Multistage Transmission Expansion Planning Research Articles

A MILP-based heuristic algorithm for transmission expansion planning problems

In the last years, a lot of effort was placed into approximated or relaxed models and heuristic and metaheuristic algorithms to solve complex problems, mainly with non-linear and non-convex natures, in a reasonable time. On one hand, approximated/relaxed mathematical models often provide convergence guarantees and allow the problem to be solved to global optimality. On the other hand, there is no guarantee that the optimal solution of the modified problem is even feasible in the original one. In contrast with that, the metaheuristic algorithms lack mathematical proof for optimality, but as the obtained solutions can be tested against the original problem, the feasibility can be ensured. In this sense, this work brings a new method combining exact solutions from a Mixed-Integer-Linear-Problem (MILP) Transmission Expansion Planning (TEP) model and stochastic solutions from metaheuristic algorithms to solve the non-linear and non-convex TEP problem. We identify the issues that came up with the linear approximations and metaheuristics procedures and we introduce a MILP-Based Heuristic (MBH) algorithm to overcome these issues. We demonstrate our method on a single-stage TEP with the RTS 24 nodes and on a multi-stage TEP with the IEEE 118 nodes test system. The AC TEP solution was obtained using Evolutionary Computation, while the DC TEP solution was obtained using a commercial solver. From the simulations results, the novel MBH method was able to reduce in 42% and in 85% the investment cost from an evolutionary computation solution for the single-stage and multi-stage TEP, respectively.

Co-optimization of multi-stage transmission expansion planning and grid operation

The ongoing transformation of the power system characterized by an increased share of renewable energy sources requires additional transmission capacities. Nevertheless, the need for new transmission capacities can be reduced by optimizing grid operation. This contribution presents a novel approach to the co-optimization of multi-stage transmission expansion planning and grid operation within a mixed-integer linear programming formulation. The expansion via AC systems and phase shifting transformers (PSTs) is combined with the control of PSTs and the determination of congestion management interventions such as redispatch of power plants or curtailment of renewable energies. The number of potential expansion candidates is reduced by linear programming relaxations. Exemplary results based on a synthetic test system containing 120 buses evidence the impact of the proposed approach on overall system costs. The proposed co-optimization reduces the total costs by 16.5 % when applied instead of the sole expansion via AC technology.

Hybrid Binary PSO for Transmission Expansion Planning Considering N-1 Security Criterion

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.

A novel multi-stage adaptive transmission network expansion planning to countermeasure cascading failure occurrence

This paper presents a practical/analytical multi-stage transmission expansion planning approach to mitigate the impacts of cascading failure. It combines forward pseudo-dynamic planning strategy with the proposed analytical method to identify the most critical transmission line according to its impacts on initiating and propagation of the cascading failure throughout power system. The proposed methodology decomposes the planning time horizon into several years or stages. In each stage, an identification method, based on multi decision-making vulnerable index, is applied to efficiently assign the location of the new transmission line for strengthening the transmission network. Using an adaptive threshold, another decision is made about repetition of the proposed identification method in each stage with new topology or going to the next stage. The IEEE 9-, IEEE 39-, and IEEE 118-bus test systems are investigated for the efficacy of the proposed method. The simulation results demonstrate that the proposed scheme is able to find the efficient solution in the form of one or more line(s) at each round of calculation; the solution that leads to effective mitigation against cascading failure.

Line maintenance within transmission expansion planning: a multistage framework

Maintenance in transmission networks is an economical way to reduce upgrading network costs without decreasing its reliability. Hence, new studies regarding transmission expansion planning (TEP) must take into account the effects of maintenance in order to obtain realistic and economic expansion investment plans. This work presents a novel framework for multistage TEP, considering line maintenance, i.e. the expansion cost of the transmission system, network losses, costs of old-line replacement and maintenance, cost of newly constructed line maintenance, and cost of replaced line maintenance, are simultaneously optimised. The advantage of this approach is the fact that the lifetimes of the lines that are replaced, retained, and added to the transmission system are changing during the expansion horizon. These lifetimes have an impact on the maintenance expenses. Annual maintenance costs are also affected by the inflation rate. Hence, both the lifetime and inflation rate roles are integrated into the proposed model. The robustness and effectiveness of the model are tested on the IEEE 24-bus test system, using a particle swarm optimisation algorithm. The results show that the proposed formulation finds more economic investment plans for TEP when compared with those found using static formulations considering the maintenance available in specialised literature.

AC-Based Differential Evolution Algorithm for Dynamic Transmission Expansion Planning

This work proposes a method based on a mixed integer nonlinear non-convex programming model to solve the multistage transmission expansion planning (TEP). A meta-heuristic algorithm by the means of differential evolution algorithm (DEA) is employed as an optimization tool. An AC load flow model is used in solving the multistage TEP problem, where accurate and realistic results can be obtained. Furthermore, the work considers the constraints checking and system violation such as real and power generation limits, possible number of lines added, thermal limits and bus voltage limits. The proposed technique is tested on well known and realistic test systems such as the IEEE 24 bus-system and the Colombian 93-bus system. The method has shown high capability in considering the active and reactive power in the same manner and solving the TEP problem. The method produced improved good results in a fast convergence time for the test systems.

Bilevel transmission expansion planning using second-order cone programming considering wind investment

This paper presents a new framework for bi-level multi-stage transmission expansion planning (TEP) considering wind investment. In the upper-level problem, the transmission and wind investment decisions are modeled, while in the lower-level problem, the market-clearing problem based on the alternating current-optimal power flow (AC-OPF) is formulated. Since the lower-level optimization problem is nonconvex, the second-order cone programming (SOCP) is applied to convexify this problem. Afterwards, the Karush-Kuhn-Tucker (KKT) optimality conditions are employed in order to convert the bi-level problem into a single-level problem. Due to the convexity of the lower-level problem, the KKT conditions are both necessary and sufficient. The whole problem is then solved by a commercial and powerful solver. To show the effectiveness and applicability of the proposed scheme, it is applied to two power systems, namely, IEEE 24-bus RTS and IEEE 118-bus. The numerical results illustrate the efficient performance of the proposed method. Furthermore, the results obtained from the AC-OPF-based market-clearing problem are compared with those obtained from the direct current-optimal power flow (DC-OPF)-based market-clearing problem, and the comparative analysis indicates that the latter may lead to inaccurate solutions.

An Extension of Reduced Disjunctive Model for Multi-Stage Security-Constrained Transmission Expansion Planning

This letter presents an extension of reduced disjunctive model to consider N-1 criterion in multi-stage transmission expansion planning (TEP). This extension is realized by exactly linearizing nonlinear terms induced by N-1 contingency constraints. Compared with the traditional approach, the extended RDM reduces the number of binary variables and constraints. Numerical results of three test systems indicate that the proposed approach significantly improves the computational performance without sacrificing the optimality of TEP problem.

Gini Coefficient for Voltage Security Assessment of Multi-stage Transmission Expansion Planning

Due to the voltage security uncertainty caused by construction sequence in multi-stage transmission expansion planning (MTEP) in bulk power grids, it is necessary to appropriately arrange the construction sequence of the MTEP schemes to reduce voltage security risk. The Gini coefficient is widely used to weigh the gap of residents' income distribution. In this paper, the voltage security Gini coefficient is defined as the voltage security risk index of the MTEP scheme, and is presented to quantitatively evaluate the entire voltage security of one MTEP scheme. Voltage security evaluation model of the MTEP is established based on voltage security Gini coefficient. Compared to the stabilization cost, the proposed model directly reflects the voltage security of the MTEP scheme, and the local optimum is avoided. The presented method is applied on the IEEE 118-bus 54-generator test system. Results show the validity and effectiveness of the proposed model.

Security Constrained Multi-Stage Transmission Expansion Planning Considering a Continuously Variable Series Reactor

This paper introduces a Continuously Variable Series Reactor (CVSR) to the transmission expansion planning (TEP) problem. The CVSR is a FACTS-like device which has the capability of controlling the overall impedance of the transmission line. However, the cost of the CVSR is about one tenth of a similar rated FACTS device which potentially allows large numbers of devices to be installed. The multi-stage TEP with the CVSR considering the $N-1$ security constraints is formulated as a mixed integer linear programming model. The nonlinear part of the power flow introduced by the variable reactance is linearized by a reformulation technique. To reduce the computational burden for a practical large scale system, a decomposition approach is proposed. The detailed simulation results on the IEEE 24-bus and a more practical Polish 2383-bus system demonstrate the effectiveness of the approach. Moreover, the appropriately allocated CVSRs add flexibility to the TEP problem and allow reduced planning costs. Although the proposed decomposition approach cannot guarantee global optimality, a high level picture of how the network can be planned reliably and economically considering CVSR is achieved.

A Risk-Based Approach to Multi-Stage Probabilistic Transmission Network Planning

As a result of the power industry restructuring and the increasing integration of large-scale renewable energy, power transmission expansion planning (TEP) has become a complicated decision-making process requiring risk analysis. This paper proposes a chance constrained approach to TEP. The probabilistic load curtailment degree is quantified by a capped load curtailment probability, which is incorporated into our multi-stage TEP model. Moreover, the system dynamic performance including security and stability is also realistically considered in our model through an iterative procedure. To enhance the computational efficiency, probabilistic optimal power flow (POPF) is adopted in conjunction with an evolutionary algorithm (EA). In case studies, different TEP approaches are compared, and effects of different parameter settings are also investigated. According to the simulation results, our model can not only provide information regarding risks, but also help network planners make trade-offs to select the most flexible and cost-effective planning schemes.

Multistage Transmission Expansion Planning Considering Fixed Series Compensation Allocation

This paper proposes a mathematical model for multistage transmission expansion planning (TEP) considering fixed series compensation (FSC) allocation and N-1 security constraints for both transmission lines and FSCs. FSCs can increase the transmission lines transfer capacity, but the importance of using them in TEP is to dispatch the power more efficiently, resulting in a different topology with less investment cost compared with planning without FSCs. This problem is modeled as a linear mixed binary programming problem and is solved by a commercial branch-and-cut solver to obtain the optimum solution. FSC is modeled as a fixed impedance located in the transmission lines in discrete steps and with an investment cost based on the prices of reinforcement lines. The results obtained using two known test systems show the economic benefits of using FSC in multistage TEP problems.

A PSO based approach for multi-stage transmission expansion planning in electricity markets

This paper presents a particle swarm optimization (PSO) based approach to solve the multi-stage transmission expansion planning problem in a competitive pool-based electricity market. It is a large-scale non-linear combinatorial problem. We have considered some aspects in our modeling including a multi-year time horizon, a number of scenarios based on the future demands of system, investment and operating costs, the N−1 reliability criterion, and the continuous non-linear functions of market-driven generator offers and demand bids. Also the optimal expansion plan to maximize the cumulative social welfare among the multi-year horizon is searched. Our proposed PSO based approach, namely modified PSO (MPSO), uses a diversity controlled PSO to overcome the problem of premature convergence in basic PSO (BPSO) plus an initial high diversity swarm to cover the search space efficiently. The MPSO model is applied to the Garver six-bus system and to the IEEE 24-bus test system and compared to the BPSO model and a genetic algorithm based model.

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

The transmission expansion planning (TEP) problem in modern power systems is a large-scale, mixed-integer, non-linear and non-convex problem. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. Based on the linearized power flow model, this paper presents a mixed-integer linear programming (MILP) approach that considers losses, generator costs and the N - 1 security constraints for the multi-stage TEP problem. The losses and generator cost are modeled as piecewise linear functions of the line flows and the generator outputs, respectively. The IEEE 24-bus system is used to compare the lossy and the lossless model. The results show that the lossy model provides savings in total cost in the long run. The selection of the best number of piecewise linear sections L is also shown. Then a complete planning framework is presented and a multi-stage TEP is performed on the IEEE 118-bus test system. Simulation results show that the proposed approach is accurate and efficient, and has the potential to be applied to large-scale power system planning problems.

A Strategy to Solve the Multistage Transmission Expansion Planning Problem

In this letter, a heuristic to reduce the combinatorial search space (CSS) of the multistage transmission expansion planning (MTEP) problem is presented. The aim is to solve the MTEP modeled like a mixed binary linear programming (MBLP) problem using a commercial solver with a low computational time. The heuristic uses the solution of several static transmission expansion planning problems to obtain the reduced CSS. Results using some test and real systems show that the use of the reduced CSS solves the MTEP problem with better solutions compared to other strategies in the literature.

Differential evolution algorithm for static and multistage transmission expansion planning

A novel differential evolution algorithm (DEA) is applied directly to the DC power flow-based model in order to efficiently solve the problems of static and multistage transmission expansion planning (TEP). The purpose of TEP is to minimise the transmission investment cost associated with the technical operation and economical constraints. Mathematically, long-term TEP using the DC model is a mixed integer nonlinear programming problem that is difficult to solve for large-scale real-world transmission networks. In addition, the static TEP problem is considered both with and without the resizing of power generation in this research. The efficiency of the proposed method is initially demonstrated via the analysis of low, medium and high complexity transmission network test cases. The analysis is performed within the mathematical programming environment of MATLAB using both DEA and conventional genetic algorithm and a detailed comparative study is presented.

A Metaheuristic to Solve the Transmission Expansion Planning

In this letter, a genetic algorithm (GA) is applied to solve the static and multistage transmission expansion planning (TEP) problem. The characteristics of the proposed GA to solve the TEP problem are presented. Results using some known systems show that the proposed GA solves a smaller number of linear programming problems in order to find the optimal solutions and obtains a better solution for the multistage TEP problem.