Operation Subproblem Research Articles

Bi-level robust planning of hydrogen energy system for integrated electricity–heat–hydrogen energy system considering multimode utilization of hydrogen

This paper proposes a bi-level robust planning model to address the rational configuration of a hydrogen energy system, accounting for the impact of wind power uncertainty in an integrated electricity–heat–hydrogen energy system (IEHHES) with the increasing wind power penetration. The upper-level problem aims to determine the capacity of the hydrogen energy system in this system, whereas the lower-level problem is formulated as a two-stage robust optimization model to simulate the typical daily operational scheme of the system, considering uncertain wind turbine output and the on/off switching of devices. This model considers multiple hydrogen utilization modes and the physical characteristics of various hydrogen storage tanks. The complex bi-level robust model is intractable directly. Therefore, this bi-level robust planning model is initially decomposed into planning and operation subproblems. These subproblems are then can be solved in parallel using the alternating direction method of multipliers (ADMM) algorithm; the planning subproblem, a quadratic programming model, is solved using a commercial solver; the operating subproblem, a two-stage robust optimization model, is solved using the column and constraint generation algorithm. Finally, case studies validate the advantages and effectiveness of the developed model and algorithm.

Learning-based hierarchical control for a net-zero commercial building with solar plus storage and high EV Chargers Penetration

The integration of renewable energy resources and electric vehicles in microgrids presents a significant challenge due to generation and demand uncertainty. However, our technical and market research in Solar Plus Storage microgrids, carried out as part of a US Department of Energy's Solar Prize project, demonstrates the efficacy of advanced microgrid controls in managing this uncertainty while saving billions of dollars. The control system must be equipped with advanced optimization tools and adaptive forecasting models that minimize planning errors for future optimal operation to achieve this. This study contributes to the literature by quantifying the impact of integrating adaptive learning-based forecasting tools for PV power and electrical load at the tertiary level of a hierarchical control system. Additionally, we use the developed learning forecasters and optimization algorithms of the tertiary level to solve intertwined optimal sizing and operation subproblems as a combined problem for a solar plus storage system.

Stochastic optimal planning scheme of a zero-carbon multi-energy system (ZC-MES) considering the uncertainties of individual energy demand and renewable resources: An integrated chance-constrained and decomposition algorithm (CC-DA) approach

Renewable resources stochasticity and energy demand variation are inevitable during the operation of energy systems. Thus, this paper presents novel stochastic planning and operation of a zero-carbon multi-energy system (ZC-MES) taking the uncertainties of individual energy demand and environmental conditions into consideration. The comprehensive mathematical model is developed as an optimization problem using Monte Carlo scenario generation, fast forward scenario reduction approach, chance-constrained programming, duality theory, and big-M linearization approach. Furthermore, benders decomposition is applied to split the large-scale optimization problem into an investment master problem (MP) and operation subproblem (SP), which are then solved iteratively. The obtained results indicate that by considering all the energy demand uncertainties as an individual entity in the model, the selected capacities of PV, AC, and HWS increase by 60%, 21%, and 10.6%, respectively, while, WT, WSHP, BES, and EC reduce by 14%, 15%, 11%, and 1.09%, respectively. Also, the optimal operation cost for the proposed model reduced by 5–10% compared to other scenarios, however, its annualized investment cost is 3–12% higher but the overall economic implication is optimal. In summary, the underlying reason for this optimal result is the combination of energy storage temporal arbitrage and energy output shifting technique that was implemented by the algorithm to maintain an optimal interrelationship balance and to favour the optimal sizing of the chosen technologies.

Economic and Environmental Policy Analysis for Emission-Neutral Multi-Carrier Microgrid Deployment

Energy and global climate change crises are correlated issues since energy generation currently contributes to nearly 40% of global greenhouse gas emissions, and inevitably the escalating energy demand realization exacerbates the ongoing undesirable circumstances. As a viable solution against the concerns above, microgrid deployments with low-emission on-site resources have been receiving increasing attention from power decision-makers. Thus, this study scrutinizes the technical and financial sustainability of deploying a net-zero emission multi-carrier microgrid and determines the optimal generation configurations. Besides, the proposed emission-neutral multi-carrier microgrid model provides insights into the economic prominence of renewable energy incentives together with regulations for the short-term deployment of green resources. The objective of the proposed model is to minimize the multi-carrier microgrid deployment costs associated with the investment, operation, maintenance, energy demand shifting, monthly peak demand charge, emission, and reliability. Furthermore, load prioritization and a novel demand shifting of demand response schemes are propounded to maintain at least the continuous flow of energy for high-prioritized loads. The customer multi-carrier microgrid deployment problem is disintegrated into an investment master problem and an operation subproblem. The results indicate that notable electrical peak mitigation of about 7–23% is procured by employing the demand response scheme. Furthermore, the sensitivity analysis illustrates that renewable penetration of 30% along with dispatchable resources is required to procure the targeted share of green resources within microgrids. Finally, the economic and environmental merits of the proposed emission-neutral multi-carrier microgrid are ensured with savings and the discounted payback period of 131% and 3.977 years, respectively.

Reliability-Constrained Power System Expansion Planning: A Stochastic Risk-Averse Optimization Approach

This work presents a methodology to incorporate reliability constraints in the optimal power systems expansion planning problem. Besides Loss Of Load Probability (LOLP) and Expected Power Not Supplied (EPNS), traditionally used in power systems, this work proposes the use of the risk measures VaR (Value-at-Risk) and CVaR (Conditional Value-at-Risk), widely used in financial markets. The explicit consideration of reliability constraints in the planning problem can be an extremely hard task and, to minimize computational effort, this work applies the Benders decomposition technique splitting the expansion planning problem into an investment problem and two subproblems to evaluate the system's operation cost and the reliability index. The operation subproblem is solved by Stochastic Dual Dynamic Programming (SDDP) and the reliability subproblem by Monte Carlo simulation. The proposed methodology is applied to the real problem of optimal expansion planning of the Bolivian power system.

Reliability-based planning of district integrated energy system considering distributed energy storage and demand response

Flexibility tools like demand response, distributed storage and integration of other energy networks are all key aspects of efficient utilisation of the electrical grid. This study presents a complete model for the reliability-based planning of district integrated energy systems (IESs) considering distributed energy storage and integrated demand response. First, an optimal planning model of district IES is proposed to determine the type and capacity of new facilities to be invested over the planning horizon, for minimising total investment and operation costs. Furthermore, a joint N−1 and N−k reliability criterion is introduced to construct the complete reliability-based planning model for economical and reliable planning solutions. The proposed model is solved via a heuristic algorithm, by iteratively solving a base-case master problem and two operation subproblems to check N−1 and N−k criteria. Numerical case studies demonstrate the effectiveness of the proposed reliability-based planning model and methodology. Results show that the model can promote the flexibility of distribution systems while ensuring reliability and economy.

Distributed multi-scenario optimal sizing of integrated electricity and gas system based on ADMM

The evolution and application of energy conversion equipment such as gas turbines and power to gas (P2G) has greatly improved the coupling characteristics of integrated electricity and gas system (IEGS). Therefore, it is necessary to take natural gas system into consideration when coping with the optimal sizing problems for electricity system. However, it is difficult to solve the problem based on a single typical scenario during the long-term planning period. This paper proposes a distributed multi-scenario optimization framework based on alternating direction multiplier method (ADMM), decoupling the original optimal sizing problem into an investment sub-problem and multiple operation sub-problems considering multiple scenarios. In addition, this paper establishes a bidirectional coupling IEGS model which includes the dynamic characteristic of the gas system and uncertainties of renewable energy and load. In order to evaluate the feasibility, the proposed framework and model are applied to a modified IEEE 33 nodes system combined with 7 nodes gas system. Case studies are presented to further study the impact of operation flexibility, lifetime loss and cost reduction potential of battery energy storage system (BESS). The results indicate that the proposed framework can effectively deal with the multi-scenario optimal sizing problem of IEGS. Moreover, this method also have a good performance in analyzing the influence of flexibility, battery lifetime and multi-stage investment strategy.

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

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

Effective Dynamic Scheduling of Reconfigurable Microgrids

This paper develops an effective model for microgrid optimal scheduling with dynamic network reconfiguration. Network reconfiguration can effectively alter local power flow and thus provide an opportunity to reduce microgrid distribution network losses during grid-connected operation (supporting microgrid economic objectives) and to reduce potential load curtailments during the islanded operation (supporting microgrid reliability objectives). The proposed optimal scheduling model is decomposed into a grid-connected operation master problem and an islanded operation subproblem. A novel and highly accurate dynamic linear power flow model, with the ability of line switching, is developed and included in both problems. The optimal schedule determined in the master problem is assessed to meet the microgrid islanding feasibility in the subproblem. If infeasible, the decision variables are amended using the islanding cuts, which will accordingly revise the network reconfiguration, as well as the schedule of dispatchable units, energy storage, and adjustable loads. The simulation results on a test microgrid demonstrate the effectiveness and satisfying performance of the proposed model.

Coordinate Planning of Multiple Microgrids and Distribution Network with Mixed AC/DC Interconnection Method

This work explores the coordinate planning methods of multiple microgrids and distribution network with mixed AC/DC interconnection method which consider the coupling influence of interconnection structure and operation mode. The structure and evaluation model of the multiple microgrids system were discussed, and then system planning models were established. In order to solve the complicated combinatorial model, the benders decomposition methods were used to divide the problem into benders master problem, reliability sub-problem and operation sub-problem. Simulation results on the multiple microgrids test system with distribution network show that the proposed methods are effective.

Robust Co-Optimization Planning of Interdependent Electricity and Natural Gas Systems With a Joint N-1 and Probabilistic Reliability Criterion

As the sharp growth of gas-fired power plants and the new emergence of power-to-gas (PtG) technology intensify the interdependence between electricity and natural gas systems, it is imperative to co-optimize the two systems for improving the overall efficiency. This paper presents a long-term robust co-optimization planning model for interdependent systems, for minimizing total investment and operation costs. Beside generators, transmission lines, gas suppliers, and pipelines, PtGs and gas compressor stations are also considered as investment candidates to effectively handle wind power uncertainties in the power system and compensate pressure losses in the gas network. Furthermore, the proposed model includes a joint N-1 and probabilistic reliability criterion to promote economical and reliable planning solutions. The proposed model is solved via a decomposition approach, by iteratively solving a base-case master problem and two operation subproblems to check N-1 and probabilistic reliability criteria. Numerical case studies illustrate the effectiveness of the proposed robust co-optimization planning approach.

Network expansion planning with microgrid aggregators under uncertainty

In this paper, a bi-objective robust model is proposed for network expansion planning (NEP) considering the integration of the microgrid aggregators. The objectives include minimization of both the expansion cost and transmission lines loading index. Forced outages of system components are taken into account as the system uncertainties. A hybrid method as the combination of gravitational search algorithm (GSA) and primal-dual interior point (PDIP) method is employed to solve the nonlinear programming (NLP) problem of the NEP. In the proposed hybrid method, the operation sub-problems are solved by the PDIP method under the worst-case single component contingencies, while the expansion plan is defined as scenario independent variables obtained by the GSA algorithm. To detect the worst-case single component contingencies with the severest effects on the system security, a subsidiary optimization problem is solved for each load level of the system. A realistic network of Qom as a part of Tehran Regional Electric Company, Iran, as well as IEEE 118-bus test system are analysed to evaluate the efficiency of the proposed method. A key conclusion is that the stochastic model may not provide sufficient security level, and a robust model is required to ensure the system security against the severe contingencies.

Security-Constrained Co-Optimization Planning of Electricity and Natural Gas Transportation Infrastructures

This paper presents a co-optimization planning model that considers the long-term interdependency of natural gas and electricity infrastructures. The model incorporates the natural gas transportation planning objective in the co-optimization planning of power generation and transmission systems. The co-optimization planning model is decomposed into a least-cost master investment problem for natural gas and electricity systems which interacts with two operation subproblems representing the feasibility (security) and the optimality (economic) of the proposed co-optimization. In addition, the natural gas subproblem would check the feasibility of fuel supply transportation system as part of the proposed co-optimization planning. The co-optimization planning of electricity and natural gas infrastructures would satisfy the desired power system reliability criterion. The iterative process will continue between the co-optimization investment and the operation subproblems until an economic, secure, reliable, and fuel-supply feasible planning for the two interdependent infrastructures is obtained. Numerical simulations demonstrate the effectiveness of the proposed co-optimization planning approach.

Microgrid Planning Under Uncertainty

This paper presents a model for the microgrid planning problem with uncertain physical and financial information. The microgrid planning problem investigates the economic viability of microgrid deployment and determines the optimal generation mix of distributed energy resources (DERs) for installation. Net metering is considered for exchanging power with the main grid and lowering the cost of unserved energy and DER investments. A robust optimization approach is adopted for considering forecast errors in load, variable renewable generation, and market prices. The microgrid islanding is further treated as a source of uncertainty. The microgrid planning problem is decomposed into an investment master problem and an operation subproblem. The optimal planning decisions determined in the master problem are employed in the subproblem to examine the optimality of the master solution by calculating the worst-case optimal operation under uncertain conditions. Optimality cuts sent to the master problem will govern subsequent iterations. Numerical simulations exhibit the effectiveness of the proposed model and further analyze the sensitivity of microgrid planning results on variety levels of uncertainty.

An effective method for generation expansion planning in restructured power systems with considering emission

This paper represents a generation expansion planning (GEP) in the restructured power systems. For decoupling generation expansion planning from transmission expansion planning, a new method as T-index is used. The Benders’ decomposition is implemented to reduce the complexity of problem. The Benders’ decomposition divides the main problem into two subproblems—the first subproblem is the master problem which wants to maximize profits of each GENCO (PBGEP), and the second subproblem is the security problem which wants to satisfy security network constraints (SCGEP). Also, the second subproblem is divided into several subproblems such as feasibility subproblem, security-constrained unit commitment subproblem, T-index subproblem and optimal operation subproblem. Outputs of this algorithm included the place, type, size, and timing for the adding of new units. Also, we calculate value of each GENCO’s profit and total profit. The value of the generated emission is one of the factors for generation expansion planning in this paper. This constraint is applied in GEP to reach allowable value for total generated emission. Finally, an application of the proposed method is discussed and concluded.

Microgrid Optimal Scheduling With Multi-Period Islanding Constraints

This paper presents a model for microgrid optimal scheduling considering multi-period islanding constraints. The objective of the problem is to minimize the microgrid total operation cost which comprises the generation cost of local resources and cost of energy purchase from the main grid. The microgrid optimal scheduling problem is decomposed into a grid-connected operation master problem and an islanded operation subproblem. The microgrid capability in operating in the islanded mode for multiple hours is scrutinized by a T-τ islanding criterion. The integer scheduling decisions determined in the master problem will be examined against the microgrid islanding feasibility in the subproblem. The scheduling decisions will be revised using proper islanding cuts if sufficient generation is not available to guarantee a feasible islanding. Islanding cuts will revise generating units, energy storage systems, and adjustable loads schedules. Any change in the schedule of adjustable loads outside the operating time interval specified by consumers is penalized by an inconvenience factor in the objective. Numerical simulations demonstrate the effectiveness of the proposed microgrid optimal scheduling model and explore its economic and reliability merits.

Decomposition approach for generation and transmission expansion planning with implicit multipliers evaluation

In an electric power systems planning framework, decomposition techniques are usually applied to separate investment and operation subproblems to take benefits from the use of independent solution algorithms. Real power systems planning problems can be rather complex and their detailed representation often leads to greater effort to solve the operation subproblems. Traditionally, the algorithms used in the solution of transmission constrained operation problems take great computational advantage with compact representation of the model, which means the elimination of some variables and constraints that don't affect the problem's optimal solution. This work presents a new methodology for solving generation and transmission expansion planning problems based on Benders decomposition where the incorporation of the traditional operation models require an additional procedure for evaluating the Lagrange's multipliers associated to the constraints which are not explicitly represented yet are used in the construction of the Benders cuts during the iterative process. The objective of this work is to seek for efficiency and consistency in the solution of expansion planning problems by allowing specialized algorithms to be applied in the operation model. It is shown that this methodology is particularly interesting when applied to stochastic hydrothermal problems which usually require a large number of problems to be solved. The results of this methodology are illustrated by a Colombian system case study.

Quarter-Hourly Operation of Hydropower Reservoirs with Pumped Storage Plants

This paper formulates a short-term operation problem to determine the optimal quarter-hourly generation schedules of multiple hydropower reservoirs with pumped-storage plants. The model is a comprehensive one that incorporates the plant-based operating zones (PBOZ), the upper and lower bounds on hydrowide power, the hydraulic coupling, and the requirements for generating power and releasing water with a fluctuation tolerance. A new procedure that includes three key techniques makes the problem easier to solve. First, the original problem is temporally decomposed into several quarter-hourly reservoir operation subproblems by dividing the planning horizon into subhorizons. Second, the plant-based operating zones that are integer variables are separately determined with dynamic programming (DP) after solving an hourly reservoir operation problem, which also derives a target-guiding trajectory for the subproblems. Third, iteratively linearizing the constraints simplifies the problems and having nonlinear objective functions guarantees the convergence of the procedure. As part of the software developed for Wuling Power Cooperation, Ltd., the present model and procedure are practical and efficient in aiding users in operating the reservoirs and scheduling the hydropower generation.

Generation expansion planning: an iterative genetic algorithm approach

The generation expansion-planning problem (GEP) is a large-scale stochastic nonlinear optimization problem. To handle the problem complexity, decomposition schemes have been used. Usually, such schemes divide the expansion problem into two subproblems: one related to the construction of new plants (investment subproblem) and another dealing with the task of operating the system (operation subproblem). This paper proposes an iterative genetic algorithm (IGA) to solve the investment subproblem. The basic idea is to use a special type of chromosome, christened pointer-based chromosome (PBC), and the particular structure of that subproblem, to transform an integer constrained problem into an unconstrained one. IGA's results were compared to those of a branch and bound (B&B) algorithm-provided by a commercial package-in three different case studies of growing complexity, respectively, containing 144, 462, and 1845 decision variables. These results indicate that the IGA is an effective alternative to the solution of the investment subproblem.

Generation Expansion Planning: An Iterative Genetic Algorithm Approach

The generation expansion planning problem (GEP) is a large-scale stochastic nonlinear optimization problem. To handle the problem complexity, decomposition schemes have been used. Usually, such schemes divide the expansion problem into two subproblems: one related to the construction of new plants (investment subproblem) and another dealing with the task of operating the system (operation subproblem). This paper proposes an iterative genetic algorithm (IGA) to solve the investment subproblem. The basic idea is to use a special type of chromosome, christened the pointer-based chromosome (PBC), and the particular structure of that subproblem, to transform an integer-constrained problem into an unconstrained one. IGA's results were compared to those of a branch and bound algorithm (provided by a commercial package) in three different case studles of growing complexity, respectively containing 144, 462, and 1845 decision variables. These results indicate that the IGA is an effective altemative to the solution of the investment subproblem.