Expansion Planning Model Research Articles

Machine Learning-Enhanced Benders Decomposition Approach for the Multi-Stage Stochastic Transmission Expansion Planning Problem

The necessary decarbonization efforts in energy sectors entail integrating flexible assets and increased levels of uncertainty for the planning and operation of power systems. To cope with this in a cost-effective manner, transmission expansion planning (TEP) models need to incorporate progressively more details to represent potential long-term system developments and the operation of power grids with intermittent renewable generation. However, the increased modeling complexities of TEP exercises can easily lead to computationally intractable optimization problems. Currently, most techniques that address computational intractability alter the original problem, thus neglecting critical modeling aspects or affecting the structure of the optimal solution. In this paper, we propose an alternative approach to significantly alleviate the computational burden of large-scale TEP problems. Our approach integrates machine learning (ML) with the well-established Benders decomposition to manage the problem size while preserving solution quality. The proposed ML-enhanced Multicut Benders Decomposition algorithm improves computational efficiency by identifying effective and ineffective optimality cuts via supervised learning techniques. We illustrate the benefits of the proposed methodology by solving multi-stage TEP problems of different sizes based on the IEEE24 and IEEE118 test systems, while also considering energy storage investment options..

Expansion planning of hybrid electrical and thermal systems using reconfiguration and adaptive bat algorithm

_ This study introduces a comprehensive model for the concurrent expansion planning of various energy systems and their associated equipment. The need to reduce network costs, emissions, losses, and feeder loading, as well as to enhance network reliability and voltage profile, mandates the utilization of proper multi-objective planning models that respect all network constraints. The introduced framework includes units for generating both electrical and thermal energies. The model leverages conventional expansion alternatives such as the installation of new lines, network reconfiguration, rewiring, and the addition of new thermal and electrical generating units to the network. Expansion planning involves determining the optimal time, location, and type of new installations to meet future energy demands while minimizing costs and emissions. Reconfiguration refers to altering the network topology to improve reliability and reduce losses. The proposed expansion planning is formulated as a discrete, nonlinear, and non-convex optimization problem, which is solved using the Self Adaptive Learning Bat Algorithm (SALBA). This algorithm improves convergence speed and increases the diversity of the search population, enhancing the likelihood of finding the global optimum. Numerical simulations of the proposed methodology on two modified standard IEEE test systems corroborate the efficacy and feasibility of the suggested approach. Key innovations include the comprehensive modeling for concurrent expansion planning, the use of an advanced optimization algorithm, and a focus on reducing costs, emissions, losses, and feeder loading while enhancing network reliability and voltage profile.

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.

Rational capacity investment for renewable hydrogen-based steelmaking systems: A multi-stage expansion planning strategy

To improve energy efficiency and mitigate environmental impact, the iron and steel industry (ISI) is responsible for implementing a low-carbon transition. The renewable hydrogen-based steelmaking system (RHSS) has emerged as an innovative energy system in the pathway of reducing the carbon footprint of ISI. Nonetheless, the sustainable development requirements of RHSS emphasize the critical need for well-planned capacity investments to boost its economic viability. This study introduces a novel planning strategy for RHSS referred to as a multi-stage expansion planning (MSEP) model, which is aimed to minimize the levelized cost of crude steel over the planning horizon from 2025 to 2050 (EU climate neutrality year). The MSEP model incorporates the construction sequence and dynamic techno-economic parameters to formulate investment strategies that adapt to changing system requirements and external conditions over the planning horizon. To address the complexity of the MSEP model, a rolling-horizon approach (RHA) is proposed to solve the model sequentially while integrating updated information. The proposed approach is benchmarked against both the single-stage approach and the perfect-sight approach through case studies. The numerical results show that the proposed RHA (i) guarantees a rational capacity investment strategy for RHSS considering the construction sequence and dynamic techno-economic parameters over multiple planning stages; (ii) achieves a reduction in the levelized cost of crude steel by approximately 50% relative to the single-stage approach; (iii) resolves the convergence issues encountered with the perfect-sight approach while achieving an optimal solution in a reasonable time frame. Additionally, sensitivity analysis evaluates the uncertainties of multiple factors on the planning results, while the robustness analysis confirms the applicability and adaptability of RHA across various scenarios.

Insights from a Comprehensive Capacity Expansion Planning Modeling on the Operation and Value of Hydropower Plants under High Renewable Penetrations

This paper presents a quantitative assessment of the value of hydroelectric power plants (HPPs) in power systems with a significant penetration of variable renewable energy sources (VRESs). Through a capacity expansion planning (CEP) model that incorporates a detailed representation of HPP operating principles, the study investigates the construction and application of HPP rule curves essential for seasonal operation. A comparative analysis is also conducted between the proposed rule curve formulation and alternative modeling techniques from the literature. The CEP model optimizes installed capacities per technology to achieve predefined VRES penetration targets, considering hourly granularity and separate rule curves for each HPP. A case study involving twelve reservoir hydropower stations and two open-loop pumped hydro stations is examined, accounting for standalone plants and cascaded hydro systems across six river basins. The study evaluates the additional generation and storage required to replace the hydropower fleet under high VRES penetration levels, assessing the resulting increases in total system cost emanating from introducing such new investments. Furthermore, the study approximates the storage capabilities of HPPs and investigates the impact of simplified HPP modeling on system operation and investment decisions. Overall, the findings underscore the importance of reevaluating hydro rule curves for future high VRES penetration conditions and highlight the significance of HPPs in the energy transition towards carbon neutrality.

Merchant EV charging station expansion planning

The significant expansion of Electric Vehicles (EV) creates an uncertain load demand that may pose many challenges to conventional planning methods, especially at the distribution network level. The development of EV technology requires charging infrastructure, which must be considered in the Distribution System Expansion Planning (DSEP). Due to the presence of EV and the load they impose on the distribution system, the planning of EV charging stations is done simultaneously with the DSEP so that the system operator can properly consider the technical constraints of the network and operational constraints. This paper presents a bi-level model for EV charging station expansion planning. The main purpose of the first level problem is expansion planning of charging stations and distribution system. But the charging stations are mostly built by a merchant investor, and they do so when it is profitable and has a reasonable risk. Therefore, the merchant investor should be encouraged to build a charging station in the planned areas. For this reason, in the second level problem, the profitability of the charging station and its risk are examined. To solve this problem, genetic algorithm (GA) has been used. Finally, to test the proposed model, the simulation was performed on a modified 69-bus IEEE network.

Multiobjective Stochastic Power System Expansion Planning Considering Wind Farms and Demand Response

In recent years, due to the increase in electricity consumption and environmental problems, power system expansion planning requires new technologies. In this regard, the incorporation of renewable energy sources (RESs) and utilization of demand response (DR) programs need disruptive variations in the present power system configurations. This paper proposes a mixed-integer linear robust multiobjective model for generation and transmission expansion planning (GEP-TEP) taking into account wind farms (WFs) and a DR program based on time-of-use pricing. The suggested model is presented via mixed-integer nonlinear programming (MINLP) at the first stage and then transformed into mixed-integer linear programming (MILP) using the Big M linearization technique. Moreover, long- and short-term uncertainties of load demand and WFs are incorporated into the recommended model to achieve more accurate results. The interval-based method is applied for taking into account long-term uncertainties while the scenario-based stochastic model is applied for modeling short-term uncertainties in the recommended GEP–TEP model. Lastly, the suggested model is investigated on various standard test systems to evaluate the effectiveness of the GEP-TEP model.

Hydrothermal simulations in Brazil using batteries - First Results

The share of renewable energy sources has increased worldwide, especially those considered unconventional (i.e. without considering hydropower). Besides proved as economically competitive, these sources cause less environmental impacts when compared to other sources of traditional power generation such as coal and oil. However, solar and wind power plants are intermittent, i.e., the generation varies according to the availability of the respective natural resources and therefore are considered non-dispatchable by the System Operator (SO). Because of that, the electrical systems must be able to somehow compensate the variability from the non-dispatchable energy sources to meet the supply-demand equilibrium. Storage technologies such as electrochemical (e.g. batteries) and electromechanical (e.g. flywheel) could be used in that sense. Recent developments of these technologies opened space for several ancillary services and products to be offered by the storage systems to the electrical system. In addition to that, the sustained reduction in operation and maintenance (O&M) costs summed to the payments for providing ancillary services could make some of these technologies economically attractive, under certain conditions. Given this new scenario, the representation of these storage systems in the expansion planning and power systems mathematical models becomes necessary. In this study, we simulated the Brazilian electrical system at 2035, considering batteries (corresponding to 7% of the installed capacity) and a 30% share of unconventional renewable energy in the system generation capacity.

A generation and transmission expansion planning model for the electricity market with decarbonization policies

Globally, the power sector must undergo a profound transition to achieve the decarbonization development targets. Various roadmaps are implemented, but only from a macro perspective, lacking the consideration of the electricity market rules. In this paper, we develop and present a market-driven generation and transmission expansion planning (MGTEP) model considering the effectiveness of the electricity market. Specifically, generation and transmission companies incorporate hourly market trading and annual capacity investment into strategic decisions to maximize their profits, with the supply function equilibrium model to analyze bidding behaviors. An equivalent quadratic programming formulation is deployed to solve the trilevel MGTEP model. Meanwhile, the MGTEP model is coupled with decarbonization policies to support the state and federal government in assessing energy transition strategies. We implement the MGTEP model with carbon emission allowance and carbon tax policies for the southern China electricity market to achieve carbon peaking by 2030. Carbon emission allowance adopts an intensity-based cap based on generation companies' historical output. The case study results show that 50 % carbon emission allowance or 400 CNY/t carbon tax is required but with several drawbacks, including unsatisfactory decarbonization effect, excessive economic sacrifice, etc. Finally, the case study is extended to dual-track policies with different combinations of policies. An optimal combination is 70 % carbon emission allowance and 160 CNY/t carbon tax. In this case, the power sector's carbon dioxide emissions and electricity prices in the southern China electricity market would increase to 554.6 Mt and 864.34 CNY/MWh in 2030, respectively, along with a carbon price of 850 CNY/t.

Developing a new flexibility-oriented model for generation expansion planning studies of renewable-based energy systems

This paper presents a flexibility-oriented generation expansion planning (GEP) model with the goal of increasing renewable energy penetration. The model incorporates GEP and unit commitment while considering improved reserve requirements. Utilizing GEP and unit commitment results in considering short-term operational constraints. Furthermore, given the increase in renewable portfolio standards (RPS) and the need for accurate reserve requirements determination, it is essential to consider improved reserve requirements in the proposed model. Moreover, this model utilizes a metric that measures power system flexibility deficiency and leads to flexible power system expansion by integrating it into the objective function. The flexibility-oriented GEP model is developed using mixed-integer linear programming and applied to a scaled-sized case study representing the national power system of Iran with a twenty-year planning horizon. The results show that neglecting improved reserve requirements leads to plans short on flexibility, and considering these requirements substantially declines the upward flexibility violation costs by 68% under the base scenario and 87% under increasing non-hydro RPS scenario. Furthermore, using the flexibility metric coupled with improved reserve requirements changes the optimal path for power system expansion and reduces the risk of flexibility deficiency. Also, increasing RPS by 35% would strongly depend on developing fast-response dispatchable generation units in the years before renewable energy resources expansion; however it doesn’t impose a significant extra cost of planning and the total cost will increase just by 9.43%.

Stochastic model for active distribution networks planning: An analysis of the combination of active network management schemes

The widespread adoption of distributed generation (DG) is changing the operation of distribution networks. To increase the control of power flows and avoid the detriments of DG intermittency, active distribution networks (ADN) emerge as a feasible solution. In this paper, we propose a convex model for ADN expansion planning. Four active network management (ANM) schemes are considered: DG active power curtailment, DG reactive power control, on-load tap changer (OLTC) tap adjustment, and shunt compensation device control. The problem is formulated as a mixed integer second-order cone programming problem (MISOCP) using the distflow equations and second-order cone relaxations (SOCR). By scenario analysis, we address the uncertainty associated with power demand, renewable generation, and electricity prices. The proposed model is used to study the benefits of different combinations of ANM schemes to a modified IEEE 33-bus system and compare them with the individual benefits of each scheme. The results indicate that ANM schemes can reduce total network costs, reduce losses, delay network reinforcement, and improve the voltage profile. In addition, some combinations of schemes develop synergies in which the combined economic benefits are greater than the sum of the individual benefits.

Comprehensive optimization framework for transmission expansion planning with fractional frequency transmission system

AbstractThe Fractional Frequency Transmission System (FFTS) operates with low frequency to decrease the electrical length of AC transmission lines, consequently enhancing transmission capacity. The integration of renewable energy sources via FFTS will significantly impact power system planning. This paper presents a Fractional Frequency Transmission Expansion Planning (FF‐TEP) model, which considers the interaction between FFTS and the industrial‐frequency power grid. This model addresses the challenges posed by the integration of offshore wind power through FFTS, and takes several key factors into account, including the active power coupling of Modular Multilevel Matrix Converter (M3C), inverter capacity, and converter transformer capacity. To address the non‐convexity caused by AC power flow, this paper introduces a Genetic‐Particle Swarm Optimization algorithm (G‐PSO) with dynamic penalties tailored to the M3C structure. This approach incorporates both crossover and mutation operators from Genetic Algorithms (GA) into Particle Swarm Optimization (PSO). The penalty function dynamically adapts according to the M3C structure, resulting in improved global optimization while maintaining computational efficiency. The results of two case studies demonstrate that FFTS can significantly enhance transmission capacity while reducing cable charging power. This reduces investment costs and decreases voltage offset issues.

Stochastic MILP Model for Merging EV Charging Stations with Active Distribution System Expansion Planning by considering Uncertainties

Radial Power Distribution Networks (PDNs) often suffer from limited reliability, flexibility, and efficiency, leading to service interruptions. Planning for radial PDNs is essential to enhance redundancy resilience, reduce disruptions, and improve overall efficiency. However, traditional PDN planning methods have become obsolete due to the proliferation of Distributed Generation (DG) resources and energy storage systems. Additionally, the rise of Electric Vehicles (EVs) demands sophisticated charging infrastructure planning. This article presents a Mixed-Integer Linear Programming (MILP) model for joint expansion planning of PDN and Electric Vehicle Charging Stations (EVCSs). The model takes into account the construction or reinforcement of substations and circuits, along with the integration of EVs, the installation of DGs, and the placement of capacitor banks, all regarded as traditional conventional expansion options alternatives. To address uncertainties associated with DG generation, conventional loads, and EV demand, our model identifies optimal installation and asset locations. We formulate this as a stochastic scenario-based program with chance constraints for Power Distribution Network Expansion Planning (PDNEP), minimizing investment, operational, and energy loss cost costs over a planning horizon. Through two deterministic and stochastic approaches, encompassing six case studies on an 18-node test system, we evaluate the effectiveness of our model. Results are further validated on a 54-node system, confirming the model’s robustness. Notably, the numerical findings underscore the substantial cost reduction achieved by including EVCSs in the stochastic expansion planning approach, demonstrating its cost-effectiveness. In case study I, where all EVs charge at home during peak hours, it’s the worst case for the PDN. The 54-node system, more complex, demands longer computational time. In the 18-node system, costs improve from 9.97% (case study II) to 3.96% (case study VI) versus the worst-case (case I). In the 54-node system, improvements range from 10.47% (case study II) to 1.40% (case study VI). As a result, In comparative analyses against deterministic and stochastic approaches, our model consistently outperforms in diverse test case studies. The proposed model’s adaptability to address uncertainties underscores its suitability for solving the PDNEP problem in PND.

An expansion planning model for strategic visioning of active distribution network in the presence of local electricity market

AbstractEmergence of different stakeholders with contrary objectives in active distribution network (ADN) requires for a fair network expansion planning that considers all of the contrary objectives. This paper provides an expansion planning model for ADN strategic visioning from electric distribution stakeholders' organization (EDSO) perspective, which takes into account the objectives of all stakeholders. The stakeholders are network owner, active customers (ACs), consumers, and environmental regulatory body (ERB). The proposed model is multistage bi‐level, where the upper‐level minimizes the present value of the total costs imposed to all ADN stakeholders and the lower‐level minimizes the total generation costs within the distribution‐level electricity market. The Karush–Kuhn–Tucker optimality conditions and the linearization techniques are employed through which the model is converted to mixed integer linear programming which can be tackled effectively. The model provides a visionary expansion plan that policymaker must legislate to realize it. Effectiveness of the model in providing a visionary expansion plan considering EDSO's perspective in making cost effective planning decisions per social welfare goals is verified through several case studies on 33‐bus standard test system. According to the simulation results, transition from DSO to EDSO in the presence of low‐capacity ACs improves social welfare by 5%. But this improvement is up to 70% in the presence of high‐capacity ACs.

Demand response programs: Comparing price signals and direct load control

Canada's electric power system is responsible for approximately 9 % of national emissions, 53 % of which occur in the province of Alberta. Integrating new variable renewable energy resources is a key part of the supply-side decarbonization pathway, while end-use electrification unlocks further opportunities on the demand side. The inherent variability of variable renewable energy output necessitates network flexibility. Supply-side flexibility solutions require significant investment, but demand-side management programs have potential to deliver network flexibility at a lower cost. An integrated framework consisting of demand and supply models investigates the efficacy of demand response programs for improving network flexibility in Alberta's power system, as measured by multiple operational metrics. The framework is applied to two demand response programs: real-time pricing and direct load control. These programs are assessed for two generation capacity mixes derived from an expansion planning model. Results indicate that substantial network flexibility benefits are achievable in a zero-emission power system via both programs resulting in avoided wind curtailment by 7.7 %. Improvement in operational costs, up to 1.4 % of the base output, is also observed in all scenarios accompanied by savings in household power bill expenditure by up to 15 %. These improvements, however, are only achieved fully when sufficient flexible load is provided.

Harmonized geospatial data to support infrastructure siting feasibility planning for energy system transitions

Climate change, energy system transitions, and socioeconomic change are compounding influences affecting the growth of electricity demand. While energy efficiency initiatives and distributed resources can address a significant amount of this demand, the United States will likely still need new utility-scale generation resources. The energy sector uses capacity expansion planning models to determine the aggregate need for new generation, but these models are typically at the state or regional scale and are not equipped to address the wide range of location- and technology-specific issues that are increasingly a factor in power plant siting. To help address these challenges, we have developed the Geospatial Raster Input Data for Capacity Expansion Regional Feasibility (GRIDCERF) data package, a high-resolution product to evaluate siting suitability for renewable and non-renewable power plants in the conterminous United States. GRIDCERF offers 264 suitability layers for use with 56 power plant technologies in a harmonized format that can be easily ingested by geospatially-enabled modeling software allowing for customization to robustly address science objectives when evaluating varying future conditions.

A Wasserstein Distance-Based Distributionally Robust Chance-Constrained Clustered Generation Expansion Planning Considering Flexible Resource Investments

This paper proposes a distributionally robust chance-constrained (DRCC) model for the clustered generation expansion planning (CGEP) of power systems. The proposed two-stage model minimizes the first-stage total cost along with the second-stage expected penalty cost with the worst-case probability distribution of renewable energy generation. A unit commitment model with flexibility constraints is embedded into the planning model, and the uncertainty is modeled via a Wasserstein distance (WD)-based ambiguity set. Demand-side resources (DSR) and concentrating solar power (CSP) plants are considered as candidates in the DRCC-CGEP model to enhance system flexibility, and the solution efficiency is improved through unit clustering. Furthermore, based on strong duality theory along with affine decision rule and conditional-value-at-risk approximation method, the proposed planning model is reformulated as a tractable mixed-integer linear programming problem. Numerical results show that the proposed WD-based DRCC-CGEP model is effective in improving the economics of the planning decisions while ensuring system reliability and maintaining computational efficiency.

Chance-constrained multi-stage stochastic energy system expansion planning with demand satisfaction flexibility

A classic multi-period stochastic energy system expansion planning (ESEP) model aims to address demand uncertainty by requiring immediate demand satisfaction for all scenarios. However, this approach may result in an expensive system that deviates from the planner’s long-term goals, especially when facing unexpectedly high demand scenarios. To address this issue, we propose a chance-constrained stochastic multi-stage ESEP model that allows for a portion of demand to remain unmet in specific periods while still ensuring complete demand satisfaction during most of the planning horizon, including the final period. This approach provides more time flexibility to build infrastructure and assess needs, ultimately reducing costs and allowing for a broader view of infrastructure planning options. To solve the chance-constrained stochastic model, we introduce a binary-search-based progressive hedging algorithm heuristic, which is particularly useful for large-scale models. We demonstrate the effectiveness and benefits of implementing the chance-constrained model through a case study of Rwanda using real-world data.

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.

Optimization-based expansion planning for power and hydrogen systems with feedback from a unit commitment model

This paper presents a novel long-term model for the joint expansion planning of power and hydrogen systems with short-term operational considerations. We propose linear reserve constraints with adjustable parameters within the planning model to address the reliability requirements from significant levels of variable renewable generation. These adjustable parameters are calibrated using an iterative training methodology that connects the long-term planning model with a short-term unit commitment model. A crucial aspect of our methodology is the iterative improvement of investment decisions through the feedback obtained by evaluating the operational performance of the investment decisions in different scenarios computed under the unit commitment model. Computational experiments in a case study of a large-scale Chilean power-hydrogen system show the effects of the proposed methodology on capacity expansion recommendations, where a correct balance between variable and flexible technologies is obtained. Moreover, when simulating the operation of the system for a full year, we observe that the proposed methodology generates an investment plan that achieves a lower total cost compared to other methodologies commonly used in the literature. Additional experiments in 100% renewable scenarios show how conventional methodologies reaches levels of not-supplied-energy between 2%–7%, while the proposed methodology achieves less than 1% in the same metric.