Expansion Planning Problem Research Articles

A comprehensive stochastic-based adaptive robust model for transmission expansion planning

To address various uncertainties appearing in the transmission expansion planning (TEP) problem, appropriate tools such as stochastic programming (SP) or robust optimization (RO) are required. On the other hand, both long-term (LT) and short-term (ST) uncertainties must be well captured to acquire the most reliable and robust solution. The current works model the LT uncertainty by RO and the ST uncertainty by SP, forming a two-stage adaptive robust optimization problem. In contrast, this paper presents a novel approach in which the SP and RO are simultaneously utilized to cope with each type of uncertainty, i.e., LT and ST uncertainty. Unlike the current methods with bilinear terms appearing in the subproblems, the trilinear terms appear in the objective function of the proposed approach, which are linearized accordingly. In addition, we propose a mixed-integer bilinear programming (MIBP) model to specify the rectangles used as uncertainty sets, which is further solved using Konno's algorithm. A standard column-and-constraint (CCG) generation solves the established tri-level structure. Two case studies are used to implement the formulation developed in this work. Results signify the effectiveness of the proposed method.

Long-Term Multiyear Transmission Expansion Planning in Turkish Power System

To sustain the clean energy transition without interruption and to ensure the reliable operation of the transmission system, it is required to have enough additional transmission capacity in the future horizons. The transmission expansion planning (TEP) problem is a core issue in deciding additional transmission capacity in the planning activities. TEP aims to find the best expansion plan while satisfying technical and economic constraints. In this study, a new binary version of the original FBI algorithm called the BFBI (binary forensic-based investigation) algorithm is developed to solve the binary TEP problem. The effectiveness and performance of the developed BFBI are assessed by implementing it in two different test systems: the standard Garver 6-bus test system and the modified 400 kV Turkish grid. Seasonal scenarios are created for 5- and 10-year planning periods to cover all possible generation and load conditions and to assess the impact of the increased share of RES on the grid in the TEP studies conducted for the modified 400 kV Turkish grid created as a bulk realistic grid. The TEP problem is solved by including investment, reliability, and operational costs in two different objective functions for cases while considering the N-1 contingency criterion. The efficacy and robustness of the BFBI algorithm are justified by comparing it with well-known algorithms such as GA and PSO.

Transmission expansion planning in a wind-dominated power system: A closed-loop approach

The current paradigm for the transmission expansion planning (TEP) problem follows an open-loop (OL) approach. This approach first executes an accuracy-oriented forecasting method to predict the available wind power, demand, and spinning and non-spinning reserve (SR and NSR) requirements. Afterward, the TEP problem is solved based on these predictions. However, this OL model does not necessarily obtain a better expansion plan in terms of the real system cost (RSC) against the actual realization of wind and demand. This article contributes to the existing literature by developing a closed-loop (CL) strategy for the TEP problem using a cost-oriented prediction method. In this novel cost-oriented methodology, the RSC assesses the forecasting data quality rather than the statistical indices (accuracy-oriented). In this regard, a bilevel programming model is established to train the predicted data to minimize the system RSC. The upper level trains the predictors for wind power and SR/NSR requirements, while the two lower-level problems formulate the unit commitment (UC)-based TEP and the economic redispatch (ERD) problem. The bilevel programming that contains integer variables at both levels is solved by the reformulation and decomposition (R&D) technique. The numerical results on the IEEE 118-bus grid illustrate the cost-effective advantages of the CL-TEP method.

Active Distribution Network Expansion Planning With Dynamic Thermal Rating of Underground Cables and Transformers

The rapid development of renewable distributed generation in active distribution networks (ADNs) imposes an increasing burden on the transfer capability of the ADNs, bringing new challenges to the distribution network expansion planning (DNEP) problem. Dynamic thermal rating (DTR), which evaluates the equipment rating based on the actual weather conditions and equipment thermal states, can enhance the equipment transfer capability to support the integration of renewable distributed generation. In this paper, we propose a DNEP model of ADNs incorporating the DTR of cables and transformers, given that underground cable feeder is preferred in the rapid urbanization trends. Then, we derive a linear reformulation of the original DNEP model and propose a modified Benders decomposition (MBD) algorithm to solve the DNEP model. To select more effective representative day scenarios, we propose a cost-based clustering method for representative day selection applicable to solving the DNEP model. Case studies based on the IEEE 33-node system and the PG&E 69-node system show that the implementation of DTR saves 14.7% and 15.1% of the investment costs of the two systems respectively. The effectiveness of the MBD algorithm and the cost-based clustering method is also verified by the case studies.

Efficient expansion planning of modern multi-energy distribution networks with electric vehicle charging stations: A stochastic MILP model

This paper presents a stochastic Mixed-Integer Linear Programming (MILP) model developed to address the collaborative expansion planning of modern multi-energy distribution networks, taking into account the integration of Electric Vehicle Charging Stations (EVCSs) in the presence of uncertainties. The model is comprehensively formulated to encompass Distributed Generation (DG) resources, Electric Vehicles (EVs), and Capacitor Banks (CBs), alongside traditional expansion options like substations and circuit construction/reinforcement. The essence of this Distribution System Expansion Planning (DSEP) problem formulation lies in its stochastic approach, featuring chance constraints to effectively manage and address uncertainties. The central objective of the model is to minimize the total investment and operational expenditures associated with the DSEP problem over a designated planning horizon. The rigorous application of optimization techniques ensures the convergence of the MILP model, thereby delivering an efficient and reliable solution. The model's effectiveness is initially assessed using an 18-bus system, followed by comprehensive testing on a larger 123- bus system to gauge its robustness. Thorough performance evaluations are conducted across various case studies, encompassing both the 18- bus and 123- bus systems, culminating in the validation of the model's resilience, scalability, and replicability. These case studies encompass deterministic and stochastic methodologies across six distinct scenarios. The numerical outcomes conclusively demonstrate that the DSEP solution, when utilizing the stochastic approach without considering EVCSs, is associated with elevated costs. However, with a strategic allocation strategy for EVCSs, noteworthy reductions in investment expenditures related to substations, lines, and overall costs are notably achieved. The incorporation of uncertainty management within the DSEP problem underscores the flexibility and adaptability intrinsic to the proposed stochastic MILP model. These attributes render it ideally suited to effectively orchestrating the expansion of multi-energy distribution networks in the presence of EVCSs, thereby enhancing its utility and relevance in addressing modern energy distribution challenges.

Distributed coordinated planning for cross-border energy system: An ADMM-based decentralized approach

Cross-border interconnection and trade (CBIT) can effectively leverage the differences in resource endowments and energy demand between regions and countries, making cross-border cooperation a potential option for addressing the high penetration of variable renewable energy. This paper presents centralized and decentralized planning approaches for the cross-border energy transmission expansion planning (TEP) problem. The proposed centralized mixed-integer second-order cone programming (MISOCP) model collaboratively optimizes the expansion of national energy networks, while considering the impact of CBIT. To protect the privacy of energy data in each country, the alternating direction method of multipliers (ADMM) algorithm is extended to decompose the centralized optimization formulation into mutually independent sub-optimization issues, and adaptively adjust the penalty parameters and Lagrangian multipliers to improve convergence. This study also quantifies the effect of cross-border cooperation in such co-expansion problems as a comparative consideration. Numerical simulations on the modified cross-border integrated energy network validates the correctness and effectiveness of the proposed model and solution methodology. The results show that cross-border cooperation can reduce a country's internal energy network congestion, thus postponing the expansion investment decisions. It also shows that the distributed coordinated planning is more efficient in terms of lower cost and renewable generation curtailment that than independent optimization method. Therefore, cross-border collaboration brings economic, environmental, and renewable integration benefits to interconnected countries.

Developing an Integration of Smart-Inverter-Based Hosting-Capacity Enhancement in Dynamic Expansion Planning of PV-Penetrated LV Distribution Networks

With the penetration of distributed energy resources (DERs), new network challenges arise that limit the hosting capacity of the network, which consequently makes the current expansion-planning models inadequate. Smart inverters as a promising tool can be utilized to enhance the hosting capacity. Therefore, in response to technical, economic, and environmental challenges, as well as government support for renewable resources, especially domestic solar resources located at the point of consumption, this paper is an endeavor to propose a smart-inverter-based low-voltage (LV) distribution expansion-planning model. The proposed model is capable of dynamic planning, where multiple periods are considered over the planning horizon. In this model, a distribution company (DISCO), as the owner of the network, intends to minimize the planning and operational costs. Optimal loading of transformers is considered, which is utilized to operate the transformers efficiently. Here, to model the problem, a mixed-integer nonlinear programming (MINLP) model is utilized. Using the GAMS software, the decision variables of the problem, such as the site and size of the installation of distribution transformers, and their service areas specified by the LV lines over the planning years, and the reactive power generation/absorption of the smart inverters over the years, seasons, and hours are determined. To tackle the operational challenges such as voltage control in the points of common coupling (PCC) and the limitations in the hosting capacity of the network for the maximized penetration level of PV cells, a smart-inverter model with voltage control capability in PCC points is integrated into the expansion-planning problem. Then, a two-stage procedure is proposed to integrate the reactive power exchange capability of smart inverters in the distribution expansion planning. Based on the simulations of a residential district with PV penetration, results show that by a 14.7% share of PV energy generation, the loss cost of LV feeders is reduced by 28.3%. Also, it is observed that by optimally making use of the reactive power absorption capability of the smart inverters, the hosting capacity of the network is increased by 50%.

Autonomous topology planning for distribution network expansion: A learning-based decoupled optimization method

The distribution of urban electricity load is highly uneven in both space and time, posing significant challenges to the problem of distribution network expansion planning (DNEP). An autonomous topology planning method for distribution network expansion is proposed to address that, driven by a learning-based decoupled optimization approach. The planning problem is decoupled from the impact of distribution network operation and used as reinforcement cost prediction for autonomous planning after the generation of topology schemes. First, a reinforcement model of the original distribution network is built that considers the actual distance calculation method of load nodes. Then an effective method for generating historical operation samples is designed, followed by the development of a learning-based reinforcement cost prediction model for the original distribution network based on operation state learning using XGBoost, which enables the prediction of said costs under different scenarios. Utilizing a distribution network topology generating method driven by the adjustable weight minimum spanning tree (AWMST) algorithm, an autonomous topology expansion planning strategy generation method employing the learning-based decoupled optimization approach is established. The feasibility and superior analysis of the proposed method is verified and analyzed on an actual urban distribution network case with simulation scenarios. The results show that the proposed method is faster and more flexible to deal with the distribution network planning problem brought about by rapid load growth in urban distribution networks.

Stochastic expansion planning of integrated energy system: A benders-based decomposition approach

This paper introduces a two-stage stochastic optimization model for the renewables-transmission expansion planning (RTEP) problem to obtain the optimal size and site of the renewable energy generating unit, as well as the investment decisions related to transmission lines and gas pipelines. The uncertainties associated with demand growth and stochastic renewable sources production levels are considered via a series of scenarios, and then, the scenario-reduction approach, i.e., the k-medoids method, is applied to reduce the computation burden. In addition, the gas flow-pressure difference steady-state formulations in the expansion planning model are reconstructed convexly using second-order cone constraints. A Benders-based decomposition method is adopted as a solution methodology in the co-planning problem. The proposed model was simulated on a modified IEEE 39-bus and Belgian gas-20 energy test network, and the simulation results validate the correctness and applicability of the presented approaches.

AC Transmission Network Expansion Planning Using the Line-Wise Model for Representing Meshed Transmission Networks

In this paper, a Line-Wise (LW) formulation of the AC Transmission Network Expansion Planning (AC-TNEP) problem for meshed transmission networks is proposed. The proposed formulation is then relaxed using a novel Quadratic Convex (QC) relaxation that can handle the mixed-integer nature of the problem and be solved efficiently using commercial solvers. The exact and relaxed formulations have been integrated into an algorithm for solving the AC-TNEP problem that has been introduced as an enhancement of an existing algorithm in the literature for obtaining feasible solutions of the AC-TNEP problem upon the use of convex relaxations to solve it. The AC-TNEP problem is solved for different scenarios that involve test cases ranging from 6 to 118 buses. The obtained solutions for the 6-bus to 46-bus test cases are shown to be globally optimal or reinforced to identical or better than the available solutions in the literature. Moreover, as distinguished from solutions in the literature, the proposed algorithm does not utilize approximations and heuristic constraints that are used to ease solving the AC-TNEP problem and were found to potentially lead to locally optimal solutions. Furthermore, the proposed algorithm is used to solve the AC-TNEP problem for the 87-bus and 118-bus test cases to establish its ability to solve for larger test cases. Extensions of the proposed algorithm to account for Reactive Power Planning (RPP) and dynamic planning are studied to further demonstrate its merits.

Impact of Electricity Price Expectation in the Planning Period on the Evolution of Generation Expansion Planning in the Market Environment

With the continuous promotion of China’s electricity market reform, the introduction of competition in the power generation market provides a new research direction for the generation expansion planning (GEP) problem, which is of great significance in the promotion of the optimization of the power energy structure. In the context of marketization, the electricity price expectation during the planning period is a key factor of GEP for independent power generation groups. There is some literature showing that the electricity price expectation in the planning period can be estimated according to certain laws of market supply and demand, while it seems to us that a future Pay as Bid (PAB) mechanism is better to determine the electricity price expectation. In this paper, to explore the impact of these two different electricity price formation mechanisms on the evolution of the generation market, a multi-agent framework is first established to describe the interaction process among the generation market agents; then, a GEP model for independent power generation groups is developed in the market competition environment, and four representative scenarios are finally designed for detailed comparative studies. Based on these case studies, the conclusion can be summarized as: (1) the PAB bidding mechanism has a lower electricity price and higher market installed capacity almost all the time during the whole planning period for all four scenarios; (2) it is more important that PAB can reduce the impact of parameter uncertainty in the laws of market supply and demand, which can obtain more reliable and reasonable results regarding the long-term evolution of the generation market.

A Bilevel Stochastic Optimization Framework for Market-Oriented Transmission Expansion Planning Considering Market Power

Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush−Kuhn−Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants.

Improved binary particle swarm optimization for the deterministic security-constrained transmission network expansion planning problem

- This paper proposes an improved version of Binary Particle Swarm Optimization (BPSO) to solve the security-constrained transmission network expansion planning (TNEP) problem using the DC network model. Some modifications, such as superior population configurations, are made to improve the efficiency of the BPSO by adapting it to the needs of the TNEP to obtain better results. A parallel implementation of the improved BPSO reduces execution times. Transmission losses are included using a quadratic function and piecewise linear approximation approach. Considering transmission losses in the long-term planning horizon can avoid underinvestment in network capacity and result in a different network expansion plan. The proposed approach is validated with numerical simulations of the classic Garver system, and its performance is tested on the IEEE 24-bus and 118-bus systems for a ten-year planning horizon. The simulation results are compared to those obtained from classic BPSO to verify the efficiency of the improved version of the BPSO.

Power Distribution Expansion Planning in the Presence of Wholesale Multimarkets

By deregulating the countries' electricity industry, the market players must adapt their performance to the deregulated environment. In this article, a risk-based stochastic optimization framework is proposed to model the participation of distribution system operator (DSO) in distribution expansion planning (DEP) problems in the presence of electricity wholesale multimarkets. Based on the proposed methodology in this article, the DSOs will be able to invest in the DEP by taking the benefits and imposed risks of the existing electricity multimarkets, i.e., forward contract, day-ahead, and balancing markets, to manage the risks of long-term uncertainties. The DSOs, who are the only retail suppliers in a specific region, can cover their DEP costs by offering fair retail prices to the retail consumers. Besides, DSOs could form diverse long- and short-term portfolios from the different electricity markets to procure the forecasted real loads and loss power of the network over the planning horizon. The diverse portfolio of the suppliers and a fair retail price can satisfy the DSOs to consider the multimarkets in the DEP process. Furthermore, the risk of uncertainties is modeled using the method of conditional value at risk (CVaR). Based on the obtained results, the DSO can reduce network loss costs by procuring power from markets rather than increasing the installed branches' ampacity by considering multimarkets and market price uncertainties. Besides, the obtained profit of DSO is increased by 12.16% in the proposed electricity multimarket environment.

Multi-objective transmission expansion planning based on Pareto dominance and neural networks

• A novel TEP approach to consider the reliability criterion over the optimization. • The probabilistic feature of reliability is considered in the TEP problem. • The multi-objective TEP problem is solved in an efficient manner by the ND-MCS. • The proposed ND-MCS leads to a more targeted and efficient search in solution space. • The planner decisions can be made by applying a fuzzy criterion after the convergence. This paper presents an algorithm to solve the multi-objective transmission expansion planning (TEP) problem including the investment and reliability criteria. The reliability is considered by using the Expected energy not supplied (EENS) index. The main contribution consists on handling the reliability criterion in the optimization process, which tends to provide solutions with better trade-off between the mentioned criteria. For that purpose, a novel probabilistic algorithm called non-dominated Monte Carlo simulation (ND-MCS) is proposed to allow solving the multi-objective TEP problem with suitable computational effort and efficacy even considering the probabilistic feature of reliability in the optimization. In addition, a Support Vector Machine (SVM) network is applied embedded within the ND-MCS. The proposed methodology integrates the Pareto dominance method as a convergence criterion to MCS and a fuzzy criterion to support the decision making. The effectiveness of the proposed approach is tested in three systems, including a practical Brazilian network.

Robust Dynamic TEP With an Security Criterion: A Computationally Efficient Model

This paper presents a hybrid column-and-constraint-generation augmented-Lagrangian algorithm to efficiently solve the robust security-constrained dynamic transmission expansion planning (TEP) problem. The column-and-constraint generation algorithm separates the TEP problem into a master problem and a set of subproblems decomposable by time period. Additionally, the computationally expensive master problem is decomposed into three computationally efficient sub-master problems: an upper-master quadratic problem, a middle-master quadratic unconstrained binary problem, and a lower-master quadratic unconstrained problem. A set of auxiliary variables are used to relax as real ones the binary variables corresponding to the status of candidate transmission lines enabling the master problem decomposition. The solutions of the three sub-master problems are coordinated using a three-block alternating direction method of multipliers algorithm to enforce binary variables to be binary. An initialization strategy based on load shedding is used to enhance the performance of the proposed algorithm. Simulation results on the IEEE 118-bus test system show the efficient performance of the proposed algorithm for solving security-constrained dynamic TEP problems.

Application of hierarchical clustering on electricity demand of electric vehicles for GEP problems

Increasing fossil fuel consumption and consequently the effects of greenhouse gases (GHGs) on the environment and economy are a major concern for all nations and governments. Electric vehicles (EVs) with plug-in capabilities have the potential to ease such problems. However, the extracted power from the grid for charging the EVs' batteries will significantly impact daily power demand. To satisfy the increasing demand and ensure generation capacity adequacy, the generation expansion planning (GEP) problem is solved to determine the investment decisions for electricity generation sources. Even though there are no centralized utilities for generation planning in most markets, there is still a need to realistically solve the GEP problems and find the optimal investment decisions to tailor the incentives used by most governments to guide the market. There is also a need for a tool to analyze the effect of different charging power levels, charging policies, and penetration levels. The main goal of this paper is to provide a tool to determine realistic optimal investment plans and evaluate different cases. It is also very important to consider the stochastic nature of the electricity demand in GEP problems. We propose a scenario-based stochastic programming model to incorporate the variability in the electricity demand due to EV charging through a set of scenarios generated by Monte Carlo Simulation. The methodology starts with applying a simulation method to generate the electricity demand of EVs by considering all the possible factors affecting EVs' demand. Each iteration of this simulation represents a possible demand profile as a result of penetrating the EVs into the market. Using all these demand profiles in GEP is preferable, but it is not computationally efficient. Computational tractability is achieved by using the clustering technique to reduce the size of such scenarios. We propose clustering methods to select a representative set from the data sets generated by the simulation and integrate EVs into GEP problems by using the selected set. The GEP models are defined to represent EVs' demand explicitly and then solved to imply the benefit of the suggested methods. The results show that GEP models with a representative set produce more realistic solutions than the GEP models including only average EVs demand. To select representative sets, different clustering techniques and distance measurements are used and compared with respect to their performances. Two different methods are defined to choose the best number of clusters: the silhouette coefficient method and the

A data‐driven inertia adequacy‐based approach for sustainable expansion planning in distributed generations‐penetrated power grids

Reduced rotational inertia in power grids due to increasing penetration levels of distributed generations (DGs) may lead to degraded performance of the traditional frequency control scheme. In response to this challenge, inertia adequacy has recently emerged as a new research area in modern power systems. Accordingly, an attempt is made in this paper to tackle inertia adequacy in the generation expansion planning (GEP) problem. This in turn helps to realize sustainable economic development. For this purpose, the inertia adequacy constraint is tied to the frequency stability metrics. In other words, minimum permissible inertia that satisfies frequency dynamic standards is defined as an inertia adequacy constraint in the GEP formulation. Further, an experimentally validated model of a cluster of DGs is employed to realize a penetrated power grid to deal with sustainable planning development. Finally, an iterative-based algorithm is proposed to expand the system with minimum cost and with the highest permissible penetration level of DGs. The effectiveness of the proposed algorithm is examined in the Garver test system.

Towards a new effective strategy to obtain optimal radial structure in power distribution networks: Graph theory-based topology assessment

Power distribution networks (PDNs) are principally operated and planned in a radial—open-loop—structure to satisfy several techno-economic goals. It is, therefore, indispensable to develop new practical strategies to rigorously investigate the radial structure-related limitation in the operation and planning of the PDNs. In this study, after a thorough and critical review of existing strategies in the literature, a new effective graph theory-based topology assessment strategy (GT-ToST) is outlined to examine the radial structure-related limitation. Then, both the distribution branch reconfiguration (DBR) problem and the multi-stage joint distributed generation and distribution network expansion planning (DG&DNEP) problem (most appropriate for the short and long-term horizons, respectively) are employed to explore the feasibility and practicality of the newly proposed strategy compared to the existing ones. The proficiency of the proposed strategy is investigated for the DBR problem with a modified 33-bus PDN and a modified real-world 177-bus PDN in Rio de Janeiro, as well as for the DG&DNEP problem with a modified 27-bus PDN and a modified real-world 104-bus PDN in the northeast part of Brazil. The obtained results from the illustrative examples and case studies prove the effectiveness of the proposed GT-ToST compared to the existing strategies.

Robust Transmission Expansion Planning of Ultrahigh-Voltage AC–DC Hybrid Grids

With the ever-increasing installation of large-capacity ultrahigh-voltage direct current (UHVdc) links, the “strong dc link and weak ac network” issue has become prominent for many regional grids in China. The transmission expansion planning (TEP) problem of such grids has been facing a significant challenge to cope with the coordination between the UHVdc links and the ultrahigh/high voltage alternating current (UHVac/HVac) network. To handle this issue, this article proposes a multistage robust TEP (RTEP) model of ultrahigh-voltage ac–dc hybrid grids. This model explicitly takes into account multiple types of uncertainties, i.e., credible contingencies occurring in the ac network, large power imbalances due to the UHVdc bipole blocking, as well as the long-/short-term uncertainty. Wasserstein metric is used to reformulate the uncertainty set and the worst-case constraints. A column-and-constraint generation based solution approach is developed in order to ensure tractability of the RTEP model. The effectiveness of the proposed RTEP is verified by numerical testing on a practical large-scale power grid.