Feasible Operating Region Research Articles

Assuring optimality in surrogate‐based optimization: A novel theorem and its practical implementation in pressure swing adsorption optimization

AbstractSurrogate‐based optimization has gained significant traction in several engineering fields, given its ability to handle complex systems without significant computational burdens. However, surrogate models are approximations and may have limitations, including the possibility of artificial minima. The main contribution of this work is the derivation of a robustness test that guarantees the optimality of surrogate‐based optimization. The derivation of this metric is based on the universal approximation theorem. The full framework proposed in this work is also composed by a sampling sizing methodology to randomly select samples within a feasible operating region (FOR) resulting from the optimization population, reducing the computational cost of the analysis and avoiding biases in the robustness calculation. The applicability and importance of this methodology are demonstrated through a case study of a complex chemical process—a pressure swing adsorption (PSA) unit—which presents a high computational cost to solve optimization problems. The results highlight the need and importance of evaluating the optimality of surrogate‐based optimization schemes.

Flexibility enhancement of urban energy systems through coordinated space heating aggregation of numerous buildings

Due to the intrinsic flexibility of thermal energy in buildings, collective space heating can potentially offer significant benefits to urban energy systems. In this context, this study introduces a novel thermal energy normalisation approach to capturing the collective indoor temperature dynamics of clustered buildings. The feasible operational region of the normalised equivalent building thermal energy model is derived from individual building parameters and temperature requirements through the constraint-tightening technique. By employing the thermal energy normalisation approach, the aggregate flexibility of building populations is quantified and integrated into the energy management optimisation problem for the urban energy system operator. To associate the response of the normalised equivalent building model and individual building models, a deadbeat controller is designed to synchronise the energy levels and realise robust operation for buildings. Through a series of case studies, the simulation results demonstrate that the proposed preheating coordination strategy can facilitate energy savings for energy system operation, cost-effectively perform congestion management to ensure no local network is overloaded, and ensure the satisfaction of indoor temperature requirements.

Analyzing impact of network constraints on feasible operation region of the radial distribution networks

Recently, there has been lot of research on finding the feasible operating region (FOR) of the active distribution network (ADN) to provide ancillary services to the transmission grid. The current focus of research is on finding methods that can accurately determine the shape of the FOR and have fast computation time. However, there is little focus on analyzing how network constraints impact the shape of the FOR. This paper attempts to address this issue and provides a mathematical derivation of how network constraints, such as cable loading and voltage limits, would influence FOR. The approach is based on a linear distflow mathematical analysis. The relations derived in the analysis are verified with numerical simulation on radial low-voltage (LV) and medium-voltage (MV) networks. The results show that cable loading constraints cut the FOR in a circular way and voltage constraints cut the FOR with a straight line of slope −ϵ, which is the ratio Rn/Xn of the path from root node to the node under analysis of the radial distribution network.

Feasible operation region estimation of virtual power plant considering heterogeneity and uncertainty of distributed energy resources

The concept of the virtual power plant (VPP) has attracted extensive attention due to its distinguished capability of integrating various types of distributed energy resources (DERs). Defining the feasible operation region (FOR) is a crucial prerequisite for VPP's participation in the provision of power system services. However, considering the heterogeneity and uncertainty of DERs, it is always a challenging task to calculate the accurate FOR of VPP. In this paper, we propose a novel internal resource aggregation approach to estimate the FOR of VPP. The design of the proposed aggregation model consists of two stages. In the first stage, all the operational constraints of various DERs at the same node are expressed with a unified polytope form, and then these constraints are aggregated into one single polytope operation constraint by the computational geometry method. In the second stage, based on the aggregated polytope operation constraint at each node, combined with the dynamic line rating (DLR) and network constraints, a data-driven distributionally robust FOR estimation problem is formulated to determine the boundaries of the FOR. Numerical experiments have been conducted to validate the feasibility and superiority of the proposed approach and its applicability in handling multi-period FOR estimation.

Combined heat and power economic emission dispatch using dynamic switched crowding based multi-objective symbiotic organism search algorithm

Combined heat and power economic emission dispatch (CHPEED) problem is a highly complex, non-linear, non-convex multi-objective optimization problem due to two conflicting objectives and various operational constraints such as valve-point loading effect, power transmission loss, prohibited operating zone, and the feasible operating region of combined heat and power unit. In order to overcome these challenges, it is necessary to design an algorithm that exhibits a search behavior, which is suitable for the characteristics of objective and constraint space of the CHPEED problem. For these reasons, a dynamic switched crowding based multi-objective symbiotic organism search (DSC-MOSOS) algorithm was designed to meet the requirements and geometric space of the CHPEED problem. By applying the DSC method in the MOSOS algorithm, it was aimed to improve the exploration ability, to strengthen exploitation-exploration balance, and to prevent the catching into local solution traps. A comprehensive experimental study was carried out to prove the performance of the proposed algorithm on IEEE CEC 2020 multi-modal multi-objective problems (MMOPs) and CHPEED problem. In the experimental study conducted among eleven versions of MOSOS variations created with DSC-method and the base MOSOS algorithm on IEEE CEC 2020 MMOPs, according to Friedman scores based on the four performance metrics, the base MOSOS algorithm ranked the last. In other experimental study, the best DSC-MOSOS variant was applied to solve the CHPEED problem, where 5-, 7-, 10- and 14-unit test systems and eight case studies were considered. The important points of this study were that 10-unit and 14-unit test systems were presented to the literature, and the prohibited operating zone was considered in CHPEED problem for the first time. According to the results obtained from eight case studies obtained from the DSC-MOSOS and fourteen competitor algorithms, while the improvement in cost was between 0.2% and 16.55%, the reduction of the emission value was between 0.2 kg and 42.97 kg compared to the competitor algorithms. On the other hand, the stability of the DSC-MOSOS and the base MOSOS was evaluated using stability analysis. While the MOSOS algorithms was not able to perform a success in any case study, the DSC-MOSOS was achieved an average success rate with 91.16%. Thus, the performance of the DSC-MOSOS over the MOSOS was verified by the results of experimental studies and analysis.

Plant‐wide control for processes with recycle and narrow feasible sets

AbstractRecycling mass and energy is a feature in almost all plants and industries. It is reported as an inevitable characteristic in actual industries due to differences between the designed processes and implementation. When a process is set, engineers identify inefficiencies in the planned performance and utilize recycles to try to reduce this difference. However, although recycles help in improving a plant's overall performance compared with a serial arrangement, its effect on dynamic plant behaviour is seldom considered, and these changes begin to impact the features of processes like controllability and stability. Similarly, even though recycles affect the feasible region of individual equipment, its effect is not verified. Based on the aforementioned background, several studies have demonstrated that advanced control strategies allow for the improvement of the dynamic behaviour of complex plants. Different techniques, such as model‐based predictive control and plant‐wide control (PWC), also show that their implementation reduces the effects of recycles. However, there is no explicit methodology to design these controllers and address the impacts of recycles on dynamic behaviour and feasibility. Additionally, there is no tuning procedure to design controllers that optimize the dynamic performance of plants, including the control system. In this context, this work presents an analysis to characterize the effects of recycles on the dynamic behaviour of plants, including how they affect the feasible operating region. Based on the previous analysis, a control methodology is also proposed to design the PWC strategy, explicitly addressing the dynamical phenomena of recycles in processes.

A Novel Model-Free Deep Reinforcement Learning Framework for Energy Management of a PV Integrated Energy Hub

This paper utilizes a fully model-free and data-driven deep reinforcement learning (DRL) framework to develop an intelligent controller that can exploit information to optimally schedule the energy hub with the aim of minimizing energy costs and emissions. By posing the energy hub scheduling problem as a multi-dimensional continuous state and action space, the proposed deep deterministic policy gradient (DDPG) method enables more cost-effective control strategies. The method can lead to a more efficient operation by considering nonlinear physical characteristics of the energy hub components like nonconvex feasible operating regions of combined heat and power (CHP) units, valve-point effects of power-only units, and fuel cell dynamic efficiency. Moreover, to provide great potential for the DDPG agent to learn an optimal policy in an efficient way, a hybrid forecasting model based on convolutional neural networks (CNNs) and bidirectional long short-term memories (BLSTMs) is developed to overcome the risk associated with PV power generation that can be highly intermittent, particularly on cloudy days. The effectiveness and applicability of the proposed scheduling framework in reducing energy costs and emissions while coping with uncertainties are demonstrated by comparing it against conventional robust optimization and stochastic programming approaches as well as state-of-the-art DRL methods in different case studies.

Metaheuristic Framework for Material Screening and Operating Optimization of Adsorption-Based Heat Pumps.

The current methods applied to material screening for adsorption-based heat pumps are based on a fixed set of temperatures or their independent variation, providing a limited, insufficient, and unpractical evaluation of different adsorbents. This work proposes a novel strategy for the simultaneous optimization and material screening in the design of adsorption heat pumps by implementing a meta-heuristic approach, particle swarm optimization (PSO). The proposed framework can effectively evaluate variable and broad operation temperature intervals to search for viable zones of operation for multiple adsorbents at once. The criteria for selecting the adequate material were the maximum performance and the minimum heat supply cost, which were considered the objective functions of the PSO algorithm. First, the performance was assessed individually, followed by a single-objective approximation of the multi-objective problem. Next, a multi-objective approach was also adopted. With the results generated during the optimization, it was possible to find which adsorbents and temperature sets were the most suitable according to the main objective of the operation. The Fisher-Snedecor test was applied to expand the results obtained during PSO application and a feasible operating region built around the optima, enabling the arrangement of close-to-optima data into practical design and control tools. This approach allowed for a fast and intuitive evaluation of multiple design and operation variables.

Economic Dispatch of Combined Heat and Power Plant Units within Energy Network Integrated with Wind Power Plant

Cogeneration, also known as a combined heat and power (CHP) system, produces both power and heat simultaneously. It reduces the operating costs and emissions by utilising waste heat from steam turbines and contributes to incapacitating the intermittency of renewable energy. The CHP-economic dispatch (CHP-ED) is needed to overcome the load dynamics as well as renewable intermittency. In this work, a CHP system connected with a wind power plant is considered for analysing the CHPED within a typical power system area. This study examines, the CHPED with and without a wind integrated energy network. The main objective of this work is to minimise the total operating cost, while meeting the generators’ constraints and prioritising the wind power output. The feasible operating region, valve point loading impact, and prohibited working regions of the CHP plants are taken while finding a CHPED solution with an integrated wind turbine. To find a CHPED solution, an optimisation algorithm was applied and the algorithm was based on selecting the best and worst scenarios. A typical 48-unit structure was used for validating the considered technique’s success for CHPED with/without a wind power plant. In our investigation, we found that operational costs were significantly reduced with a wind energy system. The presented methodology will be useful for the CHPED process of the decentralised CHP units for promoting further integration of the wind turbines and other distributed clean energy resources.

Coordinated Vertical Provision of Flexibility From Distribution Systems

The large dispersion of flexibility providing units among all voltage levels of the power system requires large, comprehensive grid models to assess the impact of flexibility usage during system operation. For this reason, aggregation methods are used to enable distributed concepts. This paper proposes a decentralized and hierarchical approach for the practical implementation of coordinated, vertical flexibility provision across multiple voltage levels, with the feasible operation region as an interface between adjacent grids. A top-down disaggregation process, based on a linear OPF model, is introduced in this paper. It is used during a flexibility provision request to distribute the requested operation point change to the underlying flexibility providing units. The objective function for this disaggregation process is chosen according to operational aspects. Both implemented methods for aggregation and disaggregation of flexibility consider grid constraints. The proposed concept is field tested during regular grid operation in a real distribution system. The results of the conducted studies show that accurate system operation in the more volatile distribution systems requires shorter time intervals compared to the transmission system. Good results with small control deviations were achieved by using time intervals of one minute for the MV and ten seconds for the LV level.

Novel Framework for Simulated Moving Bed Reactor Optimization Based on Deep Neural Network Models and Metaheuristic Optimizers: An Approach with Optimality Guarantee.

Model-based optimization of simulated moving bed reactors (SMBRs) requires efficient solvers and significant computational power. Over the past years, surrogate models have been considered for such computationally demanding optimization problems. In this sense, artificial neural networks-ANNs-have found applications for modeling the simulated moving bed (SMB) unit but not yet been reported for the reactive SMB (SMBR). Despite ANNs' high accuracy, it is essential to assess its capacity to represent the optimization landscape well. However, a consistent method for optimality assessment using surrogate models is still an open issue in the literature. As such, two main contributions can be highlighted: the SMBR optimization based on deep recurrent neural networks (DRNNs) and the characterization of the feasible operation region. This is done by recycling the data points from a metaheuristic technique-optimality assessment. The results demonstrate that the DRNN-based optimization can address such complex optimization while meeting optimality.

Feasible operation region of an electricity distribution network

In the course of net zero carbon transition, electricity distribution networks are faced with great challenges brought by increasing total and peak demand due to the electrification of transport and heat, as well as the significant uncertainties from renewable power generation and customer behaviors (such as electric vehicle travelling behaviors). Therefore, distribution network operators (DNOs) need effective tools to assess the capability of distribution networks in integrating generation and demand to conduct active management and efficient expansion of networks. However, conventional scenario-based assessment methods only provide conservative and limited information on the network capability, also with exponentially increased computational burden. By contrast, another stream of methods with different philosophy, named as operation region-based methods, describe the overall picture of the network capability analytically with little computational power needed. However, the existing linearized analytical regions, which are mainly applied to electricity transmission networks, cannot describe the capability of distribution networks accurately enough. To solve these problems, a novel feasible operation region (FOR) method with quadratic analytical expressions was proposed to characterize the range of the operating states of distribution networks, where the thermal and voltage constraints will not be violated. The FOR is a geometry in a high-dimensional space, and thus a high-dimensional error analysis approach was further developed for validating the proposed method. The boundary errors are described by multiple distance functions and operational indices, and the conservativeness of the analytical boundaries are quantified. An 11 kV radial distribution network from the United Kingdom Generic Distribution System (UKGDS) was used for the case study. The simulation results show that the quadratic analytical boundaries well approximated the real boundaries of FOR. The maximum errors for thermal and voltage boundaries would maximally cause an overcurrent up to 116 % and an undervoltage down to 0.96p.u., which are able to satisfy the requirements of engineering practice. Compared to the existing linear approximation (termed as hyperplane expressions) of FOR boundaries, the proposed quadratic expressions were proved to have higher accuracy.

Energy Storage Facilities Impact on Flexibility of Active Distribution Networks: Stochastic Approach

• A stochastic economical flexibility evaluation method is proposed. • The probability distribution function of the network's flexibility is provided. • The flexibility that storage systems provide for distribution networks is quantified. • The PV generation and energy storage impacts on the flexibility are shown. • The storage capacity should be adopted for the secure distribution grid operation. Deriving benefits from a variety of flexible sources to lower or even eliminate renewable energy resources challenges is an imperative issue in the management of power systems. Constructing a well compatible flexibility evaluation method that encompasses cost minimization and flexibility improvement is crucial to tackle this. In this paper, a stochastic economical flexibility evaluation method is proposed based upon the envelope of the feasible operation region to the uncertain space. The probability distribution function of the network's flexibility is provided for each hour. Furthermore, the flexibility that storage systems as a flexible source provide for the distribution networks is quantified. The flexibility sensitivity to the storage facility capacity is scrutinized. The simulation results show the impact of PV generation and energy storage systems on the flexibility improvement. Moreover, the sensitivity outcomes reveal that which storage capacity should be adopted for the secure distribution grid operation.

Comparative study for four technologies on flexibility improvement and renewable energy accommodation of combined heat and power system

Insufficient flexibility of the combined heat and power (CHP) system brought by its inherent heat-electricity coupling limitation reduces its renewable energy consumption capacity. Accordingly, this paper integrates four technologies, including the electric boiler, heating energy storage, electrical energy storage and bypass compensation technology, into the CHP system for more flexibility. The flexibility improvement indicator and the operational model for the integrated CHP systems are developed from the feasible operation region perspectives. Besides, an operational optimization considering the punishment for renewable energy curtailment and load shedding is proposed to evaluate performance improvement quantitatively. Combined with the energy efficiency distribution within the feasible operation region, the operating performance promotion contributed by the technology integration is analyzed using a 350 MW CHP system. The results show that integrating the bypass compensation technology can increase the maximum heat-electricity ratio by 160.3% and the electricity adjustment capacity under the heating load of 375 MW by 90.95%in the same flexibility improvement rate. Besides, the electric boiler and bypass compassion technology effectively reduce total coal consumption due to their effectiveness in improving renewable energy consumption and the high energy efficiency distribution within the newly added feasible operation region. However, they hardly handle the load shedding. Inversely, the electrical and heating energy storage systems can address the load shedding but improve weakly renewable energy accommodation under a high renewable penetration rate.

Bifurcation Stability Analysis of the Synchronverter in a Microgrid

Synchronized converters are being studied as a viable alternative to address the transition from synchronous generation to power-electronics-based generation systems. One of the important features that make the synchronous generator an unrivaled alternative for power generation is its stability properties and inherent inertial response. This work presents a stability analysis of a synchronverter-based system conducted through the bifurcation theory to expose its stability regions in a grid-connected configuration with an aggregate load model conformed by a ZIP model and an induction motor model. One and two-parameter bifurcation diagrams on the gain, load, and Thévenin equivalent plane are computed and analyzed. All the results confirm the strong stability properties of the syncronverter. Some relevant findings are that the reduction in a droop gain or time constant results in Hopf bifurcations and inertia reduction, but the increase in the time constant leads to decoupling between the reactive and active power loops. It is also found that the increment of a specific time constant (τf>0.02 s) increases the stability region on the droop gains plane to all positive values. It is also found that a low lagging power factor reduces the feasible operating and stable operating regions. For a lagging power factor above 0.755, subcritical Hopf bifurcation disappears, and also, the feasible operating solution overlaps the stability region. Finally, it is also found how the Thévenin equivalent affects the stability and that the stability boundary is delimited by Hopf bifurcations. The bifurcation diagrams are numerically computed using XPP Auto software.

Peak regulation performance study of GTCC based CHP system with compressor inlet air heating method

Improving the peak regulation performance of GTCC (gas turbine combined cycle) based CHP (combined heating and power) system helps to increase the renewable energy consumption and increase the profit of the GTCC based CHP system. In this paper, the effects of different compressor inlet air temperatures on both key parameters and the thermal performance and economic performance of the GTCC based CHP system are studied and feasible operating regions of the GTCC based CHP system are obtained. Finally, taking the heating characteristic day as an example, peak regulation performances and profit change of the GTCC based CHP system are analyzed. The results show that the compressor inlet air heating method helps to enlarge the operation region of the GTCC based CHP system under the same output power. From the heating characteristic days of period 1 to period 4, the renewable energy consumptions of the GTCC based CHP system are increased by 252.15 MW, 380.17 MW, 300.8 MW and 239.96 MW, respectively. From the perspective of technical economic performance, the net annual revenue of the GTCC based CHP system is increased by 181.83 × 104 $. The dynamic payback period is 3.3 years.

Flexible operation of integrated energy system with HVDC infeed considering multi-retrofitted combined heat and power units

For the coal-dominated power system, facilitating the thermo-electric decoupling of combined heat and power (CHP) units through flexibility retrofit technologies is an effective approach to strengthen the peak-shaving capacity of the system and promote wind accommodation. This paper focuses on exploiting the flexible regulation potential of the large-scale CHP units in the power and heat integrated energy system (PHIES) with high voltage direct current (HVDC) transmission infeed, in order to well deal with the dual peak-shaving pressure arising from the HVDC delivery power and the high share of fluctuant wind power. The internal and external retrofit technologies including zero output of low-pressure cylinders (ZO-LPC), bypass compensation heating (BCH), and thermal energy storage (TES) are adopted for CHP units as retrofit options. Firstly, the PHIES including multi-retrofitted CHP units, HVDC transmission systems, and a high share of wind power is described and modeled. Then, a two-stage day-ahead scheduling model based on the improved information gap decision theory (IGDT)-stochastic method is proposed considering the probability distribution information of uncertain variables. Finally, an annual system-wide benefits evaluation framework is formulated to assess the economic and environmental benefits of multi-retrofitted CHP units and compare the system gain value of different retrofit projects. Numerical results indicate that the thermo-electric feasible operating regions of CHP units can be comprehensively expanded with the cooperation of the proposed retrofit technologies, so as to greatly relieve wind curtailment and reserve risk of the whole system. Moreover, sensitivity analysis for diverse operation features of HVDC and different wind power installed capacity is illustrated to further verify the robust adaptability and effectiveness of multi-retrofitted CHP units in the PHIES with HVDC infeed.

Identification and quantification of the flexibility potential of a complex industrial process for ancillary services provision

As the share of variable renewable energy sources in the electricity generation mix increases, so does the need for power system flexibility. Demand side flexibility has been identified as a great opportunity to facilitate the integration of this volatile production. An important part of demand side flexibility is the modulation of the consumption of industrial processes. With the emergence of ancillary services markets, operating industrial processes in a flexible manner might generate additional value. This paper proposes a flexibility assessment tool to quantify the potential of a given industrial plant for grid services provision. We start by formulating the feasible operating region of a given industrial asset, generating a set of operating points and their corresponding power ramping potential. A weekly simulation is then performed which leads to a set of most-observed operating points, themselves leading to a set of potential ancillary services bids from the industrial process.

An iterative quota calculation method for congestion management and optimal grid utilization

A quota-based approach can help grid operators deal with congestions in distribution grids in a non-discriminatory way for customers. The quota limits the maximum feed-in or consumption of a group of flexibility providing units (FPU) within a grid cluster. The novel iterative quota calculation (IQC) method is introduced in this paper. In this approach, the maximal active power limits of the FPU are constantly adapted, and the feasible operating region (FOR) of the grid is computed. The quota is computed from the resulting FORs after ensuring that the FPU operation cannot cause grid instability. The proposed method is compared to a previously developed static approach in a real LV grid. Results show the benefits of adding reactive power to the quota calculation, especially in distribution grids with inadequate reactive power compensation.

Review of Methodologies for the Assessment of Feasible Operating Regions at the TSO–DSO Interface

The Feasible Operating Region (FOR) is defined as a set of points in the PQ plane that includes all the feasible active and reactive power flows at the Transmission System Operator (TSO)–Distribution System Operator (DSO) interconnection. Recent trends in power systems worldwide increase the need of cooperation between the TSO and the DSO for flexibility provision. In the current landscape, the efficient and accurate estimation of the FOR could unlock the potential of the DSO to provide flexibility to the TSO. To that end, much existing research has tackled the problem of FOR estimation, which is a challenging problem. However, no research that adequately organizes the literature exists. This work aims to fill this gap. Three categories of FOR estimation methods were identified: Geometric, Random Sampling, and Optimization-Based methods. The basic principles behind each method are analyzed and the most significant works involving each method are presented. For the reviewed works, we focus on the types of flexibility providing units included in the FOR estimation, the examination of time dependence, and the monetization of the FOR. Finally, the strengths and weaknesses of each category of methods are compared, providing a holistic review of the available FOR estimation methods.