A Mixed-Integer Linear Programming Approach for Multi-Stage Security-Constrained Transmission Expansion Planning

Transmission expansion planning using multivariate interpolation

With increasing penetration of renewable energy sources and electric vehicles (EVs) in power grids, developing appropriate models for power system planning is of great importance. This article proposes a novel gray wolf optimization (GWO) algorithm-based transmission expansion planning (TEP) method considering renewable energy sources and EVs and evaluates the performance of alternating current power flow (ACPF) and direct current power flow (DCPF) models in the TEP problem in terms of accuracy, run-time, and objective functions. The uncertainty associated with renewable energy sources, EVs, and loads are explicitly modeled in this study using probability density functions (pdfs) and the Copula approach. The proposed GWO-based TEP method is validated by case studies using the IEEE 24-bus reliability test system (RTS) and IEEE 118-bus test system. The ACPF model leads to fewer transmission lines and lower costs than the DCPF model in most scenarios.

This paper studies transmission expansion planning (TEP) problem considering effects of wind farms on transmission network congestion, power system reliability, line repair, and operational costs of wind and generating units in a deregulated environment. Transmission congestion is modeled using difference between local marginal prices (LMPs) of start and end buses of each line that is multiplied by its power flow. In this way, wind units can efficiently affect network congestion through decrease in lines loading and LMPs of buses. Transmission system reliability is modeled using load shedding (LS) index as well as outage rate and outage duration of a single line or simultaneous outage of a line and a wind unit. Also, generation reliability is formulated using loss of load, value of lost load, and LS criteria due to outage rates and outage durations of generating and wind units considering line limits. In addition, the effect of wind units on repair cost of transmission lines is modeled by the relationship among wind generation, line failure rates and lines loading. Operational cost includes cost of network losses, pollution penalty, fuel expenses, and generation cost of wind units. In order to more efficiently investigate the effect of wind power on TEP problem, the proposed model was tested on the IEEE Reliability Test System (IEEE RTS) for different scenarios, and the results were discussed.

Generation and transmission expansion planning with high penetration of wind farms considering spatial distribution of wind speed

This paper proposes a deterministic two-stage mixed integer linear programming (TSMILP) approach to solve the reserve constrained dynamic economic dispatch (DED) problem considering valve-point effect (VPE). In stage one, the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming (MILP) problem, which can be solved by commercial solvers. In stage two, based on the solution obtained in stage one, a range compression technique is proposed to make a further exploitation in the subspace of the whole solution domain. Due to the linear approximation of the transmission loss, the solution obtained in stage two dose not strictly satisfies the power balance constraint. Hence, a forward procedure is employed to eliminate the error. The simulation results on four test systems show that TSMILP makes satisfactory performances, in comparison with the existing methods.

A linearized formulation of AC multi-year transmission expansion planning: A mixed-integer linear programming approach

Cancer chemotherapy is a form of treatment in which both healthy and diseased tissues are adversely affected by dosing; this requires the clinician make decisions , which balance the effectiveness of treatment with toxicity effects, financial, and logistical constraints. This work presents a model-based approach for chemotherapy treatment scheduling that accounts for both drug toxicity constraints and the dosing constraints associated with clinical practice. A mixed-integer linear programming (MILP) approach is applied to a nonlinear system considered previously in an optimal control framework by Martin and Teo (1994). The nonlinearities in the pharmacodynamic PD model were eliminated by logarithmic transform and both the pharmacokinetic (PK) and PD models were converted into algebraic constraints by discretizing the system over the treatment window. This formulation also accounts for the toxicity constraints and allows for the easy incorporation of dosing constraints, which would be encountered during the course of treatment. MILP results are shown for three cases considered in R. Martin and K.L. Teo (1994): highly effective drug, moderately effective drug, and a drug with very little effect on the tumor. In the limit of the discretization timestep and delivery interval approaches zero, the MILP algorithm returns the optimal control solution. Like the optimal control solution, most of the drug is delivered at the end of the treatment cycle, which results in the minimal final cancer cell population. The MILP approach results in a problem which can be solved to optimality and can easily be augmented with constraints which give the problem more clinical relevance.

Transmission expansion planning (TEP) is a complex decision making process that requires comprehensive analysis to determine the time, location, and number of electric power transmission facilities that are needed in the future power grid. This chapter discusses the TEP problem in modern power systems, including the TEP process, available software tools, and mathematical models for TEP problems.

This paper presents a multistage transmission expansion planning (TEP) which alleviates the level of transmission congestion during the planning horizon. Due to the combinatorial nature of the proposed TEP model, a Benders decomposition approach intertwined with a manipulated disjunctive model is applied to decompose the original TEP problem into a master problem and two sub-problems standing for system security and optimal operation. The security sub-problem applying the N-1 contingency criterion to assess the transmission system security. Besides, the optimal operation sub-problem makes it possible for the proposed TEP model to fulfill the optimal operation as well as to calculate the difference between system lacational marginal prices (LMPs) for all buses. Also, this model appends a specific term into the TEP objective function as the congestion level (CL) reflecting the degree of market competitiveness. Therefore, the proposed TEP model minimizes the total costs comprising the investment cost of candidate transmission lines as well as the level of transmission congestion. The proposed approach is applied to the northeastern area of the Iranian power grid.

The transmission network expansion planning is necessary for supplying the future needs, considering load growth. Furthermore, in restructured environments, transmission lines provide the required infrastructure for creating a competitive environment. In recent years, there has been a significant advancement in storage technologies. This advancement leads to using energy storage systems to postpone the construction or replacement of transmission lines. Therefore, in this paper, the problems of transmission expansion planning and energy storage systems deployment are investigated simultaneously. Considering the presence of storage devices and their effect on network operation cost, in this paper, the operation cost is modeled as an independent objective function along with investment cost. Moreover, the problems of transmission and storage expansion planning are modeled as a tri-objective optimization problem with the objectives of reducing costs and increasing the social welfare index in the power market. The multi-objective shuffled frog leaping evolutionary algorithm is used to solve these problems. The presented model for expansion planning is implemented and analyzed on IEEE 24-bus test system in the presence and absence of energy storage systems, and the effect of change in the price of energy storage systems is studied. The results of this research show that as the technology advances and the storage costs decrease, energy storage systems can play a pivotal role in reducing expansion planning costs of the power network and improving market-based indices in the restructured environment.

Network Expansion Planning (NEP) plays a pivotal role in the development of power systems. It involves investing in new generating units and transmission lines to meet growing load demands and ensure a reliable electricity supply. Historically, the incorporation of demand response (DR) factors in power system planning has been limited due to their complexity and evaluation challenges. However, with advancements in smart grid technologies, increased integration of renewable energy, and the emergence of flexible loads, the inclusion of DR models has become crucial for enhancing power system reliability. While numerous studies have delved into generation and transmission expansion planning (GTEP) problems, only a few have explored the integration of network payment schemes and DR within the GTEP framework. This study proposes a multi-annual generation and transmission expansion planning model that incorporates three network payment schemes and two DR techniques. The objective is to secure financing for new generating units and transmission lines while minimizing the overall system cost. The proposed models employ the mixed-integer linear programming (MILP) optimization method and are validated using a modified IEEE 24-bus system. Two key system performance metrics, namely the network congestion index and network saturation index, are employed to assess system reliability and effectiveness. These results demonstrate that the integration of network payment schemes and DR techniques into the generation and transmission expansion planning model can lead to a cost reduction of 32.1% as compared to base model, reduced power system congestion and saturation (22.1%, 2.73%) to allow more renewable energy integration and enhanced power system reliability and operational flexibility.

This paper presents an hybrid method based on the metaheuristic Particle Swarm Optimization (PSO) and quadratic programming (QP) for solving the multi-stage transmission expansion planning (TEP) problem. PSO solves the investment problem and QP solves the operational cost problem. Transmission losses and the N-1 security criterion are included in this model to give a more comprehensive approach. Undertaking a complete N-1 security analysis for any network topology is time consuming. To improve the convergence speed and to reduce computational effort, Line Outage Distribution Factors (LODF) are used to calculate the line's post-contingency power flows. The proposed approach is initially validated through numerical simulations of the classic Garver's system, and its performance is later tested and compared with other in the literature on the IEEE 24-bus system.

The expected deployment of massive renewable energy sources (RES, mainly of wind and solar) at a continental or even intercontinental level creates very complex transmission expansion planning (TEP) problems. Both the size of the system and the level of uncertainty are huge. Solving a TEP problem for such big networks under high levels of uncertainty demands an exceptionally huge computational effort when using reasonably precise models. Conventional modeling approaches and solution strategies cannot be directly reproduced in this case due to their computational limitations. In this paper, we show a systematic way of approaching the problem, which deals both with modeling and with solution strategy aspects. We formulate the TEP problem as a two period stochastic linear programming problem characterized by common investment decisions to all scenarios in the first period and scenario-dependent decisions in the second period. In order to make it tractable, we devise a solution strategy based on decomposing the problem into successive optimization phases. Each phase uses the results of the previous one to reduce the search space. This reduction in complexity allows each phase to use more complex models with a similar computational load. Each optimization phase could be defined and solved as an independent problem, thus, allowing the use of specific decomposition techniques, or parallel computation when possible. A modified Garver's system is used to illustrate the methodologies. Test results from IEEE-300 bus system show that the proposed solution strategy is very effective. And, integrating the proposed solution strategy in the solution process contributes to a significant reduction in computational effort while fairly maintaining optimality of the solution.

This paper shows a methodology for solving the Transmission Expansion Planning (TEP) problem when Multiple Generation Scenarios (MGS) are considered. MGS are a result of the market based environment introduced by electricity deregulation. The solution to this problem is carried out by using multiobjective evolutionary strategies for the optimization process, implementing a new hybrid modified NSGA-II/Chu-Beasley algorithm. The proposed methodology is validated using the 6-bus Garver system and the IEEE-24 bus system. The TEP is based on the DC model of the network and non-linear interior point method is used to initialize the population. A set of Pareto optimal expansion plans with different levels of cost and load shedding is found for each system, showing the robustness of the proposed approach.

An integrated transmission expansion planning and battery storage systems placement - A security and reliability perspective