In order to reach the goal of achieving carbon peak by 2030 and carbon neutrality by 2060, the construction of new power systems with new energy sources as the main body continues to advance in china (Xu et al., 2021). Due to the limited distribution of traditional fossil fuels in China, renewable energy sources such as wind power and photovoltaic power generation will gradually become the main form of energy in the future power system (Xu et al., 2022). By 2020, the installed capacity of wind power and photovoltaic power has exceeded 24.3% of the total installed capacity of power generation, and the installed capacity of grid-connected renewable energy power generation has maintained rapid growth in China. The high proportion of distributed renewable energy connected to grid significantly affects the operation mode of the power grid. Because the operation state of the distribution network is complex and changeable and the control objects are diverse, higher requirements are put forward for the measurement and control level of the power system.

A high proportion of renewable energy is a key feature of future energy systems (Xu, 2019). PIoT provides an effective solution for the efficient operation of distribution networks with renewable energy. PIoT fully applies advanced information and communication technologies such as artificial intelligence and 5G to realize real-time connection between devices in the power system, so that the system state of each link of power production, transmission, and consumption can be fully perceived and controlled. Specifically, affected by natural conditions, renewable energy generation has the characteristics of intermittence and volatility. With the continuous operation of renewable energy generation grids, the energy storage capacity of lithium-ion batteries will also continue to decrease. Using a large number of STDs arranged around the power generation equipment to collect data and calculate, the output power of renewable energy generation equipment in the future can be predicted and the health status of lithium-ion batteries can be estimated, which can control the efficient and stable operation of the power grid (Huang and Wei, 2020; Zhang et al., 2020; Qin et al., 2023). PIoT connects power grid enterprises, power generation enterprises, power users, suppliers, and their equipment to achieve data sharing and ensure the intelligent management of the power grid without increasing the complexity of the physical connection structure of the power grid.

With the continuous construction of PIoT, the number of STDs has exploded, resulting in a huge amount of STDs’ data that need to be stored, processed, and analyzed. The traditional data processing method is used to transmit the data to the remote cloud center server (RCCS) with strong computing power for calculation. However, due to the heterogeneous and large number of STDs in the PIoT environment, the unified upload of computing tasks to the RCCS will cause network congestion, and the RCCS is arranged at the remote end of STDs. The transmission delay generated by the STD uploading data will greatly increase the completion time of the overall task, thus affecting the real-time performance of the computing task. As an extension and supplement of cloud computing, edge computation solves this problem well. Edge computation technology enables many computing tasks to be completed by local devices without being handed over to the RCCS. The task processing is completed at the edge node close to STDs, and the edge server (ES) can respond to the STD’s requests and tasks in a shorter time. However, ESs typically offer fewer computing and storage resources than RCCS. If STDs have many computing tasks, they cannot execute all of them simultaneously. Therefore, the edge computation research has focused on computing task allocation (Bi et al., 2020; Pham et al., 2020; Song et al., 2020; Wei et al., 2020; Zhu and Zhou, 2021).

Generally, a computing task allocation scheme comprises of two parts: offloading decision and resource allocation decision (Chen et al., 2022a; Chen et al., 2022b; Deng et al., 2022; Fang et al., 2022; Wang et al., 2022; Yue et al., 2022; Zhou et al., 2022; Zhou and Zhang, 2022). The former serves to determine which tasks should be performed on ESs or RCCS. The latter specifies the amount of computing and storage resources allocated to each STD by ESs or RCCS. By caching applications and their associated databases on ESs, ESs can perform tasks that require these applications, which is called service cache (Xu et al., 2018). Nowadays, in most computation offloading schemes, all services required by STDs’ computing tasks have been cached by ESs. The RCCS can cache all types of services because of its massive storage capacity. However, due to its limited storage resources, there are only a few services that an ES can cache. Accordingly, a joint optimization scheme for service cache updating and computing task allocation (JOSSCUCTA) for PIoT including renewable energy sources was proposed. The contribution of this article mainly included the following three parts:

• JOSSCUCTA was proposed and established as a mathematical model of mixed-integer non-linear programming (MINLP).

The remainder of this paper is organized as follows: a review on related work on computing task allocation is provided in Section 2. A cloud-edge-end collaboration edge computation network framework is proposed and JOSSCUCTA is proposed and established as an MINLP problem in Section 3. Section 4 provides a solution to the MINLP problem using the OA method. In Section 5, simulation results are analyzed, and conclusion is reported in Section 6 .

Based on optimization objectives, computing task allocation schemes can be categorized into four types: schemes with minimum delay, with minimum consumption of energy, with minimum trade-off between delay and consumption of energy, and with optimization of other performance indicators. Liu et al. (2016) adopted the Markov decision process to establish the computing task allocation scheme optimization model with minimum delay under the power constraint of terminal equipment. Based on experimental results, the scheme greatly reduced computing delay compared to the local computing and cloud computation schemes. Similarly, to obtain a computing task allocation scheme with the shortest latency in an ultra-dense network under the power constraints of terminal equipment, Chen and Hao (2018) demonstrated the computing task allocation problem as an MINLP problem using software-defined networking. According to experimental results, the method can reduce delay by 20% compared with baseline schemes. Xing et al. (2018) introduced a time-division multiple-access communication protocol under the scenario that each STD has several computing tasks. These tasks can be offloaded simultaneously to many ESs and can be completed in parallel. The performance and energy consumption of local computing and computing on ESs were analyzed under the framework of the protocol to develop an optimization model with minimum delay. Zhang et al. (2017) proposed an intelligent vehicle computing task allocation scheme model that utilized a Stackelberg game theory method to determine the task offloading decision with minimum delay, thereby maximizing the efficiency of the vehicle and edge devices. Ning et al. (2018) proposed a partial allocation scheme for computation tasks that minimizes total amount of computing delay and transmission delay when computing tasks may be separated into numerous modules. Considering that STDs communicate with ESs via wireless access networks and communication resources are limited in the edge computation system, STDs’ energy consumption can be minimized by computing task allocation (Zhao et al., 2017). In order to determine the optimal c computing task allocation scheme, computer resource allocation and wireless network resource allocation were optimized simultaneously. The simulation results showed that this model had a better energy-saving effect. Because the data source is always far away from the remote cloud, computing tasks with delay constraints can only be offloaded to ESs for execution. Therefore, Guo and Liu (2018) investigated an edge computing network architecture based on a fiber–wireless network and proposed an ES and a remote cloud collaborative computing task allocation scheme with the minimum energy consumption of terminal equipment under delay constraints. STDs’ energy usage can be reduced by offloading computing tasks to idle wireless devices nearby. Therefore, Cao et al. (2018) proposed an edge computing network architecture composed of STDs, help devices, and an access point device. Lan et al. (2019) developed a computing task allocation scheme that provided the optimal allocation decision while optimizing bandwidth resources, CPU frequency of STDs, and transmission power, which was modeled as an MINLP problem. Meng et al. (2019) proposed an online scheduling algorithm that optimized the allocation decision of computation tasks, the allocation of network bandwidth, and computing resources so that most tasks can be completed before the deadline. Lin and Shen (2015) aimed at optimizing the quality of the users’ experience while playing interactive games. A cloud–fog system was designed to reduce delay and improve coverage using response time, network congestion, and service coverage as indicators of users’ experience.

Taking Eqs 9, 10 into the objective function of P 0 , we obtain f Γ = 1 n ∑ i = 1 n x i l 2 v i p i c i + x i e 2 p i b i r i + v i c i e + x i c 2 p i b i r i + b i R + v i c i c + 1 n ∑ j = 1 m y j 1 − y j s m j R 0 . (12)

It can be proved that if the integer variables X and Y are relaxed to real variables, Eq. 12 is a convex function. Therefore, the optimization model P 0 is an MINLP problem which can be resolved using the OA method. This method can reduce the complexity of optimization problems by transforming MINLP into a non-linear programming (NLP) problem and a mixed-integer linear programming (MILP) problem. Because the objective function of the optimization model P 0 is non-linear and suppose a real variable τ satisfies the constraint f Γ ≤ τ , the optimization model P 0 can be transformed into an equivalent optimization model P 1 as follows: P 1 : ⁡ min ⁡ τ , s . t . f Γ ≤ τ , C 1 ∼ C 7 . (13)

Let X ¯ h and Y ¯ h be the certain values of the integer variables X and Y, respectively, satisfying the constraint C 1 ∼ C 7 . By substituting them into the optimization model P 1 , an NLP problem P 2 can be obtained: P 2 : ⁡ min ⁡ τ , s . t . 1 n ∑ i = 1 n x ¯ i l h 2 v i p i c i + x ¯ i e h 2 p i b i r i + v i c i e + x ¯ i c h 2 p i b i r i + b i R + v i c i c + 1 n ∑ j = 1 m y ¯ j h 1 − y j s m j R 0 ≤ τ C 1 ∼ C 7 , (14)

The interior point method can be used to solve the optimization model P 2 . Suppose the values of the optimal variables are Γ h ≜ < X ¯ h , Y ¯ h , C ¯ e h > , the upper bound of the optimization objective function value of P 0 can be updated by calculating f Γ h . Using the tangent function of the non-linear convex function to replace the non-linear function itself, the OA method relaxes the non-linear constraint into a linear constraint, thereby transforming the MINLP problem into an MILP problem. Let p h Γ = f Γ h + ∇ X , Y , C e f Γ | Γ = Γ h Γ − Γ h . (15)

Add p h Γ ≤ τ to the optimization model P 1 , and replace the non-linear constraint f Γ ≤ τ . The optimization model P 1 is transformed into an MILP problem. P 3 : ⁡ min ⁡ τ , s . t . p h Γ ≤ τ , C 1 ∼ C 7 . (16)

By solving the optimization model P 3 , the optimal objective function value τ and the integer optimization variable values X ¯ h + 1 and Y ¯ h + 1 can be obtained, and the lower bound of the optimization objective value can be updated with the function value τ . The integer optimization variable values X ¯ h + 1 and Y ¯ h + 1 are substituted into the optimization model P 2 to realize the iterative calculation of the lower and upper bounds of the optimization target value of P 0 . The algorithm steps of solving the optimization model P 1 using the OA method are shown in Algorithm 1

Algorithm 1

The JOSSCUCTA scheme based on the OA method.

input: w i , y j s , ε ;

An evaluation of the efficiency of JOSSCUCTA is conducted in this section. The specific simulation environment is as follows: the simulation in this paper was conducted using MATLAB. The edge computation system includes one RCCS, one WiFi wireless access point, one ES, and multiple STDs. STDs are randomly distributed in a square area, and the center of the area is deployed with one wireless access point and one ES. Channel gain is h i u p = d i − 4 , and d i is the distance between wireless access point and STD i. c i satisfies the uniform distribution U ∼ 0.8,1 G s y c l e s / s . p i u p = 100 m v , B i = 1 M b p s , and σ 2 = − 174 d b m / H z . b i satisfies the distribution U ∼ 0.5,1 M b p s . The ES and the RCCS computing resource are 15 G s y c l e s / s and 100 G s y c l e s / s , respectively. The ES’s storage resource is m e = 35 M b p s . There are five services, and the storage space required by each service obeys the distribution U ∼ 10,20 M b p s . The efficiency of JOSSCUCTA was verified by comparing with the following computing task allocation schemes:

• All local: STDs perform all computing tasks locally.

To verify whether JOSSCUCTA can reduce the average system latency of all STDs’ computing tasks when the ES has not cached services required by STDs, experiments 1 and 2 assume that services required by all STDs are not cached by the ES. The simulation scenario of experiment 1 is as follows: there are five STDs that require five servers, or that require two services. A comparison of the average system latency of different computing offloading schemes as the number of computing tasks of each STD increases is illustrated in Figure 2. As each computing task requires more and more computing resources, the average system latency of different task allocation schemes is compared, as shown in Figure 3.

Figures 2, 3 show that as the number of computing tasks on each STD increases or the computing resources required to perform each computing task increase, the average system latency of all computation offloading schemes increases. Because each STD’s total computing tasks require more computing resources and each STD or the ES has constant computing resources, each computing task is allocated fewer resources. As a result, the average system latency increases.

The average system latency of JOSSCUCTA increases as the number of servers required by STDs increases because the more STDs need the same service, the earlier the service is downloaded from the RCCS to the ES. The average system latency of all local is the highest among all computation offloading schemes, which indicates that computing intensive tasks are hardly to perform locally. SE3CSCU has higher average system latency than JOSSCUCTA because without service cache updating, computing tasks of STDs can only be offloaded to the RCCS.

The simulation scenario of experiment 2 is that the server required by each STD in the edge computation system is different. As shown in Figure 4, the average system latency of JOSSCUCTA gradually increases as the number of STDs increases when there are fewer STDs in the edge computation system. This is because the ES allocates fewer computing resources to each task when STDs offload more computing tasks to it. However, with an increasing number of STDs, more computing tasks are executed on the RCCS to obtain a smaller execution delay. Thus, average system latency does not continue to increase. Meanwhile, in computing task allocation schemes of all local and all offloading, the average execution latency does not increase or decrease consistently as it depends on computing resource requirements, computing resources supplied by all STDs, and transmission latency.

To verify whether JOSSCUCTA can reduce the average system latency of all STDs’ computing tasks when the ES has not cached part of the services required by STDs, the simulation scenario of experiment 3 is that the edge computation system contains five STDs, and each of them requires different services. The ES has cached three services which are required by first to third STDs, and there is no enough storage capacity in the ES to cache more servers. Figure 5 illustrates the comparison of all computing offloading schemes when the number of computing tasks of the fourth and fifth STDs increases.

In Figure 5, we can see even if the services cached in the ES are all required by STDs and the ES has no more storage resources to cache other services, JOSSCUCTA can reduce the average system latency. Because an STD has many computing tasks, it will increase transmission latency to offload them to the RCCS. JOSSCUCTA can download the service required by the STD to the ES, reducing the transmission latency of these computing tasks. To cache the new service, the ES needs to delete services required by other STDs with a small number of computing tasks and perform their computing tasks on the RCCS. Even though the total execution latency of these STDs has increased, it remains that the pros outweigh the cons.

The simulation scenario of experiment 4 is that there are two categories of STDs in the edge computation system. The services required by one category of STDs have been cached on the ES, and there are no more storage resources to cache other services on the ES. The services required by another category of STDs are not cached by the ES, but they are the same services. Figure 6 shows the comparison of all computing offloading schemes as the number of the second category of STDs increases.

We can see that when there are fewer STDs of the second category, the average system latency of JOSSCUCTA is the same as that of SE3CSCU, as shown in Figure 6 because server cache updating does not occur. However, as more and more STDs need the same service, JOSSCUCTA improves performance further. This is because the required service can be downloaded to the ES through service cache updating. Therefore, JOSSCUCTA can effectively adapt quickly to the changing service requirements of many STDs.

Massive heterogeneous data in PIoT with renewable energy need to be processed, and the demand for computing power and communication resources has increased dramatically. Edge computation can significantly improve the computational performance of the smart power grid. However, as the categories of computing tasks increase in PIoT and ESs are equipped with limited storage resources, ESs cannot cache all types of services required by STDs’ computing tasks. Therefore, this article proposed JOSSCUCTA for PIoT with renewable energy sources and established it as an MINLP problem. Simulation experiments showed that the JOSSCUCTA scheme can effectively reduce the average system latency of all STDs’ computing tasks when the ES has not cached or cached part of the services required by computing tasks.