Decentralized Operations of Industrial Complex Microgrids Considering Corporate Power Purchase Agreements for Renewable Energy 100% Initiatives in South Korea

Abstract

With the rise of environmental policies and advanced technologies, power systems are transitioning from centralized to decentralized systems, incorporating more distributed energy resources (DERs). This shift has increased interest in the operational functions of microgrids (MGs). The “Renewable Energy 100%” (RE100) campaign is pushing companies to adopt renewable energy. In South Korea, industrial complex microgrids (ICMGs) aim to achieve RE100 through corporate power purchase agreements (PPAs) with renewable energy providers. ICMGs need to operate in both grid-connected and islanded modes, facing challenges in power transactions due to different operating agents. This study proposes a decentralized optimal power flow (OPF) method using the separable augmented Lagrangian relaxation (SALR) algorithm to solve these power transaction problems without disclosing internal information. The proposed method decomposes the centralized OPF problem into subproblems for each ICMG and solves them in a distributed manner, sharing only transaction prices and amounts. Numerical results from the case study validate the effectiveness of the proposed method.

1. Introduction

In the decentralized electrical grid environment, microgrids (MGs) may become important components of the decentralized power system, which actively participate in local balancing by providing both energy and ancillary services that currently belong to the primary functions of the traditional grid.

MGs are localized self-controllable entities with multiple loads and distributed energy resources (DERs) that can be operated in various types for economic and reliability purposes. Moreover, MGs can be operated by connecting to the main power grid in grid-connected mode, as well as in islanded mode, for serving MG loads during failures of the main grid. The main advantage of an MG is its capability of connecting or disconnecting from the main grid according to its operation modes: grid-connected or islanded. By applying changeable operation modes, MGs can act as autonomously operating entities in a decentralized grid environment. The transaction of energy between MGs, even in disconnected states, may enhance their function as autonomous entities in power systems.

Traditional MGs rely on fossil fuels, but now low-carbon MGs are emerging, which predominantly run on renewable energy. Recently, an increasing number of commercial and industrial companies have implemented low-carbon microgrids for “Renewable Energy 100%” (RE100) implementation. The RE100 campaign is an abbreviation of 100% renewable energy, and it is a campaign that aims to procure 100% of the electricity used by companies through renewable energy. With the proliferation of the RE100 campaign, South Korea is making efforts to procure 100% of the electricity used by companies in the microgrid through renewable energy by forming the “Industrial Complex Microgrid (ICMG) for RE100 Implementation”. In South Korea, ICMGs can implement RE100 through corporate PPA with renewable energy sources. The operator of an ICMG can optimize day-ahead scheduling by considering PPAs, which balance hourly demand with dispatchable generators, renewable energy generators, and power transactions between adjacent ICMGs or the main grid. In the case of electric power transactions through corporate PPA, ICMGs must purchase all generated renewable energy because cherry-picking is prohibited. Under corporate PPA, an insufficient power supply is supplemented by the main grid through time-of-use tariff rates within the industrial complex. Conversely, excess renewable energy supply in ICMG can be sold to the wholesale market at an hourly system marginal price (SMP).

In order to determine the amounts of transacted energy within a group of interconnected ICMGs, the energy flows between adjacent ICMGs need to be determined by solving the scheduling problem of those ICMGs. With the assumption that a central coordination system exists for the energy transaction of ICMGs and is allowed to gather the internal information from each ICMG, the scheduling problem can be easily solved by applying the traditional centralized OPF method if all ICMGs disclose the internal information to the central system, such as load, generation amount, and various grid parameters. However, if the ICMGs are owned and operated by different entities and each entity prefers to protect the internal information instead of disclosing it for its own economic benefits, centralized scheduling through the central system can be limited due to the potential for information security problems. Therefore, a decentralized scheduling method for interconnected ICMGs needs to be developed where the energy transaction of ICMGs can be scheduled in a distributed manner without disclosing the internal information of ICMGs to the central system.

This paper proposes a decentralized OPF method for the energy transaction problem of interconnected ICMGs using the SALR algorithm that can decompose the centralized OPF problem into the local subproblems of each ICMG with separable quadratic terms and solve the decomposed subproblems in a distributed manner using iteration procedures. The proposed method aims to determine the optimal amounts of transacted energy between two ICMGs while minimizing their generation cost. The SALR-based decentralized OPF method can search a transaction convergence point between two ICMGs while only sharing the information of the transaction price and the transacted amount through the iteration procedure. The iteration procedure includes the update step, which enables an augmented Lagrangian multiplier to determine the amount of transacted energy, and the derived multiplier can be economically interpreted as a unit price of the transacted energy. The validity of the proposed method is provided through a case study of two interconnected ICMG systems.

1.1. Literature Reviews

Various studies have presented centralized and decentralized methods for energy management and the optimal scheduling of MGs to enhance the operational function of MGs as independent entities in decentralized grid environments. Internal information disclosure and sharing could become a major issue for facilitating energy transactions among interconnected MGs when the energy transaction is scheduled by a centralized coordination system. With increasing attention being paid to the optimal operation of interconnected MGs, the energy management methods for MGs have been studied in both centralized and decentralized approaches. The centralized approach is characterized by a central controller that gathers the required information about MGs in order to dispatch the controllable resources according to the different operation objectives [1,2,3,4]. The decentralized approach proposes a multi-agent-based energy management system for the optimal operation of MGs [5,6,7]. Recently, alongside the introduction of new renewable energy resources that improve traditional design methods [8], decentralized energy management systems (EMSs) have been implemented for the operation of distribution networks considering user privacy [9] and have also been applied to networked microgrids (MGs) [10].

From the perspective of the interconnected MGs, the optimal operation schedule can be easily derived by solving the traditional centralized OPF problem if all the interconnected MGs can share the internal information on their load, generation, and grid [11] or be operated by a central EMS [12,13,14]. However, increasingly, MGs are owned and operated by different entities. Each MG may prefer to protect internal information and solve the energy transaction problem in a protected manner since the centralized scheduling system can disclose the internal system and operation information of MGs.

The energy transaction problem of MGs has been studied for various grid environments, such as industrial, logistics, and building sectors [15,16,17,18,19,20], considering the probabilistic characteristics of the energy system [21]. In order to solve the energy transaction problem, a distributed convex optimization framework was proposed for energy transactions between islanded MGs without the central coordinator [22]. A recent study presents a privacy-preserving distributed optimal scheduling method for the expected energy exchanges among interconnected MGs, considering information security problems [23].

Moreover, numerous strategies have been developed to tackle the unit commitment issue, including priority list techniques, dynamic programming approaches, integer and linear programming, mixed integer programming, and the Lagrangian relaxation method [24,25,26,27,28,29]. The Lagrangian relaxation technique was first introduced in [30] during the late 1970s, specifically to address the unit commitment challenge. Employing the Lagrangian relaxation method enables the division of the original unit commitment issue into separate subproblems by easing the coupling constraints. It is acknowledged that the classical Lagrangian relaxation (CLR) approach may result in solutions that oscillate around the optimal one due to the duality gap not closing entirely in non-convex problems such as unit commitment [31]. To address the oscillation issue caused by the non-zero duality gap in non-convex problems, the augmented Lagrangian relaxation (ALR) method [32] was proposed to enhance the Lagrangian function by incorporating additional quadratic penalty terms. Nevertheless, the added quadratic terms in the Lagrangian function are not separable across individual generators. The non-separable nature of the quadratic penalty terms poses a significant challenge when applying the ALR method to decompose the unit commitment problem into distinct subproblems. To address a mathematical programming problem, the SALR [33,34] algorithm was developed as a decomposition approach in a distributed framework. By relaxing complex constraints, the SALR algorithm converts linear or nonlinear programming problems into an augmented Lagrangian function with separable quadratic components [35,36]. As mentioned in the above references, the proposed mathematical model is already well-established in the state-of-the-art literature. However, with the growing societal demand for RE100 implementation by companies within ICMGs, there has been limited research on decentralized operations considering PPAs between companies and renewable energy providers using this mathematical model.

1.2. Contributions

The major contributions are described below:

• Decentralized OPF Method for RE100 Implementation in ICMGs: Even though the proposed mathematical model is already well-established in the state-of-the-art literature, there has been limited research on decentralized operations considering corporate PPAs between companies and renewable energy providers using this mathematical model, despite the growing societal demand for RE100 implementation by companies within ICMGs. In particular, the focus on RE100 implementation through corporate PPAs is a novel area that has not been extensively explored in the existing literature. Therefore, this paper contributes by proposing a decentralized OPF method using the SALR algorithm to address power transactions between interconnected ICMGs for RE100 implementation through corporate PPAs. This approach aims to reduce power transaction costs for ICMGs while enabling companies to achieve their sustainability goals for RE100 implementation.
• Power Transactions Considering the Privacy of Internal Data in Grid-Connected and Islanded Modes: Our method addresses the unique challenges of managing power transactions between ICMGs in both grid-connected and islanded modes, depending on whether the ICMG is connected to the main power system. In each mode, internal power usage data of different ICMG operating entities must be shared, which can lead to information security issues for RE100 participating companies within the ICMGs. The proposed method determines optimal energy transactions between two ICMGs by sharing only transaction prices and amounts, using iterative updates of augmented Lagrangian multipliers. These multipliers can be economically interpreted as the unit prices of transacted energy. Therefore, this paper demonstrates that power transactions can be optimized using the SALR algorithm without disclosing internal information in each mode, providing ICMG operators with an operational strategy to address information security concerns.
• Economic Analysis and Practical Insights through Scenario and Sensitivity Analysis: This paper includes detailed economic analyses and sensitivity studies, providing practical insights into the feasibility and benefits of our approach in real-world scenarios. In the case study, we conducted sensitivity analysis based on actual time of use (ToU), supplementary supply (SSR) tariff scenarios, and PPA network fees in South Korea to assess the economic viability of the proposed method. By understanding how different tariff structures impact energy costs and generation, decision-makers can gain insights into which tariff plan to adopt and determine the appropriate PPA amounts for RE100 implementation.

2. Decentralized Operation Method for Power Transactions between ICMGs

ICMGs that implement RE100 are emerging as a primary solution to manage local DGs and loads as a single balancing entity in decentralized electrical grid environments with the distinctive capability to connect or disconnect from the main grid according to their grid-connected or islanded operation modes. This study focuses on industrial complex-based multi-agent microgrids, thus presenting unique structures and operating goals different from most of the operational microgrids with a single owner. Figure 1 shows the transaction structure of two interconnected ICMGs.

An optimal scheduling problem of interconnected ICMGs, including energy transactions, can be easily solved by using a traditional centralized OPF method under the condition that all ICMGs would share internal information for load, generation, and grid with one another. However, if the ICMGs are owned and operated by different entities, the internal information sharing of those ICMGs for energy transactions might be limited due to potential internal information security problems. Thus, an effective OPF method needs to be developed to solve the energy transaction problem of interconnected ICMGs without disclosing important internal information.

This chapter describes an SALR-based decentralized OPF method that can solve the energy transaction problem of ICMGs in a distributed power system, focusing on those that have entered into corporate PPAs with renewable energy for RE100 implementation while only sharing transaction prices and transacted energy information.

2.1. Centralized Optimal Power Flow Model

This study proposes a rational business model for operating a multi-agent industrial complex microgrid. During the grid-connected mode, the objective of microgrid operation is to maximize the social welfare of ICMG while allowing individual microgrid agents to pursue their individual operation goals. During the islanded mode, the ICMG operation objective supplies loads of multiple agents to minimize the social welfare loss of the industrial complex. During both grid-connected and islanded modes, the ICMG operator is responsible for ICMG operation, considering corporate PPAs with renewable energy.

During the grid-connected and islanded modes, it is assumed that companies in each ICMG have corporate PPAs with renewable energy to implement RE100. The ICMG operator needs to schedule the power transactions of the microgrid so that companies within the ICMG can purchase power through the corporate PPA. The network of each ICMG could be regarded as an energy source when each ICMG has surplus electricity from renewable energy. On the other hand, the network of each ICMG could be regarded as a sink when each ICMG has a shortage of electricity.

In the grid-connected mode, the electricity purchase or sale prices from the main grid impact the optimal operation of each ICMG. The time-of-use (ToU) tariff option is available for industrial complexes due to their industrial and commercial loads when an ICMG needs to buy electricity from the main grid in the grid-connected mode. Meanwhile, an ICMG could sell extra electricity to the main grid at the system marginal price when the ICMG has surplus electricity.

In the islanded mode, the electricity purchase or sale prices from other ICMGs impact the optimal operation of each ICMG. Market clearing pricing (MCP) is used for electricity transactions between ICMGs. After collecting generation and demand bids from all ICMG agents, the EMS of the ICMG clears the ICMG market and determines MCPs for each scheduling period. ICMG agents pursue their specific objectives to implement RE100 through scheduled decision-making, while the objective of the ICMG system operator is to maximize ICMG social welfare by balancing supplies and demands. After the market is cleared, MCPs are distributed to individual agents to refine their bids. This procedure is formulated as an iterative model involving the ICMG system operator and individual ICMG partners.

As an example, suppose there is a power system with a set of ICMGs that are interconnected and operated in grid-connected mode. Let each ICMG generate or transact electrical energy with the main grid or adjacent ICMGs in order to maintain the internal power balance according to a preset operation schedule. When an ICMG transacts electrical energy with the main grid or a set of adjacent ICMGs and operates a controllable generation unit, the internal power balance of ICMG i may be described as follows:

$$P_{i,t}^L=P_{i,t}^R+P_{i,t}^G+T_{i,t}$$

(1)

where $t$ is the time index and the unit of $t$ is hours, $t$ has a value from 1 to 24 for one day, $i$ is the index of industrial complex microgrids, $P_{i,t}^L$ is the forecasted load of ICMG $i$ at time $t$, $P_{i,t}^R$ is the forecasted renewable generation in ICMG $i$ at time $t$, $P_{i,t}^G$ is the scheduled dispatchable generation in ICMG $i$ at time $t$, and $T_{i,t}$ is the transacted electrical energy between ICMG $i$ and the connected grid with ICMG $i$.

Each variable of Equation (1) can be expressed as follows:

$$P_{i,t}^L={\sum }_{l\in {\Psi }_{Load,i}}{P}_{i,l,t}^L,P_{i,t}^R={\sum }_{r\in {\Psi }_{RE,i}}{P}_{i,r,t}^R,P_{i,t}^G={\sum }_{k\in {\Psi }_{DG,i}}{P}_{i,k,t}^G$$

(2)

$$T_{i,t}={\sum }_{m\in {\Psi }_{ICMG,i}}\left(T_{im,t}^M+T_{mi,t}^M\right)+{\sum }_{j\in {\Psi }_{ICMG,i}}{T}_{ij,t}^A$$

(3)

where $l$ is the index of loads, $r$ is the index of renewable energy resources, $k$ is the index of dispatchable generators, $j$ is the index of the adjacent ICMG from ICMG $i$, $m$ is the index of the main grid, ${\Psi }_{Load,i}$ is the set of loads in ICMG $i$, ${\Psi }_{RE,i}$ is the set of renewable energy generators in ICMG $i$, ${\Psi }_{DG,i}$ is the set of dispatchable generators in ICMG $i$, ${\Psi }_{ICMG,i}$ is the set of adjacent ICMGs and the main grid connected with ICMG $i$, $P_{i,l,t}^L$ is the load of company $l$ in ICMG i at time $t$, $P_{i,r,t}^R$ is the forecasted generation of renewable energy source $r$ in ICMG $i$ at time $t$, $P_{i,k,t}^G$ is the scheduled generation of dispatchable generator $k$ in ICMG $i$ at time $t$, $T_{im,t}^M$ is the transacted electrical energy from the main grid $m$ to ICMG $i$, and $T_{ij,t}^A$ is the transacted electrical energy from ICMG $j$ to ICMG $i$.

In grid-connected mode, the value of $T_{ij,t}^A$ is “0” because it is much cheaper for individual ICMGs to buy electricity from the main grid than from adjacent ICMGs in cases of an electricity shortage across all ICMGs. Since power transactions with adjacent ICMGs are not carried out, power information is not shared between ICMGs.

It is assumed that the energy management system (EMS) exists for the optimal scheduling of ICMGs by an ICMG operator. The EMS may coordinate the power generation and the energy transaction of each ICMG to minimize the total generation cost based on the gathered microgrid system operation information from the ICMGs. Under further assumptions that all the ICMGs agree to follow the scheduling result from the EMS, the objective of the OPF problem for a set of ICMGs to minimize the total generation cost by implementing the RE100 campaign is presented as follows:

$$\underset{P_{i,k,t}^G,\hspace{0.33em}{P}_{i,r,t}^{R\_PPA},\hspace{0.33em}{T}_{i,t}}{\mathit{Minimize}}{\sum }_t^{24}\left\{\begin{array}{c}{\sum }_{i\in {\Psi }_{ICMG}}{\sum }_{k\in {\Psi }_{DG,i}}(C_{i,k}^G\times P_{i,k,t}^G)\\ +{\sum }_{i\in {\Psi }_{ICMG}}{\sum }_{r\in {\Psi }_{RE,i}}(C_{i,r}^{R\_PPA}\times P_{i,r,t}^{R\_PPA})\\ +{\sum }_{i\in {\Psi }_{ICMG}}{\sum }_{m,j\in {\Psi }_{ICMG,i}}(C_i^T\times T_{i,t})\end{array}\right\}$$

(4)

where ${\Psi }_{ICMG}$ is the set of ICMGs, $C_{i,k}^G$ is the generation cost function of scheduled dispatchable generator $k$ in ICMG $i$, $C_{i,r}^{R\_PPA}$ is the corporate PPA cost function of scheduled renewable energy source r in ICMG i, $C_i^T$ is the cost function of transacted power in ICMG I, and $P_{i,t}^{R\_PPA}$ is the contracted amount of power between companies and renewable energy in ICMG $i$ at time $t$. The objective function (4) is subject to the following operating constraints.

(1) Cost function of dispatchable generators: the cost function of dispatchable generators is represented as a quadratic polynomial function:

$$C_{i,k}^G\left(P_{i,k,t}^G\right)=a_{i,k}+b_{i,k}\times \left(P_{i,k,t}^G\right)+c_{i,k}\times {\left(P_{i,k,t}^G\right)}^2,\hspace{1em}\forall i,k,t$$

(5)

where $a_{i,k}$, $b_{i,k}$, and $c_{i,k}$ are the coefficients of the cost function of dispatchable generator $k$ in ICMG $i$, respectively.

(2) Generation limits of dispatchable generators: the generation amount of dispatchable generators is maintained between its minimum and maximum generation limits:

$$P_{i,k,t}^{G\_min}\le P_{i,k,t}^G\le P_{i,k,t}^{G\_max},\hspace{1em}\forall i,k,t$$

(6)

where $P_{i,t}^{G\_min}$ and $P_{i,t}^{G\_max}$ are the sum of the minimum and maximum generation limits of dispatchable generators in ICMG $i$ at time $t$.

(3) Power balance equation: the power balance equation is the same as the previously described Equation (1). Each variable in Equation (1) is expressed as in Equations (2) and (3), so combining Equations (1)–(3) can be represented as follows:

$$P_{i,l,t}^L=P_{i,k,t}^G+P_{i,r,t}^R+\left(T_{im,t}^M+T_{mi,t}^M+T_{ij,t}^A\right),\hspace{1em}\forall i,j,m,l,k,r,t$$

(7)

Additionally, the load of each ICMG is equal to the total generated power of an ICMG and its transacted power with other interconnected ICMGs or the main grid. In grid-connected mode, if the value of $T_{i,t}$ is greater than “0”, it means that the power is supplied to the ICMG $i$ from the main grid. Conversely, If the value of $T_{i,t}$ is less than “0”, it means that the power of the ICMG $i$ goes out to the main grid or adjacent ICMG.

(4) PPA constraints: companies in each ICMG have a power purchase agreement (PPA) with renewable energy to implement RE100:

$$0\le P_{i,t}^{R\_PPA}\le P_{i,t}^R\hspace{1em}\forall i,t$$

(8)

$P_{i,t}^{R\_PPA}$ is determined by comparing the $P_{i,t}^R$ and $P_{i,t}^L-P_{i,t}^{G\_min}$ values. The values for $P_{i,t}^{R\_PPA}$ can be expressed as shown in

Table 1. The determination of the corporate PPAs and power transactions.

$\mathbf{Compare}\mathbf{the}{\mathit{P}}_{\mathit{i},\mathit{t}}^{\mathit{R}}$$\mathbf{and}{\mathit{P}}_{\mathit{i},\mathit{t}}^{\mathit{L}}-{\mathit{P}}_{\mathit{i},\mathit{t}}^{\mathit{G}\_\mathit{m}\mathit{i}\mathit{n}}$	${\mathit{P}}_{\mathit{i},\mathit{t}}^{\mathit{R}\_\mathit{P}\mathit{P}\mathit{A}}$
$P_{i,t}^R\le P_{i,t}^L-P_{i,t}^{G\_min}$	$P_{i,t}^{R\_PPA}=P_{i,t}^R$
$P_{i,t}^R>P_{i,t}^L-P_{i,t}^{G\_min}$	$P_{i,t}^{R\_PPA}=P_{i,t}^L-P_{i,t}^{G\_min}$

below.

(5) Cost function of transacted power in ICMG i: the cost function of transacted power in ICMG i is represented as a linear polynomial function:

$$C_i^T\left(T_{i,t}\right)=\left\{\begin{array}{c}\left(C_t^{SMP}\times T_{im,t}^M\right)+\left(C_t^{ToU}\times T_{mi,t}^M\right)\\ +\left(C_t^{MCP}\times T_{ij,t}^A\right)\end{array}\right\},\hspace{1em}\forall i,j,m,t$$

(9)

where $C_t^{SMP}$ is the system marginal price at time $t$, $C_t^{ToU}$ is the price of the ToU tariff for industrial service at time $t$, and $C_t^{MCP}$ is the market clearing price of ICMG at time $t$.

In grid-connected mode, it is assumed that the connection between ICMGs is disconnected, and the value of $T_{ij,t}^A$ is “0” in this study because it is much cheaper for individual ICMGs to buy electricity from the main grid than from an adjacent ICMG in cases of an electricity shortage across all ICMGs. Since power transactions with adjacent ICMGs are not carried out, power information in each ICMG is not shared with each other. On the other hand, the value of $T_{im,t}^M$ is “0” because the main grid is disconnected due to certain circumstances within ICMGs in islanded mode.

(6) Transacted power equality constraints between ICMGs: the transacted energy between ICMGs should be equal:

$$T_{ij,t}^A+T_{ji,t}^A=0,\hspace{1em}\forall i,j,t$$

(10)

(7) Transacted power limits between ICMGs: the transacted energy between interconnected ICMGs needs to be agreed upon within a predefined maximum limit:

$$\left|T_{ij,t}^A\right|\le T_{ij}^{Max},\hspace{1em}\forall i,j,t$$

(11)

where $T_{ij}^{Max}$ is the maximum limit of the transacted power between ICMG $i$ and $j$.

(8) Transacted power limit constraints between the main grid and ICMG i: the transacted energy between the main grid and ICMG i needs to be agreed within a predefined maximum limit:

$$\left|T_{im,t}^M\right|\le T_{im}^{Max},\hspace{1em}\forall i,j,t$$

(12)

where $T_{im}^{Max}$ is the maximum limit of the transacted power between ICMG $i$ and the main grid $m$.

2.2. Decomposition of Centralized OPF Problem Using the SALR Algorithm

For the centralized OPF model presented in Section 2.1, the overall cost is minimized according to the convexity of both objective function and constraints, and the centralized OPF problem expressed in Equations (4)–(12) has a global solution.

The essential assumption is that EMS needs to gather all power information from each ICMG to solve the centralized OPF problem. However, companies within the ICMG may be reluctant to share their power information in a central EMS if the ICMGs are owned and operated by different agents due to information security concerns.

These ICMGs may prefer to protect their internal power information in order to maximize their economic profits instead of sharing their data with a central EMS, especially transaction prices in the sale of electrical energy between interconnected ICMGs. In this study, the decentralized OPF method with the SALR algorithm is applied for interconnected ICMGs to solve centralized operation problems about power transactions while limiting the information shared on the transaction price and transacted power in order to avoid potential power information security issues.

To solve a mathematical programming problem, the SALR algorithm was designed as a decomposition technique in a distributed method. The SALR algorithm transforms linear or nonlinear programming problems into an augmented Lagrangian function with separable quadratic terms by relaxing complicating constraints.

The optimal solution can be obtained by solving the decomposed subproblems since the augmented Lagrangian function has a decomposable structure. In this problem, the SALR is applied to decompose the centralized OPF problem into the local subproblems of each ICMG by decoupling the existing coupling constraints with the adjacent ICMGs. The decomposed subproblems of each ICMG can be solved with limited information for other interconnected ICMGs and the rest of the system. The framework of the proposed SALR-based decentralized OPF method for the energy transaction problem of two interconnected ICMGs is illustrated in Figure 2.

Since this paper only addresses energy transactions between two interconnected ICMGs, the coupling constraints of the centralized OPF problem are exclusively represented in Equation (10) among the mentioned equations. By applying the SALR algorithm, the coupling constraint of the energy transaction equality is relaxed, and the relaxed transacted energy variable is added to the objective function in Equation (4) in terms of the associated augmented Lagrangian multipliers and additional penalty terms. The objective function (4) is transformed into an augmented form. The transformed objective function (13) can be defined as a separable augmented Lagrangian function as follows:

$$\begin{array}{l}L\left(P_{i,k,t}^G,P_{i,r,t}^{R\_PPA},T_{i,t},{\lambda }_{ij}\right)≔\\ \hspace{1em}{\displaystyle \sum _t^{24}}\left\{\begin{array}{c}{\displaystyle \sum _{i\in {\Psi }_{ICMG}}}{\displaystyle \sum _{k\in {\Psi }_{DG,i}}}{C}_{i,k}^G\left(P_{i,k,t}^G\right)+\\ {\displaystyle \sum _{i\in {\Psi }_{ICMG}}}{\displaystyle \sum _{r\in {\Psi }_{RE,i}}}{C}_{i,r}^{R\_PPA}\left(P_{i,r,t}^{R\_PPA}\right)\\ +{\displaystyle \sum _{i\in {\Psi }_{ICMG}}}{\displaystyle \sum _{m,j\in {\Psi }_{ICMG,i}}}{C}_i^T\left(T_{i,t}\right)\end{array}\right\}+{\displaystyle \sum _t^{24}}{\displaystyle \sum _{i\in {\Psi }_{ICMG}}}{\displaystyle \sum _{j\in {\Psi }_{ICMG,i}}}\left\{\begin{array}{c}{\lambda }_{ij}{T}_{ij,t}^A+\\ \alpha \cdot T_{ij,t}^A\left(T_{ij,t}^A+T_{ji,t}^A\right)\\ +\beta \cdot {‖T_{ij,t}^A+T_{ji,t}^A‖}^2\end{array}\right\}\end{array}$$

(13)

where ${\lambda }_{ij}$ is the augmented Lagrangian multiplier for the amount of energy transaction between ICMG $i$ and $j$, and $\alpha$ and $\beta$ are the parameters of the penalty term, respectively.

When the amount of transacted energy between two interconnected ICMGs is converged in (13), the energy transaction cost can be represented as the augmented Lagrangian multiplier times the transacted energy, and thus, the converged value of the multiplier can be economically interpreted as the unit price for the transacted energy between two interconnected ICMGs. Given the values of the augmented Lagrangian multipliers ${\lambda }_{ij}$ and the transacted energy $T_{ji}$, the separable augmented Lagrangian function (13) is decomposed into subproblems that can be solved in a distributed manner. The subproblem of ICMG $i$ is formulated as follows:

$$\underset{P_{i,k,t}^G,\hspace{0.33em}{P}_{i,r,t}^{R\_PPA},\hspace{0.33em}{T}_{i,t}}{\mathit{Minimize}}{L}_i\left(P_{i,k,t}^G,P_{i,r,t}^{R\_PPA},T_{i,t}\right)$$

(14)

Subject to constraints of Equations (5)–(12).

Under convexity and regularity conditions [33], the dual function of ICMG can be defined from the Lagrangian function of the subproblem as follows:

$${\varphi }_i\left(\lambda \right)=\underset{P_{i,k,t}^G,\hspace{0.33em}{P}_{i,r,t}^{R\_PPA},\hspace{0.33em}{T}_{i,t}}{\mathit{Minimize}}L\left(P_{i,k,t}^G,P_{i,r,t}^{R\_PPA},T_{i,t},{\lambda }_{ij}\right)$$

(15)

The dual problem is then defined as follows:

$$\underset{\lambda }{\mathit{Maximize}}{\sum }_{i\in {\Psi }_{ICMG}}{\varphi }_i\left(\lambda \right)$$

(16)

$$\lambda \ge 0$$

(17)

where λ is the vector of the augmented Lagrangian multipliers. This is subject to the constraints of Equations (5)–(12) and (17).

Figure 3 below shows the framework of the SALR-based decentralized OPF method for the energy transaction problem of two interconnected ICMGs and the relationships among the equations.

The resulting dual problem shows that the SALR-based decentralized OPF method transforms the centralized OPF problem into subproblems that can be locally optimized by searching the set of energy transaction prices so as to maximize the dual functions of each ICMG. Therefore, the dual challenge of the decentralized OPF problem can be solved in a distributed manner, including the updating procedure of the augmented Lagrangian multipliers. The optimal value of the augmented Lagrangian multiplier can be searched through the iteration procedure in Section 2.3, including the multiplier updating method.

2.3. Solution Searching Procedure for SALR-Based Decentralized OPF Method

The augmented Lagrangian relaxation (ALR) method [31], which enhances the Lagrangian function by incorporating additional quadratic penalty terms, has been proposed to address the problem of solution oscillation resulting from the non-zero optimality gap in non-convex problems. However, these quadratic terms are not separable at the level of individual generators, creating significant challenges when attempting to decompose the optimization problem into independent subproblems using the ALR method. In this paper, we applied a separable augmented Lagrangian relaxation method aimed at solving the optimization problem. This approach ensures a separable structure by integrating quadratic terms alongside additional auxiliary terms within the augmented Lagrangian function. The proposed decentralized OPF method with the SALR algorithm relaxes the coupling constraints of the centralized OPF problem and decomposes the problem into the subproblems of each ICMG, thus solving the scheduling problem of interconnected ICMGs in a distributed manner.

In this section, an iteration procedure is proposed to search for the optimal solution of the decomposed subproblems with the updated augmented Lagrangian multiplier using the mismatch in the transacted energy between two ICMGs. The proposed iteration procedure to determine the optimal solution of the subproblems proceeds as shown in the following four steps:

• Step 1: Initialization.

Initialize the augmented Lagrangian multipliers ${\lambda }_{}^{\left(0\right)}$, the updating parameter ${C_i^T}^{\left(0\right)}$, and penalty parameters $\alpha$ and $\beta$ in Equation (13). At this point, since the value of the penalty parameters is crucial for the convergence and stability of the algorithm, the penalty parameters $\alpha$ and $\beta$ are chosen from values between 0 and 3, as referenced in [29].

• Step 2: Subproblem Solving.

Solve the subproblems (14)–(17) of each ICMG.

• Step 3: Multiplier Updating.

Calculate the mismatch in the transacted energy between ${T_{ij,t}^A}^{(n-1)}$ and ${T_{ji,t}^A}^{(n-1)}$ and then update the augmented Lagrangian multiplier ${\lambda }^{(n-1)}$ in a way to maximize the dual problem using the updating parameter ${C_{ij}^T}^{(n-1)}$ as follows:

$${\lambda }^{\left(n\right)}={\lambda }^{(n-1)}+{C_{ij}^T}^{(n-1)}\left({T_{ij,t}^A}^{(n-1)}+{T_{ji,t}^A}^{(n-1)}\right)$$

(18)

• Step 4: Convergence Checking.

Set the duality gap tolerance value ϵ, which is used as the stopping criterion. At this point, ϵ is set to ϵ = 0.1 in the case study based on reference [29]. If the mismatch of transacted energy, representing the optimality gap, is less than the tolerance value ϵ,

$$\left|{T_{ij,t}^A}^{(n-1)}+{T_{ji,t}^A}^{(n-1)}\right|\le ϵ$$

(19)

then stop. Otherwise, increase the updating parameter and go back to Step 2.

The fundamental idea of the updating multiplier is to set the initial updating parameter ${C_{ij}^T}^{\left(0\right)}$ with a small value and then gradually increase the value according to the resulting mismatch of the transacted energy between two interconnected ICMGs. Two heuristic methods are applied to increase the updating parameter based on the change in the transacted energy mismatch.

The first heuristic method increases the updating parameter ${C_{ij}^T}^{\left(n\right)}$ only when the mismatch has been increased compared with the last iteration. On the other hand, the second method increases the updating parameter when the mismatch has not reduced from the last iteration compared with $M$ previous iterations. The two presented heuristic updating methods can be summarized as follows:

$${C_{ij}^T}^{\left(n\right)}=a\cdot {C_{ij}^T}^{\left(n-1\right)}$$

(20)

if

$$\left|{T_{ij,t}^A}^{(n-1)}+{T_{ji,t}^A}^{(n-1)}\right|\ge b\cdot \left|{T_{ij,t}^A}^{\left(n-2\right)}+{T_{ji,t}^A}^{\left(n-2\right)}\right|$$

(21)

$$\left|{T_{ij,t}^A}^{(n-1)}+{T_{ji,t}^A}^{(n-1)}\right|\ge \frac{\left({\sum }_{m=0}^{M-1}\left|{T_{ij,t}^A}^{\left(n-m-2\right)}+{T_{ji,t}^A}^{\left(n-m-2\right)}\right|\right)}{M}$$

(22)

where $a$, $b$, and $M$ are parameters whose suitable values are chosen heuristically.

3. Case Study

The proposed decentralized OPF method for the energy transaction problem of interconnected ICMGs is applied to simulate the hourly energy transaction of two interconnected ICMGs in grid-connected and islanded modes for the forecasted day-ahead 24 h loads and generations from renewable energy sources.

The proposed decentralized OPF method was tested using the example system with two interconnected ICMGs: ICMG A and ICMG B. It is assumed that each ICMG is operated by its own microgrid energy management system (EMS) in grid-connected or islanded mode with different load levels and dispatchable generators. Both ICMG A and B have a dispatchable generator with different cost functions; a photovoltaic (PV) generation system is installed in ICMG A and a wind generation system is installed in ICMG B as renewable energy resources (RESs), respectively. It is assumed that the energy transaction between ICMG A and B is accomplished according to the unit price for transacted energy without disclosing the information on internal load and generation between the two ICMGs. The configuration of the test system is shown in Figure 4.

The two ICMGs coordinate their own dispatchable generators and energy transactions for 24 h for the forecasted loads and generations from their RESs. It is assumed that both the dispatchable generator and the PV generation system in ICMG A are set to have a 300 MW installed capacity. The dispatchable generator and the wind generation system in ICMG B are also assumed to have 400 MW and 200 MW installed capacities, respectively. The amount of the transacted energy between ICMG A and B is limited to 150 MW.

Table 2. Technical constraints and cost coefficients of the dispatchable generators in ICMGs.

ICMG	Technical Constraints		Cost Coefficients
	Min. Power [MW]	Max. Power [MW]	${\mathit{a}}_{\mathit{i}}$ [KRW]	${\mathit{b}}_{\mathit{i}}$ [KRW/kWh]	${\mathit{c}}_{\mathit{i}}$ $[\mathbf{KRW}/{\mathbf{k}\mathbf{W}\mathbf{h}}^2$]
A	60	300	218.849077	1.332569	0.001186
B	80	400	150.827614	1.498456	0.001089

summarizes the technical constraints and the generating cost coefficients of the dispatchable generators. The table was reconstructed by referring to the corresponding data in Reference [37].

The load patterns of ICMG A and B were obtained from the Korean Statistical Information Service (KOSIS) [38] and scaled up. The two obtained load patterns show different daily patterns. The ICMG A has a load pattern that remains high during evening hours, and the daily peak occurs at 20 h. Unlike ICMG A, the load of ICMG B is concentrated in the daytime, and the daily peak takes place right before noon.

Figure 5 shows the forecasted 24 h load and renewable energy generation patterns of ICMG A and B by subtracting the renewable generation from the load of the two ICMGs, respectively. ICMG A maintains high load levels during night-time, whereas the PV system is generated during daytime between 7 h and 17 h when the forecasted loads are relatively low. Therefore, the load patterns of ICMG A show that a certain portion of its PV generation is curtailed during daytime unless there is any external power transfer, and its dispatchable generator generates up to the forecasted load levels after 17 h. Moreover, the PV generation of ICMG A can be further curtailed in order to satisfy the minimum generation constraint of the dispatchable generator. For the ICMG B case, since relatively low wind generation levels are forecasted during the daytime during the high load level, the generation burden of the dispatchable generator is expected to increase compared with night-time. Applying this test system of the two interconnected ICMGs, the proposed decentralized OPF was simulated using MATLAB 8.5 and GAMS 22.5.

3.1. Numerical Results of Grid-Connected Mode

In grid-connected mode, the system marginal price (SMP) is forecasted based on the day-ahead price of the generation scheduling program in the main grid. Notably, the balancing service in grid-connected mode is targeted at electric service providers seeking to engage in transactions with the transmission system operator (TSO) when they have surplus or insufficient electricity during PPA transactions. In instances of surplus supply, renewable energy operators can vend excess power to the wholesale market at the SMP price. Conversely, when facing insufficient supply, two tariff plans are considered for the analysis of complementary supply in South Korea.

• Tariff plan 1: Purchasing insufficient electricity from the retail market through the time of use (ToU) tariff plan.
• Tariff plan 2: Renewable energy providers purchase insufficient electricity from the retail market through the supplementary supply rate (SSR) and sell them to consumers for the balancing service.

Table 3. Price comparison between the ToU and SSR tariff plans (units: Won/kWh).

Seasons	Summer		Spring and Autumn		Winter
	ToU	SSR	ToU	SSR	ToU	SSR
Off Peak	49.5	65.0	49.5	65.0	56.6	65.0
Medium	101.8	95.8	71.9	70.8	101.8	79.1
Peak	183.1	136.2	102.2	81.6	158.0	96.7

below shows a price comparison between the time of use (ToU) and the supplementary supply rate (SSR) tariff plan in the seasons [39]. The ToU tariff rates implemented in the test system are derived from the retail prices applicable to industrial and general load categories in South Korea. When the renewable energy generated in the ICMG falls short, and the cost of generation under the ToU rate plan proves more economical than that of dispatchable generators, the ICMG operator procures electricity from the main grid at either the ToU or SSR tariff plan. In the case study, the ToU and SSR tariff rates for the summer season—shown in Table 3—were applied.

Within the grid-connected mode, the electricity price from the main grid is significantly cheaper than the transaction price from adjacent ICMGs during electricity shortages across all ICMGs. As a result, power transactions with adjacent ICMGs are not carried out in the grid-connected mode, leading to a lack of power information exchange between them. Details of the SMP, ToU, and SSR tariff rate information for the test system in the grid-connected mode are provided in

Table 4. SMP, ToU, and SSR tariff price information of the test system (units: Won/kWh).

Time	0–1	1–2	2–3	3–4	4–5	5–6	6–7	7–8	8–9	9–10	10–11	11–12
SMP	73.12	72.32	71.38	71.25	71.34	71.38	73.12	72.98	71.38	70.98	70.98	70.95
ToU	49.5	49.5	49.5	49.5	49.5	49.5	49.5	49.5	49.5	101.8	183.1	183.1
SSR	65.0	65.0	65.0	65.0	65.0	65.0	65.0	65.0	65.0	95.8	136.2	136.2
Time	12–13	13–14	14–15	15–16	16–17	17–18	18–19	19–20	20–21	21–22	22–23	23–24
SMP	70.94	70.94	78.51	70.94	71.93	73.48	73.74	76.32	75.95	75.95	75.95	74.04
ToU	101.8	183.1	183.1	183.1	183.1	101.8	101.8	101.8	101.8	101.8	101.8	49.5
SSR	95.8	136.2	136.2	136.2	136.2	95.8	95.8	95.8	95.8	95.8	95.8	65.0

below.

Each ICMG can be analyzed by considering two scenarios (ToU and SSR tariff plans) in grid-connected mode. Additionally, this study focuses on two ICMGs where electricity users have entered into corporate PPAs with renewable energy developers to implement the RE100 initiative. While it is assumed that the Corporate PPA price is fixed at 110 (Won/kWh), the PPA network fee causes differences in the RE100 implementation costs for companies within the ICMG. Therefore, this paper analyzes the sensitivity of RE100 implementation costs to changes in the PPA network fee for each ICMG. Three levels of PPA network fees are used to analyze the sensitivity of the RE100 implementation costs.

Table 5. Scenarios for the tariff plans and network fees used for the sensitivity analysis of each ICMG in grid-connected mode.

Names of Scenarios		ICMG A		ICMG B
		ToU	SSR	ToU	SSR
PPA Network Fee	15 [Won/kWh]	A-ToU-1	A-SSR-1	B-ToU-1	B-SSR-1
	10 [Won/kWh]	A-ToU-2	A-SSR-2	B-ToU-2	B-SSR-2
	20 [Won/kWh]	A-ToU-3	A-SSR-3	B-ToU-3	B-SSR-3

below shows the scenarios for the tariff plans and network fees used for the sensitivity analysis of each ICMG in grid-connected mode.

In scenarios A-ToU-1~3 and A-SSR-1~3, power transactions occur for 24 h at ICMG A. As depicted in Figure 6, power transactions from ICMG A to the main grid are scheduled during the daytime, ranging from 9:00 to 16:00. The power transaction price from ICMG A to the main grid depends on the SMP of the wholesale market.

In scenarios A-ToU-1~3, the power transaction price from the main grid to ICMG A depends on the ToU tariff of the retail market, while in scenarios A-SSR-1~3, it depends on the SSR tariff of the retail market.

By examining Figure 6, it can be observed that the optimization results vary depending on whether the ToU tariff or the SSR tariff is used. In scenarios A-ToU-1~3, where the ToU tariff is applied, the generation output of the dispatchable generator is higher compared to scenarios A-SSR-1~3.

Table 6. The results of determined 24 h dispatchable generation cost, transactions, and generation prices for ICMG A in grid-connected mode.

ICMG A (Dispatchable Generators)	Total Amount of Generation (kWh)		Generation Cost (Won)
Scenarios A-ToU-1~3	1,632,000		138,811,200
Scenarios A-SSR-1~3	1,602,000		132,971,580
ICMG A (RES, etc.)	Price (Won/kWh)	Total amount of Electricity (kWh)	Total revenue (Won)
Renewable Energy (PPA)	110	1,045,000	114,950,000
Wholesale (SMP)	70.94~78.51	658,000	47,329,130
Scenarios A-ToU-1~3	49.5/101.8/183.1	2,364,000	157,864,300
Scenarios A-SSR-1~3	65.0/95.8/136.2	2,394,000	180,588,800
Scenarios of PPA Network fee	15 (A-ToU/SSR-1)	1,045,000	15,675,000
	10 (A-ToU/SSR-2)		10,450,000
	20 (A-ToU/SSR-3)		20,900,000
Ratio of RE100 (%)	(1,045,000/5,041,000) × 100 = 20.73[%]
Offsetting Carbon Credits (Won)	$1045\left[\mathrm{MWh}\right]\times 0.459[{\mathrm{t}\mathrm{C}\mathrm{O}}_2$$\mathrm{eq}/\mathrm{MWh}]\times 17,000[\mathrm{Won}/{\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq] = 8,154,135 [Won]

below shows the results of the determined 24 h dispatchable generation cost, transactions, and generation prices for scenarios A-ToU-1~3 and A-SSR-1~3 of ICMG A in grid-connected mode.

In grid-connected mode, companies in ICMG A collectively consume a total of 5,041,100 kWh of power. During this period, the power supplied through the corporate PPA amounts to 1,045,000 kWh, indicating an RE100 implementing rate of 20.73%, regardless of the scenarios. As of 2022, the emission factor, meaning the quantity of emissions in tons of carbon dioxide equivalent per megawatt-hour (unit: ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq/MWh), is 0.459 [40]. At this time, assuming a price of 17,000 Won per 1 ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq, the carbon emission offset cost is 8,154,135 Won.

In scenarios B-ToU-1~3 and B-SSR-1~3, power transactions occur continuously for 24 h at ICMG B. As illustrated in Figure 7, power transactions from ICMG B to the main grid are scheduled during night-time, specifically from 00:00 to 05:00 and from 20:00 to 24:00. The power transaction price from ICMG B to the main grid is determined by the SMP of the wholesale market. In scenarios B-ToU-1~3, the power transaction price from the main grid to ICMG B is influenced by the ToU tariff of the retail market, whereas in scenarios B-SSR-1~3, it is affected by the SSR tariff of the retail market.

Table 7. The results of the determined 24 h dispatchable generation cost, transactions, and generation prices for ICMG B in grid-connected mode.

ICMG B (Dispatchable Generators)	Total Amount of Generation (kWh)		Generation Cost (Won)
Scenarios B-ToU-1~3	2,513,000		320,776,200
Scenarios B-SSR-1~3	2,226,000		236,321,300
ICMG B (RES, etc.)	Price (Won/kWh)	Total amount of Electricity (kWh)	Total revenue (Won)
Renewable Energy (PPA)	110	2,759,000	303,490,000
Wholesale (SMP)	70.94~78.51	299,000	21,948,970
Scenarios B-ToU-1~3	49.5/101.8/183.1	1,208,000	137,753,300
Scenarios B-SSR-1~3	65.0/95.8/136.2	1,477,000	156,894,200
Scenarios of PPA Network fee	15 (B-ToU/SSR-1)	2,759,000	41,385,000
	10 (B-ToU/SSR-2)		27,590,000
	20 (B-ToU/SSR-3)		55,180,000
Ratio of RE100 (%)	(2,759,000/6,480,000) ×100 = 42.58[%]
Offsetting Carbon Credits (Won)	$2759\left[\mathrm{MWh}\right]\times 0.459[{\mathrm{t}\mathrm{C}\mathrm{O}}_2$$\mathrm{eq}/\mathrm{MWh}]\times 17,000[\mathrm{Won}/{\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq] = 21,528,477[Won]

below shows the results of the determined 24 h dispatchable generation cost, transactions, and generation prices for scenarios B-ToU-1~3 and B-SSR-1~3 of ICMG B in grid-connected mode.

In grid-connected mode, companies in ICMG B collectively consume a total of 6,480,000 kWh of power. During this period, the power supplied through the corporate PPA amounts to 2,759,000 kWh, indicating an RE100 implementing rate of 42.58%, regardless of the scenario. As of 2022, the emission factor, meaning the quantity of emissions in tons of carbon dioxide equivalent per megawatt-hour (unit: ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq/MWh), is 0.459. At this time, assuming a price of 17,000 Won per 1 ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq, the carbon emission offset cost is 21,528,477 Won.

3.2. Numerical Results of Islanded Mode

To illustrate the effectiveness of the proposed decentralized OPF method for the energy transaction problem in islanded mode, Figure 8 shows the scheduling results for the energy transactions between ICMGs when the test system is solved using the proposed decentralized OPF method.

The power transactions from ICMG A to ICMG B are scheduled during the daytime, spanning from 8:00 to 17:00. Conversely, transactions from ICMG B to ICMG A occur during the night-time, covering the hours from 0:00 to 8:00 and from 17:00 to 24:00.

The scheduling results of power transactions from ICMG A to ICMG B align with forecasted periods of high PV generation for ICMG A and high load levels for ICMG B. Conversely, the scheduling results of power transactions from ICMG B to ICMG A correspond to forecasted periods of high wind generation for ICMG B and high load levels for ICMG A, respectively. The quantities of transacted energy per hour converge to optimal points where transaction profits and cost reductions can be maximized between ICMGs. These quantities are determined within a limit of 150 kW, representing the maximum transacted energy allowed between the two ICMGs.

Table 8. The results of the determined 24 h dispatchable generation cost, transactions, generation prices, and market clearing price for ICMG A in islanded mode.

ICMG A	Total Amount of Generation (kWh)		Generation Cost (Won)
Dispatchable Generators	3,213,000		547,101,207
ICMG A (RES, etc.)	Price (Won/kWh)	Total amount of Electricity (kWh)	Total revenue (Won)
Renewable Energy (PPA)	110	1,409,000	154,990,000
MCP (From ICMG A to B)	97.33~181.18	947,000	106,330,869
MCP (From ICMG B to A)	161.44~230.23	1,072,000	181,821,658
Scenarios of PPA Network fee	15	1,409,000	21,135,000
	10		14,090,000
	20		28,180,000
Ratio of RE100 (%)	(1,409,000/5,041,000) × 100 = 27.95[%]
Offsetting Carbon Credits (Won)	$1409\left[\mathrm{MWh}\right]\times 0.459[{\mathrm{t}\mathrm{C}\mathrm{O}}_2$$\mathrm{eq}/\mathrm{MWh}]\times 17,000[\mathrm{Won}/{\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq] = 10,994,427 [Won]

below shows the results of the 24 h dispatchable generation cost of ICMG A and the results of the 24 h transaction, generation price, and market clearing price (MCP) of ICMG A in islanded mode.

Table 9. The results of the determined 24 h dispatchable generation cost, transactions, generation prices, and market clearing price for ICMG B in islanded mode.

ICMG B	Total Amount of Generation (kWh)		Generation Cost (Won)
Dispatchable Generators	3,547,000		599,671,974
ICMG B (RES, etc.)	Price (Won/kWh)	Total amount of Electricity (kWh)	Total revenue (Won)
Renewable Energy (PPA)	110	3,058,000	336,380,000
MCP (From ICMG A to B)	97.33~181.18	947,000	106,330,869
MCP (From ICMG B to A)	161.44~230.23	1,072,000	181,821,658
PPA Network fee	15	3,058,000	45,870,000
	10		30,580,000
	20		61,160,000
Ratio of RE100 (%)	(3,058,000/6,480,000) × 100 = 47.19[%]
Offsetting Carbon Credits (Won)	$3058\left[\mathrm{MWh}\right]\times 0.459[{\mathrm{t}\mathrm{C}\mathrm{O}}_2$$\mathrm{eq}/\mathrm{MWh}]\times 17,000[\mathrm{Won}/{\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq] = 23,861,574 [Won]

below shows the results of the 24 h dispatchable generation cost of ICMG B and the results of the 24 h transaction, generation price, and market clearing price (MCP) of ICMG B in islanded mode.

In islanded mode, companies in ICMG A collectively consume a total of 5,041,100 kWh of power. During this period, the power supplied through the corporate PPA amounts to 1,409,000 kWh, indicating an RE100 implementing rate of 27.95%. As of 2022, the emission factor, meaning the quantity of emissions in tons of carbon dioxide equivalent per megawatt-hour (unit: ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq/MWh), is 0.459. At this time, assuming a price of 17,000 Won per 1 ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq, the carbon emission offset cost is 10,994,427 Won.

Companies in ICMG B collectively consume a total of 6,480,000 kWh of power in islanded mode. During this period, the power supplied through the corporate PPA amounts to 3,058,000 kWh, indicating an RE100 implementing rate of 47.19%. As of 2022, the emission factor, meaning the quantity of emissions in tons of carbon dioxide equivalent per megawatt-hour (unit: ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq/MWh), is 0.459. At this time, assuming a price of 17,000 Won per 1 ${\mathrm{t}\mathrm{C}\mathrm{O}}_2$eq, the carbon emission offset cost is 23,861,574 Won.

Figure 9 below shows the results of transaction price and transacted energy between ICMG A and B. In islanded mode, electricity clearing between ICMGs relies on market clearing pricing (MCP). The EMS of each ICMG gathers bids from all agents regarding generation and demand, then clears the market and establishes MCPs for each scheduling period. These MCPs are then provided to individual agents so they can adjust their bids after market clearance. This process is structured as an iterative model involving the ICMG system operator and individual ICMG partners. Moreover, MCP is determined based on electricity transactions between ICMGs in the islanded mode of this test case. For instance, in ICMG A, solar generation is high during the daytime, so electricity is transferred from ICMG A to ICMG B, with MCP influenced by the generation cost of ICMG A’s dispatchable generators. Conversely, during evening hours, wind generation in ICMG B is high, resulting in electricity being transferred from ICMG B to ICMG A, with MCP influenced by the generation cost of ICMG B’s dispatchable generators.

The proposed SALR-based decentralized OPF method was also compared with the Classical Lagrangian Relaxation (CLR)-based decentralized OPF method for computation efficiency. The CLR-based decentralized OPF method solves the test system for 24 h.

The CLR-based decentralized OPF method replaces the augmented Lagrangian term of the objective function with the classical Lagrangian term and solves the test system problem with the proposed constraints using the sub-gradient method. All optimality gap results in the case study have values smaller than the tolerance value ϵ, indicating that all results are optimal.

Table 10. Hourly iteration number and simulation time for CLR and SALR algorithms.

Methods	Iteration Number		Simulation Time
	CLR	SALR	CLR	SALR
Min	59	55	2.0 s	1.7 s
Max	690	79	25.4 s	3.1 s
Average	314	60	11.4 s	2.3 s

below shows the hourly iteration number and simulation time for CLR and SALR algorithms.

Table 10 summarizes the results of the iteration numbers and the computation times for the SALR and CLR algorithms, which are necessary to reduce the mismatches in the hourly transacted energy under a tolerance value of 0.1 MW according to the proposed convergence procedure in Section 2, respectively.

The results show that the SALR-based decentralized OPF method approaches the convergence point more efficiently than the CLR-based method at one-fifth of the iteration numbers and simulation times on average. Table 10 also shows that the differences in the maximum iteration numbers and computation times are substantially enlarged.

4. Conclusions

Microgrids will become the key operational components of future power systems, provided that the current power system evolves from the traditional centralized electrical grid environment to the decentralized electrical grid environment. This evolution is expected, given the continuous developments in disruptive technologies and increasing concerns about the natural environment. Furthermore, as the RE100 campaign gains momentum, South Korea has taken the lead in creating an ‘Industrial Complex Microgrid for RE100 Implementation’ with the goal of sourcing 100% of electricity consumed by industrial complex companies from renewable sources. This paper delineates a systematic approach to renewable energy procurement through corporate power purchase agreements, streamlining the integration of RE100 initiatives within industrial complexes.

Moreover, the managerial implications of this study are significant and multifaceted, especially in the context of optimizing energy management in ICMGs.

• Cost Reduction: By implementing the proposed decentralized OPF method, companies can achieve significant cost savings with the offsetting carbon credits. The sensitivity analysis of PPA network fees indicates that careful management and negotiation of these fees can lead to lower overall costs for implementing RE100 initiatives.
• Enhanced Decision-Making: The detailed analysis of different tariff plans (ToU and SSR) provides valuable insights for decision-makers. By understanding how different tariff structures impact energy costs and generator dispatch, managers can make more informed decisions about which tariff plan to adopt.
• Sustainability Goals: Our study demonstrates how corporate PPAs with renewable energy developers can be effectively managed to achieve RE100 targets. This not only helps in reducing the carbon footprint but also enhances the company’s reputation as a leader in sustainability.
• Strategic Planning: The findings from our study can aid in long-term strategic planning. By understanding the cost implications and operational impacts of different energy management strategies, companies can better plan their investments in renewable energy and energy efficiency technologies.

This paper also presents a decentralized OPF method for the energy transaction problem of interconnected ICMGs using the SALR algorithm. The proposed method solves the problem in a decomposed manner with an iteration procedure. In the iteration procedure, an augmented Lagrangian multiplier can be computed, and the computed multiplier is economically interpreted as a unit price of the transacted energy. In order to illustrate the effectiveness of the proposed method, a case study was conducted on two interconnected MGs in grid-connected and islanded modes.

In the future, the proposed decentralized OPF method will be applied to an expanded case study where energy transactions occur among multiple interconnected ICMGs. When energy transactions occur among multiple interconnected ICMGs, more coupling equality or inequality constraints will be considered. Additionally, uncertainties such as fluctuating renewable energy generation, varying load demands, and potential grid disruptions are not extensively addressed in this study. However, the impact of these uncertainties will be investigated in future research. Moreover, the solution searching procedure will be improved following further studies on both an effective method for updating the augmented Lagrangian multiplier and a generalized criterion for conducting energy transaction convergence checking. The decentralized energy transaction problem of ICMGs will also be addressed via the incorporation of internal and external operational ICMG uncertainties and the scheduling of energy storage systems.