Multi-period Optimal Power Flow Problem Research Articles

The promise of EV-aware multi-period optimal power flow problem: Cost and emission benefits

Increased electric vehicle (EV) penetration brings considerable challenges to the daily planning of the power grid operations. A careful coordination of the grid operations and charging schedules is needed to alleviate these challenges, and turn them into opportunities. For this purpose, we study the Multi-Period Optimal Power Flow problem (MOPF) with electric vehicles under emission considerations. We integrate three different real-world datasets: household electricity consumption, marginal emission factors, and EV driving profiles. We present a systematic solution approach based on second-order cone programming to find globally optimal solutions for the resulting nonconvex optimization problem. To the best of our knowledge, our paper is the first to propose such a comprehensive model integrating multiple real datasets and a promising solution method for the EV-aware MOPF Problem. Our computational experiments on various instances with up to 2000 buses demonstrate that our solution approach leads to high-quality feasible solutions with provably small optimality gaps. In addition, we show the importance of coordinated EV charging to achieve significant emission savings and reductions in cost. In turn, our findings can provide quantitative insights to decision-makers on how to incentivize EV drivers depending on the trade-off between cost and emission.

Efficient Reallocation of BESS in Monopolar DC Networks for Annual Operating Costs Minimization: A Combinatorial-Convex Approach

This article deals with the solution of a mixed-integer nonlinear programming (MINLP) problem related to the efficient reallocation of battery energy storage systems (BESS) in monopolar direct current (DC) grids through a master–slave optimization approach. The master stage solves the integer nature of the MINLP model, which is related to the nodes where the BESS will be located. In this stage, the discrete version of the vortex search algorithm is implemented. To determine the objective function value, a recursive convex approximation is implemented to solve the nonlinear component of the MINLP model (multi-period optimal power flow problem) in the slave stage. Two objective functions are considered performance indicators regarding the efficient reallocation of BESS in monopolar DC systems. The first objective function corresponds to the expected costs of the annual energy losses, and the second is associated with the annual expected energy generation costs. Numerical results for the DC version of the IEEE 33 bus grid confirm the effectiveness and robustness of the proposed master–slave optimization approach in comparison with the solution of the exact MINLP model in the General Algebraic Modeling System (GAMS) software. The proposed master–slave optimizer was programmed in the MATLAB software. The recursive convex solution of the multi-period optimal power flow problem was implemented in the convex discipline tool (CVX) with the SDPT3 and SEDUMI solvers. The numerical reductions achieved with respect to the benchmark case in terms of energy loss costs and energy purchasing costs were 7.2091% and 3.2105%, which surpassed the results reached by the GAMS software, with reductions of about 6.0316% and 1.5736%.

Congestion mitigation in unbalanced residential networks with OPF-based demand management

This paper proposes a novel congestion mitigation strategy for low voltage residential feeders in which the rising power demand due to the electrification of the transport and heating systems leads to congestion problems. The strategy is based on requiring residential customers to limit their demand for a certain amount of time in exchange for economic benefits. The main novelty of the method consists of combining a thorough representation of the network physics with advanced constraints that ensure the comfort of residential users, in a scalable manner that suits real systems. The mitigation strategy is presented from a DSO perspective, and takes the form of contracts between users and system operator. The focus on user comfort aims to make the contracts appealing, encouraging users to voluntarily enroll in the proposed mitigation scheme. The presented solution is implemented as a mixed-integer multi-period optimal power flow problem which relies on a linearized three-phase power flow formulation. Calculations on 100 real-life distribution feeders are performed, to analyze the congestion-relieving potential of several possible system operator-user contracts. From a planning perspective, the results can help the system operator define contractual terms that make a specific congestion mitigation scheme effective and viable. From an operational perspective, the same calculations can be used to optimally schedule power reduction on a day-ahead basis.

BELTISTOS: A robust interior point method for large-scale optimal power flow problems

Optimal power flow (OPF) problems are ubiquitous for daily power grid operations and planning. These optimal control problems are nonlinear, non-convex, and computationally demanding for large power networks especially for OPF problems defined over a large number of time periods, which are commonly intertemporally coupled due to constraints associated with energy storage devices. A robust interior point optimization library BELTISTOS is proposed, which allows fast and accurate solutions to single-period OPF problems and significantly accelerates the solution of multi-period OPF problems via the aid of structure-exploiting algorithms. Adhering to high reporting standards for replicable and reliable analysis, BELTISTOS is compared with interior point optimizers within the software package MATPOWER and evaluated using large scale power networks with up to 193,000 buses and problems spanning up to 4800 time periods. • BELTISTOS optimization library provides structure-exploiting interior point methods. • BELTISTOS accelerates convergence of multi-period optimal power flow problems. • BELTISTOS provides algorithms with significantly lower memory footprint.

Optimal Power Flow in Distribution Networks Under N – 1 Disruptions: A Multistage Stochastic Programming Approach

Contingency research to find optimal operations and postcontingency recovery plans in distribution networks has gained major attention in recent years. To this end, we consider a multiperiod optimal power flow problem in distribution networks, subject to the N – 1 contingency in which a line or distributed energy resource fails. The contingency can be modeled as a stochastic disruption, an event with random magnitude and timing. Assuming a specific recovery time, we formulate a multistage stochastic convex program and develop a decomposition algorithm based on stochastic dual dynamic programming. Realistic modeling features, such as linearized AC power flow physics, engineering limits, and battery devices with realistic efficiency curves, are incorporated. We present extensive computational tests to show the efficiency of our decomposition algorithm and out-of-samplex performance of our solution compared with its deterministic counterpart. Operational insights on battery utilization, component hardening, and length of recovery phase are obtained by performing analyses from stochastic disruption-aware solutions. Summary of Contribution: Stochastic disruptions are random in time and can significantly alter the operating status of a distribution power network. Most of the previous research focuses on the magnitude aspect with a fixed set of time points in which randomness is observed. Our paper provides a novel multistage stochastic programming model for stochastic disruptions, considering both the uncertainty in timing and magnitude. We propose a computationally efficient cutting-plane method to solve this large-scale model and prove the theoretical convergence of such a decomposition algorithm. We present computational results to substantiate and demonstrate the theoretical convergence and provide operational insights into how making infrastructure investments can hedge against stochastic disruptions via sensitivity analyses.

Multi-period optimal power flow for identification of critical elements in a country scale high voltage power grid

The paper focuses on the identification and numerical ranking of critical elements in a power transmission network. This problem is closely linked to the identification of critical infrastructure in a power grid. A quantitative ranking of the power system elements is necessary for the prioritization of actions enhancing system resilience, as the most critical elements require higher attention ensuring protection, functionality, redundancy and reliability. The paper presents a methodological approach based on alternating current multi-period optimal power flow problem formulation and application on a reference network replicating a country scale system. The multi-period optimal power flow method was tested and applied to the reference system and a number of critical elements were identified. The paper further discusses possible protection and mitigation measures.

Hierarchical and Robust Scheduling Approach for VSC-MTDC Meshed AC/DC Grid With High Share of Wind Power

This paper proposes a novel hierarchical and robust scheduling paradigm for the emerging voltage source converter (VSC) based multiterminal high voltage direct current (VSC-MTDC) meshed AC/DC hybrid system with high share of wind power. Considering the multilevel structure of the VSC-MTDC meshed AC/DC system, the scheduling problem is decomposed into three interactive levels according to the hierarchical analytical target cascading (ATC) technique. The low level is a two-stage adaptive robust security-constrained unit commitment problem for the AC system, which is solved by the column-and-constraint generation (C&CG) algorithm; the middle level is a day-ahead power transmission optimization problem for the VSC stations, where a day-ahead operation model for the VSC station is presented to fully use its flexible and controllable power adjustment capability to promote wind power accommodation; and the high level is a multi-period optimal power flow problem for the DC grid. An integrated ATC and C&CG algorithm is proposed to enable the hierarchical and robust scheduling. The parallel solution is used to accelerate the hierarchical scheduling. Simulations show that this formulation is effective in dealing with wind power uncertainty, promoting wind power accommodation, and improving the calculation efficiency.

Security-Constrained Day-Ahead Operational Planning for Flexible Hybrid AC/DC Distribution Networks

A new active network management framework is presented based on a multi-period optimal power flow problem that is bounded by security constraints at the distribution level for upholding the security of supply. This can be achieved through active engagement with flexible demand and distributed generation to prepare for contingency events in day-ahead operational planning. This framework is coupled with a flexible hybrid AC/DC medium voltage (MV) distribution network topology. It contains an integrated multi-terminal medium voltage DC (MVDC) interface for a seamless interaction and integration of the flexible demand and generation on both AC and DC sides of the hybrid network. The active energy management framework when coupled with a flexible hybrid AC/DC topology provides unprecedented degrees of flexibility as well as security of operation under a variety of conditions. To this end, the 75-bus UK generic distribution network has been modified and converted into a hybrid AC/DC network using the integrated MVDC interface. This framework is then deployed to minimise operational costs to the network operator, considering costs of schemes such as distributed generation curtailment and flexible demand shifting, as well as network losses. Results show a significant improvement in operational costs when the network operates as a flexible hybrid when compared to a pure AC or a more conventional AC/DC hybrid.

Active Distribution Grids Offering Ancillary Services in Islanded and Grid-Connected Mode

Future Active Distribution Grids (ADGs) will incorporate a plethora of Distributed Generators (DGs) and other Distributed Energy Resources (DERs), allowing them to provide ancillary services in grid-connected mode and, if necessary, operate in an islanded mode to increase reliability and resilience. In this paper, we investigate the ability of an ADG to provide Frequency Control (FC) in grid-connected mode and ensure reliable islanded operation for a pre-specified time period. First, we formulate the operation of the grid participating in European-type FC markets as a centralized multi-period optimal power flow problem with a rolling horizon of 24 hours. Then, we include constraints to the grid-connected operational problem to guarantee the ability to switch to islanded operation at every time instant. Finally, we explore the technical and economic feasibility of offering these services on a balanced low-voltage distribution network. The results show that the proposed scheme is able to offer and respond to different FC products, while ensuring that there is adequate energy capacity at every time step to satisfy critical load in the islanded mode.

Decentralized Dynamic Power Management with Local Information

The multi-period version of the optimal power flow can tackle the power dispatch problem of modern distribution system with distributed renewable energy sources and energy storage system. In this paper, a communication-efficient decentralized optimization algorithm (DOA) for the multi-period optimal power flow problem is presented. Firstly, the power management of modern distribution system is modelled as a linear conic optimization problem based on the conically relaxed power flow equations. Secondly, some ancillary variables at the junction bus are introduced to decompose the distribution system into several separate parts. Moreover, the DOA based on the extended version of Alternating Direction Method of Multipliers (ADMM) is proposed. The DOA evolves by partial local message exchanges without central coordination. Finally, the colouring scheme, which is in accord with the network colouring used in communication protocols to avoid packet collisions, is applied in the decentralized algorithm as well.DOI: 10.5755/j01.eie.25.1.22734

Distributed transactive energy trading framework in distribution networks

In this paper, we propose a novel transactive energy trading (TET) framework to deal with the economic issues in energy trading and the technical issues in distribution system operation in a holistic manner. In particular, we innovatively integrate a bilateral energy trading mechanism with the optimal power flow (OPF) technique to increase economic benefits to individual participants, and meanwhile ensure the reliability and security of the system operation. In order to resolve the inherent conflict of interests, Nash bargaining theory is used to model the TET problem, which is further decomposed into a multiperiod OPF problem and a payment bargaining problem. Moreover, we develop an efficient distributed algorithm for solving the TET problem base on alternating direction method of multipliers (ADMM). Instead of directly solving optimization subproblems like most ADMM-based distributed algorithms, we derive closed-form solutions to all subproblems to significantly improve the computational efficiency. Finally, numerical tests on the IEEE 37-bus and 123-bus distribution systems demonstrate the effectiveness of our proposed framework and the efficiency of our distributed algorithm.

Equilibrium of Interdependent Gas and Electricity Markets With Marginal Price Based Bilateral Energy Trading

The increasing interdependencies between natural gas systems and power systems create new business opportunities in coupled energy distribution markets. This paper studies the marginal price based bilateral energy trading on the equilibrium of coupled natural gas and electricity distribution markets. Convex relaxation is employed to solve a multiperiod optimal power flow problem, which is used to clear the electricity market. A successive second-order cone programming approach is utilized to solve a multiperiod optimal gas flow problem, which is used to clear the gas market. In addition, the line pack effect in the gas network is considered, which can offer storage capacity and provide extra operation flexibility for both networks. In both problems, locational marginal energy prices are recovered from the Lagrangian multipliers associated with nodal balancing equations. Furthermore, a best-response decomposition algorithm is developed to identify the equilibrium of the coupled energy markets with bilateral gas and electricity trading, which leverages the computational superiority of SOCPs. Cases studies on two test systems validate the proposed methodology.

ADMM-Based Multiperiod Optimal Power Flow Considering Plug-In Electric Vehicles Charging

When plug-in electric vehicles (PEVs) participate in grid operation, the intertemporal feature of PEVs charging transforms the traditional optimal power flow (OPF) problem into multiperiod OPF (MOPF) problem. In the case that the population of PEVs is huge, the large number of variables and constraints renders the centralized solution technique unsuitable to solve the MOPF problem. Therefore, a distributed algorithm based on alternating direction method of multipliers is developed to decompose the MOPF into two update steps that are solved in an alternating and iterative style. To improve the solution efficiency, the second update step is transformed into a Euclidean projection problem by approximating the original objective with a surrogate function. Then, a projection algorithm is utilized to solve the approximate problem. Numerical results show that this reformulated model obtains suboptimal solutions with small relative error, but gains considerable speed-up. Furthermore, its scalability and effectiveness are tested in the 119-bus and 906-bus distribution networks.

Hybrid Stochastic-Deterministic Multiperiod DC Optimal Power Flow

Stochastic optimal power flow (OPF) formulations that minimize the expected operating costs over forecast scenarios generally result in lower costs than the standard (deterministic) OPF problem for power systems with significant forecast error, for example, from renewable energy sources. However, this type of stochastic OPF problem is more computationally demanding than the deterministic OPF, and even more so when storage units or ramp-constrained generators are included, as they require solving a multi-period OPF problem. We propose a hybrid method approaching the cost performance of the stochastic OPF problem and the computational burden of the deterministic OPF problem. Our method decomposes the problem into stochastic and deterministic subproblems, and relies on Benders’ Cuts to interface them. We present three versions of the method, which achieve different cost/computational burden trade-offs. The versions can be parametrized so that they scale well with the problem dimension. For one of the versions, we develop a multi-dimensional formulation of the Sandwich Algorithm , which is used to iteratively approximate a convex function. Through a case study using a 118-bus system, we find that our hybrid method achieves between 25% and 81% of the cost improvement of the stochastic OPF, but requires only 12 to 41% of the increased computation time required by the stochastic OPF. Both the hybrid method and the multi-dimensional Sandwich Algorithm can be used for problems outside of the field of power systems.

An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty

Renewable energy sources such as wind and solar have received much attention in recent years, and large amounts of renewable generation are being integrated into electricity networks. A fundamental challenge in power system operation is to handle the intermittent nature of renewable generation. In this paper, we present a stochastic programming approach to solve a multiperiod optimal power flow problem under renewable generation uncertainty. The proposed approach consists of two stages. In the first stage, operating points of the conventional power plants are determined. The second stage realizes generation from the renewable resources and optimally accommodates it by relying on the demand-side flexibilities. The proposed model is illustrated on a 4-bus and a 39-bus system. Numerical results show that substantial benefits in terms of redispatch costs can be achieved with the help of demand side flexibilities. The proposed approach is tested on the standard IEEE test networks of up to 300 buses and for a wide variety of scenarios for renewable generation.

Simultaneous integrated optimal energy flow of electricity, gas, and heat

In this paper, an integrated approach to optimize electrical, natural gas, and district heating networks simultaneously is studied. Several interdependencies between these infrastructures are considered in details including a nonlinear part-load performance for boilers and CHPs besides the valve-point effect for generators. A novel approach based on selecting an appropriate set of state-variables for the problem is proposed that eliminates the addition of any new variable to convert irregular equations into a regular set while the optimization problem is still solvable. As a large optimization problem, the optimal solution cannot be achieved by conventional mathematical techniques. Hence, it is better to use evolutionary algorithms instead. In this paper, the well-known modified teaching–learning based optimization algorithm is utilized to solve the multi-period optimal power flow problem of multi-carrier energy networks. The proposed scheme is implemented and applied to a typical multi-carrier energy network. Results are compared with some other conventional heuristic algorithms and the applicability and superiority of the proposed methodology is verified.

Stochastic optimal power flow based on conditional value at risk and distributional robustness

We present a computationally-efficient approach for solving stochastic, multiperiod optimal power flow problems. The objective is to determine power schedules for controllable devices in a power network, such as generators, storage, and curtailable loads, which minimize expected short-term operating costs under various device and network constraints. These schedules are chosen in a multistage decision framework to include planned power output adjustments, or reserve policies, which track errors in the forecast of power requirements as they are revealed, and which may be time-coupled. Such an approach has previously been shown to be an attractive means of accommodating uncertainty arising from highly variable renewable energy sources. Given a probabilistic forecast describing the spatio-temporal variations and dependencies of forecast errors, we formulate a family of stochastic network and device constraints based on convex approximations of chance constraints, and show that these allow economic efficiency and system security to be traded off with varying levels of conservativeness. Our formulation indicates two broad approaches, based on conditional value and risk and distributional robustness, that provide alternatives to existing methods based on chance and robust constraints. The results are illustrated using a case study, in which conventional generators plan schedules around an uncertain but time-correlated wind power injection.