Multi-period AC Optimal Power Flow Research Articles

A Fully-Decentralized Transactive Energy Management Under Distribution Network Constraints via Peer-to-Peer Energy Trading

Peer-to-peer (P2P) energy trading is seen as a promising method for distributed transactive energy (TE) management. Since distribution network is used for electricity transfer, physical constraints should be imposed during the P2P trading. In this paper, we propose a P2P-based distributed TE management approach considering distribution network constraints and product differentiation for P2P energy trading between different buses. A multi-period AC optimal power flow (OPF) model is used to monitor power flow in distribution system, and the exactness of second-order cone relaxation is recovered by the convex-concave procedure, making sure that P2P transactions do not violate network constraints. Moreover, we propose a fully-decentralized variant of alternating direction method of multipliers for clearing P2P transactions in a fully-decentralized manner under AC power flow constraints. Our proposed variant does not need any interactions with the central supervisor in comparison with the traditional one. Finally, numerical results on IEEE 33-bus and 141-bus distribution systems verify the effectiveness of our proposed method in ensuring physical feasibility, lowering data communication and protecting data privacy during P2P energy trading.

A Multi-Period Charging Service Pricing Game for Public Charging Network Operators Considering the Dynamics of Coupled Traffic-Power Systems

The proliferation of electric vehicles (EVs) couples the operations of traffic systems and power systems, necessitating the interdependent traffic-power modeling to optimize the on-road EV charging decisions. In this paper, the multi-period charging service pricing interactions between multiple charging network operators (CNOs) are discussed considering the dynamics of traffic-power systems. A multi-period user equilibrium model considering mixed vehicle types is formulated to describe the possible vehicle trip transitions between different periods in urban transportation network. For the power distribution network, a convexified multi-period AC optimal power flow model is adopted for local electricity market clearing. With the dynamics of traffic-power systems, the pricing interaction between multiple CNOs is a non-cooperative game. We analyze the existence of Nash Equilibrium with fixed-point theory, and propose an iterative method based on the best response strategy to find <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -Nash Equilibrium. Numerical studies based on an interdependent power-traffic system consisting of two 18-node power distribution networks and one revised Nguyen-Dupuis transportation network demonstrate that with the proposed CNOs’ charging pricing strategy, the CNOs’ service profits can increase by 1%-3% while the PDNs’ operation costs decrease about 1%-2% for the interdependent traffic-power system.

Three Solution Approaches to Stochastic Multi-Period AC Optimal Power Flow in Active Distribution Systems

This paper proposes three novel solution approaches (A1, A2, A3) to solve stochastic multi-period AC optimal power flow (S-MP-OPF) for day-ahead flexibility procurement from distributed energy resources (DER) in active distribution systems (ADSs). The S-MP-OPF is a mixed-integer nonlinear programming (MINLP) problem due to the binary variables modeling the operation of storage devices and flexible loads. The proposed three approaches have a shared common first step, which resorts to a new mixed-integer linear programming (MILP) model approximation of the S-MP-OPF problem. The MILP model employs second-order Taylor series expansion of trigonometric terms and formulates the linear approximations relying on variables such as square of voltage magnitude and voltage angle difference. This first step serves also the purpose of fixing the binary variables to the values computed by the MILP problem. Then, the approach A1 only checks the AC feasibility of MILP solution while approaches A2 and A3 further optimize continuous variables. Specifically, the sophisticated heuristic approach A2 employs sequential linear programming and AC power flow while the approach A3 models and solves directly the remaining nonlinear programming (NLP) problem. The performances of these approaches, a benchmark MINLP solver, and a state-of-the-art method are thoroughly compared in three radial or weakly meshed ADSs of 34, 31, and 191 nodes, respectively. The numerical results indicate that, albeit the approach A2 performs best overall, these approaches present distinct accuracy vs speed trade-offs, which make them suitable to problems of different sizes and diverse accuracy or speed requirements.

A novel two-stage TSO–DSO coordination approach for managing congestion and voltages

This paper proposes a novel approach to TSO–DSO coordination in day-ahead operation planning for the procurement of ancillary services (AS) such as congestion management and voltage control. The approach overcomes two major issues hindering practical applicability of existing TSO–DSO coordination mechanisms, namely the computational complexity due to the large number of times the TSO and DSO problems are resolved as well as the inability to map analytically the cost and amount of flexibility at DSO level into TSO problem. To this end, a two-fold novelty of our approach consists of the decomposition of the overall AS problem into two sequential stages, which seek the procurement of: (i) “active power related” AS (i.e., for congestion management) and then (ii) the “reactive power related” AS (i.e., for voltage support), respectively as well as a fast approximation of the cost of aggregated active and reactive power flexibilities of active distribution systems (ADSs). Unlike existing mechanisms, the proposed approach considers real-world challenging aspects such as the N-1 security at TSO level and operation uncertainties at both TSO and DSO levels. Accordingly, the approach relies on tailored versions of stochastic multi-period AC security-constrained optimal power flow (S-MP-SCOPF) at TSO level and stochastic multi-period AC optimal power flow (S-MP-OPF) at DSO level, which are formulated as non-linear programming (NLP) problems. The importance and performance of the proposed approach are illustrated on a power system connecting a 60-bus transmission system (under 33 N-1 contingencies) with five 34-bus ADSs.

BATTPOWER application: Large-scale integration of EVs in an active distribution grid – A Norwegian case study

With the considerable increase of Distributed Energy Resources (DER), reliable and cost-effective operation of distribution grids becomes challenging. The efficient operation relies on computationally dependable and tractable optimisation solvers, which may handle: 1) non-linear AC power flow constraints, and 2) time-linking variables and constraints and objectives of DER, over the operational horizon. In this paper, we introduce an application of a high-performance MultiPeriod AC Optimal Power Flow (MPOPF) solver, called “BATTPOWER”, to simulate active distribution grids for a near-future scenario. A large-scale Norwegian distribution grid along with a large population of Electric Vehicles (EV) are here taken as the case-study. We suggest and analyse three operational strategies (in terms of control of charge scheduling fleet of EV) for the Distribution System Operator (DSO): (a) uncoordinated charge scheduling, (b) coordinated charge scheduling with the objective of energy cost-minimisation without operational constraints of the grid, and (c) coordinated charge scheduling with the objective of energy cost-minimisation along with the operational constraints of the grid. The results demonstrate that the uncoordinated charging would lead to: 1) overloading of lines and transformers when the share of EVs is above 20%, and 2) higher operational costs than the proposed control strategies of (b) and (c). In strategy (b) operational line/transformer limits are violated when the populations of EVs are growing above 36%. This implies that current market design must be altered to allow active control of a large proportion of DERs within grid operational limits to achieve cost minimization at system level. To our knowledge, the work presented in this paper is the first ever attempt to do a comprehensive analysis of the impact of EV charging demand on a real Norwegian distribution grid. Moreover, the inference of the analysis says that the Norwegian distribution networks are more prone to congestion problems than the voltage problems for the EV demand which includes a smart charging scheme accounting for grid conditions.

Heuristic Application on Energy Storage System Allocation in Wind Integrated Power System

Increasing penetration of renewable energy significantly alters the network power flow in terms of direction as well as magnitude. The intermittent and uncertain nature of renewable inputs is a major concern since the power flow in the system is affected considerably. Hence to support bulk integration of renewable energy in the power system, bulk or distributed energy storage systems can be implemented. The energy storage system is utilized to absorb the excess power and meet the demand to avoid violation of system constraints. In this work, a multi-period ac optimal power flow (OPF) problem with energy storage systems (ESSs) is formulated and a set of candidate buses for ESS installation are identified based on economic criterion. A novel hybrid approach of conventional cum heuristic method, newton raphson based particle swarm optimization (NRPSO) method is proposed to optimize the allocation problem. Tests are carried out on IEEE 14-bus system and modified IEEE 14–bus system integrated with wind generation for variable load condition using MATLAB, to assess the optimal location of energy storages on system operation.

A Novel Tractable Methodology to Stochastic Multi-Period AC OPF in Active Distribution Systems Using Sequential Linearization Algorithm

The ongoing transition of passive distribution networks to active distribution systems (ADSs) calls for the development of sophisticated and tractable tools to address the needs and challenges of future ADSs. In this regard, this work proposes a novel tractable methodology for flexibility procurement via stochastic multi-period AC optimal power flow (S-MP-OPF). The first novelty of the proposed methodology is the formulation of a new mixed-integer linear programming (MILP) model, which develops novel linear approximations for all nonlinear constraints (i.e., active and reactive power flows and branch currents) that ensure tractability. The proposed linearization approach relies on the second-order Taylor series expansion of trigonometric terms, does not hinge on the flat-voltage, near-voltage and small angle assumptions, and formulates the linear approximations using square of voltage magnitude and voltage angle difference variables. The second novelty is a sophisticated heuristic sequential linearization algorithm (SLA) which incorporates and improves the accuracy of the MILP model in an iterative manner. The bench-marking of proposed SLA is done on a 34-bus ADS for a comprehensive set of flexible options, whereas its versatility and scalability is demonstrated on real-world 31-bus weakly-meshed and 191-bus radial ADSs. Extensive numerical analyses show that the proposed SLA leads to a highly accurate and feasible solution with small optimality gap within few iterations, under normal and stressed operating conditions, outperforms alternative methods in terms of solution accuracy and computational efficiency, and is scalable to large S-MP-OPF problems.

Comparative Performance of Multi-Period ACOPF and Multi-Period DCOPF under High Integration of Wind Power

Today, the power system operation represents a challenge given the security and reliability requirements. Mathematical models are used to represent and solve operational and planning issues related with electric systems. Specifically, the AC optimal power flow (ACOPF) and the DC optimal power flow (DCOPF) are tools used for operational and planning purposes. The DCOPF versions correspond to lineal versions of the ACOPF. This is due to the fact that the power flow solution is often hard to obtain with the ACOPF considering all constraints. However, the simplifications use only active power without considering reactive power, voltage values and losses on transmission lines, which are crucial factors for power system operation, potentially leading to inaccurate results. This paper develops a detailed formulation for both DCOPF and ACOPF with multiple generation sources to provide a 24-h dispatching in order to compare the differences between the solutions with different scenarios under high penetration of wind power. The results indicate the DCOPF inaccuracies with respect to the complete solution provided by the ACOPF.

BATTPOWER Toolbox: Memory-Efficient and High-Performance Multi-Period AC Optimal Power Flow Solver

With the introduction of massive renewable energy sources and storage devices, the traditional process of grid operation must be improved in order to be safe, reliable, fast responsive and cost efficient, and in this regard power flow solvers are indispensable. In this paper, we introduce an Interior Point-based (IP) Multi-Period AC Optimal Power Flow (MPOPF) solver for the integration of Stationary Energy Storage Systems (SESS) and Electric Vehicles (EV). The primary methodology is based on: 1) analytic and exact calculation of partial differential equations of the Lagrangian sub-problem, and 2) exploiting the sparse structure and pattern of the coefficient matrix of Newton-Raphson approach in the IP algorithm. Extensive results of the application of proposed methods on several benchmark test systems are presented and elaborated, where the advantages and disadvantages of different existing algorithms for the solution of MPOPF, from the standpoint of computational efficiency, are brought forward. We compare the computational performance of the proposed Schur-Complement algorithm with a direct sparse LU solver. The comparison is performed for two different applicational purposes: SESS and EV. The results suggest the substantial computational performance of Schur-Complement algorithm in comparison with that of a direct LU solver when the number of storage devices and optimisation horizon increase for both cases of SESS and EV. Also, some situations where computational performance is inferior are discussed.

Graph-Based Modeling and Decomposition of Energy Infrastructures

Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these problems as graph-structured optimization problems, and illustrate how their structure can be exploited at the modeling level (for parallelizing function/derivative computations) and at the solver level (for parallelizing linear algebra operations). Specifically, we present a restricted additive Schwarz scheme that enables flexible decomposition of complex graph structures within an interior-point algorithm. The proposed approach is implemented as a general-purpose nonlinear programming solver that we call MadNLP.jl; this Julia-based solver is interfaced to the graph-based modeling package Plasmo.jl. The efficiency of this framework is demonstrated via problems arising in transient gas network optimization and multi-period AC optimal power flow. We show that our framework accelerates the solution (compared to off-the-shelf tools) by over 300%; specifically, solution times are reduced from 72.36 sec to 23.84 sec for the gas problem and from 515.81 sec to 149.45 sec for the power flow problem.

A Real-Time Optimization with Warm-Start of Multiperiod AC Optimal Power Flows

We present a real-time optimization strategy based on warm-start for solving a moving horizon of multiperiod AC optimal power flow (ACOPF) problems. In each horizon, ACOPFs are temporally interlinked via generator ramp constraints, and we assume that each horizon needs to be solved every few seconds or minutes. We introduce two approximate tracking schemes that closely follow a solution path consisting of strongly regular points. We present theoretical results bounding the tracking error by the square of the parameter changes between time periods. Experimental results for networks of sizes up to 9K buses show a fast computation time while maintaining a good solution quality, thus making our approach well suited for real-time circumstances.

Exploiting OLTC and BESS Operation Coordinated with Active Network Management in LV Networks

The large number of small scale Distributed Energy Resources (DER) such as Electric Vehicles (EVs), rooftop photovoltaic installations and Battery Energy Storage Systems (BESS), installed along distribution networks, poses several challenges related to power quality, efficiency, and reliability. Concurrently, the connection of DER may provide substantial flexibility to the operation of distribution grids and market players such as aggregators. This paper proposes an optimization framework for the energy management and scheduling of operation for Low Voltage (LV) networks assuring both admissible voltage magnitudes and minimized line congestion and voltage unbalances. The proposed tool allows the utilization and coordination of On-Load Tap Changer (OLTC) distribution transformers, BESS, and flexibilities provided by DER. The methodology is framed with a multi-objective three phase unbalanced multi-period AC Optimal Power Flow (MACOPF) solved as a nonlinear optimization problem. The performance of the resulting control scheme is validated on a LV distribution network through multiple case scenarios with high microgeneration and EV integration. The usefulness of the proposed scheme is additionally demonstrated by deriving the most efficient placement and sizing BESS solution based on yearly synthetic load and generation data-set. A techno-economical analysis is also conducted to identify optimal coordination among assets and DER for several objectives.

Efficient Allocation Strategy of Energy Storage Systems in Power Grids Considering Contingencies

This paper addresses the allocation of Energy Storage Systems (ESSs) in power grids by finding the optimal number of ESSs and their locations and sizes with the goal of improving reliability in contingency states. We propose a contingency-sensitivity-based heuristic to decide the optimal number of ESSs and the most effective locations for ESSs support, while circumventing the combinatorial nature of the siting problem. A contingency sensitivity index (CSI) is proposed which represents the impacts of contingencies on the network buses. The CSI ranks the buses, such that those with higher impacts have the privilege for installing ESSs. For the ESSs being fixed, the sizing is formulated as a multi-period AC optimal power flow (OPF) problem and solved by Self-Organizing Hierarchical Particle Swarm Optimization with Time Varying Acceleration Coefficients (HPSO TVAC). The optimal ESSs sizes are selected by minimizing a total cost, which includes investment cost of storage devices, bus voltage deviation cost and average network losses cost. Uncertainties of the renewable generation are accounted by considering different realizations of the generation profiles, then, ESSs sizes are selected by taking the worst case approach. The proposed methodology has been demonstrated on the modified IEEE 30-bus system and Tunisian Grid. The obtained results show the effectiveness of the proposed methodology and the related reliability merits.

Optimal Operation of Electric Railways With Renewable Energy and Electric Storage Systems

This paper proposes a methodology for optimal operation of railway electric energy systems considering renewable energy sources (PV panels and wind turbines), regenerative braking capabilities and hybrid electric energy storage systems (ultracapacitors and batteries). The uncertainties associated to renewable energies are taken into account through a scenario tree approach. All these elements are integrated into a multi-period AC optimal power flow problem. This problem is then cast as a large-scale nonlinear optimization problem. The aim is to study the potential for energy and economic savings of the railway operation as well as energy storage systems behavior. A real case study is analyzed for a Spanish high-speed railway line. Results are reported for several cases comparing four different operation modes.

The Adaptive Robust Multi-Period Alternating Current Optimal Power Flow Problem

This paper jointly addresses two major challenges in power system operations: 1) dealing with non-convexity in the power flow equations, and 2) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period AC optimal power flow problem (AC-OPF) with detailed modeling considerations, such as reactive capability curves of conventional and renewable generators and transmission constraints. This paper then applies strong second-order cone programming (SOCP)-based convex relaxations of AC-OPF combined with the use of an alternating direction method to identify worst-case uncertainty realizations, and also presents a speed-up technique based on screening transmission line constraints. Extensive computational experiments show that the solution method is efficient and that the robust AC OPF model has significant advantages both from the economic and reliability standpoints as compared to a deterministic AC-OPF model.

Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation

Renewable generation and energy storage are playing an ever increasing role in power systems. Hence, there is a growing need for integrating these resources into the optimal power flow (OPF) problem. While storage devices are important for mitigating renewable variability, they introduce temporal coupling in the OPF constraints, resulting in a multiperiod OPF formulation. This paper explores a solution method for multiperiod AC OPF that combines a successive quadratic programming approach (AC-QP) with a second-order cone programming (SOCP) relaxation of the OPF problem. The SOCP relaxation's solution is used to initialize the AC-QP OPF algorithm. Additionally, the lower bound on the objective value obtained from the SOCP relaxation provides a measure of solution quality. This combined method is demonstrated on several test cases with up to 4259 nodes and a time horizon of eight time steps. A comparison of initialization schemes indicates that the SOCP-based approach offers improved convergence rate, execution time, and solution quality.

Sensitivity Analysis on Locations of Energy Storage in Power Systems With Wind Integration

The penetration of renewable energy sources, particularly wind energy, into power systems has been rapidly increasing in recent years. However, the integration of wind power has posed many challenges for power system operation. For instance, this type of energy source is relatively variable and unpredictable. The installation of this renewable source might require the grid to transmit power at full capacity and some transmission lines could become congested. As a result, in some operating conditions, wind power could be curtailed, which will drive up costs for system operators. One of the actions that can be taken to support the integration of the wind is using energy storage systems. In this paper, a multiperiod ac optimal power flow problem with battery energy storages (BESs) is formulated and sets of candidate buses for BES installation are identified based on an economic criterion. Tests are carried out on IEEE 14-bus and IEEE 118-bus systems to assess the robustness of storage location on system operation.

Optimal Sizing and Control of Energy Storage in Wind Power-Rich Distribution Networks

This paper presents a planning framework to find the minimum storage sizes (power and energy) at multiple locations in distribution networks to reduce curtailment from renewable distributed generation (DG), specifically wind farms, while managing congestion and voltages. A two-stage iterative process is adopted in this framework. The first stage uses a multi-period AC optimal power flow (OPF) across the studied horizon to obtain initial storage sizes considering hourly wind and load profiles. The second stage adopts a high granularity minute-by-minute control driven by a mono-period bi-level AC OPF to tune the first-stage storage sizes according to the actual curtailment. Congestion and voltages are managed through the optimal control of storage (active and reactive power), on-load tap changers (OLTCs), DG power factor, and DG curtailment as last resort. The proposed storage planning framework is applied to a real 33-kV network from the North West of England over one week. The results highlight that by embedding high granularity control aspects into planning, it is possible to more accurately size storage facilities. Moreover, intelligent management of further flexibility (i.e., OLTCs, storage, and DG power factor control) can lead to much smaller storage capacities. This, however, depends on the required level of curtailment.

Information Gap Decision Theory-Based Congestion and Voltage Management in the Presence of Uncertain Wind Power

The supply of electrical energy is being increasingly sourced from renewable generation. The variability and uncertainty of renewable generation, compared to a dispatchable plant, is a significant dissimilarity of concern to the traditionally reliable and robust power system. This change is driving the power system toward a more flexible entity that carries greater amounts of reserve. For congestion management purposes, it is of benefit to know the probable and possible renewable generation dispatch, but to what extent will these variations effect the management of congestion on the system? Reactive power generation from wind generators and demand response flexibility are the decision variables here in a risk averse multiperiod AC optimal power flow (OPF) seeking to manage congestion on distribution systems. Information Gap Decision Theory is used to address the variability and uncertainty of renewable generation. In addition, this work considers the natural benefits to the congestion on a system from the over estimation of wind forecast; providing an opportunistic schedule for both demand response nodes and reactive power provision from distributed generation.

Minimizing the Reactive Support for Distributed Generation: Enhanced Passive Operation and Smart Distribution Networks

Renewable distributed generation (DG), primarily wind power, will represent the lion's share of the new generation capacity that will be connected to distribution systems. However, while both firm and variable generation present our traditionally passive distribution networks with well-established technical challenges, the requirements and practices related to the power factor operation of these generation plants might lead to undesirable effects at the transmission level with the reactive power support needed by high penetrations of DG capacity potentially impacting on weak areas of the transmission grid. In this work, this problem is formulated as the minimization of the reactive support for DG and is investigated using two different operational perspectives: adopting passive but enhanced power factor and substation settings, and implementing Smart Grid control schemes. These two approaches are modeled using a tailored multi-period AC optimal power flow technique that caters for the variability of demand and generation, and considers N-1 contingencies. The results demonstrate that the enhanced passive approach is able to achieve a performance almost as good as Smart Grid control without the need for any additional investment.