Transmission Expansion Planning Model Research Articles

Security‐constrained transmission expansion planning using linear sensitivity factors

Formulating power flow equations with linear sensitivity factors (LSFs) reduces the number of variables and constraints, and consequently, the computational burden of power systems’ optimisation problems. This study proposes a transformative, computationally efficient model for transmission expansion planning (TEP). While the existing TEP models use bus voltage angles, the proposed TEP takes advantages of LSFs to formulate an optimisation. LSFs allow to omit voltage angles from the formulation and replace all nodal power balance constraints by one equivalent constraint. Thus, the proposed model includes less number of variables and constraints compared with the classical angle-based model. These features significantly reduce computational costs of TEP and enhance its scalability, especially for large-scale systems. Load and generation uncertainties are modelled using a data-driven approach, and N − 1 security criteria are taken into account to ensure system security. All equations under normal and N − 1 conditions are considered using data of the complete network graph. Simulation results show that the proposed model provides the same results as the conventional angle-based model while being much faster (more than 58% based on the authors’ case studies) and computationally more efficient.

Efficient linear network model for TEP based on piecewise McCormick relaxation

This study presents a novel scheme for transmission expansion planning (TEP) based on piecewise McCormick relaxation. The model presented considers investment and operation cost and identifies the transmission lines to be built. Since the AC power flow equations are inherently non-convex and non-linear, the resulting TEP model will be a highly complex optimisation problem, in which the optimal global solution is not guaranteed to be found by the existing techniques. This study aims to transform the non-linear model of the power network into a novel linear one. The model proposed is much more precise compared with the DC approach, while the global solution is guaranteed to be found by the off-the-shelf solvers. This accurate transformation from a non-convex and non-linear AC-TEP formulation into a linear-TEP model enables the planner to get more insight into the power flow of the power system. The TEP problem is formulated as a mixed-integer linear programming problem and is solved using the efficient commercial solvers. The results of the case studies show the tractability and exactness of the proposed model as well as its superiority over the state-of-the-art schemes.

Incorporating Massive Scenarios in Transmission Expansion Planning With High Renewable Energy Penetration

High renewable energy penetration profoundly increases the diversity of operating statuses for the power system. Therefore, massive operating scenarios need to be considered in transmission expansion planning (TEP) to fully reflect the impact of renewable energy on power system operation. Usually, representative scenarios need to be selected to reduce the computational burden of TEP. However, the impact of abandoning many scenarios is unclear because investment decisions are highly non-linear with respect to the input scenarios. In this paper, we propose a TEP model to effectively consider massive scenarios without reduction. We use Benders decomposition to divide the TEP problem into an investment master problem and many operation subproblems. Multiple parametric linear programming (MPLP) is applied to cluster the operation subproblems in each iteration. Here, only one operation subproblem needs to be solved in each cluster, and the results of other subproblems in the same cluster can be analytically obtained. The clustering process is objective-based and self-updated dynamically during each iteration so that the effects of all the scenarios on investment decisions are considered. The efficiency improvement and effectiveness of the proposed method are illustrated through case studies on the modified Garver's 6-bus, IEEE RTS-79, IEEE RTS-96, and realistic-sized test system.

AC load flow based model for transmission expansion planning

This paper proposes an accurate model to solve the transmission network expansion planning (TNEP) problem. The TNEP problem is solved using a linear DC model, a mixed integer linear DC model, and the proposed accurate exact mixed integer non-linear AC model. A 19 bus system which is a part of the 220 kV Egyptian transmission network is used for the verification of the proposed load flow models. The proposed exact non-linear AC load flow based model that considered control of active and reactive power flow in the network and considered the power losses in the system yielded promising results when compared to DC load flow based linear and mixed integer linear models. It provided a planned network with least number of added lines and consecutively with the least cost.

A Multistage Robust Transmission Expansion Planning Model Based on Mixed Binary Linear Decision Rules—Part I

This two-paper series introduces a new multistage robust approach for solving the transmission expansion planning (TEP) problem under the uncertainty of loads and wind power productions. The proposed multistage robust TEP model is formulated using mixed binary and linear decision rules, which aims at finding a solution withstanding any realization of the uncertain parameters belonging to a set-based uncertainty model. The robustness of the optimal expansion plan can be adjusted by the budget of uncertainty. The first part of this two-paper series presents the extended and compact formulations for a deterministic TEP problem. Then, the compact formulation of the TEP problem under the uncertainty of loads and wind power productions is introduced as a multistage robust optimization problem, which is reformulated using mixed binary and linear decision rules. The extended formulation of these decision rules, as functions of uncertain parameters, is presented in this part as well.

Clustering‐based chance‐constrained transmission expansion planning using an improved benders decomposition algorithm

This study presents a chance-constrained transmission expansion planning (TEP) approach considering the uncertainty of renewable generation and load. On the basis of the underlying idea of density-based clustering techniques, a novel scenario generation method is presented to characterise the uncertainty sources in the form of representative scenarios. Then, the chance constraints imposed on the sampling scenarios are incorporated into the TEP model to avoid uneconomical transmission investment. The authors further develop an improved Benders decomposition (BD) algorithm with specialised Benders cuts to solve the chance-constrained TEP problem. Numerical examples are given to verify the validity of the proposed TEP approach in simulating uncertainties and providing reasonable planning schemes. Their results on two test systems also demonstrate that the proposed BD algorithm is computationally efficient in solving this kind of chance-constrained TEP problem.

Short‐circuit‐constrained transmission expansion planning with bus splitting flexibility

Incorporation of the short-circuit level constraints in the transmission expansion planning (TEP) has a direct impact on the final solution. Conventionally, in TEP models, a substation is tackled as a single node where are all transmission lines, power transformers, and generating units are connected to each other. However, bus splitting is a common option in most substations that divides the connected elements into two groups. Doing so, bus splitting can alter the flow path impedances and accordingly manage the short-circuit levels. Here, the short-circuit level constraints are modelled in terms of conventional TEP and bus splitting decision variables. The modelling process is very complex and some non-linear terms appear in the models. To have a tractable model in real-world problems, the non-linearities are converted to linear equivalents making the final TEP model conforming the mixed-integer linear programming format. The performance of the proposed model is examined on the 24-bus reliability test system. The results show that incorporation of the bus splitting option in the TEP problem decreases the total cost of the optimal expansion plan.

Power network planning considering trade‐off between cost, risk, and reliability

Summary Over the past few years, the penetration of renewable distributed generation (DG) into power systems has increased markedly. Given the intermittency and uncertainty of renewables, demand response (DR) resources play an important role in balancing power supply-demand and shaving peak demand. In order to evaluate the system performance under contingencies, a risk factor is explicitly defined in this paper. This risk factor realistically considers the cost and the feasibility of corrective control (CC) actions. This risk factor is incorporated into our multi-objective transmission expansion planning (TEP) framework, which handles conflicting objectives of cost, risk, and reliability. The proposed model is numerically verified on the modified IEEE 118-bus and IEEE 24-bus RTS systems. Comparative studies with simplified versions of TEP models have also been undertaken. To sum up, the proposed approach should be considered as a risk-based, decision support tool, providing system operators or network planners with opportunities to make tradeoffs between cost, risk and reliability.

Assessing the impact of sampling and clustering techniques on offshore grid expansion planning

Due to the ongoing large-scale connection of non-dispatchable renewable energy sources to the power systems, short- to long-term planning models are challenged by an increasing level of variability and uncertainty. A key contribution of this article is to explore and assess the implications of different dimension reduction approaches for long-term Transmission Expansion Planning (TEP) models. For the purpose of this study, a selection of sampling and clustering techniques are introduced to compare the resulting sample errors with a variety of sampling sizes and two different scaling options of the original data set. Based on the generated samples, a range of TEP model runs are carried out to investigate their impacts on investment strategies and market operation in a case study reflecting offshore grid expansion in the North Sea region for a 2030 scenario. The evaluations show that dimension reduction techniques performing well in the sampling and clustering process do not necessarily produce reliable results in the large-scale TEP model. Future work should include ways of incorporating inter-temporal constraints to better capture medium-term dynamics and the operational flexibility in power system models.

How to build an electric power transmission network considering demand side management and a risk constraint?

The increasing penetration of intermittent renewable energy poses plenty of challenges to electricity networks. Moreover, following the applications of intelligent electricity networks, demand response (DR) has attracted a great deal of attention due to its positive effects on shaving peak demands and balancing power supply and demand. On the other hand, when DR reaches a critical market level, the market behavior of DR becomes a meaningful uncertainty to the networks as well. Therefore, power transmission expansion planning (TEP) becomes a complicated decision-making process requiring risk analysis. This paper proposes a probabilistic approach to TEP contemplating risk. The conventional reliability criterion is replaced by a risk constraint. In addition, the TEP problem is decomposed into a master investment problem and two slave subproblems, i.e., optimal operation and feasibility check subproblems. The proposed TEP model is tested on the Garver’s six-bus and the modified IEEE 24-bus RTS and Polish 2383-bus systems. According to the numerical results, the proposed TEP model is superior compared to the conventional reliability-driven TEP from three perspectives: (1) It has incorporated a risk constraint and hence can help network planners understand the variants of risk and provide the opportunity to make trade-offs between cost, reliability and risk. (2) It still enforces the reliability criterion and is more cost-effective when the wind power uncertainty becomes higher in the future. (3) It allows risk-analysis, giving decision-makers the flexibility to choose a plan according to their individual risk-aversion levels and understand the multiple outcomes.

When doing nothing may be the best investment action: Pessimistic anticipative power transmission planning

Abstract A fundamental challenge in power system planning is how to handle the interactions of participants’ behaviors in deregulated markets. This is important due to the high cost involved in their decisions. Proactive or anticipative transmission expansion planning models have been proposed by some authors to jointly model the interactions among deregulated electricity market participants making market-driven investment decisions. Several works have shown that a Transmission Network Planner can increase social welfare by anticipating line expansion planning to generation expansion equilibrium and market outcomes. However, proactive transmission expansion decisions may lead to suboptimal solutions when the generation expansion equilibrium problem have multiple solutions (i.e., leading to higher total costs and lower social welfare). We propose a methodology to study the potential impacts of proactive expansion planning on generation expansion decisions. The resulting formulation is stated as a mathematical program subject to an equilibrium problem with equilibrium constraints (EPEC). To deal with this problem, we also propose an approach to derive tractable EPEC solutions with global optimality guaranteed based on a column-and-row generation algorithm. Our numerical results shows that a proactive investment plan can lead to higher total cost than not investing at all because of the existence of multiple market-driven generation expansion equilibria. We show that the proposed algorithm significantly reduce the time of computation up to two orders of magnitude with respect to existing methodologies.

Modelling probabilistic transmission expansion planning in the presence of plug‐in electric vehicles uncertainty by multi‐state Markov model

Increasing penetration of plug-in electric vehicles (PEVs) in the power system makes a need to consider the impact of PEVs on the transmission expansion planning (TEP) studies especially for large-scale PEV parking lots. Modelling of PEVs (as vehicle to grid (V2G)) is highly dependent on the owner's behaviour. In this study, a systematic method based on multi-state Markov model is utilised to represent the uncertainty of V2G's presence. To investigate the impact of PEVs, a probabilistic TEP in the presence of V2Gs (P_TEPV2G) is proposed. In the proposed TEP model, the objective function consists of the total line and risk costs (RCs). Moreover, the optimal place and capacity of PEV parking lots are considered as the decision variables. It is assumed that there is an electric vehicle fleet operator for the management of electric vehicles. Because P_TEPV2G is a complex and non-linear optimisation problem, an improved cuckoo search algorithm (ICS) is utilised to effectively solve the problem. On the IEEE 24-bus system, simulation results show that the availability of the PEVs at the proper bus leads to decreasing RC and deferring construction of new transmission lines.

Transmission expansion in an oligopoly considering generation investment equilibrium

Transmission expansion planning (TEP) is a sophisticated decision-making problem, especially in an oligopolistic electricity market in which a number of strategic (price-maker) producers compete together. A transmission system planner, who is in charge of making TEP decisions, requires considering the future generation investment actions. However, in such an oligopolistic market, each producer makes its own strategic generation investment decisions. This motivates the transmission system planner to consider the generation investment decision-making problem of all producers within its TEP model. The strategic generation investment problem of each producer can be represented by a complementarity bi-level model. The joint consideration of all bi-level models, one per producer, characterizes the generation investment equilibrium that identifies the future evolution of generation investment in the market. This paper proposes a tri-level TEP decision-making model to be solved by the transmission system planner, whose objective is to maximize the social welfare of the market minus the expansion costs, and whose constraints are the transmission expansion limits as well as the generation investment equilibrium problem. This model is then recast as a mixed-integer linear programming problem and solved. Numerical results from an illustrative example and a case study based on the IEEE 14-bus test system demonstrate the usefulness of the proposed approach.

Probabilistic transmission expansion planning considering distributed generation and demand response programs

Transmission expansion planning (TEP) is generally determined by peak demands. To improve the efficiency and sustainability of energy systems, attention has been paid to demand response programs (DRPs) and distributed generation (DG). DRPs and DG will also have significant impacts on the controllability and economics of power systems, from short-term scheduling to long-term planning. In this study, a non-linear economic design for responsive loads is introduced, based on the price flexibility of demand and the customers' benefit function. Moreover, a probabilistic multi-objective TEP model which considers DRPs is also proposed. A probabilistic analysis method, the so-called Monte-Carlo simulation method, is implemented to handle the uncertainty of the loads, DRPs and DG in the TEP problems. Due to the problems' non-convex formulations, a non-dominated sorting differential evolution program is used to solve the TEP problems. The proposed TEP model can find the optimal trade-off between transmission investment and demand response expenses. The planning methodology is then demonstrated on an IEEE 118-bus system in order to show the feasibility of the proposed algorithm.

Analysis of transmission expansion planning considering consumption-based carbon emission accounting

Consumption-based carbon emission accounting is able to clarify consumers’ responsibility for the carbon emissions from a power system. The responsible amount of carbon emissions for each consumer can be calculated based on the power consumption and the accordant carbon emission flow (CEF). Distribution of the CEF in the network may vary significantly under different transmission network configurations, resulting in different attributed carbon emission responsibilities of consumers. This paper describes how transmission expansion planning (TEP) and consumption-based carbon emission accounting affect each other. A novel TEP model considering the consumption-based carbon emission accounting is presented. A new index named CO2 allocation equity coefficient (CAEC) is introduced to quantify the equity performance of the consumption-based carbon emission accounting system. As such, the requirement for different equity performances can be explicitly incorporated into the TEP model as a constraint to determine its effect on TEP. The proposed TEP model is tested on Garver’s 6-bus system and a modified IEEE 39-bus system. The results show that the methodology is able to obtain the transmission expansion planning, in general, more lines must be planned to achieve better equity performance, with more even consumption-based carbon emission, but leading to an overall increasing tendency in the annualized transmission investment cost.

Multi‐objective transmission expansion planning in a smart grid using a decomposition‐based evolutionary algorithm

The integration of large-scale renewable energy and demand response (DR) resources in smart grids have brought in emerging challenges for transmission expansion planning (TEP), particularly in terms of system security. The conventional TEP models have not fully addressed the cost and the feasibility of corrective control (CC) actions such as generation rescheduling and load curtailment under contingencies. Moreover, the optimality of CC depends on the pre-contingency state, the post-contingency state, as well as the existence and viability of the involved CC actions. In this study, first the authors have given the explicit definition of CC risk index (CCRI), which evaluates the expected system performance under a set of contingencies (i.e. risk of incurring security issues). With the authors’ improvement, the CCRI is now mathematically tractable and may have wide applications to TEP problems. Afterwards, the authors have proposed a multi-objective TEP framework with tradeoffs between cost and risk. A relatively new yet superior multi-objective evolutionary algorithm called the multi-objective evolutionary algorithm (MOEA)/D is introduced and employed to find Pareto optimal solutions. The proposed model is numerically verified on the modified IEEE RTS 24-bus and 118-bus systems. According to the simulation results, the proposed model can provide information regarding variants of risks and coordinate the optimum planning and DR solutions.

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.

Strategic multiyear transmission expansion planning under severe uncertainties by a combination of melody search algorithm and Powell heuristic method

In this paper, a new strategic multiyear model is presented for Transmission Expansion Planning (TEP) in deregulated environments. This methodology is based on a tri-level decision making whose fundamental elements are pool-based electricity market and strategic behavior of market participants. In addition, to minimize risks of planning arising from severe uncertainties, an information gap decision theory (IGDT) is used. By using the IGDT, the TEP model is formulated for the risk-averse and risk-seeker decision makers through the robustness and opportunity models, respectively. The offered model is formulated as a non-convex mixed-integer non-linear optimization problem. With this regards, a combination of melody search algorithm and improved Powell heuristic method is widely used to determine the optimal solution. The planning methodology has been applied to the IEEE 30-bus test system and to the large-scale Iranian 400-kV transmission grid. Simulation results demonstrate the feasibility and effectiveness of the proposed model, and the fact that it can be profitable for the real-world networks.

Comprehensive power transfer distribution factor model for large‐scale transmission expansion planning

Transmission expansion planning (TEP) is an important and computationally expensive decision-making process in power systems. Expression of the power flows using power transfer distribution factors (PTDFs) could potentially reduce the size and computational cost of the TEP. However, this formulation does not lend itself easily for this problem as the system topology changes in the course of the optimisation procedure. This study presents a PTDF-based TEP model devoid of voltage angles and nodal power balances, while producing the same solution as angle-based TEP models. The proposed model is capable of monitoring a limited number of transmission lines that have significant impact on the system's reliable and optimal operation. It thus considerably reduces the number of constraints and results in a scalable optimisation problem. The proposed model is highly advantageous especially for the TEP of large-scale power systems. The numerical results provide an indication for the effectiveness of the proposed model.

A Probabilistic Transmission Planning Framework for Reducing Network Vulnerability to Extreme Events

The restructuring of electric power industry has brought in plenty of challenges for transmission expansion planning (TEP), mainly due to uncertainties. The commonly used probabilistic TEP approach requires the network to meet an acceptable risk criterion. However, a series of blackouts in recent years caused by extreme weather-related events have raised the concerns about network vulnerability through calculating the expected risk value. In this paper, we have proposed the concept that TEP should be economically adjusted in order to make network less vulnerable to extreme events (EEs) caused by climate change, e.g., floods or ice storms. We firstly give the explicit definitions of economic adjustment (EA) index and adjusted risk value. Then we formulate our model as a risk-based decision making process while satisfying the deterministic ${\rm N}-1$ criterion. The proposed approach is tested on the IEEE 118-bus system. Results based on various risk aversion levels are given and comparison studies with other risk-based TEP approaches have been done. Also, sensitivity analysis of parameter setting has been conducted. According to the numerical results, the proposed risk-based TEP model is a flexible decision-making tool, which can help decision makers make a tradeoff between economy and security.