Transmission Expansion Planning Model 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.

Integrated transmission expansion planning incorporating fault current limiting devices and thyristor-controlled series compensation using meta-heuristic optimization techniques

Transmission expansion planning (TEP) is a vital process of ensuring power systems' reliable and efficient operation. The optimization of TEP is a complex challenge, necessitating the application of mathematical programming techniques and meta-heuristics. However, selecting the right optimization algorithm is crucial, as each algorithm has its strengths and limitations. Therefore, testing new optimization algorithms is essential to enhance the toolbox of methods. This paper presents a comprehensive study on the application of ten recent meta-heuristic algorithms for solving the TEP problem across three distinct power networks varying in scale. The ten meta-heuristic algorithms considered in this study include Sinh Cosh Optimizer, Walrus Optimizer, Snow Geese Algorithm, Triangulation Topology Aggregation Optimizer, Electric Eel Foraging Optimization, Kepler Optimization Algorithm (KOA), Dung Beetle Optimizer, Sea-Horse Optimizer, Special Relativity Search, and White Shark Optimizer (WSO). Three TEP models incorporating fault current limiters and thyristor-controlled series compensation devices are utilized to evaluate the performance of the meta-heuristic algorithms, each representing a different scale and complexity level. Factors such as convergence speed, solution quality, and scalability are considered in evaluating the algorithms’ performance. The results demonstrated that KOA achieved the best performance across all tested systems in terms of solution quality. KOA’s average value was 6.8% lower than the second-best algorithm in some case studies. Additionally, the results indicated that WSO required approximately 2–3 times less time than the other algorithms. However, despite WSO’s rapid convergence, its average solution value was comparatively higher than that of some other algorithms. In TEP, prioritizing solution quality is paramount over algorithm speed.

Multi-objectives transmission expansion planning considering energy storage systems and high penetration of renewables and electric vehicles under uncertain conditions

Transmission expansion planning (TEP) integrating electric vehicles (EVs) and renewable energy sources (RESs) is pivotal for the transition toward cleaner and more sustainable energy systems. One of the biggest challenges in TEP with EVs and RESs is the uncertainty inherent in their behaviors. Managing this uncertainty is critical for ensuring the grid's reliability and resilience, and for facilitating a seamless transition to EVs. A potent method for addressing uncertainties in power systems is the application of a scenario-based approach. However, the efficiency of this approach is contingent upon an increase in the number of representative scenarios, which, in turn, escalates computational time, making solving the TEP problem a crucial task. To tackle these challenges, this paper proposes a multi-objective resilience model for TEP, to advance towards more sustainable energy systems. The model seeks to strike a balance between economic, environmental, and technical considerations by minimizing planning costs, carbon dioxide emissions, and enhancing the voltage profile. Furthermore, the paper proposes a cascaded intelligent strategy to handle uncertainties and reduce computational complexity by reducing the number of representative scenarios without compromising system reliability. The adaptive neuro-inference system is designed to manage long-term uncertainties, while two fuzzy systems are developed to address short-term uncertainties. The problem is formulated as a complex non-linear multi-objective optimization problem. To address this, a hybrid approach combining the mountain gazelle optimizer and the multi-objective salp swarm optimizer is developed to solve the problem. The efficacy of the proposed method is validated on two separate test systems, demonstrating its superiority in maintaining system reliability while reducing computing time by at least 92 % in comparison with the considered traditional methods. The results also highlight the superior performance of the proposed hybrid algorithm compared to existing meta-heuristic algorithms in solving the TEP.

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.

Security-constrained Transmission Expansion Planning with N-k Security Criterion and Transient Stability

The integration of large-scale wind power into the power system is a global trend in response to climate change, however, the intermittent nature of wind power presents new challenges for planners. Conventional transmission expansion planning (TEP) methods, which only consider N-1 static security, may not ensure the security of multiple contingencies and transient stability in a large-scale wind power integration scenario. Incorporating N-k-based static constraints and dynamic constraints, such as differential-algebraic-equations-(DAEs)-based transient stability constraints, into TEP can result in a heavy computational burden and render the TEP model intractable. This paper proposes a tractable mathematical model (S&DSTEP) for joint consideration of static and dynamic security in TEP with wind power. The uncertain wind power generation is captured through selected scenarios and the model is divided into a TEP master problem and multiple sub-problems for evaluating static security and transient stability. Static security is determined by the use of fault chain theory (FCT), avoiding the need for enumerating all N-k contingencies, thus reducing the computational burden. Transient stability is analyzed through the use of stabilizing cuts generated from the extended equal-area criteria (EEAC) rather than dynamic constraints expressed as DAEs. The proposed model is verified on the modified New England 39-bus system and IEEE 118-bus system, demonstrating its ability to consider transient stability while being more computationally efficient compared to the robust method that directly incorporates all contingency scenarios.

Bi-level transmission expansion planning considering prohibited operating zones and multi-fuel units

Transmission expansion planning (TEP) provides a solution to economically and securely expand the transmission network. In this context, the bi-level frameworks are receiving increased attention considering a DC or (linear/convex) AC economic dispatch at the lower level. However, the prohibited operating zones (POZ) and multi-fuel units (MFU) are ignored to be modeled at the lower level, while it plays a vital role in the output results. To this end, this article presents a bi-level TEP model that considers POZ and MFU. Incorporating these two issues into the lower level’s economic dispatch problem introduces more complexity to the optimization problem but provides more realistic optimal plans. Unlike the typical approaches to solving bi-level programming (BP), the formulated problem cannot be solved by Karush–Kuhn–Tucker (KKT) conditions or strong duality theory (SDT) due to binary variables at the lower level. To this end, an iterative-based reformulation-and-decomposition (R&D) technique is utilized to find the optimal solutions to the bi-level mixed-integer programming (BMIP) problem. The presented methodology is applied to the IEEE 118-bus system. The numerical results corroborate the effectiveness of the proposed structure and highlight that modeling POZ and MFU is an essential task in the TEP problems.

Transmission Expansion Planning Considering Wind Power and Load Uncertainties

Due to the rapidly increasing power demand worldwide, the development of power systems occupies a significant position in modern society. Furthermore, a high proportion of renewable energy resources (RESs) is an inevitable trend in further power system planning, due to traditional energy shortages and environmental pollution problems. However, as RESs are variable, intermittent, and uncontrollable, more challenges will be introduced in transmission expansion planning (TEP). Therefore, in order to guarantee the security and reliability of the power system, research related to TEP with the integration of RESs is of great significance. In this paper, to solve the TEP problem considering load and wind power uncertainties, an AC TEP model solved by a mixed integer non-linear programming (MINLP) is proposed, the high-quality optimal solutions of which demonstrate the accuracy and efficiency of the method. Latin hypercube sampling (LHS) is employed for the scenario generation, while a simultaneous backward reduction algorithm is applied for the scenario reduction, thus reducing the computational burden. Through this method, the reserved scenarios can effectively reflect the overall trends of the original distributions. Based on a novel worst-case scenario analysis method, the obtained optimal solutions are shown to be more robust and effective.

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.

Robust transmission expansion planning using pair-based convex hull uncertainty sets under high penetration of renewable energy generation

Robust optimization is a practical and effective mathematical framework for coping with uncertainty in the transmission expansion planning (TEP) process, while computing the full convex hull is an outstanding data-driven means of searching for robust boundaries in the uncertainty sets employed in robust TEP processes. However, computing the full convex hull becomes intractable as the number of uncertain factors increases. This study addresses this issue by proposing a two-stage, four-level robust TEP model with uncertainty sets constructed using pair-based convex hulls. Employing a pair-based convex hull enables high-dimensional uncertainty to be characterized by constructing multiple low-dimensional uncertainty sets, and thereby decreases the computational burden associated with solving the robust TEP model while reducing the conservativeness of planning solutions. The model is then solved by means of a parallel column and constraint generation method. The proposed model is demonstrated to characterize the high-dimensional uncertainty efficiently and provide TEP solutions with relatively low conservativeness and high robustness based on numerical simulations of Garver’s 6-bus and IEEE 118-bus test systems.

Transmission expansion planning with optimal transmission switching considering uncertain n-k contingency and renewables

This paper presents a novel model for transmission expansion planning (TEP) with optimal transmission switching (OTS) considering uncertain N-k contingency, renewables and loads. In the proposed approach, ambiguity set and budget uncertainty set are utilized to simultaneously characterize three types of uncertainties in power system: (1) wind power output; (2) load demands; (3) the status and probability distribution of generation and transmission N-k contingency. Accordingly, the optimal expansion plan and OTS can be obtained through a three-level model to guarantee the safety and economy of power system in the worst-case of wind power, load demand and N-k contingency. A decomposition algorithm based on benders decomposition is developed to efficiently solve the model. Cases studies on the revised IEEE 30-bus test system demonstrate that (1) the optimal expansion plan can be greatly affected by the proposed uncertainty sets, (2) the total costs can be effectively reduced by considering optimal transmission switching and (3) the decomposition method can efficiently solve the proposed TEP model.

Hybrid robust/stochastic transmission expansion planning considering uncertainties in generators’ offer prices: A second-order cone program approach

The aim of this paper is to propose a hybrid robust/stochastic model for transmission expansion planning (TEP) problem. The uncertainties related to demand and wind are modelled via stochastic programming (SP), while the uncertainties associated with the generators’ offer prices are modelled via robust optimization (RO). In this sense, an ellipsoidal uncertainty set is considered which the offer price values are known to lie in these given ellipsoids. The model presented is then divided into a master problem and several independent subproblems using a tailored implementation of Bender's decomposition (BD) method. Robust linear constraints of the lower level problems are then transformed into a convex second-order cone programming (SOCP) problem. We will apply the proposed model to IEEE-118 bus power system showing that generators’ offer price and their correlation can considerably affect the optimal plan of the transmission planning. It is observed that considering correlation among generators’ offer prices would not necessarily yield more expensive expansion plan in comparison with the case where correlation is ignored. Indeed, increase or decrease in investment cost depends on the entries of the variance-covariance matrix, network topology and the location of generators. Moreover, the results show the computational efficiency of the robust convex model.

Robust transmission expansion planning model considering multiple uncertainties and active load

Uncertainty must be well addressed in transmission expansion planning (TEP) problem, and it significantly affects the reliability and cost-effectiveness of power systems. Owing to the complex operating environment of power systems, it is crucial to consider different types of uncertainties during the planning stage. In this paper, a robust TEP model is proposed by considering multiple uncertainties and active load. Specifically, in this model, the uncertainties of wind power output and contingency probability are considered simultaneously. The uncertainties are described by scenario and interval, and the Benders decomposition technique is applied to solve the model. The feasibility and effectiveness of the proposed model are illustrated using the IEEE RTS and IEEE 118-node systems.

A linearized transmission expansion planning model under N − 1 criterion for enhancing grid‐scale system flexibility via compressed air energy storage integration

The concept of flexibility is defined as the power systems’ ability to effectively respond to changes in power generation and demand profiles to maintain the supply–demand balance. However, the inherent flexibility margins required for successful operation have been recently challenged by the unprecedented arrival of uncertainties, driven by constantly changing demand, failure of conventional units, and the intermittent outputs of renewable energy sources (RES). Tackling these challenges, energy storage systems (ESS) as one important player of the new power grids can enhance the system flexibility. It, therefore, calls for an efficient planning procedure to ensure flexibility margins by considering ESS's role in modern power systems. This paper proposes a novel mixed integer linear programming (MILP) model for transmission expansion planning (TEP) framework taking into account the role of compressed air energy storage (CAES) integration on improvements in system flexibility. The proposed framework is housed with a quantitative metric of grid-scale system flexibility, while a new offline repetitive mechanism is suggested to account for the N − 1 reliability criterion. The model is applied to different test systems, where the numerical results demonstrate the impacts of CAES units on system flexibility, investment plans, and the total costs.

A comparative analysis of generation and transmission expansion planning models for power loss minimization

In modern power systems, renewable energy resources are becoming more relevant due to their eco-friendly nature and sustainable electrification. Therefore, it is important to consider the effects of the renewable energy resources (RERs) on the generation expansion planning and transmission expansion planning (GTEP) simultaneously. The proper assessment of power losses is essential in order to adequately evaluate the consequence of renewable energy resources in power systems. This paper presents multi-objective optimization problems that are solved using DC, modified DC and AC modelling methods in order to accurately and efficiently compute electrical losses and its impacts on the expansion planning procedure. This paper develops a Mixed Integer Non-linear Programming (MINLP) problem and was solved using CONOPT and CPLEX solvers embedded in Algebraic Modelling Language. The proposed methods are evaluated and validated on three case studies: IEEE Garver’s 6 bus system, IEEE 24 bus test system and a real-world Nigeria Power System. A comparative analysis of the three modelling approaches and a sensitivity analysis of the simulation results indicate that AC solution method provide an accurate computation of power losses and efficient optimal planning strategy as compared to the modified DC method.

Robust nonlinear mathematical transmission expansion planning based on German electricity market simulation

Requirements on electrical energy transmission and the work of system operators are changing due to the shift from centralized towards decentralized generation. This leads to an increased need of transport capacities in grids. In this paper, a robust method is presented to solve the resulting transmission expansion planning (TEP) problem using a nonlinear mathematical optimization. In terms of TEP optimization successive measures are considered in the used mathematical formulation such as grid optimization, grid enhancement and grid extension. The mathematical optimization is based on a DC power flow formulation using unreduced grid models. The concept of the TEP model design and the implementation of different measures are given in detail in the paper. The applicability of the developed approach is shown by the application to a model of the German transmission grid based on a German electricity market simulation for a yearly simulation calculating an expansion demand of 3047 GWkm.

Scenario-based probabilistic multi-stage optimization for transmission expansion planning incorporating wind generation integration

Integrated transmission expansion planning (TEP) and generation expansion planning (GEP) with Wind Farms (WFs) is addressed in this paper. The optimal number of expanded lines, the optimal capacity of WFs installed capacity, and the optimal capacity of wind farms lines (WFLs) are determined through a new TEP optimization model. Furthermore, the optimum capacity additions including conventional generating units is obtained in the proposed model. The Benders decomposition approach is used for solving the optimization problem, including a master problem and two sub-problems with internal scenario analysis. In order to reduce the computational burden of the multi-year and multi-objective expansion planning problem, a multi-stage framework is presented in this paper. The uncertainties of wind speed and system demand along with contingency scenarios lead to a probabilistic optimization problem. Moreover, in the proposed model, the planning time horizon is divided into three predefined stages. This multi-stage approach is used to increase the proposed model accuracy in a power system with a high level of wind power penetration. Hence, in this paper a scenario-based probabilistic multi-stage model for transmission expansion planning is proposed, incorporating optimal WFs integration. It is recognized that high wind penetration increases the transmission expansion investment cost, but based on the reduction of the investment cost of conventional units, the total system cost will be smaller. This result emphasizes the main advantage of wind generating system over the conventional generating system. This planning methodology is applied to the modified IEEE 24-bus test system and simplified Iran 400-kV real system to show the feasibility of the proposed algorithm.

Reducing wind power curtailment by risk-based transmission expansion planning

Due to the inherent intermittency of wind power and the shortage of transmission capacity, a considerable amount of wind power cannot be delivered to load centres. The resulting curtailment of wind power poses a serious challenge to transmission planners. In this paper, we take advantages of the superquantile theory and formulate a risk-based transmission expansion planning (TEP) model to reduce the curtailment of wind power. Regarding its non-convexity and computation difficulty induced by increasing scenarios, we propose a convex relaxation method that can greatly improve computational efficiency. In the numerical study, the computational efficiency of the proposed solution strategy is verified. The comparable results demonstrate the effectiveness and superiority of the risk-based TEP model in terms of making a trade-off between the curtailment of wind power and the transmission investment cost.

Hybrid AC/DC Transmission Expansion Planning Considering HVAC to HVDC Conversion Under Renewable Penetration

In this paper, a dynamic (i.e., multi-year) hybrid model is presented for Transmission Expansion Planning (TEP) utilizing the High Voltage Alternating Current (HVAC) and multi terminal Voltage Sourced Converter (VSC)-based High Voltage Direct Current (HVDC) alternatives. In addition to new HVAC and HVDC lines, the possibility of converting existing HVAC transmission lines to HVDC lines is considered in the proposed model. High shares of renewable resources are integrated into the proposed hybrid AC/DC TEP model. Due to the intermittency of renewable resources, the planning of large-scale Energy Storage (ES) devices is considered. In order to accurately estimate the total TEP costs and hence capturing the scenarios of load and renewable generation uncertainty, using a clustering approach, each year of the planning horizon is replaced with four representative days. The proposed model is formulated as a Mixed-Integer Linear Programming (MILP) problem. Using Benders Decomposition (BD) algorithm, the proposed model is decomposed into a Master investment problem to handle the decision variables, and Sub-problems to check the feasibility of master problem solution and optimize the operation and ES investment cost. Three test systems are used as case studies to demonstrate the effectiveness of the proposed hybrid AC/DC TEP model.

Optimal planning of renewable energy systems for power loss reduction in transmission expansion planning

Purpose The purpose of this study is to address the efficiency of power losses representation while still reducing the computational burden of an optimal power flow (OPF) model in transmission expansion planning (TEP) studies. Design/methodology/approach A modified TEP model is formulated with inclusions of linearized approximation of power losses for a large-scale power system with renewable energy sources. The multi-objectives function determines the effect of transmission line losses on the optimal power generation dispatch in the power system with and without inclusion of renewable energy sources with emphasis on minimizing the investment and operation costs, emission and the power losses. Findings This study investigates the impact of renewable energy sources on system operating characteristics such as transmission power losses and voltage profile. Sensitivity analysis of the performance for the developed deterministic quadratic programming models was analyzed based on optimal generated power and losses on the system. Research limitations/implications In the future, a comparison of the alternating current OPF and direct current (DC) OPF models based on the proposed mathematical formulations can be carried out to determine the efficiency and reduction of computation process of the two models. Practical implications This paper proposed an accurate way of computing transmission losses in DC OPF for a TEP context with a view of achieving a minimal computation time. Originality/value This paper addresses the following objectives: develop a modified DC OPF with a linearized approximation of power losses in TEP problem with large integration of RES. Investigate the impact of RES on system operating characteristics such as transmission power losses and voltage profile.

Efficient sensitivity based approach for AC transmission expansion planning

AC transmission expansion planning (TEP) is a complex problem to solve due to its large scale, mixed-integer, non-linear and non-convex characteristics. This paper presents an efficient sensitivity based approach which employs the primal-dual interior point method (PDIPM), for tackling integer variables in AC TEP. PDIPM's Hessian is used to evaluate the sensitivities of the objective function with respect to the line candidates, which are then used to find a feasible AC TEP solution. The proposed approach solves this non-convex mixed integer non-linear programming problem, without resorting to any use of relaxations/approximations in the AC TEP model. Also, the need and superiority of the AC TEP over the conventional DC TEP is established by comparing both using the proposed approach. Solutions of AC TEP with reactive power planning and an integrated multistage AC TEP are also obtained to demonstrate the performance of the proposed approach. Superior solution quality and lesser computation time of the proposed approach are confirmed by comparing the same with that of the branch and bound/cut approach, constructive heuristic algorithm, merit function-based approach, conic programming and particle swarm optimisation. The studies performed for the various test cases prove the efficacy and computational efficiency of the proposed approach.