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At least 163 records · Page 9

U.S. Fusion D-Li Neutron Irradiation Facility: Fusion Prototypic Neutron Source (FPNS) Technology Study

A primary engineering challenge for the realization of fusion energy involves the development of high-performance structural and plasma-facing materials with dimensional stability and resistance to neutron degradation of mechanical properties. The harsh fusion environment, including high levels of helium production and other transmutation products along with high operating temperatures, poses an extreme challenge for materials. Identifying materials that can withstand these conditions is a high priority for fusion energy research. Critical to resolving this gap in scientific understanding is developing a neutron source facility with the ability to mimic the extreme conditions in a fusion reactor. Working with the Department of Energy (DOE) Office of Fusion Energy Sciences (FES), Oak Ridge National Laboratory (ORNL) and the Virtual Laboratory for Technology (VLT) organized a workshop to discuss the need for a Fusion Prototypic Neutron Source (FPNS). [1] While there are a variety of uses for FPNS neutrons, the main driver of US interest is expanding the scientific understanding of materials degradation in the deuterium-tritium (D-T) fusion environment. FPNS will help build the scientific foundation required to enable design of a next step fusion device. Using specifications from previous projects as a guide, key parameters were agreed upon for a near term, moderate cost US facility that would be complementary to the more extensive plans of the International Fusion Materials Irradiation Facility (IFMIF). Types of facilities that could potentially meet those criteria were identified. A scoping study for three technologies was initiated to answer three critical questions: 1) Can the concept meet the key parameters, 2) What is the estimated cost, and 3) What is the estimated schedule. One approach selected for the scoping study is a D-Li stripping source similar to the design of the IFMIF but at a lower beam power and atomic displacement rate for cost and schedule reasons. The purpose of this report is to document the results of the D-Li stripping source option study, providing answers to the three questions. The approach to generating a fusion prototypic neutron source using a deuteron beam incident on a flowing lithium target has been studied for more than 40 years. As a result of the research and development recently executed primarily in Europe and Japan, the ability of this approach to meet key parameters (damage parameters, irradiation volume) outlined in the US workshop for a near-term, moderate cost fusion prototypic neutron source facility is not in doubt. The main question that must be answered is the cost of such a facility. As a result, a strong focus was placed on understanding alternatives for developing the facility and their relative costs. The project was broken into four components for the cost estimate: the ion source, accelerator, lithium target system, and conventional facilities. The cost of the accelerator is an important cost driver for the D-Li stripping concept. To fully understand the range of the accelerator cost, multiple alternatives were considered including normal conducting and superconducting linacs and the frequency of the radiofrequency quadrupole. Multiple previous design studies dating from 1989 through 2017 were examined (costs were escalated to 2019 dollars) and compared. After analysis, two options were selected for costing, one superconducting and one room temperature. We found similar project costs for the two accelerator options, on the order of $100M including design and project management but excluding contingency. Including everything except the conventional facilities, the estimate for the neutron source facility is estimated to be $220M without contingency. Additional significant costs for the facility are the conventional costs arising from the need to construct buildings for the accelerator and target facilities, bringing electrical power to the site including a new substation, and removing the heat from the facility using heat exchangers. While ORNL would oversee this work, much of the effort would be executed by contractors. Estimates for this effort was based on similar projects that are currently being executed at ORNL or were executed at ORNL in the recent past. The estimate for conventional facilities for the neutron facility is $173M without contingency, bringing the total project cost to $393M without contingency. With a 50% contingency, the estimated cost is $589M. The estimate range was established using guidance from the Association for the Advancement of Cost Engineering (AACE). Specifically, guidance from recommended practice 17R-97 provides insight on the expected accuracy range of estimates based on the degree of project definition and the position of the project in the stage-gate process or maturity timeline. An AACE Class 5 type estimate is appropriate for concept screening. The expected accuracy range includes a low end of -50% to -20% and a high end of +30% to +100% around the estimated cost. For the D-Li stripping neutron source, a -20% to +100% cost range was applied for a recommended cost range of $471M to $1,179M. Less emphasis was placed on determining the project schedule due to the fact that the project costs were large and may eliminate this option from consideration. The development of the accelerator facility may require on the order of five years without contingency. A more realistic schedule with contingency may be seven years. However, this estimate should be scrutinized in a preconceptual design activity if a more realistic estimate is needed. Finally, one lesson learned in this process is that the requirements for a near-term, moderate cost facility drives the alternative selection toward existing facilities and infrastructure. The D-Li stripping neutron source option requires a green field site due to the lack of existing buildings and infrastructure that can be reused for this effort. As a result, the conventional facilities costs are a significant fraction of the total facility cost. Other neutron source options where buildings, electrical power, and cooling infrastructure already exist may be able to meet the requirements for a near term, moderate cost facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Enhanced Large-Signal Stability Method for Grid-Forming Inverters During Current Limiting: Preprint

Grid-forming (GFM) inverters are a promising technology for the widespread integration of renewable energy sources in future power systems. As a key element of GFM inverter control, the primary controller governs the internal reference voltage and angle. During contingencies in the grid---such as faults, voltage drops, or frequency and phase jumps---an inverter can be forced into a current-limiting mode of operation modulating inverter dynamics, and, as a result, it is prone to losing synchronism with the grid. In this paper, we propose a novel GFM primary control method with an additional synchronization term that naturally activates during contingencies to improve the dynamic response. The method allows the inverter to remain synchronized with the grid, which improves the inverter's dynamic behavior both during and after current-limiting grid conditions and enhances grid support, including voltage support using full current capacity. The method is demonstrated for voltage, frequency, and phase jumps both in a single-machine-to-infinite-bus and a network-wide electromagnetic transient simulation of the IEEE 14-bus system with 5 GFM inverters. The simulations provide insights into the proposed synchronization method and confirm the high potential of the method, which robustly secures synchronism under severe contingencies.

current limiting↗

Optimisation of dynamic reactive power sources using mesh adaptive direct search

Dynamic reactive power sources can be used to effectively mitigate the fault-induced delayed voltage recovery and transient voltage instability issues. When many var sources need to be installed at planned locations, optimisation of their sizes is a complicated non-linear optimisation problem due to its non-convexity and the dependence of the constraint on time-series trajectories of post-fault voltages. Solving this optimal sizing problem needs to utilise both a non-linear optimisation solver and a power system differential-algebraic equation solver. This study proposes a new approach for solving this problem under both a single contingency and multiple contingencies by using the mesh adaptive direct search algorithm interfaced with a power system simulator. The proposed approach is validated by case studies on a North American Eastern Interconnection model to optimise the sizes of planned STATCOMs against critical contingencies.

Huang, Weihong↗

A Solar-assisted Voltage Optimization Method for Transmission Solar Network Power System

This paper proposes a new formulation and solution algorithm that uses transmission level solar inverters to address the security-constrained optimal power flow (SCOPF) problem. The goal is to stabilize voltage fluctuations in transmission networks in base case and contingency scenarios, by using bulk solar power plant with a minimal number of post-contingency corrections. To achieve this goal, a two-stage volt/var optimization method is proposed to first correct all voltage violations with the volt-var alternating current optimal power flow (ACOPF) algorithm for a base case. Then a linearized SCOPF volt-var control algorithm is proposed to identify the corrective actions for all potential voltage violations in all contingency scenarios. The proposed method was tested and validated on a modified IEEE 118-bus system with solar photovoltaic (PV) data.

Photovoltaic, Volt/Var Control↗

Methods for Computing Physically Realistic Estimates of Electric Water Heater Demand Response Resource Suitable for Bulk Power System Planning Models

Demand response is commonly called on to reduce load during system peak times or to respond to contingency events. In future power systems with higher shares of wind and solar generation (which we describe together as variable generation [VG]), demand response could have more opportunities to provide energy shifting or operating reserve services. This report evaluates the ability of residential electric water heaters, both electric resistance water heaters (ERWHs) and heat pump water heaters (HPWHs), to provide such services starting from detailed whole-building energy models that realistically represent New England single family home stock. We use a parsimonious surrogate model to represent operational flexibility in a form suitable for linear and mixed integer programming. This enables relatively fast determination of aggregate contingency reserve resource, price-taking energy shifting outcomes, and in some cases the determination of aggregate models at the megawatt (MW) scale that can be directly included in large-scale grid models. After selecting modeling methods and parameters through various computational experiments, we find interquartile ranges of contingency reserve resource in ISO-NE for about 603,400 ERWHs of 45 MW - 69 MW for Claim10 (50 minute responses provided with 10 minutes of advanced notification) and 65 MW - 102 MW for Claim30 (30 minute responses provided with 30 minutes of advanced notification), and for about 619,000 HPWHs of 48 MW - 88 MW for Claim10 and 52 MW - 90 MW for Claim30. The overall reserve resource is up to 32% of total load for ERWHs providing Claim10 service, 47% for ERWHs providing Claim30 service, 93% for HPWHs providing Claim10 service, and 97% for HPWHs providing Claim30 service. More work is required to determine if HPWHs are inherently more suitable than ERWHs for providing contingency reserve or if these results reflect idiosyncrasies of the single family home stock model used in this study. The value of this contingency resource in a Near-term VG model of ISO-NE is $\$ 0.40$ to $\$1.20$ per water heater-year, and significantly larger, $\$ 3.80$ to $\$ 5.30$ per water heater-year in a Mid-term VG model of ISONE. Aggregating surrogate models to the MW-scale for energy shifting service is more challenging than for contingency service and we only present such results for ERWHs, because we were unable to determine satisfactory ways to deal with HPWHs' time-varying and path dependent operational characteristics. Individual surrogate models suitable for evaluating the energy shifting resource from both ERWHs and HPWHs are created, however, and dispatched against day-ahead prices from the Near-Term VG and Mid-Term VG models of ISO-NE. The individual surrogate models are able to access and potentially shift all 640 GWh of HPWH load and 1,547 GWh of ERWH load we modeled in two different single family home stock models. In contrast, the most effective model of aggregate ERWH shifting resource we created only captured 34.7% of the total ERWH load. Energy shifting affected by price-taking dispatch against modeled day-ahead energy prices produces per water heater year profits of $\$19.44$ - $\$22.93$ for individual HPWHs, $\$39.11$ - $\$40.54$ for individual ERWHs, and up to $\$4.00$ - $\$4.24$ for aggregated ERWHs, with the variations mainly due to grid conditions (more or less VG). When the supply-side response to these changes is accounted for, the per water heater year production cost savings for ISO-NE are $\$7.50$ to $\$17.70$ for the most effective set of endogenously dispatched aggregate ERWHs, $\$15.60$ to $\$15.70$ for individual ERWHs dispatched against the DA prices, and $\$10.70$ to $\$11.20$ for individual HPWHs dispatched against DA prices. Those ranges primarily represent the difference between Near-Term VG and Mid-Term VG grid conditions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Integrated Cost and Schedule using Monte Carlo Simulation of a CPM Model - 12419

This discussion of the recommended practice (RP) 57R-09 of AACE International defines the integrated analysis of schedule and cost risk to estimate the appropriate level of cost and schedule contingency reserve on projects. The main contribution of this RP is to include the impact of schedule risk on cost risk and hence on the need for cost contingency reserves. Additional benefits include the prioritizing of the risks to cost, some of which are risks to schedule, so that risk mitigation may be conducted in a cost-effective way, scatter diagrams of time-cost pairs for developing joint targets of time and cost, and probabilistic cash flow which shows cash flow at different levels of certainty. Integrating cost and schedule risk into one analysis based on the project schedule loaded with costed resources from the cost estimate provides both: (1) more accurate cost estimates than if the schedule risk were ignored or incorporated only partially, and (2) illustrates the importance of schedule risk to cost risk when the durations of activities using labor-type (time-dependent) resources are risky. Many activities such as detailed engineering, construction or software development are mainly conducted by people who need to be paid even if their work takes longer than scheduled. Level-of-effort resources, such as the project management team, are extreme examples of time-dependent resources, since if the project duration exceeds its planned duration the cost of these resources will increase over their budgeted amount. The integrated cost-schedule risk analysis is based on: - A high quality CPM schedule with logic tight enough so that it will provide the correct dates and critical paths during simulation automatically without manual intervention. - A contingency-free estimate of project costs that is loaded on the activities of the schedule. - Resolves inconsistencies between cost estimate and schedule that often creep into those documents as project execution proceeds. - Good-quality risk data that are usually collected in risk interviews of the project team, management and others knowledgeable in the risk of the project. The risks from the risk register are used as the basis of the risk data in the risk driver method. The risk driver method is based in the fundamental principle that identifiable risks drive overall cost and schedule risk. - A Monte Carlo simulation software program that can simulate schedule risk, burn WM2012 rate risk and time-independent resource risk. The results include the standard histograms and cumulative distributions of possible cost and time results for the project. However, by simulating both cost and time simultaneously we can collect the cost-time pairs of results and hence show the scatter diagram ('football chart') that indicates the joint probability of finishing on time and on budget. Also, we can derive the probabilistic cash flow for comparison with the time-phased project budget. Finally the risks to schedule completion and to cost can be prioritized, say at the P-80 level of confidence, to help focus the risk mitigation efforts. If the cost and schedule estimates including contingency reserves are not acceptable to the project stakeholders the project team should conduct risk mitigation workshops and studies, deciding which risk mitigation actions to take, and re-run the Monte Carlo simulation to determine the possible improvement to the project's objectives. Finally, it is recommended that the contingency reserves of cost and of time, calculated at a level that represents an acceptable degree of certainty and uncertainty for the project stakeholders, be added as a resource-loaded activity to the project schedule for strategic planning purposes. The risk analysis described in this paper is correct only for the current plan, represented by the schedule. The project contingency reserve of time and cost that are the main results of this analysis apply if that plan is to be followed. Of course project managers have the option of re-planning and re-scheduling in the face of new facts, in part by mitigating risk. This analysis identifies the high-priority risks to cost and to schedule, which assist the project manager in planning further risk mitigation. Some project managers reject the results and argue that they cannot possibly be so late or so overrun. Those project managers may be wasting an opportunity to mitigate risk and get a more favorable outcome. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Quantitative Risk Management - Risk Informed Decision Making on High-Risk Waste Remediation Projects - 19022

For every $1 billion invested in projects, $97 million is wasted due to poor project performance. That means 9.7% of money spent on projects is wasted due to poor risk and uncertainty management. High-risk projects, similar to those in waste remediation, have the most to lose. A solid quantitative risk management program is one of the keys to increasing the likelihood that a project will succeed. A quantitative risk program solves two major problems that challenge the effective management of risk and uncertainty: 1. Risks arise at all levels of an organization; however, not all organizational levels have an effective way to identify and resolve them. This can lead to risks that, even if identified, are not reported. 2. Decision-makers are often forced to operate solely on intuition when implementing mitigation strategies, not fully understanding the effects that certain decisions have on the program's cost and schedule. A quantitative risk program uses a risk register and builds it into the project/program integrated schedule to assess the impact of these risks, typically at the 80% confidence contingency level for specific milestones and/or project completion. Implementing a quantitative risk program drives a forward-thinking, proactive mentality to problem solving into all levels of the organization. A healthy risk program for regular reporting and communication ensures that all members of an organization are thinking about risks and using their communication channels to resolve them. It gives a method of communication and incentive for all levels in the organization and helps to ensure that risks will be reported and resolved. Pacific Northwest National Laboratory (PNNL) has developed tools and methods that provide a level of realism for analyzing different scenarios and estimating contingency that does not exist in the standard industry risk tool kit. These tools and methods provide decision-makers with actionable, quantitatively based information to guide their decision making. The first tool is a probabilistic branching risk model for mitigation strategies. Current quantitative risk analysis tools in the industry simulate two cases: fully mitigated and un-mitigated. In the fully mitigated case, the user assumes that every planned mitigation activity is successful. In the un-mitigated case, the user assumes that none are successful. The truth lies between these two extremes. The PNNL team has developed a probabilistic risk model for mitigation scenarios that includes a probability that a mitigation activity will succeed and a probability that a mitigation action will be funded. These probabilities are elicited from subject matter experts and ensure that the contingency calculations at the specified confidence are approaching reality. The second tool developed at PNNL is the Risk Box, which is a tool that integrates with different scenarios in the risk register. For example, say the user is faced with two different and mutually exclusive mitigation actions to reduce a risk. The Risk Box methodology performs the contingency calculations and then displays them on a time-phased graph that shows how each scenario reduces the risk contingency needed on the project/program. This graph then provides quantitative information to show decision-makers which mitigation action provides the greatest reduction (cost and schedule) in risk contingency for the program. Implementing these and other tools within a structured risk program increases the likelihood that a project will come in on schedule and budget, ensures that all personnel are proactively thinking about problems and resolutions, creates communication channels for all members to submit and resolve potential problems, produces a prioritized list of risk rankings to focus leadership on issues that may cause the biggest problems, and implements processes that drive updates to the risk program as the risk profile changes. PNNL has been developing these methods and using them on projects for over 20 years. They have been successfully applied on waste management projects, high-tech research and development projects, and construction projects, and they continue to be used on a number of U.S. Department of Energy projects today. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Hybrid Cascading Outage Analysis of Extreme Events with Optimized Corrective Actions

Power system are vulnerable to extreme contingencies (like an outage of a major generating substation) that can cause significant generation and load loss and can lead to further cascading outages of other transmission facilities and generators in the system. Some cascading outages are seen within minutes following a major contingency, which may not be captured exclusively using the dynamic simulation of the power system. The utilities plan for contingencies either based on dynamic or steady state analysis separately which may not accurately capture the impact of one process on the other. We address this gap in cascading outage analysis by developing Dynamic Contingency Analysis Tool (DCAT) that can analyze hybrid dynamic and steady state behavior of the power system, including protection system models in dynamic simulations, and simulating corrective actions in post-transient steady state conditions. One of the important implemented steady state processes is to mimic operator corrective actions to mitigate aggravated states caused by dynamic cascading. This paper presents an Optimal Power Flow (OPF) based formulation for selecting corrective actions that utility operators can take during major contingency and thus automate the hybrid dynamic-steady state cascading outage process. The improved DCAT framework with OPF based corrective actions is demonstrated on IEEE 300 bus test system.

Cascading outage↗

Enhanced Security-Constrained OPF With Distributed Battery Energy Storage

This paper discusses how fast-response distributed battery energy storage could be used to implement post-contingency corrective control actions. Immediately after a contingency, the injections of distributed batteries could be adjusted to alleviate overloads and reduce flows below their short-term emergency rating. This ensures that the post-contingency system remains stable until the operator has redispatched the generation. Implementing this form of corrective control would allow operators to take advantage of the difference between the short-and long-term ratings of the lines and would therefore increase the available transmission capacity. This problem is formulated as a two-stage, enhanced security-constrained OPF problem, in which the first-stage optimizes the pre-contingency generation dispatch, while the second-stage minimizes the corrective actions for each contingency. Case studies based on a six-bus test system and on the RTS 96 demonstrate that the proposed method provides effective corrective actions and can guarantee operational reliability and economy.

Wen, YF↗

Development of Extended Period Pressure-Dependent Demand Water Distribution Models

Los Alamos National Laboratory (LANL) has used modeling and simulation of water distribution systems for N-1 contingency analyses to assess criticality of water system assets. Critical components considered in these analyses include pumps, tanks, and supply sources, in addition to critical pipes or aqueducts. A contingency represents the complete removal of the asset from system operation. For each contingency, an extended period simulation (EPS) is run using EPANET. An EPS simulates water system behavior over a time period, typically at least 24 hours. It assesses the ability of a system to respond and recover from asset disruption through distributed storage in tanks throughout the system. Contingencies of concern are identified as those in which some portion of the water system has unmet delivery requirements. A delivery requirement is defined as an aggregation of water demands within a service area, similar to an electric power demand. The metric used to identify areas of unmet delivery requirement in these studies is a pressure threshold of 15 pounds per square inch (psi). This pressure threshold is used because it is below the required pressure for fire protection. Any location in the model with pressure that drops below this threshold at any time during an EPS is considered to have unmet service requirements and is used to determine cascading consequences. The outage area for a contingency is the aggregation of all service areas with a pressure below the threshold at any time during the EPS.

42 ENGINEERING↗

Topology Control for Load Shed Recovery

This paper introduces load shed recovery actions for transmission networks by presenting the dc optimal load shed recovery with transmission switching model (DCOLSR-TS). The model seeks to reduce the amount of load shed, which may result due to transmission line and/or generator contingencies, by modifying the bulk power system topology. Since solving DCOLSR-TS is computationally difficult, the current work also develops a heuristic (MIP-H), which improves the system topology while specifying the required sequence of switching operations. Experimental results on a list of N-1 and N-2 critical contingencies of the IEEE 118-bus test case demonstrate the advantages of utilizing MIP-H for both on-line load shed recovery and recurring contingency-response analysis. This is reinforced by the introduction of a parallelized version of the heuristic (Par-MIP-H), which solves the list of critical contingencies close to 5x faster than MIP-H with 8 cores and up to 14x faster with increased computational resources. The current work also tests MIP-H on a real-life, large-scale network in order to measure the computational performance of this tool on a real-world implementation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The benefits of grid-scale storage on Oahu

The Hawaiian Electric Company intends to procure grid-scale Battery Energy Storage System (“BESS”) capacity. The purpose of this study is to determine whether providing contingency reserve or time-of-day shifting is of more benefit to the Oahu grid, and to better understand the relationship between BESS size and level of benefit. This is an independent study by Sandia, and is not being used to support the regulatory case for BESS capacity by Hawaiian Electric. The study team created a production cost model of the Oahu grid using data primarily from the Hawaiian Electric Company. The proposed BESS supplied contingency reserve in one set of runs and time-of-day shifting in another. Supplying contingency reserve led to larger savings than time-of-day energy shifting. Assuming a renewable reserve and a quick-start reserve, and $15/MMBtu for Low-Sulphur Fuel Oil, the 50-MW/25-MWh, 100-MW/50-MWh, and 150-MW/75-MWh systems supplying contingency reserve provided, respectively, savings of 9.6, 15.6, and 18.3 million USD over system year 2018. Over the range of fuel prices tested, these cost savings were found to be directly proportional to the cost of fuel. Lastly, as the focus is the operational benefit of BESS capacity, the capacity value of the BESS was not included in benefit calculations.

25 ENERGY STORAGE↗

Towards smart corrective switching: analysis and advancement of PJM's switching solutions

Transmission switching, as a power flow control mechanism that can reduce costs and improve reliability, has gained a lot of attention during the last decade. Despite its benefits, industry adoption has been very limited due to its computational complexity, stability and AC performance concerns. Pennsylvania New Jersey Maryland (PJM) has published a list of corrective switching solutions to relieve actual and post‐contingency network violations. The list is developed based on operators ’ prior knowledge and offline studies. This study employs a fast AC‐based real‐time contingency analysis (RTCA) tool with corrective transmission switching (CTS) functionality to analyse PJM's switching solutions with actual PJM data. The results show that the RTCA CTS tool is almost always able to find solutions that perform better than, or equally as well as, PJM's solutions. The results also show that PJM's list identifies solutions for only 3% of the problematic contingencies with post‐contingency violations over the course of one week. The RTCA CTS tool, however, is able to find corrective TS solutions for almost all the cases. The results suggest that CTS is ripe for industry adoption. The tool provides significant savings and would pave the road towards a smarter transmission network as an essential ingredient of the future smart grid.

Balasubramanian, Pranavamoorthy↗

Transactive energy systems for distributed blackstart and service recovery

Abstract Current transactive controls use marginal benefits and marginal costs to achieve an economic market efficiency during normal grid operations. However, the transactive mechanisms designed for normal economic operations cannot be applied directly for the contingencies because the grid operations during contingencies are often dictated by technical needs rather than purely economic criteria. For instance, one of the key technical requirements for the blackstart is to have at least one blackstart capable resource cleared which cannot be ensured by the transactive mechanism designed for normal economic operations because they work primarily based on the marginal benefit and marginal cost of the participants. This article presents one of the first attempts to develop a transactive mechanism to be used during grid contingencies. A distributed blackstart and service recovery is used as an example contingency to evaluate the performance of the proposed transactive mechanism. The performance of the proposed transactive mechanism is demonstrated for various use cases using a modified IEEE‐123 node test system. The simulation results demonstrated the proof of concept of applying a transactive mechanism to enable distributed blackstart and service recovery by engaging the mix of blackstart capable and non‐capable distributed energy resources.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Financial derivative pricing under probability operator via Esscher transfomation

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing{sup 9} where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φ{sub x}(u) of X{sub t} we recuperate the Black-Scholes formula for financial derivative prices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Three-Stage Production Cost Modeling Approach for Evaluating the Benefits of Intra-Hour Scheduling Between Balancing Authorities

This paper introduces a production cost modeling approach for evaluating the benefits of intra-hour scheduling among Balancing Authorities (BAs). System operation is modeled in a three-stage sequential manner: day ahead (DA)-hour ahead (HA) real time (RT). In addition to contingency reserve, each BA will need to carry out 'up' and 'down' load following and regulation reserve capacity requirements in the DA and HA time frames. In the RT simulation, only contingency and regulation reserves are carried out as load following is deployed. To model current RT operation with hourly schedules, a new constraint was introduced to force each BA net exchange schedule deviation from HA schedules to be within North American Electric Reliability Corporation (NERC) area control error (ACE) limits. Case studies that investigate the benefits of moving from hourly exchange schedules between Western Electricity Coordinating Council (WECC) BAs into 10-minute exchange schedules under two different levels of wind and solar penetration (11% and 33%) are presented.

17 WIND ENERGY↗