 11 is total service demand versus transaction cost MnA changing condition of the change.
FIG. 12 is the profit of the ESP versus transaction cost MnChange of change
FIG. 13 is the average profit of the LEAG versus transaction cost MnChange of change
Detailed description of the preferred embodiments
The implementation mode of the invention is divided into two steps, wherein the first step is the establishment of a scene, and the second step is the implementation of the scene and an algorithm, wherein the implementation comprises the implementation of a block chain of a federation and the implementation of energy trading based on a contract theory. The established model comprises three entities of LEAG, EV and ESP as shown in figure 1, which completely corresponds to the implementation of the block chain of the alliance and the energy transaction implementation process based on the contractual theory in the invention content. Since the objective of the modeled social welfare maximization problem is a concave function, we use the CCP algorithm to solve, and the implementation flow chart of the CCP algorithm is shown in fig. 2.
1) For a system model, considering the reliable and economic operation of a power grid, in order to protect the safety of transaction information and the privacy of both transaction parties, an electric vehicle internet based on a block chain of a alliance is provided; to incentivize EVs to participate in electric energy trading, we propose an energy trading incentive mechanism based on contractual theory, and maximize the utility of each discharging EV if and only if the type of contract item selected by the discharging EV is consistent with its own type. We consider a parking lot with 20 electric vehicles and a LEAG, assuming that the discharge types of the electric vehicles follow a gaussian distribution, the battery capacity of any electric vehicle is 24 kw-hr, and the unit price γ of the discharge cost is 10 cents/kw-hr. Leag specific electricity price gammaLIs 13 cents/kwh.
2) In order to solve the problems proposed by us, firstly, a safe energy transaction mechanism based on a block chain of a federation is given, then a V2G energy transaction incentive mechanism based on contract theory is given, and finally computing task unloading based on edge computing is given.
For the implementation of the algorithm, when a V2G energy trading incentive mechanism based on contract theory is designed, because the goal of the modeled social welfare maximization problem is a concave function, the CCP algorithm is adopted for solving; in the design of a safe energy transaction mechanism based on an alliance block chain, calculation task unloading based on edge calculation is provided, and second-order Steinberg game modeling and a backward induction method are adopted for solving.
For the present invention we also performed a number of simulations comparing the proposed solution with the case of no information symmetry.
Fig. 3 and 4 show the discharge capacity L, respectivelykAnd a prize RkTheta with respect to EV typekThe variation of (2). The numerical results indicate that the discharge charge and reward monotonically increase with EV type, consistent with lemma 2. Furthermore, it is observed that a contract without information asymmetry requires much higher power on the electric vehicle than a contract without information asymmetry and provides the same reward for each EV. The reason behind this has been demonstrated in lemma 4.
FIGS. 6 and 7 show the utility U of the LEAGLAnd the effectiveness of EV
Figure GDA0002949744490000201
Type theta with EVkThe situation of the change. In the absence of information asymmetry, higher utility can be achieved by the LEAG, while the utility of any EV remains zero. The reason has been explained in the proof of the lemma 3. Thus, electric vehicles may actually benefit from information asymmetry because the LEAG cannot extract all available power from the electric vehicle without knowing the precise knowledge of its type.
FIG. 8 shows the social benefit SW vs. EV type θkUnder the condition of change, the simulation result shows that the social benefit is superior to the condition without information asymmetry under the condition of information asymmetry, because the benefit and the benefit of the LEAG cannot make up the corresponding effect of the electric automobileThe loss of use.
Fig. 9 shows the convergence performance of the proposed CCP based solution. Three initial points, { Rk，0[1]8, 10, 12, chosen to ensure the initial point's effect on convergence speed. As the number of iterations increases, all three cases converge to optimal social welfare. In particular, the initial point is { Rk，0[1]Only 25 iterations are needed to achieve convergence at 12. The reason is that 12 is closest to the average value (12.774) of the optimum prize shown in fig. 2 (b). In contrast, { Rk，0[1]The case of 8 requires more than 300 iterations.
To verify the benefits of edge calculation, we consider two cases, four and eight LEAGs, i.e., N-4 and N-8, respectively. In the case of N-4, we assume that the edge computing service is not available to the first three LEAGs, we fix their computing power to 10, 20 and 30, respectively. At the same time, we assume that a fourth LEAG can purchase service from the ESP and change the service requirements it purchases to demonstrate the impact on the likelihood of successfully creating a chunk. In the case where N is 8, the computational power of the first seven LEAGs is fixed at [ 10: 40]. A conventional scheme without edge computation assistance is used for comparison. We assume DnFollow a normal distribution, i.e.
Figure GDA0002949744490000211
Wherein μ D n200 and
Figure GDA0002949744490000212
fig. 10 shows a trend graph of the success probability of the proposed edge-based approach versus the purchased service demand. When the service requirement purchased from the ESP is 55, the simulation results show that the success probability of the proposed edge calculation-based scheme is improved by 92.4% (N-4) and 124.6% (N-8) over the success probability of the conventional scheme. The reason is that the relative computing power of the LEAGs that can obtain edge computing services can be increased by orders of magnitude compared to those that rely solely on their local computing power.
FIGS. 11, 12, 13 show the total service demand, the profit of the ESPAnd average profit to LEAG with transaction cost MnA changing condition of the change. The simulation parameter is sn，min＝90，sn，max＝210，Pc，min＝0，Pc，max＝15，Qn＝12000，γc3, 50G 1, 4G 2 and 50N. Fig. 6(a) and (b) show that the total service demand and profit of an ESP both increase monotonically with transaction fees. The reason behind this is that the increased transaction fees provide greater incentives for the LEAG to purchase more services from the ESP. This not only improves the probability of success of the LEAG, but also the profit of the ESP. In addition, it was observed that the total service demand and profit of the ESP created rewards Q with the blocknMonotonically, this is also due to higher rewards providing more incentive for the LEAG to purchase more services.
Fig. 13 shows a comparison of the average profits of the nth LEAG achieved by four different schemes: proposed solution, without the conventional solution of edge calculation, the nth LEAG always buys an aggressive solution s of maximum service volumen，maxAnd the nth LEAG always purchases a minimum amount of service sn，minThe conservative strategy of (1). It is clear that the proposed scheme outperforms the other three heuristic schemes because the strategy of the LEAG is optimized for the transaction cost. Conservative plans perform better than aggressive plans when the transaction cost is low. Purchasing more services is not worth the expectation of profit not to offset the cost of purchasing the service. In contrast, when the transaction fee is high enough, the LEAG should purchase more services to increase the chance of winning, since the expected profit is much higher than the cost of the service. In all cases, the conventional scheme without edge calculation performs worst for the reasons explained in fig. 5.
Although specific implementations of the invention are disclosed for illustrative purposes and the accompanying drawings, which are included to provide a further understanding of the invention and are incorporated by reference, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the disclosure of the preferred embodiments and the drawings, but the scope of the invention is defined by the appended claims.

Claims (3)

1. A V2G energy trading method applied to a physical network system has the advantages that an energy trading mechanism based on a block chain can meet the safety performance to a great extent, and edge calculation is applied to guarantee the efficiency of trading; a trading mechanism based on a contract theory can better stimulate the EV to participate in energy trading under the condition of asymmetric information, thereby maximizing social benefits, and is characterized in that:
1) in order to protect the safety of transaction information and the privacy of both transaction parties, a transaction mode based on a block chain of a federation is provided;
2) in order to encourage EV to participate in electric energy transaction, an incentive compatibility mechanism based on contract theory is proposed;
3) in order to provide calculation task unloading based on edge calculation, a second-order Steinberg game modeling and a backward induction method are adopted for solving;
the step 3) specifically comprises the following steps: to win block chain mining competition, a Local Energy Aggregator (LEAG) may purchase edge computing services from an edge computing service provider (ESP) to expand its computing power; we assume that there are N Local Energy Aggregators (LEAGs) and that the set of Local Energy Aggregators (LEAGs) is denoted as
Figure FDA0002949744480000011
The service requirement of the nth Local Energy Aggregator (LEAG) is denoted as sn(ii) a For the nth Local Energy Aggregator (LEAG), the probability of success P of block creationnI.e. depends on two factors: its relative hash capability Pn，hAnd its block isolation probability Pn，oIt is explained as follows:
the relative hash capability of the nth Local Energy Aggregator (LEAG) is defined as the ratio of its computational capability to the total computational capability, i.e.:
Figure FDA0002949744480000012
wherein P isn，hIs greater than 0 and
Figure FDA0002949744480000013
after finding a valid proof of operation, the nth Local Energy Aggregator (LEAG) must broadcast the created block to other Local Energy Aggregators (LEAGs) to reach consensus; if the nth Local Energy Aggregator (LEAG) happens to select a large block that propagates slowly due to data size, the block is more likely to be dropped due to high transmission delay; therefore, the chance that the nth Local Energy Aggregator (LEAG) wins the block mining competition will be reduced, a phenomenon known as islanding; by assuming that the block propagation times follow a poisson distribution, the block isolation probability is expressed as:
Figure FDA0002949744480000021
where T represents the expected inter-block time, the bitcoin is 10 minutes, Δ T (D)n) Is expressed as size DnIs defined as the relative propagation time of the block of (a):
Δt(Dn)＝t(Dn)-t(0)
wherein, t (D)n) For propagation of a signal of size DnT (0) represents the delay of the communication channel, i.e. the time required to transmit the block header, t (0) is the constraint t (0) ≧ dcC is a boundary where dcRepresents the transmission distance, c represents the speed of light;
found by investigation that t (D)n) Can be prepared by using the same at DnThe first order taylor series expansion near 0 is approximated as:
Figure FDA0002949744480000022
the second term of the above equation is related in part to the carrying capacity of the communication channel and can be written as Shannon-Hartley's theorem
Figure FDA0002949744480000023
Wherein G is1And G2Respectively representing channel capacity and coding gain; therefore, by at (D)n)＝t(Dn) -t (0) is taken
Figure FDA0002949744480000024
And
Figure FDA0002949744480000025
Δt(Dn) Is written as:
Δt(Dn)＝t(Dn)-t(0)≈Dn/(G1G2)
probability of success P of block creationnGiven by:
Figure FDA0002949744480000026
once the consensus process is successful, the nth LEAG will receive revenue, which consists of two parts: reward contribution Q to creation of a blocknAnd a transaction fee Mn(ii) a The net revenue for the nth Local Energy Aggregator (LEAG) can be calculated as the expected profit minus the cost of service:
Un，b(sn)＝(Qn+Mn)Pn(sn)-pcsn
wherein p iscIs the unit price of the edge computing service;
the utility of an edge computing service provider (ESP) is defined as the total revenue gained by providing the service minus the operating cost, i.e.:
Figure FDA0002949744480000027
wherein gamma iscIs the unit cost of service provisioning;
since edge computing service providers (ESPs) are dominant over LEAGs, edge computing service providers (ESPs) andcompetitive interactions between Local Energy Aggregators (LEAGs) can be simulated as a two-stage stainberg leader follower game; in the first stage, the edge computing service provider (ESP) determines the price per service (p)cAnd obtain revenue from a Local Energy Aggregator (LEAG) for resolving the offloaded workload verification problem; in a second phase, the Local Energy Aggregator (LEAG) acts as a follower and determines the need for service to be purchased; the two-stage stainberg leads the formulation of the follower game as follows:
step 1: service price optimization problem:
Figure FDA0002949744480000031
s.t.C5：pc，min＜pc＜pc，max
wherein p isc，minAnd pc，maxRespectively representing minimum and maximum ranges of service unit prices;
step 2: service demand optimization problem
Figure FDA0002949744480000032
s.t.C6：sn，min＜sn＜sn，max
Wherein s isn，minIs the minimum computational resource (hash capability) required by the nth Local Energy Aggregator (LEAG), sn，maxRepresents the maximum resource that an edge computing service provider (ESP) can provide;
optimal price and optimal service demand can be achieved by using backward induction:
1) solution of the second stage optimization problem: first, a service price p is givencSolving a second stage service demand optimization problem for each Local Energy Aggregator (LEAG); during service demand optimization, each Local Energy Aggregator (LEAG) competes with each other to maximize its own relative hashing capabilityTo quantize, and thus maximize, its likelihood of successfully creating a block; from formulas
Figure FDA0002949744480000033
It can be seen that the relative hashing capability of the nth Local Energy Aggregator (LEAG) is not only dependent on its policy snBut also on other Local Energy Aggregators (LEAG) policies, e.g.
Figure FDA0002949744480000034
n' ≠ n; therefore, competition among N Local Energy Aggregators (LEAGs) can be simulated as an N-person non-cooperative game, and the optimal strategy of the nth Local Energy Aggregator (LEAG) is expressed as
Figure FDA0002949744480000041
And order
Figure FDA0002949744480000042
Representation collection
Figure FDA0002949744480000043
A set of best policies of other Local Energy Aggregators (LEAGs) than the nth Local Energy Aggregator (LEAG); we have the following attributes:
theorem 3: nash equilibrium: the set of best service requirement policies, i.e.
Figure FDA0002949744480000044
Nash equilibrium of the N-person non-cooperative game in the second stage is formed;
theorem 4: presence of nash equilibrium: the N-person non-cooperative game in the second stage has Nash equilibrium;
theorem 5: optimal response: in view of
Figure FDA0002949744480000045
Best response function of nth Local Energy Aggregator (LEAG)
Figure FDA0002949744480000046
Given below;
theorem 6: uniqueness of nash equilibrium: if the condition is
Figure FDA0002949744480000047
If yes, then the Nash equilibrium of the second stage N-person non-cooperative game is unique;
based on the optimal service demand strategy of all Local Energy Aggregators (LEAGs) obtained in the second stage, the problem of service price optimization in the first stage can be solved; by substituting nash equilibrium of the second stage N-player non-cooperative game
Figure FDA0002949744480000048
Edge computing service provider (ESP) UEThe utility of (a) can be written as:
Figure FDA0002949744480000049
then we can get the following properties:
theorem 7: the concavity is as follows: the service price optimization problem is a standard convex optimization problem;
theorem 8: stenberg equilibrium: nash equilibrium of N-person non-cooperative game in second stage
Figure FDA00029497444800000410
And first phase service price optimization problem optimal solution
Figure FDA00029497444800000411
Constituting a steinberg equilibrium.
2. The method according to claim 1, wherein the step 1) specifically comprises: initially, each electric vehicle must register with a legal authority to obtain its public, private and certificate; public or private keys may be generated and distributed by an authority; the certificate represents the unique identity of the electric automobile by binding registration information of the certificate, each electric automobile has a set of wallet address issued by an organization, and in the initialization process, the electric automobile can search the nearest wallet address used by a Local Energy Aggregator (LEAG) and verify the integrity of the wallet, and then the electric automobile downloads corresponding data from a memory server;
the Local Energy Aggregator (LEAG) then develops a contract that specifies the performance, i.e. the relationship between the energy required to discharge the EV and the reward, i.e. the discharge EV payment in terms of energy coins, in which each different performance reward association is defined as a contract item, which usually contains a variety of contract items, then the Local Energy Aggregator (LEAG) broadcasts the contract and each EV selects its desired contract item to maximise its return, after the energy transaction, if the corresponding contract item has been successfully completed, the discharge EV will receive the specified reward, the energy coin is transferred from the Local Energy Aggregator (LEAG) to the address of the wallet federation of the EV, the authenticity of the payment can be verified by checking the last block of the block chain, the Local Energy Aggregator (LEAG) creates a new transaction record, which must first be verified by the electric vehicle and digitally signed, then uploading and publishing the audit;
all transaction records collected by the Local Energy Aggregator (LEAG) over a period of time will be encrypted, digitally signed, then organized into blocks, invalid transactions will be discarded, each new block linked to the previous block in the federation blockchain by a cryptographic hash, then, similar to the proof of work in bitcoin, each authorized Local Energy Aggregator (LEAG) in the federation blockchain competes for creating blocks by finding valid proof of work, i.e., hash values that meet certain difficulty requirements;
if the Local Energy Aggregator (LEAG) has limited computational power, it may purchase edge computing services from an edge computing service provider (ESP), the compute-intensive workload verification process is then handled by nearby edge compute nodes with powerful computing power, and the probability of success of block creation will be significantly increased, first the Local Energy Aggregator (LEAG) that found a valid proof of work broadcasts the created block to all authorized Local Energy Aggregators (LEAGs) in the network, next each Local Energy Aggregator (LEAG) reviews and validates the transaction records in the received block, and selects whether to accept the new chunk, if a new chunk is accepted by all Local Energy Aggregators (LEAGs), i.e., consensus is achieved, it will be appended at the end of the current federation block chain, and the Local Energy Aggregator (LEAG) that created this block will be awarded a certain number of energy coins.
3. The method according to claim 1, wherein the step 2) specifically comprises: the EV type is defined as follows:
definition 1: considering a parking lot with K discharging EVs, these EVs can be sorted and classified into K types according to their preference, if the set of electric vehicle types is expressed as: theta ═ theta1，...，θk，...，θKThen we get θ1＜...＜θk＜...＜θK，k＝1，...，K.
Further derivation we derive type θkCan be defined as:
Figure FDA0002949744480000061
wherein the parameters
Figure FDA0002949744480000062
For residual capacity, parameter χ (d)k) Indicating the distance d traveledkMinimum amount of power required, parameter Ek，maxIs the battery capacity;
in the case of asymmetric information, the Local Energy Aggregator (LEAG) does not know the specific type of each EV, but only the probability distribution of each type, we assume that the Local Energy Aggregator (LEAG) knows that there are K types of discharging cars and that one discharging car belongs to the type θkProbability P ofkThen, then
Figure FDA0002949744480000063
A contract composed of K contract items, which is not the same contract provided for different types of EVs, but different contract items designed for K discharge EV types; e.g. specific to type thetakThe designed contract item is expressed as (L)k，Rk) Wherein L iskRepresents the required power, RkRepresenting the resulting special reward, the contract being expressed as:
Figure FDA0002949744480000064
wherein
Figure FDA0002949744480000065
Considering this K type of discharging car, the expected utility of the Local Energy Aggregator (LEAG) is calculated as follows:
Figure FDA0002949744480000066
wherein gamma isLIs the unit electricity price of the Local Energy Aggregator (LEAG);
accepting contract item (L)k，Rk) Type theta ofkThe utility function of the electric vehicle is expressed as:
Figure FDA0002949744480000067
where gamma is the unit price of the cell discharge, thetakm(Rk) Is of type thetakR of (A) to (B)kThe value of (D); function m (R)k) Is RkWhere m (0) is 0, m' (R)k) > 0 and m' (R)k) < 0, without loss of generality, m (R)k) Can be defined as a quadratic function:
Figure FDA0002949744480000071
where a and b are assumed to be constant and must satisfy m' (R)k) > 0 and m' (R)k)＜0；
The expected social benefit is the sum of the total utility of the Local Energy Aggregator (LEAG) and K EVs:
Figure FDA0002949744480000072
the social welfare maximization problem under asymmetric information is described as follows:
Figure FDA0002949744480000073
s.t.C1：θkm(Rk)-γLk≥0，(IR)
C2：θkm(Rk)-γLk≥θkm(Rk′)-γLk′，(IC)
C3：0≤R1…＜Rk＜…＜RK
C4：Lk≤θk
Figure FDA0002949744480000074
wherein C1, C2 and C3 represent IR, IC and monotonicity constraints, respectively, and C4 represents LkThe upper limit of (d);
definition 2: the IR, IC and monotonicity constraints are defined as follows:
personal rational constraints (IR constraints): for collections
Figure FDA0002949744480000075
Is any one of the types thetakIf it selects the contract item (L)k，Rk) That it will getObtaining positive return;
incentive compatibility constraints (IC constraints): IC constraints ensure the self-revealing nature of contracts, for collections
Figure FDA0002949744480000076
Is any one of the types thetakIf and only if it selects a contract item (L) designed for its own typek，Rk) The maximum return is obtained only when the user wants to use the mobile phone;
monotonicity constraint: for collections
Figure FDA0002949744480000077
Is any one of the types thetakOf the type θk-1Is high, but has a specific type of thetak+1EV of (2) is low;
based on IR, IC and monotonicity constraints, the following properties can be derived:
introduction 1: for collections
Figure FDA0002949744480000078
Is any one of the types thetakIf θ is equal tok＞θk′Then Rk＞Rk′(ii) a When theta isk＝θk′When R isk＝Rk′；
2, leading: for L in set Ck，RkThe following inequalities are satisfied:
0≤R1＜…＜Rk＜…＜RK
0≤L1＜…＜Lk＜…＜LK
Figure FDA0002949744480000081
in the information asymmetry scenario, we define sufficient requirements for contract feasibility:
theorem 1: contract feasibility: set C when and only when the following conditions are satisfiedAny one of contracts (L)k，Rk) It is feasible:
a：0≤R1＜…＜Rk＜…＜RKand 0. ltoreq.L1＜…＜Lk＜…＜LK
b：θ1m(R1)-γL1≥0
c: for K e {2, …, K }, there is γ Lk-1+θk-1[m(Rk)-m(Rk-1)]≤γLk≤γLk-1+θk[m(Rk)-m(Rk-1)]
By eliminating the IR constraint and the IC constraint, the K IR constraints and the K (K-1) IC constraints are respectively reduced to 1 and K-1, so that the social welfare maximization problem under the asymmetric information can be converted into:
Figure FDA0002949744480000082
s.t.C1：θ1m(R1)-γL1≥0，(IR)
C2：θkm(Rk-1)-γLk-1≥θkm(Rk)-γLk，(IC)
C3，C4，k＝2，…，K
because the goal of the social welfare maximization problem is a concave function, convex programming cannot be directly applied, and a CCP algorithm is adopted for solving;
denotes fk(Rk)＝θkm(Rk) Due to fk(Rk) With respect to RkIs differentiable, so fk(Rk) Can be expanded by using its first order taylor series as:
Figure FDA0002949744480000083
wherein R isk，o[τ]Represents the initial point of the iteration τ;
thus, constraint C2, having a difference of two concave functions, is converted to a difference of a concave function and an affine function, written as
Figure FDA0002949744480000091
By using
Figure FDA0002949744480000092
Instead of C2, social welfare maximization is transformed into a convex programming problem and can be easily solved by using the Karush-Kuhn-Tucker (KKT) condition, at each iteration τ, by solving the transformed convex problem to obtain a locally optimal solution
Figure FDA0002949744480000093
And
Figure FDA0002949744480000094
then, the initial point of the Taylor series expansion at the iteration of τ +1 is defined as
Figure FDA0002949744480000095
Next, repeating the iteration to find a new locally optimal solution;
the iterative process terminates until a predefined stopping criterion is met;
theorem 2: convergence property: at any iteration τ, obtained
Figure FDA0002949744480000096
And
Figure FDA0002949744480000097
is feasible; in addition to this, the present invention is,
Figure FDA0002949744480000098
is non-regressive and will converge to the maximum social benefit, i.e.:
Figure FDA0002949744480000099
in the absence of information asymmetry, we have:
and 3, introduction: in contract design without information asymmetry, contract items (L) in any set Ck，Rk) All should satisfy thetakm(Rk)＝γLk(ii) a That is, the yield for any EV is 0;
thus, by forcing the benefit of each EV to be 0, the social benefit is equivalent to that of a Local Energy Aggregator (LEAG), and the corresponding optimization problem is expressed as:
Figure FDA00029497444800000910
s.t.C1：θkm(Rk)-γLk＝0
C2：0≤R1＜…＜Rk＜…＜RK
Figure FDA00029497444800000911
to solve this problem, we must find the solution of K quadratic equations, i.e.
Figure FDA00029497444800000912
Let R bek1And Rk2Are two solutions to the kth quadratic, the optimal solution is given by:
Figure FDA00029497444800000913
and (4) introduction: in contract design when there is no information asymmetry, for any oneEV type thetak，RkAre all fixed, with thetakIs irrelevant.
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