Distributed Energy Dispatch for Geo-Data Centers Port Microgrid

Abstract

With the development of port automation and artificial intelligence, coordination with multi-geographic data centers (Geo-DCs) has become a viable solution to address the issue of limited port computing resources. This study proposes a distributed energy dispatch method for the port microgrid coordinated with Geo-DCs (Geo-DCPM), aimed at reducing port carbon emissions and operational costs. Consider the single point of failure problem and high construction costs of centralized data centers. Geo-DCs are first introduced to solve the problem of insufficient computing resources in ports. An energy consumption calculation model for Geo-DCs is established, considering the data load delay constraint and the data space transfer constraint caused by specific delay-sensitive loads in the port microgrid. Then, an energy dispatch model (EDM) is constructed for the Geo-DCPM, taking into account carbon capture costs. Moreover, based on mixed-integer linear programming, a distributed algorithm is proposed to solve the EDM problem. Finally, the simulation results verify the effectiveness of the proposed method. Compared with the centralized algorithm, the packet loss rate of the distributed algorithm combined with Geo-DCs is significantly lower, reduced by about 70%.

1. Introduction

Ports play a crucial role in international shipping logistics, with a significant number of ships docking at ports annually and emitting carbon dioxide [1]. To develop green ports, there is a growing interest in utilizing renewable energy in the port microgrid, involving various technical challenges. As the key to improving energy efficiency, the energy dispatch problem has been widely focused on [2].

The purpose of energy dispatch is to reduce port operating costs and ensure reliable port operation [3]. Luo [4] presents an energy management model considering the uncertainties of various renewable energy sources. Gu [5] uses CCHP equipment to ensure the smooth operation of microgrids under multi-energy flow interaction. Iris [6] investigates the energy management problem of smart grid seaports, considering the energy consumption generated by shore power yards and ships passing by. Alasali [7] constructs an energy control model of the low-voltage distribution network considering the energy consumption of electric cranes. Mao [8] proposes an integrated energy system dispatch model that considers port power supply management and berth allocation. The above-mentioned research focuses on port energy management and involves many aspects, such as renewable energy uncertainty, integrated energy systems, and various energy-consuming equipment at the port, with a view to reducing operating costs while ensuring reliable port operation. In addition to energy consumption, carbon emission is also a pressing issue that requires attention [9,10]. Among various methods of reducing carbon dioxide emissions, carbon capture is the most effective approach for port microgrid [11,12,13]. Therefore, the operating cost and constraints of the carbon capture device should be modeled in the EDM of the Geo-DCPM.

Many centralized algorithms are proposed to solve the energy dispatch problem. Sahoo [14] proposes a centralized energy management approach for hybrid microgrid systems containing solar cells. Moeini-Aghtaie [15] proposes a genetic algorithm (MAGA) to solve energy network problems. However, considering the single point failure problem of centralized algorithms [16,17,18] and the distributed structure of port microgrids, many distributed methods have been proposed. Huang [19] proposed a delay-free-based distributed algorithm to solve the economic dispatch problem of microgrids. Chen [20] proposed a distributed fast economic dispatch algorithm to ensure the optimal allocation of distributed energy resources. Zhong [21] designs a distributed intelligent system to improve the efficiency and reliability of energy systems. Chang [22] proposes a byzantine-resilient distributed peer-to-peer energy management approach to minimize operating costs. Liu [23] proposes a distributed adjustable robust optimal scheduling algorithm to reduce operation costs. According to the above research, various methods, including ADMM [24], the double Newton descent method [25], the gradient descent method [26], and the subgradient descent method [27] can be used to solve the port energy dispatch problem in the disturbed pattern. The complement of the above-distributed algorithms relies on information transmission and distributed computation, which require a large amount of computing resources. However, the computing resources of most port microgrids are limited, and it may not be possible to complete distributed economic dispatch by relying only on its own computing resources. Therefore, how to increase computing resources to effectively handle port operations and achieve the goal of economic dispatch is an issue that requires focus.

As an effective way to optimize resource utilization, data centers have highly concentrated computing capabilities and powerful data processing capabilities, which can solve the problem of insufficient computing resources [28,29,30,31]. There has been some research about the energy management of the data center power system. To minimize daily electricity bills, Tian [32] proposes an optimal energy management method of an integrated energy system with a data center. Ding [33] considers waste heat generated from data center operations to minimize the operating costs of data center microgrids. He [34] develops an energy-efficient data center cooling to achieve minimal system energy consumption. Khan [35] establishes energy management models that take into account IT equipment performance degradation and improper thermal conditions in IT rooms to minimize the operation cost. In the previous research, the utilized centralized data centers pose the risk of single points of failure, as consolidating large amounts of data can lead to network congestion, low data transfer speeds, and increasing heat generation. Although waste heat recovery and data processing delay constraints are considered in some research, energy consumption costs increase rapidly. The optimal energy management solutions in the existing studies are obtained by centralized algorithms to coordinate with the centralized data center, which is unsuitable for distributed port microgrids. Then, Geo-DCs are introduced to solve the problem of insufficient computing resources in port microgrids, but few papers focus on the impact of Geo-DCs. Therefore, how to efficiently and safely implement a distributed economic dispatch method for port microgrids, with low energy consumption caused by Geo-DCs, needs to be studied.

To solve the above problems, this paper proposes a distributed energy dispatch method for Geo-DCPM based on a dual decomposition mixed-integer linear programming algorithm. The main contributions are as follows:

• Considering that the computing power resources of the port are limited, the Geo-DCs are introduced to increase the computing power resources of the port without the construction cost of the data center. Unlike centralized data centers, Geo-DCs can improve disaster recovery capabilities and ensure port business continuity.
• An energy dispatch model of the Geo-DCPM is constructed, aiming at minimizing the operation cost of Geo-DCPM. A Geo-DC energy consumption calculation model is constructed to achieve reasonable allocation and efficient utilization of computing resources with the coordination of Geo-DCs. To reduce carbon emissions, the carbon capture cost is also considered in the energy dispatch model.
• A distributed algorithm based on a dual decomposition mixed-integer linear programming algorithm is proposed to solve the energy dispatch problem of Geo-DCPM. Geo-DCPM has a lower packet loss rate and is more suitable for distributed structures.

The remainder of this paper is arranged as follows: Section 2 establishes an energy consumption model of Geo-DCs. Section 3 constructs an energy dispatch model for Geo-DCPM and presents a distributed energy dispatch algorithm based on dual decomposition mixed-integer linear programming. In Section 4, simulation cases are used to verify the effectiveness of the proposed distributed energy dispatch strategy in different scenarios. Section 5 summarizes the paper.

2. Structure and Model of Geo-DCPM

2.1. Geo-DCPM Structure

To increase the computing resources of the distributed port microgrid, the Geo-DCPM is constructed by coordinating multi-geographic data centers with port microgrids. The main components of a data center are divided into four parts: the IT equipment power usage (servers and storage), the cooling system power usage, the other equipment power usage (lighting, security, fire safety), and the power transmission and distribution system power usage. As shown in Figure 1, the power supply side includes the wind turbine, the photovoltaic panel, the water turbine, and fuel engine equipment, and the demand side of the port includes ships, logistics transportation equipment, refrigerated storage equipment, etc. To reduce port carbon emissions, carbon capture equipment is also used.

Geo-DCs can contain multiple geographically distinct nodes, which can be located in different cities, regions, or even countries, as shown in Figure 2. Different from centralized data centers, these nodes are interconnected through high-speed networks and use load-balancing technology to distribute data, which can efficiently allocate and utilize resources and improve disaster recovery capabilities. However, since it is located in many different cities, the impact of network connection quality on Geo-DCs cannot be ignored. If the connection quality between some nodes is poor, it may affect the transmission speed and real-time performance of data.

2.2. Geo-DC Energy Consumption Model

To establish an energy consumption calculation model for Geo-DCs, differences in equipment and data load types across different data centers are usually ignored. Therefore, some assumptions of the Geo-DCs consumption are given first [36].

Assumption 1. 

There is a time slot set $T=\left\{1,2,\cdots ,t\right\}$, which matches the power system dispatch plan time, and its time period is one hour.

Assumption 2. 

Port data loads are all latency-sensitive data loads.

Assumption 3. 

The delay bound D does not exceed the length of one time slot.

Assumption 4. 

Data center servers are all homogeneous.

Under the above assumptions, the energy consumption generated by Geo-DCs for data processing is expressed as

$$P_{IDC}^{n,t}=P_{cool}^{n,t}+P_{IT}^{n,t},$$

(1)

where $P_{IDC}^{n,t}$ is the power consumption of the data center at time t; $P_{cool}^{n,t}$ and $P_{IT}^{n,t}$ are the air conditioning equipment and active powers of the data center servers at time t, respectively; and n is the number of nodes. Among them

$$\begin{array}{c}{P}_{cool}^{n,t}=\frac{Q_c^n}{EE{P}^n}·n_{cool}^n\Delta t\hfill \\ P_{IT}^{n,t}=m^{n,t}{P}_{fmin}^n+\left(P_{fmax}^n-P_{fmin}^n\right)u^{n,t}{m}^{n,t}\hfill \end{array},$$

(2)

where $Q_c^n$ is the cooling power of the air conditioner; $EE{P}^n$ is the energy efficiency coefficient of the air conditioner; $n_{cool}^n$ is the number of air conditioners; $m^{n,t}$ is the number of active servers at time t; $P_{fmax}^n$ and $P_{fmin}^n$ are the peak power and silent power of a single server in the Geo-DCs when no tasks are being processed; and $u^{n,t}$ is the average utilization of the Geo-DC server.

To ensure the reliable operation of Geo-DCs, the constraints need the following:

• Server average utilization constraint To achieve the effective resource utilization in the Geo-DCs, a reasonable average utilization constraint is set as

  $$u^{n,t}=\frac{{\displaystyle \sum _{\delta =1}^{\Phi }}{\lambda }_{\delta }^{n,t}}{m^{n,t}{\mu }^{n,t}},0\le u^{n,t}\le U_{max}^n,$$

  (3)

  where ${\lambda }_{\delta }^{n,t}$ is the data load allocated from the frontend portal server to the Geo-DCs at time t; $\Phi$ is the frontend portal set, and the frontend portal server set is defined as $\delta \left(\delta \in \Phi \right)$; ${\mu }^{n,t}$ is the average service rate of the active servers in the Geo-DCs; and $U_{max}^n$ is the upper limit of CPU utilization of a single server.
• Server number constraint The number of servers in the Geo-DCs is limited and can be expressed as

  $$0\le m^{n,t}\le M^n,$$

  (4)

  where $M^n$ is the total number of servers in the Geo-DCs.
• Data load processing latency constraint To ensure the smooth operation of the port, the Geo-DC needs to process the data load within the delay time. The M/M/1 queuing model is used to estimate the average residence time of the data load in the Geo-DCs. The average residence time does not exceed the delay limit D. The functional relationship is

  $$0<\frac{1}{{\mu }^{n,t}-\frac{{\displaystyle \sum _{\delta =1}^{\Phi }}{\lambda }_{\delta }^{n,t}}{m^{n,t}}}\le D,$$

  (5)

  where ${\displaystyle \sum _{\delta \in \Phi }}{\lambda }_{\delta }^{n,t}$ is the total data load arriving at the data center at time t, and D is the delay limit of data load processing. When ${\displaystyle \sum _{\delta \in \Phi }}{\lambda }_{\delta }^{n,t}=0$, the minimum number of active servers $m^{n,t}=0$ is considered to satisfy the delay constraint. Based on this Equation (5), it is rewritten as

  $$m^{n,t}\ge \frac{1}{{\mu }^{n,t}-\frac{1}{D}}\sum _{\delta =1}^{\Phi }{\lambda }_{\delta }^{n,t},$$

  (6)
• Data load balancing constraint The data load in the Geo-DCs needs to be consistent to ensure the normal operation of the port. Due to the huge amount of data and the huge span of time and space, packet losses may occur. Therefore, the functional relationship between the input and output data loads of data centers distributed at different power nodes is expressed as

  $$\left(1-\chi \right)L_{\delta }^t\le \sum _{n_{IDC}=1}^{I_{IDC}}\sum _{\delta =1}^{\Phi }{\lambda }_{\delta }^{n,t}\le L_{\delta }^t,$$

  (7)

  where $L_{\delta }^t$ is the total data load sent from the front end at time t, and $\chi$ is the packet loss rate during data transmission.
• Data center space-time transmission constraint To meet the service quality of the data center, the data load can be transferred to other data centers for processing. The spatiotemporal transmission characteristics of the data center can be expressed as

  $$\sum _{\delta \in \Phi }{\lambda }_{\delta }^{n,t}=L_{local}^{n,t}+L_z^{n,t},$$

  (8)

  $$L_z^{n,t}=\sum _{n_{IDC}=1}^{I_{IDC}}{B}_{i,j}\left(Z_J^{n,t}-Z_C^{n,t}\right),$$

  (9)
  $$\left(1-\chi \right)L_{\delta }^t\le \sum _{n_{IDC}=1}^{I_{IDC}}{L}_{local}^{n,t}\le L_{\delta }^t,$$

  (10)

  $$-\chi L_{\delta }^t\le Z_J^{n,t}-Z_C^{n,t}\le 0,$$

  (11)

  $$0\le {\lambda }_{\delta }^{n,t}\le {\lambda }_{\delta ,max}^{n,t},$$

  (12)

  where $L_{local}^{n,t}$ is the workload arriving at the Geo-DCs at time t; $L_z^{n,t}$ is the workload allocated from space-time transmission at time t; $B_{i,j}$ is the communication association matrix of the Geo-DCs; $Z_J^{n,t}$ and $Z_C^{n,t}$ are the space-time transfer accepted by the data center at time t load, and the transferred data load, and ${\lambda }_{\delta ,max}^{n,t}$ is the highest load that the data center can withstand at time t.

The energy consumption calculation model of Geo-DCs consists of Equations (1)–(12). As mentioned above, since Geo-DCs are distributed in different cities, the data migration will occur during work. Therefore, the operating cost of Geo-DCs includes the power consumption cost and the data migration cost, which can be expressed as

$$C_{IDC}^{n,t}=K_{IDC}^{n,t}{P}_{IDC}^{n,t}+\gamma Z_J^{n,t},$$

(13)

where $C_{IDC}^{n,t}$ is the Geo-DC operating cost, $K_{IDC}^{n,t}$ is the cost coefficient of port processing data at time t, and $\gamma$ is the unit bandwidth cost of the Geo-DC load transfer.

3. Distributed Energy Dispatch for Geo-DCPM

Aiming at minimizing the operating cost of Geo-DCPM, a distributed energy dispatch model is proposed in this section.

3.1. Energy Dispatch Model

To solve the problem of port environmental pollution, the carbon capture is applied to deal with carbon emissions in this paper. Then, the Geo-DCPM operational cost consists of the power supply cost, the carbon capture cost, and the Geo-DC operation cost, and the objective function is designed to minimize the operating cost, which can be expressed as

$$minF=F_1+F_2+F_3,$$

(14)

where F is the total operation cost of the Geo-DCPM; and $F_1,F_2$, and $F_3$ are power supply cost, carbon capture cost, and Geo-DC operation cost, respectively. Among them,

$$\begin{array}{c}{F}_1=F_w+F_{pv}+F_{fu}+F_h+F_{wq}\\ F_2=K_c{\displaystyle \sum _{n_c=1}^{I_c}}{P}_c^n\\ F_3={\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{C}_{IDC}^{n,t}\end{array},$$

(15)

where $F_w={\displaystyle \sum _{n_d=1}^{I_d}}{a}_w{P}_w^n,F_{pv}={\displaystyle \sum _{n_d=1}^{I_d}}{a}_{pv}{P}_{pv}^n,F_{fu}={\displaystyle \sum _{n_d=1}^{I_d}}{a}_{fu}{P}_{fu}^n,F_h={\displaystyle \sum _{n_d=1}^{I_d}}{a}_h{P}_h^n$, and $F_{wq}=K_f{\displaystyle \sum _{n_c=1}^{I_c}}{P}_f^n$ are the wind power generation costs, photovoltaic power generation costs, hydropower generation costs, fossil fuel power generation costs, and wind abandonment penalty fee, respectively; $P_w^n,P_{pv}^n,P_{fu}^n$, and $P_h^n$ are the wind turbine output power, photovoltaic output power, hydraulic output power, and fossil fuel generator output power; $a_w,a_{pv},a_{fu}$, and $a_h$ are the cost coefficients of each power generation equipment; $P_f^n=q_f{P}_w^n$ is the power consumption of the wind abandonment volume; and $K_f$ is the wind abandonment cost coefficient. $F_1$ can be rewritten as $F_i={\displaystyle \sum _{n_d=1}^{I_d}}{a}_i{P}_i^n$. $P_i^n$ is the engine output power, $a_i$ is the cost coefficient of the power generation equipment, and i is the number of equipment. $P_c^n={\gamma }_c{q}_c{x}_c{\lambda }_t{P}_{fu}^n$ is the power consumption of the carbon capture equipment, $K_c$ is the carbon capture cost coefficient, ${\gamma }_c$ is the energy consumption required to capture unit carbon dioxide, $q_c$ is the carbon emission intensity of fossil fuel combustion, $x_c$ is the capture level, ${\lambda }_c$ is the flue gas split ratio, and $q_f$ is the wind abandonment level.

To ensure the reliable operation of the Geo-DCPM, the constraints need the following:

• Power balance constraint To ensure stable operation, the power generation capacity of the port must meet the total load demand as follows:

  $$P_{load}+\sum _{n_c=1}^{I_c}{P}_c^n+\sum _{n_d=1}^{I_d}{P}_f^n+\sum _{n_{IDC}=1}^{I_{IDC}}{P}_{IDC}^{n,t}\le \sum _{n_d=1}^{I_d}{P}_i^n,$$

  (16)

  where $P_{load}$ is the total port load demand. At the same time, Equation (16) is a global coupling constraint.
• Power generation equipment capacity constraint Port power generation equipment needs to operate stably within a certain range as follows:

  $$\begin{array}{c}{P}_w^{min}\le P_w^n\le P_w^{max},P_{pv}^{min}\le P_{pv}^n\le P_{pv}^{max}\hfill \\ P_{fu}^{min}\le P_{fu}^n\le P_{fu}^{max},P_h^{min}\le P_h^n\le P_h^{max}\hfill \end{array},$$

  (17)

  where $P_w^{min},P_w^{max},P_{pv}^{min},P_{pv}^{max},P_{fu}^{min},P_{fu}^{max},P_h^{min}$, and $P_h^{max}$ are the upper and lower power limits of each power generation equipment, respectively.
• Carbon capture equipment constraint The energy consumption level of port carbon capture equipment need to be limited to ensure the sustainability and economy of the port equipment as follows:

  $$\sum _{n_c=1}^{I_c}{P}_c^n\ge {\gamma }_c{q}_c{x}_c{\lambda }_t\sum _{n_d=1}^{I_d}{P}_{fu}^n,$$

  (18)

  $$P_c^{min}\le P_c^n\le P_c^{max},$$

  (19)

  where $P_c^{min}$ and $P_c^{max}$ are the upper and lower power limits of the carbon capture equipment, respectively. At the same time, Equation (18) is a global coupling constraint.
• The Geo-DC transport constraint To meet the computing power needs of the port, reduce delays, and improve the operational efficiency and reliability of the port, the Geo-DC transport constraint is as follows:

  $$\left\{\begin{array}{c}{m}^{n,t}\ge \frac{1}{{\mu }^{n,t}-\frac{1}{D}}{\displaystyle \sum _{\delta =1}^{\Phi }}\left(L_{local}^{n,t}+{\displaystyle \sum _{j\in Q}}{B}_{i,j}\left(Z_J^{n,t}-Z_C^{n,t}\right)\right)\\ 0\le L_{local}^{n,t}+{\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{B}_{i,j}\left(Z_J^{n,t}-Z_C^{n,t}\right)\le {\lambda }_{\delta max}^{n,t}\\ \left(1-\chi \right)L_{\delta }^t\le {\displaystyle \sum _{\delta =1}^{\Phi }}{\lambda }_{\delta }^{n.t}\le L_{\delta }^t\\ \left(1-\chi \right)L_{\delta }^t\le {\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{\displaystyle \sum _{\delta =1}^{\Phi }}{\lambda }_{\delta }^{n,t}\le L_{\delta }^t\\ -\chi L_{\delta }^t\le Z_J^{n,t}-Z_C^{n,t}\le 0\\ 0\le m^{n,t}\le M^n\end{array}\right.,$$

  (20)
  At the same time, the data transmission constraints in Equation (20) are global coupling constraints.

In summary, the energy dispatch model of Geo-DCPM consists of Equations (14)–(20), which can be summarized as

$$\left\{\begin{array}{c}\begin{array}{c}\min {\displaystyle \sum _{i=1}^I}{F}_i\left(P_i^n\right)\\ st:\left\{\begin{array}{c}\begin{array}{c}-{\displaystyle \sum _{n_d=1}^{I_d}}{P}_i^n+{\displaystyle \sum _{n_d=1}^{I_d}}{P}_f^n+{\displaystyle \sum _{n_c=1}^{I_c}}{P}_c^n+\\ {\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}\left(P_{cool}^{n,t}+m^{n,t}{P}_{fmin}^n+\left(P_{fmax}^n-P_{fmin}^n\right)/{\mu }^{n,t}{\displaystyle \sum _{\delta =1}^{\Phi }}\left(L_{local}^{n,t}+{\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{B}_{i,j}\left(Z_J^{n,t}-Z_C^{n,t}\right)\right)\right)\le -P_{load}\end{array}\\ {\gamma }_c{q}_c{x}_c{\lambda }_t{\displaystyle \sum _{n_d=1}^{I_d}}{P}_{fu}^n-{\displaystyle \sum _{n_c=1}^{I_c}}{P}_c^n\le 0\\ \begin{array}{c}\left(1-\chi \right)L_{\delta }^t\le {\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{\displaystyle \sum _{\delta =1}^{\Phi }}{L}_{local}^{n,t}+{\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{B}_{i,j}\left(Z_J^{n,t}-Z_C^{n,t}\right)\le L_{\delta }^t\\ \left(1-\chi \right)L_{\delta }^t\le {\displaystyle \sum _{n_{IDC}=1}^{I_{IDC}}}{L}_{local}^{n,t}\le L_{\delta }^t\\ -\chi L_{\delta }^t\le Z_J^{n,t}-Z_C^{n,t}\le 0\end{array}\end{array}\right.\\ \Gamma ={\Gamma }_d\cup {\Gamma }_c\cup {\Gamma }_{IDC}\end{array}\\ \left\{\begin{array}{c}{\Gamma }_d^n=\left\{\left[\begin{array}{c}{P}_w^n\\ P_{pv}^n\\ P_{fu}^n\\ P_h^n\end{array}\right]\in R^{NT}\left(n=1,\cdots ,N\right)\left|\mathrm{Equations}\left(15\right)\mathrm{and}\left(17\right)\right.\right\}\hfill \\ {\Gamma }_c^n=\left\{\left[\begin{array}{c}{P}_c^n\\ 0\\ 0\\ 0\end{array}\right]\in R^{NT}\left(n=1,\cdots ,N\right)\left|\mathrm{Equations}\left(15\right),\left(18\right)\mathrm{and}\left(19\right)\right.\right\}\hfill \\ {\Gamma }_{IDC}^n=\left\{\left[\begin{array}{c}{m}^{n,t}\\ L_{local}^{n,t}\\ Z_J^{n,t}\\ Z_C^{n,t}\end{array}\right]\in R^{NT}\left(n=1,\cdots ,N\right)\left|\mathrm{Equations}\left(1\right)-\left(13\right)\mathrm{and}\left(20\right)\right.\right\}\hfill \end{array}\right.\end{array}\right.,$$

(21)

where $I_d$ is the number of electrical nodes, $I_c$ is the number of carbon nodes, and $I_{IDC}$ is the number of data center nodes. In addition, ${\Gamma }_d$ is the electric node set, ${\Gamma }_c$ is the carbon node set, ${\Gamma }_{IDC}$ is the data center node set, and $\Gamma$ is the set of all decision variables.

From Equation (21), it can be seen that the energy dispatch problem of the Geo-DCPM is a mixed-integer linear programming problem with global coupling constraints. For designing a distributed solving algorithm, global coupling constraints need to be decoupled. According to the different energy flows, carbon flows, and data flows of the Geo-DCPM, the global coupling constraints can be processed as follows:

$$\left[\begin{array}{ccc}{A}_1\hfill & B_1\hfill & D_1\hfill \\ A_2\hfill & B_2\hfill & D_2\hfill \\ A_3\hfill & B_3\hfill & D_3\hfill \end{array}\right]{\mathbb{S}}_i-C\le 0,$$

(22)

where ${\mathbb{S}}_i={\left[\begin{array}{ccccccccc}{P}_w^n& P_{pv}^n& P_{fu}^n& P_h^n& P_c^n& m^{n,t}& L_{local}^{n,t}& Z_J^{n,t}& Z_C^{n,t}\end{array}\right]}^T$ is the matrix form of decision variables. N represents the number of time slots.

$A_1=\left[\begin{array}{cccc}-I_N+q_f& -I_N& -I_N& -I_N\end{array}\right]$, $A_2=0_{1\ast 4}$, $A_3=0_{6\ast 4}$, $B_1=I_N$, $B_2=-I_N$, $B_3=0_{6\ast 1}$, $D_1=\left[\begin{array}{cccc}{P}_{fmin}^n& \frac{P_{fmax}^n-P_{fmin}^n}{{\mu }^{n,t}}& \frac{P_{fmax}^n-P_{fmin}^n}{{\mu }^{n,t}}& \frac{P_{fmin}^n-P_{fmax}^n}{{\mu }^{n,t}}\end{array}\right]$, $D_2=0_{1\ast 4}$, $D_3=\left[\begin{array}{cccc}0& I_N& I_N& -I_N\\ 0& -I_N& -I_N& I_N\\ 0& I_N& 0& 0\\ 0& -I_N& 0& 0\\ 0& 0& I_N& -I_N\\ 0& 0& -I_N& I_N\end{array}\right]$ and $C={\left[\begin{array}{cccccccc}-P_{load}& 0& L_{\delta }^t& \left(\chi -1\right)L_{\delta }^t& L_{\delta }^t& \left(\chi -1\right)L_{\delta }^t& 0& \chi L_{\delta }^t\end{array}\right]}^T$ are the global coupling constraint coefficient matrices of electrical nodes, carbon nodes and data nodes, respectively.

And the local constraint matrix can be given below

$$\begin{array}{c}-m^{n,t}+\frac{1}{{\mu }^{n,t}-\frac{1}{D}}{\displaystyle \sum _{\delta =1}^{\Phi }}\left(L_{local}^{n,t}+{\displaystyle \sum _{j\in Q}}{B}_{i,j}\left(Z_J^{n,t}-Z_C^{n,t}\right)\right)\le 0\hfill \\ \left[\begin{array}{cccc}-I_N& \frac{1}{{\mu }^{n,t}-\frac{1}{D}}& \frac{1}{{\mu }^{n,t}-\frac{1}{D}}& \frac{1}{\frac{1}{D}-{\mu }^{n,t}}\end{array}\right]\left[\begin{array}{c}{m}^{n,t}\\ L_{local}^{n,t}\\ Z_J^{n,t}\\ Z_C^{n,t}\end{array}\right]\le 0\hfill \end{array},$$

(23)

Then, when with all constraints of energy dispatch problem in matrix form, the energy dispatch model of the Geo-DCPM is as follows:

$$\begin{array}{c}min{\displaystyle \sum _{i=1}^I}{F}_i\left(P_i^n\right)\\ \mathrm{s}.\mathrm{t}.\left[\begin{array}{ccc}{A}_1\hfill & B_1\hfill & D_1\hfill \\ A_2\hfill & B_2\hfill & D_2\hfill \\ A_3\hfill & B_3\hfill & D_3\hfill \\ A_4\hfill & B_4\hfill & D_4\hfill \end{array}\right]{\mathbb{S}}_i-\left[\begin{array}{c}C\hfill \\ E\hfill \end{array}\right]\le 0\end{array},$$

(24)

where $A_4=0_{1^{\ast }}$, $B_4=0$, $D_4=\left[\begin{array}{cccc}-I_N& \frac{1}{{\mu }^{n,t}-\frac{1}{D}}& \frac{1}{{\mu }^{n,t}-\frac{1}{D}}& \frac{1}{\frac{1}{D}-{\mu }^{n,t}}\end{array}\right]$ and $E=0$ are local constraint coefficient matrices.

To solve the above energy dispatch problem, considering the distributed structure of the Geo-DCPM, a distributed algorithm should be designed.

3.2. Distributed Algorithm Based on Mixed-Integer Linear Programming

Assume that Geo-DCPM has a total of I equipment, and the communication network topology between them is a directed graph $G=\left\{V,E_k\right\}$, where V is a node set, which can be expressed as $V=\left\{1,2,3\cdots I\right\}$. The set of directed edges $E_k$ can be expressed as $E_k=\left\{\left(j,i\right):a_j^i\left(k\right)>0\right\}$. For any $i,j\in \{1,\dots ,I\}$, if there is $\eta \in (0,1)$ such that $k>0$ satisfies $a_j^i\left(k\right)\in [0,1),a_i^i\left(k\right)\ge \eta$ and $a_j^i\left(k\right)>0$, Then, there is $a_j^i\left(k\right)\ge \eta$. At the same time, for all $k\ge 0$, when $i=\{1,\dots ,I\}$, there is ${\displaystyle \sum _{j=1}^I}{a}_j^i\left(k\right)=1$; when $j=\{1,\dots ,I\}$, there is ${\displaystyle \sum _{i=1}^I}{a}_j^i\left(k\right)=1$. In this directed graph G, there is no centralized controller. All equipment nodes are connected, enabling information interaction and satisfying strong connectivity. In addition, there is a positive integer $K\ge 1$. For $\left(j,i\right)\in E_{\infty }$, every K consecutive iteration, agent i has at least one information interaction with the adjacent agent j.

Before designing the algorithm, some assumptions should be given first. This makes the distributed optimization dispatching algorithm have convergence and optimality under the communication features of time-varying multi-agent networks.

Assumption 5. 

When $i=\{1,\dots ,I\}$, functions $c_i^T{\mathbb{S}}_i:R^{NT}\to R$, ${\Gamma }_i\subseteq R^{NT}$ and $A_i{\mathbb{S}}_i-b$ are all convex.

Assumption 6. 

When $i=\{1,\dots ,I\}$, set ${\Gamma }_i$ is a compact subset of $R^{NT}$.

Assumption 7. 

There is $\tilde{\mathbb{S}}={\left[{\tilde{\mathbb{S}}}_1\dots {\tilde{\mathbb{S}}}_I\right]}^{\top }\in \mathrm{relint}(\Gamma )$, $\mathrm{relint}(\Gamma )$ is the relative interior of the set Γ, those components of ${\displaystyle \sum _{i=1}^I}{A}_i{\tilde{\mathbb{S}}}_i-b\le 0$ that are linear with $\mathbb{S}$ have ${\displaystyle \sum _{i=1}^I}{A}_i{\tilde{\mathbb{S}}}_i-b\le 0$, and the other parts are ${\displaystyle \sum _{i=1}^I}{A}_i{\tilde{\mathbb{S}}}_i-b<0$.

Assumption 8. 

When ${\left\{c\left(k\right)\right\}}_{k\ge 0}$ is a monotonically decreasing sequence of positive real numbers, and $c\left(k\right)\le c\left(r\right)$ is satisfied for all $k\ge r\ge 0$, there are: (1) ${\displaystyle \sum _{k=0}^{\infty }}c\left(k\right)=\infty$; (2) ${\displaystyle \sum _{k=0}^{\infty }}c{\left(k\right)}^2<\infty$, where $c\left(k\right)=\zeta /(k+1)$, $\zeta >0$.

When Assumptions 5–7 hold, there is strong duality and an optimal primal–dual pair $\left({\mathbb{S}}^{★},{\lambda }^{★}\right)$, ${\mathbb{S}}^{★}={\left[{\mathbb{S}}_1^{★}\dots {\mathbb{S}}_I^{★}\right]}^{\top }$ exists, so there exists.

$$L\left({\mathbb{S}}^{★},\lambda \right)\le L\left({\mathbb{S}}^{★},{\lambda }^{★}\right)\le L\left(\mathbb{S},{\lambda }^{★}\right),\lambda \in R_{+}^{NT},\mathbb{S}\in \Gamma ,$$

(25)

From Equation (24), it can be seen that the energy dispatch problem of the Geo-DCPM is globally decoupled, which is in fact a mixed-integer linear programming problem

$$\begin{array}{c}\underset{{\left\{{\mathbb{S}}_i\in {\mathbb{S}}_i\right\}}_{i=1}^I}{min}\sum _{i\in I}{c}_i^T{\mathbb{S}}_i\hfill \\ st:{\displaystyle \sum _{i=1}^I}{A}_i{\mathbb{S}}_i-b\le 0\hfill \end{array},$$

(26)

where I is the number of nodes; ${\mathbb{S}}_i\in R^n$ is the decision variable, expressed as the output of node i.

Its Lagrangian function can be expressed as

$$L(\mathbb{S},\lambda )={\displaystyle \sum _{i=1}^I}{L}_i\left({\mathbb{S}}_i,\lambda \right)={\displaystyle \sum _{i=1}^I}\left(c_i^T{\mathbb{S}}_i+{\lambda }^T\left(A_i{\mathbb{S}}_i-b\right)\right),$$

(27)

where $\mathbb{S}={\left[{\mathbb{S}}_1^{\top }\cdots {\mathbb{S}}_I^{\top }\right]}^{\top }\in \Gamma \subseteq R^n$, with $n={\displaystyle \sum _{i=1}^I}NT,\lambda \in R_{+}^{4T}$ are vectors of Lagrange multipliers.

The dual function of Equation (26) can be expressed as follows:

$$f\left(\lambda \right)=\underset{\mathbb{S}\in \Gamma }{min}L(\mathbb{S},\lambda ),$$

(28)

Since the objective function and constraint functions in the dual problem are separable, the dual function of Equation (26) can be expressed as follows:

$$f\left(\lambda \right)={\displaystyle \sum _{i=1}^I}{f}_i\left(\lambda \right)={\displaystyle \sum _{i=1}^I}{min}_{{\mathbb{S}}_i\in {\Gamma }_i}{L}_i\left({\mathbb{S}}_i,\lambda \right),$$

(29)

where $f\left(\lambda \right)$ is a concave function, expressed as the dual function of node i.

And the dual problem of Equation (26) is as follows:

$$\mathcal{D}:\underset{\lambda \ge 0}{max}{\displaystyle \sum _{i=1}^I}{f}_i\left(\lambda \right),$$

(30)

At this time, solving the dual problem (30) is equivalent to solving the original (26). Inspired by Ref. [37], a distributed algorithm based on the dual decomposition mixed-integer linear programming method is proposed, as shown in Algorithm 1.

At each iteration, each agent i calculates the value of a weighted average $l_i\left(k\right)$ based on the estimated dual variable ${\lambda }_j\left(k\right),j=1,\dots ,m$, $l_i\left(k\right)={\displaystyle \sum _{j=1}^I}{\mathrm{a}}_j^i\left(k\right){\lambda }_j\left(k\right)$. If agent i and agent j do not communicate during the iteration, $a_j^i\left(k\right)$ is 0 at this time.

Then, the local original vector ${\mathbb{S}}_i(k+1)$ is updated by minimizing $L_i$

$${\mathbb{S}}_i\left(k+1\right)\in arg\underset{\mathbb{S}}{min}\left(c_i^T{\mathbb{S}}_i\left(k\right)+l_i^T\left(k\right)A_i{\mathbb{S}}_i\left(k\right)-l_i^T\left(k\right)\frac{b}{I}\right),$$

(31)

And the dual vector is updated as follows:

$${\lambda }_i\left(k+1\right)={\left[0,l_i\left(k\right)+c_k{A}_i{\mathbb{S}}_i\left(k+1\right)-c_k\frac{b}{I}\right]}^{+},$$

(32)

To reduce the gap with the optimal solution, ${\widehat{\mathbb{S}}}_i(k+1)$ assisted iterative computation is given

$${\widehat{\mathbb{S}}}_i\left(k+1\right)=\frac{\left[{\displaystyle \sum _{r=0}^{k-1}}{c}_r{\mathbb{S}}_{ir}\right]+c_k{\mathbb{S}}_i\left(k+1\right)}{\left[{\displaystyle \sum _{r=0}^{k-1}}{c}_r\right]+c_k},$$

(33)

Algorithm 1: Distributed Mixed Integer Linear Programming Algorithm

Initialization: $k=0$, consider ${\widehat{\mathbb{S}}}_i\left(0\right)\in {\Gamma }_i,{\lambda }_i\left(0\right)\in R_{+}^{4T},i=1$,

Repeat

1: $k\leftarrow k+1$

2: Update $l_i\left(k\right)$ based on $l_i\left(k\right)={\displaystyle \sum _{j=1}^I}{\mathrm{a}}_j^i\left(k\right){\lambda }_j\left(k\right)$.

3: Update ${\mathbb{S}}_i(k+1)$ based on Equation (31).

4: Update ${\lambda }_i\left(k+1\right)$ based on Equation (32).

5: Update $\widehat{{\mathbb{S}}_i}(k+1)$ based on Equation (33).

Until convergence

Set Lagrange multipliers $\underset{k\to \infty }{lim}∥{\lambda }_j\left(k\right)-{\lambda }^{\ast }∥=0,i=1,\cdots ,m$ and the vector

$\underset{k\to \infty }{lim}dist\left(\widehat{\mathbb{S}}\left(k\right),{\Gamma }^{\ast }\right)=0$.

Since the bad estimates of the Lagrange multipliers exist in the early stages of the algorithm, it will have an impact on ${\widehat{\mathbb{S}}}_i\left(k\right)$. Through the reinitialization mechanism, ${\widehat{\mathbb{S}}}_i\left(k\right)$ will present a much better numerical behavior than ${\widehat{\mathbb{S}}}_i\left(k\right)$. Therefore, two different sequences ${\widehat{\mathbb{S}}}_i\left(k\right)$ and ${\tilde{\mathbb{S}}}_i\left(k\right)$ are used to correct ${\mathbb{S}}_i\left(k\right)$ in the designed algorithm process. Namely, ${\tilde{\mathbb{S}}}_i(k+1)$ is the weighted average and distributed optimal solution for the energy dispatch problem of the Geo-DCPM, which can be expressed as ${\tilde{\mathbb{S}}}_i(k+1)=\left\{\begin{array}{cc}{\widehat{\mathbb{S}}}_i(k+1)\hfill & k<k_{s,i}\\ \frac{{\displaystyle \sum _{r=k_{s,i}}^k}c\left(r\right){\mathbb{S}}_i(r+1)}{{\displaystyle \sum _{r=k_{s,i}}^k}c\left(r\right)}\hfill & k\ge k_{s,i}\end{array}\right.$.

4. Simulation Result

In this case, the simulation software platform is Matlab R2022a and the hardware platform is Intel(R) Core(TM) i9-13900KF CPU @ 3.00 GHz, 32 GB memory, 64-bit operating system. Some simulation cases are designed, where a Geo-DCPM consists of three wind turbines, three photovoltaic panels, three water turbines, three pieces of fuel engine equipment, three pieces of carbon capture equipment, and three data centers. According to multi-energy flow, they are divided into three electrical nodes, three carbon nodes, and three data nodes, as shown in Figure 3. The parameters of the power generation equipment are shown in

Table 1. Parameters of power generation equipment.

Equipment	${\mathit{a}}_{\mathit{i}}$	${\mathit{P}}_{\mathbf{i}}^{min}$ (kWh)	${\mathit{P}}_{\mathbf{i}}^{\mathbf{max}}$ (kWh)
PV	0.510	0	1850
W	0.525	0	1500
FU	0.551	500	950
H	0.541	0	1500

, and the parameters of other equipment are shown in

Table 2. Parameters of other equipment.

Equipment	Numerical Value
$Q_c^n$	2.057 kWh/number
$EE{P}^n$	3.4
$n_{cool}^n$	50 number
$M^n$	1500 number
${\mu }^{n,t}$	30 number/h
D	0.5 s
$\chi$	0.1
$P_{fmin}^n$	1 kWh
$P_{fmax}^n$	3 kWh
${\lambda }_{\delta ,max}^{n,t}$	35,000 number
${\gamma }_c$	0.296
$q_c$	0.3
$x_c$	0.9
${\lambda }_c$	0.128
$q_f$	0.1
$P_c^{min}$	20 kWh
$P_c^{max}$	610 kWh
$P_{load}$	3000 kWh
$K_{IDC}^{n,t}$	0.0798 $/kWh
$K_c$	7.938 $/kWh
$K_f$	0.07 $/kWh
$\gamma$	0.000875 $/number

. The adjacency matrix of the nine nodes is updated every two iterations. The energy dispatch method of the Geo-DCPM is expressed as Equation (21). Assuming that between 9 a.m. and 10 a.m., the port operating load is 3000 kWh, the port has an arrival data load of 100,000 an hour. To solve this problem, two methods, centralized algorithms and distributed algorithms, are used in different situations. The simulation results are shown in Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8. The comparison of cost results of simulation examples is shown in

Table 3. Simulation results comparison.

Case	Wind Curtailment Cost ($)	Power Supply Cost ($)	Carbon Capture Cost ($)	Data Processing Cost ($)	Data Transfer Cost ($)	Packet Loss Rate	Total Cost ($)	Case Details
4.1	24.7702	1124.2560	126.2226	837.9000	0.0000	0.10000	2115.5876	Centralized data centers and centralized algorithm [38]
4.2	29.8354	1176.9702	100.3128	853.8712	0.0000	0.03861	2163.4046	Centralized data centers [34] and distributed algorithm
4.3	28.6062	1112.2076	108.5322	805.6020	2.5984	0.02166	2059.9614	Geo-DCs and distributed algorithm
4.4	30.4500	1151.1668	103.2276	782.2948	2.6250	0.05407	2072.1792	Power equipment failure
4.5	29.8354	1178.9638	97.2706	812.7042	2.8875	0.06100	2124.0765	Computing resource demand increase

.

4.1. Case 1: By a Centralized Method

In this case, we use a centralized algorithm to solve the energy dispatch problem of the port. The Geo-DCs do not participate in the economic dispatch of the power system.

The power supply of each generating equipment is [538.57, 1850.00, 500.00, 1550.00], [1500.00, 1850.00, 500.00, 1550.00], [1500.00, 1850.00, 500.00, 1550.00]. The total power supply is 16,738.57 kWh, as shown in Figure 4a, the main power generation equipment is photovoltaic power generation equipment. Wind power generation equipment and fossil fuel power generation equipment will generate additional costs for wind curtailment and carbon emissions, so they are relatively less used. The wind power curtailment of the port wind power generation equipment is 353.857 kWh, and the wind curtailment penalty fee is 24.7702$. The carbon emission is 450 t, the operating power of the carbon capture equipment is [334.46, 610.00, 610.00], the total power consumption of the carbon capture equipment is 1554.46 kWh, the carbon capture cost is 126.2226$, the port power supply cost is 8030.40 CNY, the total power supply is 15,238.57 kWh.

Assuming that the port computing resources are sufficient, the load of the data center server is [20,000, 35,000, 35,000], the number of active servers is 1500, the spatiotemporal transfer Geo-DCs loads are all 0, and the packet loss rate generated during the processing project is 0.1, as shown in Figure 4b. During the data distribution process, the Geo-DC servers are all powered on and waiting to be used. After the data load coming from the port occupies all the computing resources of the entire data center, it will continue to be allocated to the next data center for calculation. The total power consumption of the data center processing load is 10,500.00 kWh, the cooling system power consumption is 30.25 kWh, the Geo-DC operation cost is 837.9$, the data spatiotemporal transfer cost is 0$, and the cooling system cost is 2.4388$. In conclusion, the total port operation is 2115.5876$.

Figure 4. Simulation results of the centralized method. (a) Power supply and consumption of each equip-ment; (b) Operation status of data centers.

Figure 4. Simulation results of the centralized method. (a) Power supply and consumption of each equip-ment; (b) Operation status of data centers.

4.2. Case 2: By the Proposed Distributed Method without Geo-DCs

In this case, the proposed method is used to solve the energy dispatch model of the port microgrid without Geo-DCs. The centralized data centers are utilized to perform calculations for distributed energy dispatch of the port microgrids rather than the Geo-DCs. It can be seen from Figure 5a that in the port energy dispatching, when k = 25,000, the power supply of the power generation equipment has completed the convergence, and the power supply of the generator equipment is [1450.00, 1850.00, 608.67, 1550.00], [1362.21, 1680.06, 574.68, 1407.62], [1450.00, 1850.00, 607.60, 1550.00], the total power supply power is 15,940.84 kWh, and the power supply cost is 1176.9702$. The wind power curtailment of the port wind power generation equipment is 426.221 kWh, and the wind curtailment penalty fee is 29.8354$. It can be seen from Figure 5b that when k = 25,000, the power consumption of the carbon capture equipment gradually converges. The total carbon emissions are 537.285 t. The operating power consumption of the carbon capture equipment is [397.22, 429.72, 408.44]. The total power consumption of the capture equipment is 1235.38 kWh, and the carbon capture cost is 100.3128$. It can be seen that due to wind curtailment penalties and additional costs for carbon capture, wind power generation and fuel power generation equipment supply less power.

As can be seen from Figure 5c, the data centers stabilize after about 100 iterations. The number of active servers in each data center is 1500, and the amount of data space transferred is 0. The loads received by the data centers are [29,992, 30,948, 32,062]. The packet loss rate generated during the data transmission process is 0.03861, which is 1.43 times lower than the packet loss rate of the centralized algorithm. The total power consumed by the data center’s processing load is 10,700.13 kWh, and the cooling system consumes 30.25 kWh. It can be seen from Figure 5d that the dual variables of the global power balance constraint and the global carbon capture equipment constraint converge to be consistent, and all global Geo-DC transport constraints converge to be consistent. The optimal solution is obtained. The data center operation cost is 853.8712$, and the cooling system cost is 2.4150$. In conclusion, the total port operation cost is 2163.4046$.

Figure 5. Simulation results of the proposed distributed method without Geo-DCs. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of data centers; (d) Dual variable iteration process.

Figure 5. Simulation results of the proposed distributed method without Geo-DCs. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of data centers; (d) Dual variable iteration process.

4.3. Case 3: By the Proposed Distributed Method

In this case, the proposed distributed algorithm based on dual decomposition mixed-integer linear programming is used to solve the energy dispatch problem of the Geo-DCPM. It can be seen from Figure 6a, when k = 25,000, the power supply power of the power generation equipment has completed convergence, and the power supply power of the generating equipment is [1362.21, 1680.06, 558.72, 1407.62], [1362.21, 1680.06, 575.60, 1407.62], [1362.21, 1680.06, 578.56, 1407.62]. The total power supply power of the Geo-DCPM is 15,062.55 kWh, and the power supply cost is 1112.2076$. The wind power curtailment of the port wind power generation equipment is 408.663 kWh, and the wind curtailment penalty fee is 28.6062$. As can be seen from Figure 6b, when k = 25,000, the power consumption of carbon capture equipment gradually converges. The total carbon emission is 513.864 t. The operating power consumption of carbon capture equipment is [431.71, 425.67, 479.22]. The total power consumption of the capture equipment is 1336.60 kWh, and the carbon capture cost is 108.5322$. It can be seen that because clean energy is more economical and green, photovoltaic output power is greater. The combustion of fossil fuels will produce carbon emissions, increase economic costs, and cause environmental pollution. However, to ensure the smooth operation of the port microgrid, fuel power generation equipment maintains a low power supply.

Figure 6. Simulation results of the proposed distributed method. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of Geo-DCs; (d) Dual variable iteration process.

Figure 6. Simulation results of the proposed distributed method. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of Geo-DCs; (d) Dual variable iteration process.

As can be seen from Figure 6c, the Geo-DCs tend to be stable after more than 100 iterations. The gap in the number of active servers in each data center is small, and the gap in the amount of data load spatiotemporal transfer is also small. The load received by the Geo-DCs is [33,820, 31,209, 32,808], the number of active servers is [1217, 1161, 1195], the incoming data load transmission amounts is [99, 99, 99], and the outgoing data load transmission amount is [100, 100, 100]. The packet loss rate generated during data transmission processing is 0.02166, which is 4.62 times lower than the centralized packet loss rate. The total power consumed by the Geo-DC processing load is 10095.27 kWh, the cooling system consumes 30.25 kWh, the Geo-DC operation cost is 805.6020$, the data spatiotemporal transfer cost is 2.5984$, the cooling system cost is 2.4150$. In conclusion, the total operation cost is 2059.9614$. It can be seen that each data center has remaining computing resources that can meet the increased data load demand during port emergencies.

The energy dispatch problem of the Geo-DCPM in this paper is a mixed-integer linear programming problem with global coupling constraints. The dual variables ${\lambda }_j\left(k\right)$, $j=1,\dots ,m$ of different global coupling constraints are involved in the iterative optimization process. This paper conducted 1–30,000 iterative simulations, and the results are shown in Figure 6d. It can be seen that when k = 2500, the dual variables all converge to the same value, and the dual variable values corresponding to the optimal solution of the port microgrid energy dispatch problem are obtained.

4.4. Case 4: Power Equipment Failure

In this case, to further verify the effectiveness of the proposed distributed method, it is assumed that the photovoltaic power generation equipment in the port part fails. It can be seen from Figure 7a that in the port energy dispatching, when k = 25,000, the power supply of the power generation equipment has completed convergence, and the power supply of the generator equipment is [1450.00, 1600.00, 586.12, 1550.00], [1450.00, 1600.00, 607.18, 1550.00], [1450.00, 1600.00, 580.61, 1550.00], the total power supply power is 15,569.91 kWh, and the power supply cost is 1151.1668$. The wind power curtailment of the port wind power generation equipment is 435.00 kWh, and the wind curtailment penalty fee is 30.4500$. It can be seen from Figure 7b that when k = 20,000, the power consumption of carbon capture equipment gradually converges. The total carbon emission is 530.973 t. The operating power consumption of carbon capture equipment is [415.69, 406.82, 448.76]. The total power consumption of the capture equipment is 1271.27 kWh, and the carbon capture cost is 103.2276$. It can be seen that due to the failure of some photovoltaic power generation equipment, the power generation of other equipment has increased to maintain the smooth operation of the port.

Figure 7. Simulation results of port equipment failure. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of Geo-DCs; (d) Dual variable iteration process.

Figure 7. Simulation results of port equipment failure. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of Geo-DCs; (d) Dual variable iteration process.

As can be seen from Figure 7c, the Geo-DCs tend to be stable after about 150 iterations, and the data transfer in and out is consistent. The loads received by the Geo-DCs are [29,998, 30,306, 34,289]. The number of active servers is [1133, 1139, 1225]. The amount of data transferred in is [100, 100, 100], and the amount of data transferred out is [100, 100, 100]. The packet loss rate generated during data transmission processing is 0.05407. The total power consumed by the Geo-DC processing load is 9803.20 kWh, and the cooling system consumes 30.25 kWh. It can be seen from Figure 7d that when k = 1500, the dual variables of the global power balance constraint and the global carbon capture equipment constraint converge together and the optimal solution is obtained. The cost of Geo-DC operation is 782.2948$, the data spatiotemporal transfer cost is 2.6250$, the cooling system cost is 2.4150$. In conclusion, the total operation cost is 2072.1792$. It can be seen that the proposed distributed method is effective even in the case of power generation equipment failure.

4.5. Case 5: Computing Resource Demand Increase

In this case, to further verify the effectiveness of the proposed distributed method, it is assumed that the demand for port computing resources increases. As can be seen from Figure 8a, in port energy dispatch, when k = 26,000, the power supply of power generation equipment gradually converges. Since the cost of photovoltaic power generation is low, the power supply of photovoltaic power generation equipment is the highest and the power supply of fuel power supply equipment is low. The power supply of the generator equipment is [1450.00, 1850.00, 585.99, 1550.00], [1450.00, 1850.00, 631.11, 1550.00], [1362.21, 1680.06, 599.70, 1407.62], the total power supply power is 15,966.69 kWh, and the cost of power supply is 1178.9638$. The wind power curtailment of the port wind power generation equipment is 426.221 kWh, and the wind curtailment penalty fee is 29.8354$. It can be seen from Figure 8b that when k = 25,000, the power consumption of the carbon capture equipment gradually converges, and the power consumption of each carbon capture equipment is relatively close. The total carbon emission is 545.04 t. The operating power consumption of the carbon capture equipment is [393.79, 400.18, 403.95]. The total power consumption of the carbon capture equipment is 1197.92 kWh, and the carbon capture cost is 97.2706$. As the demand for port computing resources increases, the energy consumption of Geo-DCs increases, resulting in an increase in the output power of each power supply equipment and an increase in power supply costs.

As can be seen from Figure 8c, Geo-DCs stabilize after approximately 100 iterations. Due to the large amount of data that needs to be processed, almost reaching the upper limit of each data center, the difference in the number of active servers opened in each data center is small, and the difference in data space transfer volume is also small. The load received by the Geo-DCs is [33,392, 30,177, 35,000], and the number of active servers is [1216, 1147, 1250]. The amount of data transferred in is [110, 110, 110], and the amount of data transferred out is [110, 110, 110]. The packet loss rate incurred during data transmission processing is 0.061. The total power consumed by the Geo-DC processing load is 10,184.27 kWh and the cooling system consumes 30.25 kWh. It can be seen from Figure 8d that when k = 600, the dual variables of all global coupling constraints individually converge to unity and the optimal solution is obtained. The Geo-DC operation cost is 812.7042$, the data spatiotemporal transfer cost is 2.8875$, the cooling system cost is 2.4150$. In conclusion, the total operation cost is 2124.0765$. It can be seen that the proposed distributed method is effective even when the demand for port computing power increases.

This paper first considers Geo-DCs into the port microgrid energy dispatch problem. Therefore, compared with other literature, we mainly consider the spatio-temporal transmission constraints of Geo-DCs and the distributed optimization algorithm based on mixed-integer linear programming, which are explained accordingly in the paper. This paper elaborates on it from two aspects: the comparison between Geo-DCs and centralized data centers [34] and the comparison between distributed algorithms and centralized algorithms [38]. Geo-DCs have a lower packet loss rate and less energy consumption than centralized data centers. Distributed algorithms can achieve optimal results at lower costs and packet loss rates than centralized algorithms.

Figure 8. Simulation results of computing resource demand increase. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of Geo-DCs; (d) Dual variable iteration process.

Figure 8. Simulation results of computing resource demand increase. (a) The dynamic curve of the power; (b) The dynamic curve of carbon capture power; (c) The dynamic curve of Geo-DCs; (d) Dual variable iteration process.

In conclusion, from Cases 1 to 5, the distributed results are compared with the optimal centralized results. The distributed energy dispatch cost of Case 2 is the highest. Due to the use of centralized data centers and implementation of distributed computing. As a result, the packet loss rate is reduced and the data load is increased, resulting in slightly higher costs. The distributed energy dispatch cost of Case 3 is slightly lower than the centralized optimization result, due to the fewer number of active server redundancies and litter power consumption of Geo-DCs. Regarding data center usage, centralized data centers are more expensive to use. In Case 4, due to partial damage to the port’s photovoltaic power supply equipment, the wind power supply equipment supplied more power, resulting in more wind curtailment penalties, which leads to an increase in port operating costs. In Case 5, the demand for computing power resources at the port increased, thus the power demand of Geo-DCs increased, resulting in an increase in the total cost. Therefore, the method of coordinating port microgrids with Geo-DCs is more reasonable. It is better suited to the structural and operational characteristics of port microgrids and gives the best results with lower cost and packet loss.

5. Conclusions

This paper has proposed a distributed energy dispatch method for the Geo-DCPM to reduce port operating costs, promote the development of green ports, and minimize port microgrid costs. An energy dispatch model for the port microgrid coordinated with Geo-DCs has been established. Furthermore, a distributed algorithm based on mixed-integer linear programming is proposed. Finally, the simulation results verify the effectiveness of the proposed energy dispatch method for the Geo-DCPM. The simulation results show that when Geo-DCs coordinate with the port microgrid, the data packet loss rate is reduced and the operating cost is lower. Compared with centralized data centers, distributed optimal decision-making results for Geo-DCPM can be obtained by the mixed-integer linear programming method based on dual decomposition. In this paper, only the load delay and transmission constraints of Geo-DCs are considered. In the future, a heating system may be considered in the concerned system.