Power Flow Constraints Research Articles

An ADMM-based power system partitioned black-start and parallel restoration method considering high-penetrated renewable energy

The large-scale blackouts after natural disasters have attracted much more concern these days. When a blackout occurs in a power transmission system, the whole system will be decomposed into several sub-systems and take much more time to recover. As the capacity of renewable energy continues to increase, the difficulties of the black start and restoration for a power transmission system also keep intensifying. To this end, this paper proposes a power transmission system partitioned black-start and restoration method while applying renewable energy sources to support and improve the recovery process. We first establish the power system black-start and restoration model and linearize the power flow constraints and unit generation constraints. Considering the power system can be decomposed into several sub-systems with high-capacity renewable energy sources, we propose a system partitioning method and a two-level parallel restoration model. The model realizes the independent restoration of each sub-system and is solved by the alternating direction multipliers method. Case studies on a modified New England 39-bus power system and a practical power system verify that the proposed method can offer high feasibility and effectiveness for power transmission systems with high-penetrated renewable energy sources when facing a large-scale blackout.

Multi-Source Energy Storage Stations Control Strategy Considering Implicit Linearization of The Power Flow Manifold

With the development of distributed new energy and multi-type loads, in order to realize the effective management of distributed power sources by multi-microgrids and better play the supporting role of microgrids on distributed power sources, we consider the dynamic changes of power flow in the distribution network caused by the power interaction between multi-microgrids and shared energy storage and propose an optimal dispatching strategy of multi-microgrids considering multi-source synergy considering the constraints of power flow. Since the constraint of the distribution network is a highly nonlinear mixed integer programming problem with power terms, a linearized approximation model is adopted for the power flow of the distribution network, and then a multi-objective model with minimal wind power and photovoltaic abandonment and minimum total operating cost of multi-microgrid is established. The improved IEEE18 node system is used to verify the model, and the results show that the proposed method comprehensively considers the linkage of grid-load-storage, which makes the dispatching results more realistic and more applicable.

Open capacity measurement and evaluation of n-1 security criteria considering distribution network dispatching security

In order to ensure the safety of distribution network dispatching, the open capacity evaluation, one of the distribution network operation and maintenance tools, is analyzed. Aiming at the shortcomings of traditional reactive power capacity evaluation that is too simple and cannot effectively handle multiple interconnected feeders, a new method is proposed to consider N-1 to establish security and network reconfiguration. Considering the safety factor and the minimum network loss, the open capacity is evaluated, and the interconnection switch is regenerated, which provides the best scheme for the maintenance of the distribution network. This model not only considers the power flow constraints during normal operation but also considers the switching operation constraints under fault conditions. It has the advantages of high solution quality and feasible calculation results. In order to solve the model, a two-level hybrid algorithm based on generalized Benders decomposition, a dichotomous approximation is proposed. The algorithm adopts the idea of upper approximation, lower test, and two-layer interaction. It continuously reduces the solution space through alternate iterations until the optimal solution is obtained. The test results of 22-node and 70-node systems verify the correctness and effectiveness of the model and algorithm in this paper.

Hierarchical Coordination of Transmission and Distribution System Operations in European Balancing Markets

We propose a hierarchical scheme for the coordination of transmission and distribution system operations, which is inspired by nested decomposition and tailored for integration in upcoming European balancing markets. We compare our proposal to a number of recent European research projects and pilots. We demonstrate the effectiveness of our proposal in resolving a number of transmission-distribution coordination dilemmas, including conflict resolution between network operators, self-healing, sharing charges in mutually beneficial actions, and the recursive integration of distributed resources in pan-European balancing markets. We implement a proof-of-concept market clearing platform that can match transmission and distribution system market orders, cope with non-convexities in market offers and power flow constraints, scale to systems of realistic size, and respect the decentralization of communications and information sharing which is required in European electricity markets. We demonstrate the effectiveness of our platform on large-scale instances of the Italian and Danish power systems based on data sourced from the EU Horizon 2020 SmartNet project. We demonstrate the superiority of our approach to alternative coordination schemes in terms of economic efficiency, alignment of incentives and system security.

Optimal Economic Dispatch and Power Generation for Microgrid Using Novel Lagrange Multipliers-Based Method With HIL Verification

Microgrid incorporating distributed renewable energy resources (RERs) is increasingly important owing to the goal to reach net-zero emissions by mid-century. This article deals with the optimal energy management of microgrid comprising RERs and battery energy storage system. In addition to considering power flow constraints and uncertainties of RERs, the importance of retaining profits of microgrid operators and the needs for providing extra supports to the main grid are rising. To meet all the requirements, a novel Lagrange multipliers-based method is proposed to deal with equality and inequality constraints simultaneously to directly obtain the optimal economic dispatch solution analytically. Moreover, a microgrid built in Cimei Island of Penghu Archipelago, Taiwan, is investigated to examine the compliance with the requirements of equality and inequality constraints and the performance of the Lagrange multipliers-based method. Furthermore, the comparison of the proposed method with experience-based energy management system, Newton-particle swarm optimization, and deep Q-learning network is provided to evaluate the obtained solutions. Finally, through the hardware in the loop mechanism, which is built using OPAL-RT real-time simulator with floating-point digital signal processor, the effectiveness of proposed Lagrange multipliers-based method is verified and proven to be pragmatic.

Reliability-Oriented Planning Framework for Smart Cities: From Interconnected Micro Energy Hubs to Macro Energy Hub Scale

Energy hubs, as the prospect of future energy systems, are efficient and reliable frameworks for the generation, conversion, storage, and consumption of energy in multicarrier energy systems. Existing urban facilities in smart cities (SCs) can be considered as micro energy hubs (MIEHs), whereas the SC itself can be regarded as a macro energy hub incorporating its MIEHs. Moreover, the interconnection of MIEHs is particularly important to achieve high-reliability and economical smart city energy systems (SCESs). This article presents a framework for reliability-oriented expansion planning of multicarrier energy systems in SCESs. The proposed framework tends to improve energy not supplied and customer interruption cost indices for both heat and electrical loads, as well as the energy index of reliability. The proposed multicarrier energy system facilitates interoperability between different energy carrier systems to supply electricity and heat demand simultaneously. The interconnection of MIEHs is modeled through linearized alternating current optimal power flow and natural gas network constraints, whereas full interaction of the electricity and gas networks is realized by the power-to-gas systems and combined heat and power systems. The effectiveness of the proposed mixed-integer linear programming planning model is demonstrated in the Dättwil district (Switzerland) through four scenarios, analyzing the effect of MIEH interconnection, as well as the gas and electricity interaction within an MIEH. Simulation results confirm the effectiveness of the proposed method due to a significant reduction in total investment cost and a considerable improvement in reliability indices.

Bi-objective robust planning model for optimal allocation of soft open points in active distribution network: A flexibility improvement approach

Improving system flexibility is one of the requirements of today's power grids in response to existing uncertainties and fluctuations. High penetration of renewable energy sources (RESs) poses many technical challenges to the system, making it difficult to solve unless flexibility is provided by network-side tools efficiently. In this regard, this paper uses the possibility of changing the network topology in the optimal presence of intelligent switching tools, such as soft open points (SOPs), to improve the network's operational flexibility. The penetration capacity range of RESs is defined as an index to evaluate the active distribution network (ADN) flexibility considering the different operating conditions caused by the inherent uncertainty of RESs. The more compatible a network is with a larger penetration capacity range of RESs without violating system security and power flow constraints, the more flexible the network will be in dealing with the uncertain production of such sources. The optimal site and size of SOPs, final network topology, and penetration capacity range of RESs are determined by solving a bi-objective robust optimization model cost-effectively and in a flexibility improvement approach while considering supply-side uncertainty. The proposed model is conducted on IEEE 33-bus system, and the results are presented and discussed.

Techno-Economic Energy Optimization of the Off-Grid Electrical System with Power to Gas Storage Technology

Renewable energy sources (RESs) have undeniable advantages over the recent years not only to supply electrical demand but also electrical demand. However, maximum use of the RES’s power has always been challenging as high penetration of the RESs as well as their intermittent nature might compromise the distribution networks power flow constraints. This paper proposes optimal energy operation of the off-grid distribution network (DN) with participation of the power-to-gas (PtG) storage system. In this regard, PtG system is considered as an energy supplier in the DN. The natural gas generated by using PtG is applied to backup diesel generators for meeting demand at peak times. The objective functions in the system are modeled based on technical and economic modeling including minimize the operation cost and maximize the system reliability. The optimal energy operation in the two case studies is assumed considering non-participation and participation of the PtG system. To solving of the energy optimization, particle swarm optimization algorithm is proposed. Finally, proposed case studies under numerical simulation are implemented for validation of the participation of the PtG system.

Unit commitment with AC optimal power flow constraint

Because of the enormous economic gain it may offer, unit commitment (UC) has been a primary optimization job in the daily operation planning of contemporary power systems. The AC optimal power flow (ACOPF) constraint is a method for determining the ideal load arrangement in alternating current (AC) power systems. Using unit commitment and ACOPF limitations to determine optimal load distribution is an important approach to ensure the steady functioning of power systems. The unit commitment approach with ACOPF constraint is examined in this study. The aims and contents of the study are set by analyzing the current approaches, and a piecewise linearized unit commitment method is developed that takes into consideration the ACOPF limitations and has good accuracy and practicality. Finally, to validate the method’s effectiveness, it was tested using a six-bus test system.

Risk-averse and flexi-intelligent scheduling of microgrids based on hybrid Boltzmann machines and cascade neural network forecasting

The future of energy flexibility in microgrids (MGs) is steering towards a highly granular control of the end-user customers. This calls for more highly accurate uncertainty forecasting and optimal management of risk and flexibility options. This paper presents a novel data-driven model to optimize the operation of MGs based on a risk-averse flexi-intelligent energy management system (RFEMS), considering the rising challenge of global climate change. It considers the presence of renewables, a diesel generator, and flexibility resources (FRs) containing a demand response program (DRP), distributed electric vehicles (EVs), and electric springs (ESs). In the first phase, the proposed model, by means of a novel hybrid deep-learning (DL) model, forecasts uncertain parameters associated with wind and solar generations, load demand, and day-ahead energy market price. The architecture of the proposed hybrid forecasting model is composed of several stacked restricted Boltzmann machines and a cascade neural network. In the second phase, the MG operator (MGO), based on the obtained uncertainty forecasting results, in the context of a hybrid risk-controlling model, optimizes the MG operation using the provided demand-side flexibility. The proposed optimization problem is linearized stochastic programming with robust concepts, subject to AC optimal power flow constraints, MG flexibility restrictions, and operating limits of local resources. Finally, the efficiency of the proposed RFEMS by using real German datasets on a 33-bus test MG is analyzed. Numerical results demonstrate the superior performance of the proposed forecasting model over several hybrid DL models. In particular, the root mean square error (RMSE) index for wind, solar, load, and price forecasting is improved by 53.35%, 73.24%, 80.24%, and 58.1%, respectively. Further analysis of the proposed RFEMS reveals that operating indices in two 33-bus and 69-bus test networks are significantly improved. It paves pathways to risk-averse, flexible, and economic operation of smart active distribution networks.

Community microgrid planning in Lombok Island: an Indonesian case study

Rural electrification, diesel generator replacement, and resilient electrification systems against natural disasters are among the main targets for Perusahaan Listrik Negara (PLN) in Indonesia to achieve a universally accessible, resilient, and environment-friendly electricity supply. Microgrids, therefore, become a popular and available way to achieve the aforementioned targets due to their flexibility and resiliency. This paper aims to provide a resilience-oriented planning strategy for community microgrids in Lombok Island, Indonesia. A mixed-integer linear program, implemented in the distributed energy resources customer adoption model (DER-CAM), is presented in this paper to find the optimal technology portfolio, placement, capacity, and optimal dispatch in a community microgrid. The multinode model is adopted for the planning, and hence, power flow constraints, N-1 contingency, and technology constraints are considered. The results show that the placement of photovoltaic (PV) arrays, battery energy storage systems (BESSs), and diesel generators (DGs) as backup sources in multi-node community microgrids lead to multiple benefits, including 100% rural electrification, over 25% cost savings, as well as over 22%, in particular CO2 emission reduction in multinode community microgrids.

Stochastic Coordinated Management of Electrical–Gas–Thermal Networks in Flexible Energy Hubs Considering Day-Ahead Energy and Ancillary Markets

This paper presents an optimal operation framework for electrical, gas, and thermal networks in the presence of energy hubs (EHs), so that EHs can benefit from day-ahead ancillary and energy markets. Therefore, to consider the goals of network operators (optimal operation of networks) and EHs (optimal operation in markets), the proposed model is developed in the form of a bi-level optimization. Its upper-level formulation minimizes the expected energy loss in the proposed networks based on the optimal power flow constraints and technical limits. At the lower-level problem, maximizing the expected profit of EHs in day-ahead energy and ancillary markets (including reactive and reserve regulation) is formulated based on the operational model of resources, storage devices, and responsive load in the EH framework, and the flexible constraints of EHs. This scheme includes the uncertainties of load, market price, renewable energy resources, and mobile storage energy demand, which uses the point estimation method to model them. Karush–Kuhn–Tucker is then used to extract the single-level model. Finally, by implementing the proposed scheme on a standard system, the obtained numerical results confirm the capability of the proposed model in improving the network’s operation and economic status of EHs. As a result, the proposed scheme is able to decrease operation indices such as energy losses, voltage drop, and temperature drop by approximately 28.5%, 39%, and 27.8%, respectively, compared to load flow analysis. This scheme can improve the flexibility of EHs, including non-controllable sources such as renewable resources, by nearly 100% and it obtains considerable profits for hubs.

Economic operation of networked flexi-renewable energy hubs with thermal and hydrogen storage systems based on the market clearing price model

This paper presents the energy management of flexi-renewable energy hubs in electric and thermal networks based on the market clearing price model and participation of hubs in the energy market. Renewable sources include wind sources and bio-waste units, where the latter simultaneously plays a role in electrical and thermal energy generation. Hydrogen and thermal storage are used as a source of flexibility in the hub. The proposed scheme has a two-level formulation. Its upper level considers the participation of hubs in the energy market. It maximizes the expected profit of energy hubs by observing the operational constraints of power sources and storage devices (in the form of a hub) and the hub's flexibility limitation. The lower-level problem presents the market clearing price model. In this problem, the expected operation cost of the generation units in the electric and thermal networks is minimized subject to satisfying the constraints of the optimal power flow of the mentioned networks. The Karush-Kuhn-Tucker method provides a single-level formulation of the scheme. Also, stochastic optimization is adopted to model the uncertainties of load and renewable power to examine the flexibility of energy hubs accurately. Finally, by evaluating the numerical results obtained from different study cases, the scheme can improve the operating conditions of energy networks and obtain optimal flexibility and economic conditions for energy hubs. The hydrogen storage device next to the thermal storage device can achieve 100% flexibility conditions for the hubs. Storage devices can enhance the economic status of renewable hubs by about 9.2%. The energy management of flexi-renewable hubs improves energy networks' operational and economic status by 21–24% and 8.8% compared to power flow studies.

Low-carbon economic scheduling strategy for active distribution network considering carbon emissions trading and source-load side uncertainty

The double uncertainty of the source-load side poses a new challenge to the reliability of the low carbon scheduling in the active distribution network (ADN) system. In this study, a low-carbon economic scheduling model of the ADN system is proposed, which considers step-type carbon emissions trading (CET) mechanism and source-load side uncertainty. The multi-dimensional discrete probability sequences of source-load side are converted into the global equivalent load (EL) by the proposed discretized step transformation (DST) and the convolutional sequence operation (CSO) method, and the predicted value of EL is expressed by the expected value of the EL probability sequence. By setting the probability constraint of the spinning reserve capacity, the influence of power prediction error on the ADN system is fully considered. On this basis, the chance constraint problem (CCP) is further converted to a deterministic mixed-integer linear programming (MILP) problem by linearizing power flow constraints. The proposed strategy is verified based on the IEEE 33-bus ADN system. The experimental results indicate that the system can further realize the synergy of economic benefits and environmental benefits. In addition, compared with other intelligent algorithms, the solution time of the proposed strategy is significantly reduced, and the optimization effect is greatly improved.

Small-signal stability constrained unit commitment based on decomposition and SQP-GS

This paper proposes a small-signal stability constrained unit commitment(SSSC-UC) model to ensure that the solution of SCUC can provide a sufficient small-signal stability margin. To solve the model, Benders decomposition (BD) is applied to separate the problem into a SCUC master problem, which is a mixed-integer linear programming problem, and a series of subproblems to check the AC power flow constraint and small-signal stability constraint. The small-signal stability check subproblems are non-smooth and non-linear programming problems, which are solved by Sequential Quadratic Programming with Gradient Sampling (SQP-GS). When the subproblem checks do not pass, cuts formed by the sensitivity of the spectral abscissa with respect to generator output are added to the master problem for the next iteration of the SCUC. The iteration process continues until all AC power flow and small-signal constraint violations are eliminated and a SCUC solution is found. Simulations on the New England 10-machine 39-bus system and the IEEE 54-machine 118-bus system show that our proposed SSSC-UC can guarantee small-signal stability for all time periods while SCUC cannot. Furthermore, the proposed parallel technique can speed up the computation up to 5 and 11 times respectively for the two test systems.

A techno‐economic model for enhancing PV hosting capacity through capabilities of smart inverters and soft open points

AbstractThe hosting capacity of solar photovoltaics (PVs) in the distribution network can be impacted by the violation of power flow constraints such as power loss, voltage, and line loadings. In this paper, a planning structure based on optimal PV placement and optimal operation of the smart inverters and soft open point (SOP) is proposed in order to investigate the loss of power, voltage profiles, line loadings and total operation cost of the distribution system. The stochastic nature of the daily load and PV generation is considered in power flow optimization by the proposed method. Respective objective functions are optimized using a genetic algorithm (GA) according to probabilistic power flow. While the desired objective function is optimized, the optimality of the PV locations and contribution of smart inverters and SOP is ensured through GA optimization. The proposed model is investigated through numerical analyses on IEEE 33‐bus and IEEE 69‐bus distribution systems considering different cases of reactive power supports. Developed GA is able to deal with challenges of convergence that are imposed by complex nonlinear formulations. Obtained results prove the superiority of the developed program for the investigation of the PV hosting capacity in both technical and cost aspects.

Community Resilience Optimization Subject to Power Flow Constraints in Cyber-Physical-Social Systems

This article develops a community resilience optimization method subject to power flow constraints in the cyber-physical-social systems in power engineering, which is solved using a multiagent-based algorithm. The tool that makes the nexus between the electric generation on the physical side and consumers and prosumers on the social side is the power flow algorithm. Specifically, the levels of emotion, empathy, cooperation, and the physical health of the consumers, prosumers are modeled in the proposed community resilience optimization approach while accounting for the electric power system constraints and their impact on the critical loads, which include hospitals, shelters, and gas stations, to name a few. The optimization accounts for the fact that the level of satisfaction of the society, the living standards, and the social well-being are depended on the supply of energy, including electricity. Evidently, the lack of electric energy resulting from load shedding has an impact on both the mental and the psychical quality of life, which in turn affects the community resilience. The developed constrained community resilience optimization method is applied to two case studies, including a two-area 6-buses system and a modified IEEE RTS 24-bus system.

Stochastic two-stage coordination of electric vehicles in distribution networks: A multi-follower bi-level approach

As the number of electric vehicles (EVs) continues to rise, it is essential to consider appropriate management strategies for coordinating EVs connected to different buses in the power networks. In light of this, this paper proposes a stochastic two-stage bi-level model for coordinating EVs in a distribution network with charging stations under alternating current optimal power flow (ACOPF) constraints. The scheduling problem is considered to independently minimize the costs of the distribution system operator (DSO) and EVs parked at different charging stations located at various buses of the network. In the proposed model, the DSO as the leader, and all EVs as independent followers, are individual entities who try to follow their priorities and objectives. The amount and price of exchanged power between the DSO and EVs are optimally determined in the proposed model. The proposed bi-level model has been converted to a single-level model using the Karush–Kuhn–Tucker (KKT) conditions. Afterwards, the Big M method is used to convert the non-linear equations that appear due to utilizing the KKT approach. The scenario-based uncertainty modeling is used to model the uncertainty in input data such as day-ahead and real-time market prices, EVs’ initial state of charge (SOC), and arrival/departure time. The centralized unilateral form of the model has also been developed to validate the proposed model. The results indicate that the bi-level model can lead to cost reduction for the EVs.

Coordinated active and reactive power management for enhancing PV hosting capacity in distribution networks

AbstractThis paper proposes an operational planning model based on optimal active and reactive power control strategies to enhance solar photovoltaics (PV)’ hosting capacity in distribution networks. Reactive power control is carried out through optimum static VAr compensators (SVCs) placement, while active power control is performed through flexible loads, particularly shiftable and interruptible loads. The first stage of the proposed two‐stage stochastic model assigns decision‐making regarding calculating PV hosting capacity at different nodes, in addition to the allocation and capacity of SVCs. In the second stage, the first stage decisions are assessed to ensure the power flow constraints under various uncertainties such as daily load and stochastic PV generation. The presented model is investigated through numerical analyses on modified IEEE 15‐bus and IEEE 33‐bus distribution systems considering different active‐reactive strategy cases. While most previous works only rely on one type of active or reactive power control strategy, this study investigates the challenges of the respective application of active and reactive power control in various modes of fundamental practices. The obtained results prove the superiority of the proposed hybrid active‐reactive control strategy for enhancing PV hosting capacity compared to respective active or reactive power controls.

Quantifying the benefits of shared battery in a DSO-energy community cooperation

Local energy communities are forming as a way for prosumers and consumers to invest in distributed renewable energy sources, community storage and share electricity. Meanwhile, several distribution grids have voltage problems at certain hours of the year. Local energy communities consisting of generation and storage units might be valuable flexible assets that the distribution system operator (DSO) can make use of. This article aims to study how a battery in an energy community can provide services to the distribution grid, by creating a linear optimisation model which includes power flow constraints and a battery degradation model. First, we investigate how the battery operation of an energy community impacts the voltage in the nearby buses. We find that when including the degradation model, the voltage limits are violated much less than when not including the degradation model. Next, we investigate how the battery operation differs when the energy community cooperates with an active DSO to share the battery use, and quantify how much the DSO should remunerate the energy community. We find that the energy community should get 15 € per year due to an increase in electricity and degradation costs, which equals an increase of 0.12%, compared to when the community is not providing a service. Finally, a sensitivity analysis is performed to determine which parameters are more important to consider. We find that voltage violations in the grid are sensitive to the battery replacement cost, electric vehicle charging peak and the average spot price, while the remuneration from the DSO is sensitive to the battery replacement cost. For small battery sizes and a low power-to-energy ratio, the community is not able to improve the voltage at all hours of the year.