Quantifying Benefit of Well-Located Distributed Energy Resources

In recent years, there has been a global acceleration in the adoption of distributed energy resources (DERs), due to their potential to decrease net demand and minimize costs associated with transmission and distribution networks. In practice, however, many of them are not situated in load areas, but in remote areas for return of investment, i.e., mostly characterized by high solar radiation, abundant wind resources, and relatively low land-use fees. As a result, the locational mismatches can lead to excessive network construction, significant congestion, and loss costs. To achieve cost-effective grid operation and planning results, it is crucial to locate DERs considering their system level impacts. Since the locational benefits of DERs are not fully assessed for and reflected in their field deployment process today, DERs are not induced to the appropriate sites. To fill this gap, this study quantifies the benefits of diverse DER deployment scenarios using Monte Carlo simulations and provides policy recommendations for utilities and authorities. To estimate the benefits, we conducted a long-term analysis using the transmission expansion planning approach and a short-term analysis based on the optimal power flow methodology. The proposed analysis reveals that the upper 10% scenario of the experimental group with better DER locations can achieve 27% cost reduction than that of the control group. The noteworthy improvement of the well-located scenario for the same amount of DER deployment accounts for a benefit of $1519M in the Korean power system case study.


Indices and Sets
Shadow price of the active power balance constraint of bus n at time t in year y δ q n,y,t Shadow price of the reactive power balance constraint of bus n at time t in year y μg,y,t Shadow price of the maximum active power constraint of dispatchable generator g at time t in year y ρg,y,t Shadow price of the maximum reactive power constraint of dispatchable generator g at time t in year y ν r l,y,t Binary variable that is equal to 0 if active power flow receiving through line l is negative and 1 otherwise at time t in year y.ν s l,y,t Binary variable that is equal to 0 if active power flow sending through line l is positive and 1 otherwise at time t in year y.ω l,y,t Shadow price of the maximum power flow constraint of line l at time t in year y θ n,y,t Voltage angle of bus n at time t in year y C cong n,y,t Congestion cost of bus n at time t in year y C loss n,y,t Loss cost of bus n at time t in year y f l,y,t Complex power flow through line l at time t in year y.f p,loss l,y,t Active power loss through line l at time t in year y.f p l,y,t Active power flow through line l at time t in year y.f q,loss l,y,t Reactive power loss through line l at time t in year y.f q l,y,t Reactive power flow through line l at time t in year y.p g,y,t Active power of dispatchable generator g at time t in year y.p r,y,t Active power of non-dispatchable generator r at time t in year y.q g,y,t Reactive power of dispatchable generator g at time t in year y.
rv l,y Residual value for line l in year y.x l,y Binary variable that is equal to 1 if line l is built and 0 otherwise in year y.V n,y,t Voltage magnitude of bus n at time t in year y u g,y,t Binary variable that is equal to 1 if dispatchable generator g is online and 0 otherwise at time t in year y.z g,y,t Generation cost for dispatchable generator g at time t in year y.

I. INTRODUCTION
T HE definition of distributed energy resources (DERs) pro- vided in [1] includes generating units that are connected to distribution-level voltages and can either provide support to the distribution network or serve customers through on-site production.The report also highlighted the economic benefits of DERs, noting that on-site production could save up to 30% of electricity costs associated with transmission and distribution.However, in reality, many countries are currently facing locational mismatches between demand and generation sites due to regional constraints and other practical considerations, causing a challenge in system operation and planning.To address this challenge, using continental-level transmission lines is considered as a solution.For instance, the e-Highway 2050 and Interconnections Seam projects in Europe and the United States, respectively, construct long-distance transmission lines to connect different regions [2], [3].These projects in common aim to maintain overall system balance by facilitating the efficient transfer of electricity between regions with varying levels of power demand and generation.In South Korea, a similar challenge exists due to the concentration of power generation in the Southern and Eastern regions, which requires electricity to be transferred to areas with higher demand.In the U.K., efforts are being made to study the most efficient ways to construct long-distance DC cables to transfer electricity produced from wind resources in Scottish and North Sea to Southern load centers [4].Unfortunately, however, the use of long-distance transmission lines poses several drawbacks, including increased costs associated with construction, losses, and congestion.Therefore, relying solely on this approach may not be the optimal solution to address the challenge.To identify solutions to the demand and generation mismatch, various strategies, including long-distance transmission lines, voltage source converter-based HVDC technology suitable for large-scale grid, and sector coupling technologies such as power-to-gas and power-to-heat, are being explored [5], [6], [7].
To operate and maintain the grid in a cost-efficient manner, it is crucial to strategically locate DERs at suitable sites and maximize their potential benefits to mitigate the aforementioned issues.For this reason, some utilities and research organizations have been characterizing the locational and temporal values of DERs and exploring ways to reflect these values through incentives or pricing schemes [8].One example of such a scheme is the Value Stack mechanism established by the New York State Public Service Commission, which determines compensation levels for DER installations based on their energy, capacity, environmental, demand response, and locational system relief values [9].A law concerning benefits of DERs has been passed recently in the National Assembly in South Korea.The law would require utilities to precisely assess the benefits of DERs and use this information to incentivize DERs to be located in suitable sites [10].
Well-located DERs can provide various benefits to the grid and society [11].Firstly, DERs can provide benefits by being located near the point of demand, thus avoiding the need for new generation facilities and related transmission and distribution infrastructure investments.These benefits can increase generation capacity, reduce fuel consumption of generation facilities, contribute to reducing transmission losses, and avoid the need for new transmission and distribution infrastructure through congestion relief.In particular, the National Renewable Energy Laboratory has developed a model to systematically analyze the benefits and costs of DERs based on these factors [12].Moreover, in California, the California Public Utilities Commission and each utility formed a working group and conducted the Locational Net Benefit Analysis project to evaluate deferral opportunities in distribution network planning [13].In academic research, the authors of [14] emphasized the importance of compensating DERs owners based on their contributions to the system, rather than relying on flat credits or tax credits.The authors quantified the benefits of DERs in terms of deferring infrastructure investments in distribution network.Similarly, in [15], the authors proposed a quantification framework to assess the benefits of investment deferral in distribution networks attributable to the integration of undispatchable DERs.They formulated a multi-objective problem, taking into account the benefits of network investment deferral, energy loss costs, and interruption costs.Secondly, fast-responding DERs, such as PV inverters with grid-support functionalities, can contribute to system flexibility and reliability through ancillary services, such as frequency regulation and spinning reserves, similar to traditional generators [16], [17].Through advanced grid support functions available today [18], DERs can strengthen system reliability for sensitive loads and, potentially, they can increase social benefits and energy security by providing reliable electricity near the point of demand, less relying on the transmission system.Studies have quantified the benefits that energy storage systems can provide to the grid as a type of DER [19], [20], [21], [22], [23].Lastly, DERs are mostly low-carbon sources, such as solar and wind, to reduce greenhouse gas emissions.They can also reduce potential environmental costs and provide benefits for improving the quality of life [24].Most of the aforementioned benefits of DERs are currently being compensated through a range of policies.Especially with regard to the benefits of renewable energy, countries provide compensation for facility investment and power generation through policies such as the Investment Tax Credit, Production Tax Credit, Renewable Portfolio Standard, Feed-in Tariff, Feed-in Premium, Contracts for Difference, and other similar mechanisms [25], [26].In addition, compensation can be offered to market participants who provide various services such as demand response and ancillary services [27], [28].However, the compensation for locational benefits, which can offer significant benefits in grid planning and operation, is currently underexplored and insufficient.Therefore, it is necessary to quantify those benefits and incorporate them into future policies and decision-making processes.
For these reasons, this study focuses on investigating the locational benefits of DERs and performs a quantitative evaluation of the benefits of deploying DERs in random locations through Monte Carlo simulations.Specifically, we conduct analysis with both long-term and short-term models and subsequently estimate the benefits of DERs based on both analyses.The long-term model has been developed utilizing the widely recognized transmission expansion planning (TEP) methodology to estimate the benefits of avoided investment in transmission network through a mixed integer linear programming approach.The short-term model is based on a standardized AC Optimal Power Flow (OPF) model, such as the one proposed in [29], which calculates congestion and loss costs and estimates the benefits through a non-linear programming approach.This study also conducts a case study on a reduced test system in South Korea to estimate the non-parametric probability distribution of integrated benefits.Fig. 1 illustrates the simplified model architecture and data flow.
The key contributions of this study are as follows: r By deploying DERs in various scenarios, the benefits of congestion and loss reduction were quantified through short-term analysis, as well as the benefits of avoided investment in transmission lines were also evaluated through long-term analysis.
r Based on a quantitative analysis of their benefits, we present recommendations for effective DER field Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
deployment that can be utilized by policymakers for permitting and designing renewable energy zones.
r Heuristic-based algorithms were proposed to efficiently estimate the benefits of a nationwide transmission system while saving the computational time required for the Monte Carlo simulations.The remainder of this article is organized as follows.Section II and Section III present the framework for quantifying long-term and short-term benefits, respectively.In Section IV, relevant case studies are described, and integrated benefits are estimated using Monte Carlo simulations.Finally, the conclusions and policy implications with key takeaways are presented in Section V.

II. FRAMEWORK FOR QUANTIFICATION OF LONG-TERM BENEFIT
This section identifies needs of additional transmission lines using the TEP to estimate the long-term benefits of DERs deployments.The TEP computes the differences in cost associated with network expansion between the base and well-located DER scenarios in order to estimate the long-term benefit, including avoided cost.
In Section II-A, a typical TEP formulation is presented [30].The subscripts g, y, s, l, and n, which are not explicitly specified in the equation, correspond to the sets of generators, years, snapshots, lines, and nodes, respectively.The subscript s denotes multiple critical points within the temporal set.In Section II-B, we propose a practical approach to reduce the computational time for simulations.

A. TEP Formulation
The TEP equation in this study is formulated as: where the first term of the objective function represents generation cost, the second term represents investment cost of candidate transmission lines that have been selected for construction, and the third term represents the residual value of the lines that remain after the analysis period.The discount factor α is applied to convert these terms into their present values.The parameter η l,y is defined as the residual proportion of the initial investment cost for line l constructed in year y.
Other equations used for the TEP are as follows: Equation ( 3) defines a logical constraint, which requires that the status of a transmission line built in the previous year ỹ should be maintained in year y.In other words, the transmission line should continue to operate if it was built in the previous year.Equations ( 4)-( 10) illustrate the linearization process of the quadratic generation cost function through the use of piecewise linear approximation [31].Equation ( 11) constrains the power output of the generator.Equation ( 12) determines the output of the non-dispatchable generator based on predetermined capacity factor and capacity of the generators.
where the two non-negative variables f + l,y,s and f − l,y,s are used to represent the active power flow f p l,y,s as shown in (13).These variables are utilized to indicate the direction of power Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
flow.It is important to note that these non-negative variables are not assigned simultaneously within the formulations.Eqs ( 14)-( 17) describe the linearization process of the quadratic active power loss function via piecewise linear approximation, as detailed in [30].Equation ( 18) restricts the power flow through a transmission line to its rated capacity, whereby the power flow of the line is equal to the sum of the sending and receiving flows from the nodes and the power loss.Equations ( 19)-( 20) incorporate the disjunctive factor M to circumvent the nonlinearity associated with binary decision variables.Additionally, the power flow is determined by utilizing the DC power flow model, which is an approximation of the AC power flow model.Finally, (21) represents the power balance equation of each node.

B. A Practical Approach to Reduce Computing Time 1) A Time-Consuming Problem Arising From Candidate
Lines: A national level TEP typically involves a multitude of parameters and decision variables that are associated with nodes, branches, and generators.The complexity of these planning problems may result in lengthy computation times required to solve the problem.For the reason, most TEP studies, as in [32] and [33], adopt a set of candidate transmission lines prior to optimization, rather than fully searching all possible solutions.Moreover, in the real world, candidate transmission lines may be constrained by the practical routes and standardized line parameters, which could prevent network operators from solving the TEP model using a given set.In such cases, increasing the number of candidate lines might be necessary to achieve an optimal solution to the problem, but this could potentially result in longer computation times.Additionally, increasing the size of the candidate set does not guarantee that the TEP problem can be solved in all cases.
For the aforementioned reasons, the model in this study uses a new heuristic-based algorithms.In the algorithm captured in Algorithm 1, if the TEP model is not feasible in initial set of candidate transmission lines, this model updates the line parameters within a constrained set of candidate transmission lines.Specifically, for each candidate transmission line, one candidate line is added in parallel, and candidate lines of the route made equivalent to one candidate line.The maximum active power capacity of each candidate line is then multiplied by the number of candidate lines.Accordingly, the resistance and reactance values are divided by the number of candidate lines.Once the result from the TEP model is feasible, the number of determined transmission lines is increased by the number of iterations, and the line parameters are updated to their original values.This process prevents an exponential increase in analysis time by maintaining the size of the search space, whereas there is a linear increase in analysis time due to the iteration process.
2) A Time-Consuming Problem Arising From N-1 Contingency: In our study, network security is ensured by conducting N-1 contingency analysis during the long-term planning process.This type of analysis ensures that the network can continue to operate normally in the event of a failure in one of the transmission lines.However, incorporating N-1 contingency analysis results in an exponential increase in computation time.

Remove feasible problems end while end for return the new transmission lines considering contingency
To address this issue, we divided the TEP framework into two steps.In Step 1, the model identifies new transmission lines using the TEP formulation, without considering N-1 contingency.These new transmission lines are then added to the existing set of lines before starting Step 2. In Step 2, using Algorithm 2, the model decomposes the time dimension and solves the resulting decomposed problems in parallel-processing using the TEP formulation, introducing the argument c representing failed transmission line corresponding to contingency.Afterwards, the new transmission lines that result in the least expansion cost are incorporated into the existing set.At this time, it is important to note that the timeslots during which no new transmission lines are constructed and the timeslots for which new transmission lines are added to the existing set are deemed operational in the event of an N-1 contingency.This process is repeated until all time-decomposed problems have been fully able to withstand N-1 contingency.
This long-term planning model considers only the worst-case snapshots, rather than continuous time-frame.The reinforcement of transmission lines is primarily determined by worst-case Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
scenarios that arise during periods of peak demand or high generation.The TEP problem can be efficiently solved by focusing the most impactful worst-case scenario, rather than employing an hourly resolution.As a result, it reduces the effort required to search across multiple time-frames.

III. FRAMEWORK FOR QUANTIFICATION OF SHORT-TERM BENEFIT
This section analyzes the annual operating benefits resulting from the deployment of DERs by modeling a nonlinear AC OPF to calculate Locational Marginal Price (LMP).The costs associated with loss and congestion are then calculated, and a method for estimating the benefits related to them is proposed.The loss and congestion costs are included in power supplying cost of utility which is the basis of retail tariffs for customers.The subscript t denotes the time step within the given time set.

A. AC-OPF Formulation
The objective function of the AC-OPF used in this article can be expressed as (22) which is the sum of the operating costs of generators.
Other equations for the problem formulation are as follows, with the corresponding shadow prices indicated next to each respective constraint.
p min g u g,y,t ≤ p g,y,t ≤ p max g u g,y,t : {μ g,y,t , μg,y,t }, ( q min g u g,y,t ≤ q g,y,t ≤ q max g u g,y,t : {ρ g,y,t , ρg,y,t }, (30) f l,y,t = (f p l,y,t + f p,loss l,y,t ) 2 + (f q l,y,t + f q,loss l,y,t ) 2 , (31)  ρg,y,t q g,y,t − q min g u g,y,t Equations ( 23)-( 24) represent the power equations, which indicate active and reactive flows of a transmission line expressed in terms of the equivalent pi circuit.Equations ( 25)-(26) represent the line losses.Equations ( 27)-( 28) are node balance constraints for active and reactive powers.At this point, since problems may arise in the reactive power balance when a large number of DERs are integrated, it is assumed the addition of a reactive power facility to each node.Equations ( 29)-( 30) represent the inequality constraints that impose limits on the generation of active and reactive powers for dispatchable generators.Conventional AC OPF models typically do not consider the commitment of generators.However, in this study, the commitment of generators is considered, as it varies depending on the deployment of DERs and can have a significant impact on the optimization results.
Considering this factor in a nonlinear AC-OPF can significantly increase computing time.To address this issue, some studies have employed a DC-based model to determine optimal discrete decisions, which are then used as parameters for the AC-based model [34].Therefore, this article uses a linearized DC-OPF to determine the commitment of the generators.Equations ( 31)-( 32) are constraints related to the power flowing through the transmission lines, which is the key constraint in OPF.Equations ( 33)-( 34) are the constraints on the maximum/minimum voltage and angle.Eq (35) is a lagrangian function incorporating ( 27)- (32) and their corresponding shadow prices.Lastly, (36) represents the LMP calculation using the partial derivative of the Lagrangian function [35].

B. Formulation of Congestion and Loss Cost Estimation
In power systems, congestion can occur when there are excessive power flows between nodes, leading to a mismatch between the costs paid by the load and the revenues received by the generator.Specifically, congestion on transmission lines can result in the load paying more than the original cost to the generator, resulting in an accumulated cost burden.Therefore, this article aims to use LMPs calculated through AC OPF to calculate congestion costs.LMPs, which include energy costs, congestion costs, and line losses, reflect the current congestion situation in the system and are sufficient for calculating congestion costs.
1) Congestion Cost Estimation: Based on the above, equations for calculating congestion costs expressed in the view of utilities as follows: The initial term within each square bracket in (37) represents the total cost paid by the load connected to node n for receiving power.The subsequent term represents the total amount settled to the generator for transmitting power from other nodes to node n.The third term represents the total amount settled to the generator connected to node n.Finally, the discount factor was applied to convert these terms into their present values.
2) Loss Cost Estimation: Line losses in AC power flow calculations refer to the power loss that occurs due to the resistance component of a transmission line.However, these losses can result in a mismatch between the cost paid by the load and the settlement received by the generator.Similar to congestion costs, it means that the load may end up paying a higher cost than the bid price offered by the generator due to line losses, and the load needs to minimize this cost to avoid long-term financial losses.In such a situation, an accurate calculation of the loss cost is required for the load to minimize it, and this article proposes to calculate this cost using LMP, just like congestion costs.As mentioned previously, LMP is the marginal price that reflects line losses as a price signal, so it is sufficient to use it as a basis for calculating loss costs.
Based on the above, equations for calculating loss cost can be expressed in the view of utilities as follows: The summation of the first term within each square bracket in (38) represents the total cost paid by the load on node n as it receives power, while the summation of the second term represents the total amount settled by the generator on node n as it transmits power from other nodes.Furthermore, the discount factor was applied in a similar manner as the congestion costs.

IV. CASE STUDY
The primary objective of the study is to assess the long-term and short-term benefits of DERs based on their locations using a reduced test system in South Korea.To estimate the benefits, the control group and experimental group scenarios were designed.The locational benefits of DERs were evaluated by calculating the differences in transmission expansion, loss, and congestion costs between the two groups.In this study, Monte Carlo simulation, a computational technique employing statistical sampling and probability distribution functions, was utilized to evaluate various scenarios.DERs, transmission networks, dispatchable generators, and other parameters were integrated into the Monte Carlo simulation to estimate the benefits derived from the random deployment of DERs.For the analysis, photovoltaic (PV) and wind generators, bio source, and fuel cell were considered as DERs, in accordance with the policy of South Korea.The analysis period covers three-year cycles from 2025 to 2034, and a discount rate of 4.5% is applied.Fig. 2 illustrates the total flowchart of long and short-term analysis.The proposed models for quantification of long-term and short-term was solved via Gurobi 9.1.2solver [36] and Ipopt 3.13.2solver [37] under Python environment, respectively.Corporation (KEPCO), a test system was configured by simplifying the power system of South Korea to only one node per jurisdictional region and interconnecting transmission lines between regions, as shown in Fig. 3.

A. Data Description
This resulted in a total of 10 nodes for the regions of Seoul, Gangwon, Incheon, Chungbuk, Chungnam, Gyeongbuk, Jeonbuk, Jeonnam, Gyeongnam, and Busan.An additional slack node was included for power flow calculations, resulting in a total of 11 nodes in the final test system.Intra-zone transmission lines were deleted, as each region had only one node in the test system.However, all inter-zone transmission lines were retained for benefit analysis considering the power flows.Generator specifications were maintained while being connected to the node corresponding to their respective regions.The test system comprises 11 buses and 82 lines as presented in Appendix.
2) Deployment Scenario of DERs: The overall scenario is divided into control and experimental groups based on the deployment of DERs.Scenarios of both groups were set where the total capacity of DERs remains the same as the South Korean government's deployment plan.The control group was designed based on the current DER deployment ratio, and it is used as the baseline for benefit analysis of well-located DERs.Table I shows the DER deployment capacity for each node in the control group and one selected scenario from the experimental group for total analysis period.
For the experimental group, scenarios for DER deployment were generated using a stochastic approach.First, the available capacity, deducting the already deployed capacity from the market potential in each region, was computed.Next, a weight of 1 was assigned to all regions, and a deployment probability was determined for each region using a Dirichlet distribution.The Dirichlet distribution is continuous multi-variate probability distributions in which the sum of probabilities for multi-dimensional vectors is unity, and with hyper-parameters set to 1, it becomes a uniform distribution.Finally, this process was repeated until the planned capacity for each year was fully deployed.If a particular region met its market potential during the deployment iteration, it was excluded from the subsequent iterations.Table I shows an example DER deployment scenario generated using this method.

TABLE I DER CAPACITY OF CONTROL AND SELECTED EXPERIMENTAL GROUPS DURING ANALYSIS PERIOD
3) Profiles of DERs and Loads: The profiles of PV and wind generators were generated using the average values of historical output data obtained from Korea South-East Power Co.Ltd., Korea Western Power Co.Ltd., and Korea Southern Power Co.Ltd.over a one-year period [38], [39], [40], [41].As for the bio source and fuel cell, since hourly capacity factor data were not available, a constant value was assumed for all hours.Additionally, the load profiles were constructed using the historical electricity demand data obtained from the Korea Power Exchange for the corresponding time period as the PV and wind generators [42].All profiles demonstrate a temporal resolution of one hour and cover a duration of 8760 hours.Fig. 4 illustrates the hourly average values of seasonal profiles.In the long-term framework, two temporal snapshots were employed throughout the course of a year to represent the worstcase scenarios.The first snapshot corresponds to the point when the highest capacity factor for each hourly pattern of all DERs coincides with the minimum load within the load pattern.The second snapshot represents the point when the lowest capacity factor of all DERs coincides with the peak load of the load pattern.
In the short-term framework, modified profiles with a span of 288 hours, based on hourly average values for each month, were used to reduce the computational time required for Monte Carlo simulations.

B. Results of Benefit Analysis 1) Results of Integrated Benefit Analysis:
The integrated benefit was estimated by combining the annual benefits derived from both the long-term analysis and the short-term analysis.The benefits derived from the long-term analysis are evenly divided throughout the entire analytical period, owing to the fact that the decision to construct additional transmission lines in a specific year is influenced by the cumulative integration of DERs from preceding periods.The benefits obtained from the short-term analysis yield results on an annual basis.Fig. 5 shows the non-parametric probability distribution of the integrated benefits for 2000 scenarios.The red solid line represents the upper 10% of the total integrated benefits, and the green dotted line represents the upper 25%.The total benefits for both scenarios are 1520M$ and 1495M$, respectively.Through the numerous Monte Carlo simulations, it has been confirmed that the locational benefits of DERs exhibit a certain distribution with a mean of 1414M$ and a standard deviation of 157M$.This finding holds significant potential for future decision-making processes for estimating locational benefits of DERs.
Table II shows the annual benefits for the two selected experimental scenarios, i.e., the upper 10% and 25% levels of Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the distribution.Notably, in the upper 10% scenario, benefits are lower during the early period from 2023 to 2028 since the DER capacity does not reach the critical point that causes decreased congestion and loss, resulting in marginal effects of the distributed deployment.During the later period from 2029 to 2034, on the other hand, benefits of the well-located DERs are significantly higher due to the deployment of approximately 28 GW of DERs during this period.Meanwhile, the upper 25% scenario shows a similar trend in benefits to the upper 10% scenario, albeit at a slightly lower level.This is attributed to differences in the deployment of DERs in metropolitan areas, despite both scenarios having the same number of transmission lines.Fig. 6 displays the deployment status of DERs by region based on these results.

TABLE II INTEGRATED BENEFITS OF UPPER 10% AND 25% LEVELS DURING THE ANALYSIS PERIOD COMPARED TO THE CONTROL SCENARIO
Fig. 6 illustrates that in 2022, the deployment of DERs was concentrated in the Jeonnam and Jeonbuk regions with low demand, whereas only 10% of the total DER capacity was deployed in the three high-demand regions-Seoul, Incheon, and Busan.Furthermore, there was a significant difference of approximately 3.8 times when comparing the total deployment capacity of these regions.
However, an analysis of the deployment results in 2034, based on the proposed framework, revealed a reduction of 14% in the proportion of DERs deployed in the Jeonnam and Jeonbuk regions compared to 2022.Conversely, there was a 15% increase in the proportion of DERs deployed in the Seoul, Incheon, and Busan regions compared to 2022.Additionally, the difference in total deployment capacity between these regions decreased to nearly zero.
These findings show that matching the regional generation and demand is essential to maximize the benefits of DERs and operate the system efficiently.The following subsections discuss the outcomes of the long-term and short-term benefit analysis for the upper 10% scenario.

2) Results of Long-Term Benefit Analysis:
The stochastic deployment of DERs results in avoided costs in transmission line investments, leading to long-term benefits.The avoided cost is the difference in expansion costs between the control group and the experimental group.New transmission lines will be determined when the line capacity is insufficient to deliver the required inter-region power flow.Fig. 7 illustrates the expansion cost for new transmission lines across scenarios.Among scenarios, the control group incurred the highest expansion cost, surpassing the costs incurred by  Additionally, an analysis was conducted to assess the computational performance of the proposed algorithms in Section II-B.We configured the baseline case to identify the optimal solution by iteratively increasing the total number of candidate lines without implementing the proposed Algorithms.The analysis outcomes are exhibited in Table IV, displaying both the computation time and the number of necessary candidate lines.This is done in two cases: one integrates the algorithms and the other does not.In the absence of considering N-1 contingency, only Algorithm 1 was implemented, leading to an increase in the number of candidate lines to 108, which were deemed necessary to obtain a solution for the problem.Incorporation of Algorithm 1 reduced computation time by approximately 50%, while maintaining the number of candidate lines at 36.When considering N-1 contingency, both Algorithm 1 and Algorithm In terms of optimality, it is crucial to acknowledge that all algorithms, including the no algorithm case, are unable to guarantee a global optimal solution for the entire power system due to the limited set of candidate lines.Instead, they ensure finding an optimal solution for the given set.The proposed Algorithm 1 limits the number of combinations from the set of candidate routes, possibly making it challenging to explore the optimal route.However, it significantly reduces computational time.Given that the study is based on a Monte Carlo approach, the algorithm was developed to achieve near-optimal results while minimizing computation time.The performance of the algorithm was evaluated by comparing it to existing methods, and it demonstrated an average error rate of approximately 0.005%, which is considered acceptable.On the other hand, Algorithm 2 addresses the problem by decomposing the temporal factor and sequentially identifying the least-cost results through parallel-processing, ensuring optimality.Therefore, any additional test for Algorithm 2 was not performed.
3) Results of Short-Term Benefit Analysis: The network configurations for each analysis year are determined based on long-term planning results.Generation commitment decisions and locational marginal price calculations are made using these configurations.The analysis also accounts for the variability of demand and DERs by using monthly and hourly average values of DERs profiles.All scenarios of the experimental group are used for analysis, and their short-term benefits are compared with those of the control group scenario.Monthly and hourly benefits analysis results are summed up to annual results.The time step and optimization horizon of the analysis is one hour.In 2031, due to the absence of specific generator data and load data for all nodes in the original system, the benefit was estimated using the linear interpolation method.
Table V presents the calculated loss and congestion costs of the upper 10% scenario of experimental group and control group during the analysis period, utilizing the network configurations provided in Table III.
In 2025, the experimental group deployed DERs in Incheon and Busan regions at similar levels to other regions, which is different from the control group where DERs were concentrated in Jeonnam.However, despite the changes in deployment, the total DER capacity is low, resulting in negligible cost differences when compared to the control group.
On the other hand, in 2028, there is a slight increase in the overall capacity of DERs compared to that of 2025.As a result, the experimental group experienced a reduction in costs of approximately 6M$million compared to the control group.
In 2034, the experimental group's analysis results show that while their overall congestion and loss costs have decreased due to a significant increase in DER capacity and the ability to meet the demand of nearby areas, the control group also experienced a reduction in overall congestion and loss costs due to 12 transmission line expansions.Ultimately, the cost difference between the control and experimental groups in 2034 is higher than in 2028, indicating the effectiveness of distributed DER deployment.Based on these observations, therefore, strategically distributing DERs can result in cost-effective outcomes.Furthermore, the annual analysis demonstrates that, as DER capacity increases over the years, distributing DERs would result in more significant benefits.

V. CONCLUSIONS AND POLICY IMPLICATIONS
The increasing penetration of DERs presents practical challenges, such as regional constraints and investment bias, which exacerbate the problem of early saturation and system reinforcement.In this context, this article has proposed a framework to quantitatively assess the benefits of well-located DERs.
The proposed frameworks were used to evaluate the Korean power system from year of 2023 to 2034, using Monte Carlo simulations.The long-term benefit analysis revealed that the control group resulted in a number of line constructions, while most of the experimental group required only a few line constructions.In the short-term benefit analysis, scenarios with evenly distributed DERs exhibited lower annual congestion and loss costs compared to the control group in common.
The findings of this study demonstrate that the strategic deployment of DERs can offer an economically viable solution for power system investment and operation, particularly in light of the increasing penetration of DERs.The research also offers valuable insights into the potential benefits of well-located DERs, which can guide future policies and decision-making processes.In order to site DERs in a cost-effective manner, as indicated by the findings of this study, it is necessary to artificially simulate deployment scenarios that are rarely observed in reality.
Some jurisdictions, such as the US, applying locational marginal pricing and financial transmission right in wholesale spot markets, can deliver the price signal for suitable locations to DERs.On the other hand, other jurisdictions, such as U.K. or South Korea, using a uniform pricing scheme in their wholesale markets, should find various ways to induce DERs in optimal locations to benefit the entire system operation.
It is evident that not all projects would adjust their target site solely in response to locational price factors such as the spot market prices.For this reason, it is possible to consider a regulation mechanism based on permitting process or designing renewable energy zones considering regional capacity limits according to the simulation results in this study.For instance, in case the deployment capacity in a particular area reaches its limit, new DER deployments should be directed to regions with sufficient capacity to receive the incentive.Such an approach would promote the optimal deployment of DERs.This stronger policy signifies a notable shift in the regulatory paradigm, as it involves the imposition of an upper limit on capacity, which goes beyond a mere introduction of price differentiation.Despite such policies, it can be plausible that certain project developers may still not be responsive to the quantity and price signals, as they prioritize specific project needs.To tackle this challenge, the Korean government is contemplating the adoption of licensing measures to restrict the quantity aspect, and the simulation results of this study could provide them with an initial direction.While acknowledging that limiting capacity through licensing may not perfectly align with market principles, it is believed that such a policy could yield greater public benefits.Consequently, it might be crucial to carefully evaluate multiple options, such as in [43], [44], [45], [46], to induce the cost-effective siting of DERs.
This study has the following limitations.Firstly, it did not consider resources with flexible points of connection, such as electric vehicles (EVs), in the selection of DERs.Incorporating these resources has the potential to yield different outcomes, characterized by increased long-term and short-term benefits, through the implementation of various scheduling mechanisms.Additionally, the commitment decisions for generators did not take into account operational characteristics, including start-up and shut-down constraints, as well as ramp rate limits.Moreover, the construction of transmission lines did not consider voltage and reactive power in the AC power system.DERs are typically connected at the distribution level.To conduct nationwide simulations that are computationally tractable, the study performs experiments on a reduced network that simplifies the transmission network with DERs aggregated at buses in their region.Indeed, the versatility of the proposed framework allows for potential application to larger-scale systems with higher spatial resolution, including distribution networks.While incorporating the modeling of the distribution system would have provided distribution-level impact, its complexity poses a significant challenge in implementing the same Monte Carlo approach used in this research, making this work impractical.Consequently, the modeling of the distribution system was not included in this research.Lastly, the analysis did not consider curtailment due to its limited allowance in South Korea and the fact that grid parity has not been achieved.Moreover, the absence of well-defined compensation policies for curtailment led to its exclusion from this study to prevent inaccurate estimations of benefits.However, if curtailment is considered in future research, it is expected that the number of line constructions in long-term analysis would be reduced.To perform a more sophisticated analysis, it is imperative to incorporate the aforementioned factors, potentially with a computation time reduction method refined from the ones proposed for future research.

APPENDIX THE DATA USED FOR THE TEST SYSTEM
The test system comprises 11 buses and 82 lines as presented in Table VI

Algorithm 1 :
Restructure Candidate Line Parameters.Input: initial set of candidate transmission lines Ω new L iteration i = 1 line resistance r l line reactance x l while TEP model is not feasible in given Ω new L

Fig. 2 .
Fig. 2. Flowchart of the long and short-term frameworks.

Fig. 3 .
Fig. 3. Test system from model reduction of South Korea power system comprising 11 bus and 82 lines (abstracted for illustration).

Fig. 5 .
Fig. 5. Non-parametric probability distribution of integrated benefits from Monte Carlo simulation.

Fig. 7 .
Fig. 7. Expansion cost for new transmission lines by scenarios.
Index for line and set for new candidate lines.n, Ω N Index and set for nodes.Shadow price of the minimum reactive power constraint ofdispatchable generator g at time t in year y Δf k,l,y,t Active power flow through block k of piecewise linear loss function of line l at time t in year y.Δp k,g,y,t Power produced in block k of piecewise linear generation cost function of generation g at time t in year

TABLE III RESULTS
OF A LONG-TERM BENEFIT ANALYSIS FOR THE CONTROL AND UPPER 10% EXPERIMENTAL SCENARIOS IN 2034

TABLE V RESULTS
OF SHORT-TERM BENEFIT ANALYSIS FOR THE CONTROL AND UPPER 10% EXPERIMENTAL GROUPS DURING THE ANALYSIS PERIOD 2 were used, resulting in a noteworthy reduction in computation time to approximately 1/5 of the original duration.The computation time was markedly affected by the number of candidate lines under N-1 contingency.
-IX.Table VI represents the on/off-peak demand over the analysis period.Table VII provides the average specification values of generators for 2025.The generator set varies depending on the analysis year.Due to confidentiality reasons, this article Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
TABLE VI ON/OFF-PEAK LOAD DURING ANALYSIS PERIOD TABLE VII AVERAGE SPECIFICATION VALUES OF GENERATORS BY REGION IN 2025 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE VIII AVERAGE
SPECIFICATION VALUES OF EXISTING TRANSMISSION LINES IN 2025TABLE IX AVERAGE SPECIFICATION VALUES OF CANDIDATE TRANSMISSION LINES FOR TEP SIMULATION provides limited unit level information.Table VIII displays the average specification values of transmission lines in the test system, excluding one of the double circuit lines, and presenting the average values for lines with the same route.Similarly, Table IX displays the average specification values of candidate transmission lines.The route of candidate transmission lines was made up of only those above 154 kV in existing transmission lines.Access to all relevant data presented in this article is available at https://github.com/SEND-LAB/Data.git.