Expected System Cost Research Articles

Interpreting the value of flexibility in AC security-constrained transmission expansion planning via a cooperative game framework

Security-constrained transmission expansion planning (SCTEP) is an inherently complex problem that requires simultaneously solving multiple contingency states of the system (usually corresponding to N-1 security criterion). Existing studies focus on effectively finding optimal solutions; however, single optimal solutions are not sufficient to interpret the value of flexibility (e.g., from energy storage systems) and support system planners in well-informed decision making. In view of planning uncertainties, it is necessary to estimate the contributions of flexibility to various objectives and prioritise the most effective investments. In this regard, this work introduces a SCTEP tool that enables interpreting the value of flexibility in terms of contributions to avoided load curtailment and total expected system cost reduction. Inspired by cooperative game theory, the tool ranks the contributions of flexibility providers and compares them against traditional line reinforcements. This information can be used by system planners to prioritise investments with higher contributions and synergistic capabilities.

The impact of pumped hydro energy storage configurations on investment planning of hybrid systems with renewables

The pumped hydro energy storage (PHES) systems can be installed in various configurations depending on the specific geographical and hydrological conditions. Closed-loop PHES systems are off-stream and have no natural inflow to the system. However, open-loop systems are on-stream and have natural inflows to the upper and/or lower reservoirs. In this study, we develop two-stage stochastic programming models for various PHES configurations to investigate how the choice of PHES configuration impacts the sizing decisions and costs of a hybrid system that includes a renewable power generator co-operated with PHES. Our numerical results show that using a PHES facility instead of a conventional hydropower system reduces the expected system cost and mismatched demand significantly. Open-loop PHES facilities perform better than closed-loop PHES and seawater-PHES facilities, dramatically lowering the need for fossil fuels in demand fulfillment. The most cost-efficient PHES configuration is when there is natural inflow to the upper reservoir. Using solar energy instead of wind as the renewable source significantly increases the requirement for larger upper reservoirs in on-stream open-loop PHES facilities, while reducing the expected system cost for all configurations.

Multi-interval rolling-window joint dispatch and pricing of energy and reserve under uncertainty

In this paper, the intra-day multi-interval rolling-window joint dispatch and pricing of energy and reserve is studied under increasing volatile and uncertain renewable generations. A look-ahead energy-reserve co-optimization model is proposed for the rolling-window dispatch, where possible contingencies and load/renewable forecast errors over the look-ahead window are modeled as several scenario trajectories, while generation, especially its ramp, is jointly scheduled with reserve to minimize the expected system cost considering these scenarios. Based on the proposed model, marginal prices of energy and reserve are derived, which incorporate shadow prices of generators’ individual ramping capability limits to eliminate their possible ramping-induced opportunity costs or arbitrages. We prove that under mild conditions, the proposed market design provides dispatch-following incentives to generators without the need for out-of-the-market uplifts, and truthful-bidding incentives of price-taking generators can be guaranteed as well. Some discussions are also made on how to fit the proposed framework into current market practice. These findings are validated in numerical simulations.

Enabling inter-area reserve exchange through stable benefit allocation mechanisms

The establishment of a single European day-ahead market has accomplished the integration of the regional day-ahead markets. However, reserve provision and activation remain an exclusive responsibility of regional operators. This limited spatial coordination and the separated structure hinder the efficient utilization of flexible generation and transmission, since their capacities have to be ex-ante allocated between energy and reserves. To promote reserve exchange, recent work proposed a preemptive model that withdraws a portion of the inter-area transmission capacity available from day-ahead energy for reserves by minimizing the expected system cost. This decision-support tool, formulated as a stochastic bilevel program, respects the current architecture but does not suggest area-specific costs that guarantee sufficient benefits for areas to accept the solution. To this end, we formulate a preemptive model in a framework that allows application of game theory methods to obtain a stable benefit allocation, i.e., an outcome immune to coalitional deviations ensuring willingness of areas to coordinate. We show that benefit allocation mechanisms can be formulated either at the day-ahead or the real-time stages, in order to distribute the expected or the scenario-specific benefits, respectively. For both games, the proposed benefits achieve minimal stability violation, while allowing for a tractable computation with limited queries to the bilevel program. Our case studies, based on an illustrative and a more realistic test case, compare our method with well-studied benefit allocations, namely, the Shapley value and nucleolus, and analyze the factors that drive these allocations (e.g., flexibility, network structure, wind correlations). We show that our method performs better in stability and tractability.

Competitive Energy Storage and the Duck Curve

Power systems with high penetrations of solar generation need to replace solar output when it falls rapidly in the late afternoon—the duck curve problem. Storage is a carbon-free solution to this problem. This essay considers investment in generation and storage to minimize expected cost in a Boiteux-Turvey-style model of an electric power system with alternating daytime time periods, with solar generation, and nighttime periods, without it. In the most interesting cases, if energy market prices are uncapped, all expected cost minima are long-run competitive equilibria, and the long-run equilibrium value of storage capacity minimizes expected system cost conditional on generation capacities.

Strategic network expansion planning with electric vehicle smart charging concepts as investment options

The electrification of transport seems inevitable as part of global decarbonization efforts, but power system integration of electric vehicles faces numerous challenges, including a disproportionately high demand peak necessitating expensive infrastructure investments. Moreover, long-term developments in the power sector are characterized by great uncertainty, which increases the risk of making incorrect investment decisions leading to stranded assets. A cost-effective system integration of electrified transport would therefore not be possible without the implementation of smart charging concepts in combination with strategic network expansion planning that considers the impact of uncertainties. This paper proposes investment and operation models of Grid-to-Vehicle (G2V), Vehicle-to-Grid (V2G), and Vehicle-to-Building (V2B) for the large-scale and long-term network expansion planning problem under multi-dimensional uncertainty. Additionally, it presents a multi-stage stochastic planning framework that can identify optimal investment strategies such that the expected system cost is minimized and the risk of stranded investments is reduced. The models are demonstrated on the IEEE 24-bus test system and applied in a case study of the power system of Great Britain. The results highlight G2V, V2G and V2B as effective non-network alternatives to conventional reinforcement that could generate substantial economic savings and act as hedging instruments against uncertainty. For the case of Great Britain, the Option Values of G2V, V2G, and V2B could amount to £1.2bn, £10.8bn, and £10.1bn, respectively, over a 40-year horizon. Although the quantified values are system-specific, the paper presents key observations on the role of smart charging concepts as investment options that can be generalized for any low-carbon power system.

A maintenance strategy based on system reliability considering imperfect corrective maintenance and shocks

In this study, an innovative maintenance strategy is proposed for systems subject to normal degradation and shock process. The shock process is a non-homogeneous Poisson process, and a changing factor is considered for the dependence between the normal degradation and the occurrence intensity of shocks. The system reliability is divided into three stages, based on which maintenance activities are implemented. In Stage 1 and Stage 2, when a fatal shock occurs, corrective maintenance is performed if the number of completed corrective maintenance activities does not reach the allowed limit; Otherwise, the system is replaced. Replacement is always performed once the system reliability decreases to Stage 3. Corrective maintenance is imperfect, with a perfect or minimal effect at certain probabilities. Two control variables, the allowed numbers of corrective maintenance in Stage 1 and Stage 2, are determined to minimize the expected system cost rate, by using Particle Swarm Optimization algorithm. The proposed model and method are illustrated by an example of one sliding spool. The optimal result is verified by checking the results of feasible variables. Furthermore, the proposed maintenance policy is compared with two contrastive maintenance policies. The comparison results show the necessity and effectiveness of the proposed method.

Long-Term Expansion Planning of the Transmission Network in India under Multi-Dimensional Uncertainty

Considerable investment in India’s electricity system may be required in the coming decades in order to help accommodate the expected increase of renewables capacity as part of the country’s commitment to decarbonize its energy sector. In addition, electricity demand is geared to significantly increase due to the ongoing electrification of the transport sector, the growing population, and the improving economy. However, the multi-dimensional uncertainty surrounding these aspects gives rise to the prospect of stranded investments and underutilized network assets, rendering investment decision making challenging for network planners. In this work, a stochastic optimization model is applied to the transmission network in India to identify the optimal expansion strategy in the period from 2020 until 2060, considering conventional network reinforcements as well as energy storage investments. An advanced Nested Benders decomposition algorithm was used to overcome the complexity of the multistage stochastic optimization problem. The model additionally considers the uncertainty around the future investment cost of energy storage. The case study shows that deployment of energy storage is expected on a wide scale across India as it provides a range of benefits, including strategic investment flexibility and increased output from renewables, thereby reducing total expected system costs; this economic benefit of planning with energy storage under uncertainty is quantified as Option Value and is found to be in excess of GBP 12.9 bn. The key message of this work is that under potential high integration of wind and solar in India, there is significant economic benefit associated with the wide-scale deployment of storage in the system.

Stochastic optimization for AC optimal transmission switching with generalized Benders decomposition

Optimal transmission switching is proposed in recent years to optimize the power system operational cost in deterministic studies. With the rapid growth of renewable generations, the grid uncertainties have greatly increased, which cannot be ignored in the decision-making of optimal transmission switching problems. This paper proposes a novel two-stage stochastic optimization formulation with a convex relaxation for AC optimal transmission switching problems. A generalized Benders decomposition based algorithm, including an inner loop and an outer loop, is proposed to solve the AC optimal transmission switching problem with grid uncertainties. The optimal switching plan and the expected system cost will be found in the iterative calculation without any sacrifice of accuracy. Numerical studies on the IEEE 118-bus system and the South Carolina 500-bus confirm the effectiveness of the proposed decomposition approach in solving the AC optimal transmission switching problems with grid uncertainties. The scalability analysis shows the proposed approach is efficient in dealing with a large number of scenarios.

Inspection interval optimization for a k-out-of-n load sharing system under a hybrid mixed redundancy strategy

In this paper, we optimize the periodic inspection interval for a k-out-of-n load sharing system with a mixed redundancy strategy in which the components are identical. The system is inspected at fixed intervals. If the system has any failed components, they will be detected at the end of the inspection interval. The components will be sent for repair at the beginning of the next inspection interval and will be available at the end of the interval. We assume the component's repair time is less than the inspection interval. Similarly, if the system fails to work during an inspection interval, it will be detected at the end of the interval. In the proposed hybrid mixed redundancy strategy, the system starts working with any number of components between k and n, depending on the number of the available components at the beginning of the inspection interval. We consider replacing the failed component with a new one from the standby queue using an imperfect discrete switch. Moreover, after a component's failure, its load will be shared among the remaining components, which causes an increase in their failure rates. The presented work aims to find the optimal total expected system cost per unit time by determining the number of working components at the beginning of each time interval and the inspection interval. The expected total system cost consists of the system's inspection cost, components' repair cost, system's downtime cost, and repair cost. The presented problem is solved with a full enumeration method and a new heuristic algorithm. The results show the superiority of the presented mixed redundancy strategy in comparison with the traditional strategies. Moreover, the proposed heuristic algorithm performs better in terms of computational time (up to one percent) compared to the full enumeration techniques.

Dynamic Reserve and Transmission Capacity Allocation in Wind-Dominated Power Systems

The large shares of wind power generation in electricity markets motivate higher levels of operating reserves. However, current reserve sizing practices fail to account for important topological aspects that might hinder their deployment, thus resulting in high operating costs. Zonal reserve procurement mitigates such inefficiencies, however, the way the zones are defined is still open to interpretation. This paper challenges the efficiency of predetermined zonal setups that neglect the location of stochastic power production in the system, as well as the availability, cost and accessibility of flexible generating units. To this end, we propose a novel reserve procurement approach, formulated as a two-stage stochastic bilevel model, in which the upper level identifies a number of contiguous reserve zones using dynamic grid partitioning and sets zonal requirements based on the total expected operating costs. Using two standard IEEE reliability test cases, we show how the efficient partitioning of reserve zones can reduce expected system cost and promote the integration of stochastic renewables.

Fabrication Cycle Time and Shipment Decision for A Multiproduct Intra-Supply Chain System with External Source and Scrap

Managers of today’s transnational firms, facing competitive global business environments, always intend to optimize their intra-supply chain systems to meet customers’ multiproduct demands with perfect quality goods, timely delivery, and minimum fabrication-shipping expenses. In the production units of intra-supply chain systems, random scraps are inevitable due to various unforeseen factors. Also, since the in-house capacity is limited, implementing a partial outsourcing plan can help release machine workloads, smooth production schedule, and reduce fabrication uptime. Inspired by these facts, this study explores an intra-supply chain system with random scraps and an external source. We build a mathematical model to portray the characteristics of the studied problem. Model analyses and the renewal reward theorem help us to obtain the expected system cost function. Optimization techniques and Hessian matrix equations are used to jointly decide the optimal cycle time and shipment policy that minimize the expected system cost. Through numerical illustration, we expose the individual and joint impact of diverse system features on the optimal operating policies and other crucial parameters of the studied problem, thus, facilitate managerial decision makings.

Data-Based Resilience Enhancement Strategies for Electric-Gas Systems Against Sequential Extreme Weather Events

Some extreme weather events, such as the hurricane, pass through an area sequentially and thus are called sequential extreme weather events (SEWEs). This paper proposes a data-based robust optimization (RO) model to enhance the resilience of the integrated electricity and gas system (IEGS) against SEWEs. Specifically, the SEWE strikes the IEGS sequentially. After each attack, the system state is adjusted immediately to minimize the maximized expected system cost caused by the SEWE. The attack-defense procedures are repeated alternatively during the SEWE. Preventive measures, hardening, are made in advance to reduce the impact of sequential attacks. The entire process is formulated as a multi-period RO model. It is proved that the most effective resilience enhancement strategies for this model are the same as those for a two-stage RO model, which can be solved by the nested column-and-constraint generation (C&CG) algorithm. In addition, the property of SEWEs, sequentially endangering limited regions of the IEGS, is incorporated to build a data-based uncertainty set and reduce its conservativeness. Simulation results on two IEGSs validate the effectiveness of the proposed model.

Market-based coordination of integrated electricity and natural gas systems under uncertain supply

The interdependence between electricity and natural gas systems has lately increased due to the wide deployment of gas-fired power plants (GFPPs). Moreover, weather-driven renewables introduce uncertainty in the operation of the integrated energy system, increasing the need for operational flexibility. Recently proposed stochastic dispatch models optimally use the available flexibility and minimize the total expected system cost. However, these models are incompatible with the current sequential market design. We propose a novel method to optimally define the available natural gas volume for power production scheduling, anticipating the real-time flexibility needs. This volume-based model is formulated as a stochastic bilevel program that aims to enhance the inter-temporal coordination of scheduling and balancing operations, while remaining compatible with the sequential clearing of day-ahead and real-time markets. The proposed model accounts for the inherent flexibility of the natural gas system via the proper modeling of linepack capabilities and reduces the total expected system cost by the optimal definition of natural gas volume availability for GFPPs at the forward phase. The volume-based coordination model is compared with a price-based coordination alternative, which was recently proposed. In the latter one, the natural gas price perceived by GFPPs is similarly adjusted to enhance the temporal coordination of scheduling and balancing stages. This comparison enables us to highlight the main properties and differences between the two coordination mechanisms.

An exact method for disassembly line balancing problem with limited distributional information

As an important part in product recycling, disassembly line balancing problem (DLBP) has attracted a large amount of attention. Stochastic DLBP is now a hot and challenging research topic, due to its wide applications. This work investigates a DLBP with uncertain task times, where the distributional information is limited, i.e. only the mean values and standard deviations are given, due to the lack of data. From a two-stage perspective, a disassembly process is determined and the disassembly tasks are assigned to workstations in the first stage, and the penalty cost (i.e. the recourse cost) for exceeding the cycle time is minimised in the second stage. The objective is to minimise the expected system cost. For the problem, a two-stage distributionally robust formulation is devised, to minimise the worst-case expected system cost out of all possible probability distributions. Different from literature that focuses on approximation methods to tackle the limited distributional information, an exact method, i.e. the cutting-plane algorithm, is developed. Numerical results show that compared with the state-of-the-art solution methods, our developed cutting-plane algorithm can provide more reliable solutions in term of the robustness, especially in some extreme cases.

Distributionally Robust Chance-Constrained Generation Expansion Planning

This article addresses a centralized generation expansion planning problem, accounting for both long- and short-term uncertainties. The long-term uncertainty (demand growth) is modeled via a set of scenarios, while the short-term uncertainty (wind power generation) is described by a family of probability distributions with the same first- and second-order moments obtained from historical data. The resulting model is a distributionally robust chance-constrained optimization problem, which selects the conventional generating units to be built among predefined discrete options. This model includes a detailed representation of unit commitment constraints. To achieve computational tractability, we use a tight relaxation approach to convexify unit commitment constraints and solve the model with linear decision rules, resulting in a mixed-integer second-order cone program. It is observed that the proposed model exhibits better out-of-sample performance in terms of total expected system cost and its standard deviation compared to a chance-constrained model that assumes a Gaussian distribution of short-term uncertainty. A similar observation is made when comparing the proposed model against a chance-constrained program that uses empirical renewable power generation data with unknown type of distribution, recasting as either a robust optimization or a stochastic program.

The Economic Value of Distributed Storage at Different Locations on an Electric Grid

The objective of this article is to analyze the system benefits of distributed storage at different locations on a grid that has a high penetration of renewable generation. The chosen type of distributed storage modeled is deferrable demand (e.g., thermal storage) because it is relatively inexpensive to install compared to batteries and could potentially form a large component of the peak system load. The advantage of owning deferrable demand is that the purchase of energy from the grid can be decoupled from the delivery of an energy service to customers. Consequently, these customers can reduce costs by shifting their purchases from expensive peak periods to off-peak periods when electricity prices are low. In addition, deferrable demand can provide ramping services to the grid to mitigate the uncertainty of renewable generation. The primary economic issue addressed in this paper is to determine how the storage capacity is allocated between shifting load and providing ramping services. The basic economic tradeoff is between the benefit from shifting more load from peak periods to less expensive periods, and reserving some storage capacity for ramping to reduce the amount of conventional reserve capacity purchased. Our approach uses a new form of stochastic, multi-period Security Constrained Optimal Power Flow (SCOPF) that minimizes the expected system costs for energy and ancillary services over a 24-hour horizon. For each hour, five different levels of wind generation may be realized and these are treated as different system states with known probabilities of occurring. This model is applied to a reduction of the grid in New York State and New England and simulates the hourly load on a hot summer day, treating potential wind generation at different sites as stochastic inputs. The results determine the expected amount and location of conventional generating capacity dispatched, the reserve capacity committed to maintain operating reliability, the charging/discharging of storage capacity, and the amount of potential wind generation spilled. The results show there are major differences in how the deferrable demand at two large load centers, Boston and New York City, is managed, and we provide an explanation for these differences.

Optimal parameter selection problem with application to the synchronization of delivery cycles in a supply chain with Wiener process

SummaryIn this paper, we use optimal parameter selection technique to develop two models involving single‐vendor–multiple‐buyer supply chain, which are called the dynamic independent optimization (DIO) model and the dynamic synchronized cycles (DSC) model, respectively. These models are, respectively, similar to the traditional static independent policy model and the traditional static synchronized cycle model, except that the deterministic demands of the buyers in the above two static models are now being replaced by the stochastic demands satisfying a Wiener process, which have more real‐life applications. Similar to the above static synchronized cycles model, the synchronization of the supply chain in our DSC model is also achieved by scheduling the delivery days of the buyers and coordinating them with the vendor's production cycle. Finding the optimal expected system costs of the DIO model and the DSC model involves solving optimal parameter selection problems governed by ordinary differential equations, whose final times are continuous decision variables and discrete decision variables, respectively. Computational methods have been developed for solving these problems. Numerical results show that the coordinated policy is better than the independent optimization policy, in terms of minimizing the expected system cost of the entire supply chain. Sensitivity analysis is performed to test the effect of changing the cost coefficients and the value on the performances of these models, where is the ratio of the total mean demand rate of all the buyers over the vendor's production rate.

On the Efficiency of Competitive Energy Storage

When energy storage is employed to facilitate large-scale integration of intermittent renewable electricity generation, do competitive bulk power markets continue to provide incentives for efficient investment? This essay adds competitively-supplied storage to a Boiteux-Turvey model of an electric power system with two types of periods. In the most interesting, tractable cases of this dynamic model, all efficient points are long-run competitive equilibria, and the long-run equilibrium value of storage capacity minimizes expected system cost conditional on generation capacities. But the analysis here cannot rule out the existence of inefficient equilibria.

Stochastic optimization of cellulosic biofuel supply chain incorporating feedstock yield uncertainty

Abstract The global goal to reduce dependence on fossil fuels and to mitigate greenhouse gas emissions has resulted in research focused on environment friendly and socio-economically sustainable renewable energy sources. However, commercial production of bio-energy is constrained by biomass supply uncertainty and associated costs. This study presents an integrated approach to determining the optimal biofuel supply chain considering biomass yield uncertainty. A two-stage stochastic mixed integer linear programming is utilized to minimize the expected system cost while incorporating yield uncertainty in the strategic level decisions related to biomass production and biorefinery investment. Applicability of the stochastic model is illustrated through a case study of switchgrass-based biofuel in west Tennessee.