Utility maximization energy allocation method with upper bound on allocation under random energy arrival conditions

Abstract

The utility maximization energy allocation method with upper limit of distribution under random energy arrival condition studies the off-line one-dimensional resource allocation problem of realizing the utility maximization of a convex increasing function system within a certain time under the energy causality (hard) constraint, energy saturation (soft) constraint and task executability (hard) constraint. Based on the allocation strategy of maximizing the system utility under the energy causality (causality hard constraint) and energy saturation (saturation soft constraint), the energy allocation problem under the executable hard constraint is additionally considered, and an allocation scheme of reducing the iteration number is proposed. According to the executable constraint, energy is directly allocated to the time slot originally discussed, without iteration calculation and constant checking of additional wasted energy. The utility maximization energy allocation efficiency of the increasing convex function system under the causality hard constraint, saturation soft constraint and executability hard constraint is improved.

Description

Technical Field

[0001] This invention relates to an algorithm for resource allocation in energy harvesting systems. This algorithm can maximize the system utility of a monotonically increasing convex utility function under conditions of random energy arrival, achieving one-dimensional optimal energy allocation. Background Technology

[0002] In recent years, energy harvesting systems have received widespread attention in fields such as communication systems, wearable or implantable devices, structural health monitoring systems, wireless sensor networks, and vehicle area networks. For example, EH devices can serve as Road Side Units (RSUs) in vehicle edge computing networks, performing tasks such as vehicle safety warnings, vehicle dispatching, vehicle control, and human information services. In other application examples, in fog computing scenarios, EH devices can act as human servers or fog nodes, collecting, storing, processing data, and forwarding it to the network edge (IoT gateway). Energy harvesting systems can perform various tasks, including specific functions such as sensing, transmitting, diagnosing, treating, and preventing diseases; industrial process machine monitoring and control; vehicle safety warnings, monitoring, and control; information services; and intelligent transportation. The harvested energy can be used to replenish the batteries of IoT nodes, and can come from natural resources (such as solar energy) and artificial resources. Therefore, studying the distribution of energy across time slots under conditions of random energy arrival and causal flow between time slots is of great significance for improving system performance, maximizing energy utilization, and achieving maximum system utility.

[0003] Based on a one-dimensional energy allocation method that only considers the soft constraints of energy saturation and the hard constraints of energy causality, this invention, when considering the maximum allocatable energy constraint, uses some proposed theorems and lemmas to prove that energy allocation can be achieved in a faster way without frequent iterative calculations, thus greatly improving computational efficiency.

[0004] The advantages of this invention compared to existing technologies are: based on a one-dimensional energy allocation method that only considers the soft constraints of energy saturation and the hard constraints of energy causality, it achieves fast energy allocation and improves computational efficiency when considering the maximum allocatable energy constraint. Summary of the Invention

[0005] The technical problem solved by this invention is that, based on existing strategies, a method for optimizing energy allocation in energy harvesting systems using the KKT method is proposed, which can achieve greater system utility than the tunneling strategy.

[0006] The technical solution of this invention is characterized by including the following steps:

[0007] First, an energy harvesting model is proposed, and three constraints on the energy harvesting problem are given: hard constraints on causality, soft constraints on saturation, and hard constraints on executability. An objective function is defined, and the value is maximized in the end.

[0008] Second, the problem is solved in two steps: one under hard causal constraints and soft saturation constraints, and the other under hard causal constraints, soft saturation constraints, and hard executability constraints.

[0009] Third, we first consider the problem of allocating energy to time slots under causal hard constraints and saturation soft constraints. We can employ a geometric programming tunnel policy or an Effective Encountering BoundPolicy method.

[0010] Fourth, the problem is then considered under the constraints of causality (hard constraints), saturation (soft constraints), and executability (hard constraints). Building upon the third step, since a constraint p is added to each time slot... s ≤p opt When the energy allocated is greater than p opt When it is necessary to reduce the energy consumed in allocation, we prove that p s drop to p opt This is the most appropriate approach, and we will provide proof for four different scenarios.

[0011] To maximize the system utility of a monotonically increasing convex function under random energy arrival conditions, and considering a one-dimensional allocation algorithm (ODAA - Executability Hard Constraint) under causality hard constraints, saturation soft constraints, and executability hard constraints, the algorithm includes the following steps:

[0012] 1) Ignoring the executable constraints, under the constraints of energy causality and energy saturation, if p1 = p[l1] is allocated according to a certain allocation scheme, where l1 is the largest time slot allocated to p1 starting from 0, and the energy allocated after this time slot is greater than p1;

[0013] Next, we will consider two cases of executable hard constraints and handle them separately:

[0014] ①If p1>p opt In the first constant tunnel, p is allocated from time slot 1 to time slot s. a =p opt The energy is given by s = l1, n1 = l1; if there is still unallocated energy in the time slots, return to step 1) and repeat the operation using the updated parameters as follows. n max ′=n max -i1;

[0015] If the new allocation line touches the lower bound in some time slot k1, then,

[0016] otherwise

[0017] ② Otherwise, allocate p from time slot 1 to time slot s in the first constant tunnel. a = Energy of p1, where s = l1, n1 = l1; if there is still unallocated energy in the time slots, return to step 1) and repeat the operation using the updated parameters as follows.

[0018] n max ′=n max -i1;

[0019] 2) Otherwise, without considering the executable constraints, we allocate p2 = p[l2] according to a certain allocation scheme under the energy causal constraints and energy saturation constraints. The allocation of l2 starting from 0 is the largest time slot of p2, and the energy of the allocation after this time slot is less than p2. Next, we consider two cases under the hard constraints of executableness and handle them separately.

[0020] ①If p2>p opt In the first constant tunnel, p is allocated from time slot 1 to time slot s. a =p opt The energy is given by s = l2, n1 = l2; if there is still unallocated energy in the time slots, return to step 1) and repeat the operation using the updated parameters as follows. E0′=E max ,

[0021] n max ′=n max -i1;

[0022] ② Otherwise, allocate p from time slot 1 to time slot s in the first constant tunnel. a = Energy of p2, where s = l2, n1 = l2; if there is still unallocated energy in time slots, return to step 1) and repeat the operation using the updated parameters as follows. E0′=E max , n max ′=n max -i1.

[0023] The principle of this invention is as follows: Based on a one-dimensional energy allocation method that only considers the soft constraints of energy saturation and the hard constraints of energy causality, when considering the maximum allocatable energy constraint, it is proved, using some proposed theorems and lemmas, that energy allocation can be achieved in a faster way without frequent iterative calculations, thus greatly improving computational efficiency.

[0024] The advantages of this invention compared to existing technologies are: based on a one-dimensional energy allocation method that only considers the soft constraints of energy saturation and the hard constraints of energy causality, it achieves fast energy allocation and improves computational efficiency when considering the maximum allocatable energy constraint. Attached Figure Description

[0025] Figure 1 This is the time-slot energy arrival model of the present invention.

[0026] Figure 2 This invention relates to an energy distribution strategy within an energy tunnel.

[0027] Figure 3 and Figure 4 These are different scenarios where energy consumption has been adjusted under feasibility constraints according to the present invention.

[0028] Figure 5 Two cases for the proof of Theorem 4 Detailed Implementation

[0029] We consider a time-slotted energy arrival model, where energy arrives randomly in time, such as... Figure 1 As shown. All time intervals have the same length. We assume that at time 0, the battery has an initial energy of E0 units, E max Let be the capacity of the battery. The energy collected in a given time slot is given by a saturation soft constraint, which is measured at the end of the time slot. We have s = 1, 2, ..., N+1. We consider the energy flow between time slots that satisfy both the causality hard constraint and the saturation soft constraint.

[0030] To better utilize randomly arriving harvested energy to execute tasks on the processor, the QoS of tasks on embedded systems must be maximized under several practical constraints. These constraints include:

[0031] Energy causality (hard constraint): The available energy in each time slot *s* is finite, determined by the energy at the end of the last time slot. It is impossible to utilize energy that has not yet arrived, nor is it possible to utilize the energy in the current time slot. s This refers to the energy consumed by each time slot task.

[0032]

[0033] Energy saturation (soft constraint): There is an energy capacity constraint on the available energy for task processing. It requires that the remaining energy at the end of the last time slot plus the energy arriving at that time slot be less than the battery's storage capacity; otherwise, energy will overflow from the battery, leading to energy inefficiency and a suboptimal solution. This is not a hard constraint.

[0034]

[0035] Task Executability (Hard Constraint for Executability) Constraint: The total resource utility used by all tasks within each time period must be less than a specified value. This level depends on the limited system capacity.

[0036] p s ≤p opt , s=1,2,…,N+1 (3)

[0037] Optimal resource allocation refers to maximizing the benefits of an energy supply system within a given timeframe and under certain constraints. Therefore, this objective can be expressed as:

[0038]

[0039] The objective function is about p s An increasing convex function.

[0040] The following considers energy allocation in two scenarios.

[0041] 1. One-dimensional energy allocation considering only causal hard constraints and saturation soft constraints.

[0042] Reference [1] proposes a tunneling strategy that determines the upper bound of the length of the first constant power allocation and then iteratively processes the remaining time slots in the same way, "until" the last time slot.

[0043] However, in certain extreme cases, this can lead to a suboptimal solution. For example, there might be a solution like... Figure 2 The energy harvesting case is shown. We can see that there is Scheme 1, which first allocates power using the blue power allocation line in time slots 1 and 2, and then uses the green power allocation line in time slots 3 and 4. If we use Scheme 2, allocating power using the blue line in time slot 1, and then using the red line in time slots 2 through 4, the objective function will be greater than Scheme 1. We will temporarily disregard the allocation after time slot 4. Scheme 1 is a "tunneling strategy." Therefore, we can see that the tunneling strategy is suboptimal in some cases. Based on this, we can propose a new method, namely the Effective Encountering Bound Policy, by analyzing the KKT conditions.

[0044] 2. Maximize the system utility of a monotonically increasing convex function under the condition of random energy arrival, and consider one-dimensional allocation under causal hard constraints, saturation soft constraints and executability hard constraints.

[0045] We add an additional executable hard constraint P to the problem solved in the first step. s ≤p opt , s = 1, 2, ..., N+1.

[0046] This problem is clearly more complex. When the allocated energy is greater than p opt At that time, the energy needs to be immediately corrected to be less than or equal to p. opt To conserve energy for future use, frequent correction and iterative calculations lead to continuous updates of the initial energy and time slots, resulting in low allocation efficiency. To facilitate allocation, we present Theorem 3. Furthermore, we consider designing a novel method, "One-Dimensional Allocation Algorithm Considering Hard Constraints of Executability" (ODAA, A4), which simplifies the allocation process using a one-dimensional energy allocation method that only considers causality and saturation constraints. It is worth noting that this one-dimensional energy allocation method can employ either the Tunnel Policy or the Effective Encountering Bound Policy; of course, the result corresponding to the Effective Encountering Bound Policy is optimal. Therefore, this method is independent of the one-dimensional energy allocation method that only considers causality and saturation constraints.

[0047] Theorem 3: If, considering both causal hard constraints and saturation soft constraints, a certain allocation method is used to assign p... s The optimal allocation is greater than p opt To satisfy additional hard execution constraints, p is directly allocated in the time slots under discussion. s =p opt This is the optimal way to maximize the object function under these three constraints. Even considering the wasted energy, recursive computation is unnecessary in the time slot under discussion. When the executable hard constraints are active during the time slot under discussion, if p is modified... opt When encountering a lower bound, the update of the initial energy of the time slot must be carefully calculated and discussed.

[0048] To prove Theorem 3, we first give Lemmas 1, 4, 5, and 2. We will discuss the different cases of the original distributive line under causal hard constraints and saturation soft constraints, as well as p. s Decrease to p opt The different scenarios are as follows: scenario 1.1, scenario 1.2, scenario 2.1, and scenario 2.2.

[0049] Case 1: Without considering p s ≤p opt In this situation, you encounter the underside of the tunnel.

[0050] In case 1, depending on the different situations of the early time slots and p opt The specific value depends on p. opt Adjust p s After that, there are generally two situations, namely situation 1.1 and situation 1.2.

[0051] Case 1.1: p s After being reduced, it touched the lower edge of the tunnel in time slot 1 to s. Figure 3 The tunnel only encounters the lower side at the last time slot k (k = s ~ ) below it.

[0052] Lemma 1: For case 1.1, when p s More than p opt During the allocated time slots from time slot 1 to s, p is reduced. s to p opt The energy consumption from the contact point to the lower bound is greater than before. The initial energy of the time slots discussed later is related to the previous E. max The quantities are the same.

[0053] Proof: If we reduce p s Below p opt Even though all constraints are satisfied, this will result in a lower objective function reward value in the discussion allocation slots from 1 to s. Furthermore, due to the saturation constraint, relative to p... opt Unused stored energy will be wasted, leading to energy overflow in the next time slot. If we... s The value decreases to above p opt If the value of p is less than 1, then the executable constraint is not satisfied. Therefore, in case 1.1, the value of p is reduced. s to p opt It is the best choice. The energy consumption from the contact point to the lower bound is greater than before. The initial energy of the time slots discussed later is related to the previous E. max The quantities are the same.

[0054] In the time slot allocation discussed, from time slot 1 to s, p s Reduce to p opt Then, resource allocation continues in the following time slots, with the initial energy updated to E′0 = E max Time slot s' = ss~.

[0055] Case 1.2: p sAfter lowering, at a certain encounter time slot g before the last time slot touching the lower edge, the lower side of the tunnel is touched. In case 1.2, as... Figure 4 As shown, typically, we iteratively calculate the energy distribution every time the distribution line encounters the underside of the tunnel, which involves a large amount of computation. Therefore, we provide Theorem 4 to simplify it.

[0056] Theorem 4: For case 1.2, when p s From time slot 1 to s ~ exceeding p opt When, decrease p s to p opt It eliminates the need for iterative calculations of energy allocation every time a new initial energy level and updated time slot number are encountered.

[0057] Proof: As Figure 4 As shown, if the power line encounters the lower part of the tunnel at time slot s = g, where 1 ≤ g ≤ s, we can be certain that from time slot g to s, the power line will encounter the lower end of the tunnel in every time slot, and the energy distribution will be less than p. opt This would inevitably increase energy waste. Figure 5 The red solid line .a represents the total wasted energy at the end of time slot 3, which is ④. If we calculate it iteratively in each time slot, the allocation across time slots 1 to 3 remains p. opt ,like Figure 5 As shown by the red dashed line. Each recalculated allocation strategy updates the E for each time slot. max The initial energy. At the end of time slot 1, the wasted energy is represented by ③. At the beginning of time slot 2, as E... max Initial energy update and p opt The wasted energy at the end of time slot 2 is represented by ②. The wasted energy at the end of time slot 3 is represented by ①. According to the property that opposite sides of a parallelogram are equal, equation ① + ② + ③ = ④ holds. Therefore, the graphical method proves that it is not an unnecessary iterative statement. Directly adjust to p. opt The allocation is equivalent to the allocation in iterative computation. Figure 5 .b demonstrates another kind of... Figure 5 In the same case, where ① + ② = ③, from Figure 5 .a to Figure 5 .b. We generally assume that it is unnecessary to iteratively calculate energy allocation with new initial energy and time slot number at each encounter. We also observe that when the energy line first encounters the lower bound, the initial energy of the time slots discussed later can be calculated from the last time slot. We can easily see that energy ① represents the remaining energy in the time slot. However, energy ① is wasted when the energy saturates in the next time slot. The initial energy available in subsequent time slots is always E′0 = E max .

[0058] p will decrease within the discussion interval. s to p opt Then, from time slot 1 to s, resource allocation continues in the following time slots, and the initial energy of E′0 is updated to E. max And the time slot coefficient s′=ss~.

[0059] Case 2: Without considering p s ≤p opt In this case, the upper part of the tunnel is encountered at the last time slot s.

[0060] Lower p s It is necessary. This depends on the different situations in the early time slots and p. opt There are generally two cases for the specific value of , namely case 2.1 and case 2.2.

[0061] Case 2.1: In p s After descending, it remains in the tunnel, satisfying the causal and saturation constraints from time slot 1 to s in the time slot under discussion. In this case, Theorem 5 for resource allocation is given.

[0062] Theorem 5: For case 2.1, in the time slot interval under discussion from time slot 1 to time slot s, we will... s drop to p opt Then, resources are allocated with an updated initial energy for the time slots discussed later. These resources can be calculated from time slot 1 to the last time slot s of the interval under discussion, where time slot g is the time slot where the confined power line last touches the lower edge of the tunnel.

[0063] Case 2.2: In p s After the reduction, it exceeds the lower end of the tunnel, meaning the saturation constraint is no longer satisfied. In this case, Lemma 2 for resource allocation is given.

[0064] Lemma 2: For case 2.2, reduce p in the time slot interval under discussion. s to p opt This is the optimal choice. Then, continue allocating energy to time slots after s~. After the initial energy update, calculations are only performed from time slot g, i.e., when the allocation line last encounters the lower bound, until the last time slot discussed, s~. There is no need to recalculate the allocation each time energy is replenished.

[0065] The proof of Lemma 2 is similar to that of Theorem 4.

[0066] Based on Lemmas 1, 4, 5 and 2, Theorem 3 was proved.

[0067] Based on Theorem 1, the following "One-Dimensional Allocation Algorithm Considering Hard Constraints of Executability" (ODAA-Hard Constraints of Executability, A4) is given, providing the optimal solution to the one-dimensional energy allocation problem under causal constraints, saturation constraints, and executability constraints.

[0068] In Theorem 3, the allocation method considering causal constraints and saturation constraints can be any method, not limited to the optimal method of EEBP (A2), but also including any other suboptimal allocation algorithm, such as Tunnel Policy (A1).

[0069] A one-dimensional allocation algorithm (ODAA - Executability Hard Constraint) that maximizes the system utility of a monotonically increasing convex function under random energy arrival conditions, and considering causality hard constraints, saturation soft constraints, and executability hard constraints, is characterized by the following steps:

[0070] 1) Ignoring the executable constraints, under the constraints of energy causality and energy saturation, if p1 = p[l1] is allocated according to a certain allocation scheme, where l1 is the largest time slot allocated to p1 starting from 0, and the energy allocated after this time slot is greater than p1;

[0071] Next, we will consider two cases of executable hard constraints and handle them separately:

[0072] ①If p1>p opt In the first constant tunnel, p is allocated from time slot 1 to time slot s. a =p opt The energy is given by s = l1, n1 = l1; if there is still unallocated energy in the time slots, return to step 1) and repeat the operation using the updated parameters as follows. n max ′=n max -i1;

[0073] If the new allocation line touches the lower bound in some time slot k1, then,

[0074] otherwise

[0075] ② Otherwise, allocate p from time slot 1 to time slot s in the first constant tunnel. a = Energy of p1, where s = l1, n1 = l1; if there is still unallocated energy in the time slots, return to step 1) and repeat the operation using the updated parameters as follows.

[0076] n max ′=n max -i1;

[0077] 2) Otherwise, without considering the executable constraints, we allocate p2 = p[l2] according to a certain allocation scheme under the energy causal constraints and energy saturation constraints. The allocation of l2 starting from 0 is the largest time slot of p2, and the energy of the allocation after this time slot is less than p2. Next, we consider two cases under the hard constraints of executableness and handle them separately.

[0078] ①If p2>p opt In the first constant tunnel, p is allocated from time slot 1 to time slot s. a =p opt The energy is given by s = l2, n1 = l2; if there is still unallocated energy in the time slots, return to step 1) and repeat the operation using the updated parameters as follows.

[0079] E0′=E max ,

[0080] n max ′=n mx -i1;

[0081] ② Otherwise, allocate p from time slot 1 to time slot s in the first constant tunnel. a = Energy of p2, where s = l2, n1 = l2; if there is still unallocated energy in time slots, return to step 1) and repeat the operation using the updated parameters as follows. E0′=E max , n max ′=n max -i1.

[0082] Simulation and Experiment

[0083] We present several experiments to evaluate the performance of the proposed algorithm. To compare the performance of the two algorithms, we extend the tunneling policy A1 to A1", enabling power allocation under executable constraints.

[0084] Specifically, we divide it into 3 energy-reaching scenarios and 2 different p opt Task setup simulation. Task settings A, p opt =10.8. Task settings B, p opt =9.6.

[0085] Scene 1

[0086] To evaluate the algorithm's performance, we began with extensive Monte Carlo simulations. We assumed E... max=20, E0=12, the energy arrival process is random: configuration A generally has an energy distribution between 1.4 and 4.2, and the energy distribution is uniform in each time slot between time slot 1 and 999. Figure 1 N = 999.

[0087] Scene 2

[0088] We assume E max =20, E0=12, the energy arrival process is random: configuration B generally has an energy distribution between 1.3 and 10.3, and the energy distribution is uniform in each time slot between time slot 1 and 999. Figure 1 N = 999.

[0089] Scene 3

[0090] We assume E max =20, E0=12, the energy arrival process is random: configuration C generally has an energy distribution between 5.3 and 14.3, and the energy distribution is uniform in each time slot between time slot 1 and 999. Figure 1 N = 999.

[0091] The average arrival energy for scenarios 1, 2, and 3 shows an increasing trend. We can see that for scenarios IV, V, and VI, under the same energy distribution, the average actual energy used using algorithm A2 is not always greater than the average actual energy used using algorithm A1. However, the average logarithmic reward for different algorithms all conforms to this relationship. This confirms that our proposed A4 (A2) outperforms the original A1 (A1).

[0092] Table 1 Simulation results for Scenario 1

[0093] Task Setting A A B B Algorithm A1(A1”) A2 (A4) A1(A1”) A2 (A4) <![CDATA[mean(p s )]]> 1.6546e+2 1.4912e+2 1.6461e+2 1.4900e2 <![CDATA[mean(r s )]]> 2.6391e+2 2.8009e+2 2.6307e+2 2.7997e+2

[0094] Table 2 Simulation results for scenario 2

[0095] Task Setting A A B B Algorithm A1(A1”) A2 (A4) A1(A1”) A2 (A4) <![CDATA[mean(p s )]]> 2.9475e+3 2.9202e+3 2.9423e+3 2.9190e+3 <![CDATA[mean(r s )]]> 1.0576e+3 1.0624e+3 1.0571e+3 1.0622e+3

[0096] Table 3 Simulation results for scenario 3

[0097] Task Setting A A B B C Algorithm A1(A1”) A2 (A4) A1(A1”) A2 (A4) A1(A1”) <![CDATA[mean(p s )]]> 4.9229e+3 4.9119e+3 4.9185e+3 4.9096e+3 4.9229e+3

Claims

1. A utility maximization energy allocation method with upper bound on allocation under random energy arrival condition, considering energy causality constraint, energy saturation constraint and executable hard constraints, characterized in that comprising the following steps: first, the symbols and terms are explained; Assuming initially E0 units of energy, E max is the battery capacity; E k is the energy absorbed by each time slot, measured at the end of each time slot, k is the time slot number, k = 1,..., N + 1; The following is explained about tunnel policy: P[n] = [p max [n], p0[n]] = {p | p max [n] ≤ p ≤ p0[n]), where n is the time slot number; n ub is calculated using the existing geometric programming method, and the maximum time slot is allocated in the energy allocation tunnel. n denotes the number of discrete time slots; Energy causality constraint: the available energy for each time slot s is limited by the energy at the end of the last time slot; it is not possible to use energy that has not yet arrived, nor is it possible to use energy from this time period now; represents the sum of the energy accumulations from the initial energy at the start to the arrival of the l-1th time slot; where E s represents the energy arriving at each time slot s; where p s represents the energy allocated to each time slot s; l represents the number of discrete time slots; Energy saturation constraint: there is an energy capacity constraint on the available energy for task processing; it is required that the remaining energy at the end of the last time slot plus the energy arriving at that time slot is less than the storage capacity E of the battery max ; otherwise, energy would spill from the battery, resulting in energy inefficiency, which is a suboptimal solution, which is not a hard constraint; Task enforceable hard constraints: add limit p to each time slot s ≤ p opt When the allocated energy is greater than p opt The consumed energy by the allocation needs to be reduced; p s ≤p opt , s = 1, 2,..., N + 1 (3) The optimal resource allocation means maximizing the benefit of the energy supply system under certain constraints in a certain time; therefore, this goal can be expressed as The objective function is an increasing convex function in p s ; The one-dimensional assignment algorithm (ODAA) that maximizes the system utility of a monotonically increasing convex function under the condition of random energy arrival and considers causal constraints, saturation constraints and executable hard constraints has the following steps: (1) Without considering the executable hard constraints, only under the energy causal constraints and energy saturation constraints, if the assignment pi = p[li] is made according to the assignment scheme, where li is the largest time slot that assigns pi starting from 0, and the assigned energy after this time slot is greater than pi; Next, the executable hard constraints are considered, and the following two cases are handled respectively: opt p1= p1- p a = p opt s = s + 1, n1= n1+ 1 ​ If the new assignment line touches the lower bound at a time slot k1, then, Otherwise ii. else, pi < p opt In the first constant tunnel, from time slot 1 to time slot s, p a = pi, where s = li, nl = li; if there are still time slots not allocated energy, return to step 1) to repeat the operation using the updated parameters as follows, n max ′=n max -i1; p a denotes the energy allocated to the time slot interval in the first constant tunnel; (2) Without considering the executable hard constraints, only under the energy causal constraints and energy saturation constraints, when the upper side of the tunnel is encountered, the assignment p2 = p[l2] is made according to the assignment scheme, where l2 is the largest time slot that assigns p2 starting from 0, and the assigned energy after this time slot is less than p2; Next, considering the executable hard constraints, the following two cases are handled respectively; Considering the executable hard constraints, the following two cases are handled, and the processing method comprises the following steps: opt , in the first constant tunnel, from time slot 1 to time slot s, p a = p opt is allocated, where s = l2, n1 = l2; if there are still time slots not allocated energy, return to step 1) using the updated parameters as follows, E0' = E max , ​ ii. else p2 < p opt In the first constant tunnel, from time slot 1 to time slot s, p is allocated a = p2, where s = l2, n1 = l2; if there are still time slots not allocated energy, return to step 1) using the updated parameters as follows, and repeat the operation,

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