Energy Storage System Units Research Articles

Energy storage system coordinated with phase-shifting transformer and dynamic rating equipment for optimal operation of wind-rich smart power networks

Emergence of flexibility devices into smart power systems can assist the power system operators in making effective and economical decisions for the power system scheduling. These devices include energy storage system (ESS), phase-shifting transformer (PST), dynamic transformer rating (DTR), and dynamic line rating (DLR). In this paper, an approach is proposed for optimal day-ahead scheduling of power system using coordinated operation of ESS, PST, DTR, and DLR units under high wind power penetration situation. The aim is to minimize operational, load shedding, and wind power curtailment costs by regarding all the problem constraints. All of the model's relations as well as AC power flow equations have been convexified in order to construct a mixed-integer quadratically-constrained programming (MIQCP) model whose solution will obtain global optimum results. The developed model is implemented in GAMS and applied to the IEEE 24-bus system under various case studies, and the obtained results are investigated thoroughly. By coordinated operation of the employed flexibility devices, the loading of transformers and lines reach 159 % and 246 % compared to their nominal rating without violation of temperature limitations. Through releasing the capacity of lines and transformers, the total scheduling cost is reduced by about 52 % compared to traditional operation. Also, the whole energy of wind farms is utilized without any curtailment or constraints violation.

Fuzzy Logic-Based Energy Storage Control in Smart Grids for Grid Stability

This study studies the usefulness of fuzzy logic-based control systems for improving energy storage control inside smart grids to promote grid stability. The study combines empirical data analysis, including energy storage system (ESS) specifications, smart grid operational data, fuzzy logic-based control rules, and ESS state variables, to demonstrate the suitability and efficiency of using fuzzy logic-based control mechanisms in dynamic grid environments. The examination of ESS specs revealed a wide range of maximum capacities, spanning from 100 kWh to 200 kWh. Additionally, the charge and discharge efficiencies exhibited variations, ranging from 85% to 96%. An analysis of operational data from the smart grid revealed significant variations in grid frequency, ranging from 50.0 Hz to 50.3 Hz. Voltage levels also exhibited fluctuations, ranging from 229 kV to 232 kV. Additionally, renewable energy generation from solar and wind sources showed fluctuations between 1400 kW to 1650 kW and 800 kW to 850 kW, respectively. The incorporation of linguistic factors and fuzzy rules based on grid parameters facilitated the adaptive control of ESS units in the construction of fuzzy logic-based control rules. The analysis of ESS state variables revealed dynamic changes in the state of charge, which ranged from 60% to 90%. Additionally, oscillations in available energy were observed across different timestamps and ESS units. An investigation of in state variables, revealed adaptive changes percentage change demonstrating varying degrees of variations in state of charge, available energy, and operational states at various timestamps. The results emphasize the flexibility and efficiency of control systems based on fuzzy logic in improving energy storage operations in smart grids, highlighting their capacity to improve grid stability and efficiently handle changing grid characteristics.

MPC Based Dynamic Voltage Regulation Using Grid-Side BESPS With the Consideration of Communication Delay

Battery energy storage power stations (BESPS) play an important role in the power flow regulation in large-scaled micro-grids. It is proposed that the static Var compensator (SVC) be replaced by BESPS through activation of its dynamic voltage regulation (DVR) function so that the cost of SVC can be saved. An additional controller named energy storage coordination controller (ESCC) is needed to support the control algorithm of DVR and coordinate the individual battery energy storage system units. However, communication delay between the ESCC and the commercial BESS units is compounded by the difficulty of measuring the micro-grid (MG) bus voltage by ESCC. These issues should be considered in the design of the BESPS controller to avoid compromising the micro-grid operation. In this paper, we will be investigating model predictive control (MPC), Smith Predictor and PI based control schemes to deal with the communication delay issue. Kalman Filter based observer is designed to monitor the MG bus voltage as a feedback signal of the ESCC. The stability of the proposed method is further discussed and the results using the control hardware-in-the-loop (CHIL) testing are presented.

Hierarchical Intelligent Operation of Energy Storage Systems in Power Distribution Grids

High penetration of distributed energy storage systems (ESS) offers an unparalleled opportunity to reinforce the distribution grid at the local level against upstream disruptions; however, their mass operation under uncertainty of load and renewable generation is computationally expensive. While deep reinforcement learning (DRL) has been suggested to train operator agents capable of handling uncertainty and high dimensionality of the problem, it falls short when safety and feasibility assurances are required in critical operations. This paper proposes a model for hierarchical coupling of DRL and mathematical optimization for operation of ESS in distribution grids, in order to take advantage of DRL fast response while keeping network constraints in check. In the proposed method, strategic scheduling of distributed ESS units are performed locally by fast DRL-trained agents, while critical grid-wide operations such as fault management and voltage control are performed by an optimization-based central controller. The local controller is trained by Twin Delayed Deep Deterministic Policy Gradient (TD3), whose response time is three orders of magnitude faster than stochastic optimization, while the optimality of solutions are similar in both cases.

Energy storage system impact on the operation of a demand response aggregator

In this paper, we consider a demand response (DR) aggregator responsible for participating in the wholesale electricity market on behalf of the end-users who participated in the DR programs. Thus, the DR aggregator can trade its acquired DR within the short-term electricity markets, i.e., the day-ahead and the balancing (real-time) markets. In the proposed framework, the electricity market prices are considered uncertain, and a robust optimization approach is applied to address the uncertainties to maximize the profit of the DR aggregator. A model for analyzing the impact of the energy storage system (ESS) unit on a DR aggregator's performance is developed to provide more flexibility for the consumers. The direct interactions of a DR aggregator with an ESS are neglected in many models. However, this consideration can lead to improvement in the flexibility of the aggregator and also increase the profit of the entity by trading energy in the short-term markets to charge the ESS during the low-price periods and discharge it to the market while the electricity market prices are high. Hence, it is assumed that the DR aggregator owns an ESS unit and can cover a percentage of its traded power through the ESS. An analysis of the impact of the ESS unit on the DR aggregator's performance is applied to study the most appropriate size of the ESS that can maximize the profit of the aggregator. In addition, renewable energy production is employed for end-users through the installation of rooftop photovoltaic (PV) panels. This demand-side renewable generation can provide more flexibility for the participants in DR programs. Various feasible case studies have been applied to demonstrate the model's effectiveness and usefulness, and conclusions are duly drawn. The numerical results indicate that having an ESS seems necessary when the decision-maker desires to protect its profit from the worst-case scenarios and reduces the negative effect of the uncertain parameter, i.e., the wholesale electricity market prices. Thus, it can be shown that having a greater capacity for the ESS has a significant and direct impact on increasing the profit of the aggregator even in the worst-case scenarios, where the profit rises 20 % when the budget of uncertainty in the robust optimization is equal to 12.

Using energy storage systems to extend the life of hydropower plants

Despite their advantages, distributed energy resources (DERs) bring inherent uncertainty and variability into the landscape of modern power systems. As DER penetration grows, conventional generators like hydropower plants have to respond more often to arrest the imbalance in the net load. Hydropower turbines provide their best operational performance with minimal wear and tear when operating at regions of maximum efficiency. However, the current needs for hydropower plants require them to operate under varying load conditions and thus sub-optimal operating points leading to additional stress. To relieve the hydropower plants, this paper proposes a hybridization strategy where a hydropower unit is paired with an energy storage system (ESS) to increase operational flexibility and mitigate damage to the hydro plant. Models are developed to represent the operation of the hybrid system, quantify degradation, and assess economic benefits. Moreover, an innovative controller disaggregates the market dispatch signal into separate control setpoints for the ESS and hydropower unit. In case studies performed on a real-world hydropower facility, it was found that the ESS-based hybridization can extend the life of the hydropower plant by 5% on average. The economic benefits from reduced maintenance and deferred investment are estimated to be around $3.6 million.

Optimal Configuration of Extreme Fast Charging Stations Integrated with Energy Storage System and Photovoltaic Panels in Distribution Networks

Extreme fast charging (XFC) for electric vehicles (EVs) has emerged recently because of the short charging period. However, the extreme high charging power of EVs at XFC stations may severely impact distribution networks. This paper addresses the estimation of the charging power demand of XFC stations and the design of multiple XFC stations with renewable energy resources in current distribution networks. First, a Monte Carlo (MC) simulation tool was created utilizing the EV arrival time and state-of-charge (SOC) distributions obtained from the dataset of vehicle travel surveys. Various impact factors are considered to obtain a realistic estimation of the charging power demand of XFC stations. Then, a method for determining the optimal energy capacity of the energy storage system (ESS), ESS rated power, and size of photovoltaic (PV) panels for multiple XFC stations in a distribution network is presented, with the goal of achieving an optimal configuration. The optimal power flow technique is applied to this optimization so that the optimal solutions meet not only the charging demand but also the operational constraints related to XFC, ESS, PV panels, and distribution networks. Simulation results of a use case indicate that the presented MC simulation can estimate approximate real-world XFC charging demand, and the optimized ESS and PV units in multiple XFC stations in the distribution network can reduce the annual total cost of XFC stations and improve the performance of the distribution network.

A Distributed Control Strategy for State-of-Charge Balance of Energy Storage Without Continuous Communication in AC Microgrids

With the high penetration of renewable energy sources (RES), the energy storage system (ESS) units have been employed as critical components to compensate for the power fluctuation generated by RESs in an ac microgrid. However, it's a major challenge to achieve the state-of-charge (SoC) balance of ESS units due to the difference of initial SoC values and varied capacities. To deal with this issue, a distributed event-triggered control strategy has been proposed to realize the SoC balance among ESS units by regulating the virtual resistances. Compared with existing methods, only the local SoC of each energy storage is exchanged with the neighboring ESS units. Furthermore, by employing the proposed event-triggered mechanism, the data sampling and signal transmission are only conducted when the predefined triggering condition is satisfied, which effectively saves the usage of communication resources. Moreover, the stability and inter-event interval with the proposed control strategy is analyzed in this paper. Finally, several case studies are presented in the experiment where the presented approach shows its robustness against dynamic load and unexpected single-point communication failure.

Probabilistic reliability management of energy storage systems in connected/islanding microgrids with renewable energy

• ESS scheduling has been performed in both weekly and daily modes. • Different operating strategies has been assessed. • Stochastic models of parameters in the MO scheduling are taken into account. • Impact of parameters of EES on reliability determined. Energy storage systems (ESSs) are useful devices to ensure the reliable operation of microgrids especially those with high penetration of renewable energies. The microgrid operation is highly associated with scheduling of ESS units. Therefore, in this paper, a new algorithm for ESS scheduling has been suggested in order to manage MG in a reliable manner. Because reliability considering and cost minimization are conflicting objectives in ESS scheduling, the multi-objective optimization problem should be solved for optimal scheduling of ESS. Different operating strategy have been considered and their impact on ESS scheduling in the microgrid has been investigated. In order to properly consider the uncertainties associated with the multi-objective scheduling problem, probabilistic models have been presented for the parameters in the network and they are expressed as mixed integer linear programming (MILP) problems. Non-dominated sorting teaching learning-based optimization (NSTLBO) algorithm is employed to solve the MO problem. Scheduling plan is performed on both weekly and daily horizons in connected/islanding microgrid modes. By implementing this method on a modified 33-bus IEEE test system, the results endorse the effectiveness of the proposed scheme for enhancing the reliability of MGs.

Design of Virtual Inertia Controller for DC Microgrid Using Zero Placement Technique

With DC microgrids becoming popular, the concept of virtual inertia control (VIC) is gaining attention to minimize the DC bus voltage fluctuations caused by intermittent sources and loads. VIC scheme controls the power electronic converter (PEC) to achieve a smooth voltage profile. However, the intrinsic output impedance of the converter acts as an output disturbance and distorts the inertial response. An additional feed-forward controller has been used in previous works to mitigate this. However, the design proposed in this paper eliminates the additional controller while achieving a smooth voltage profile. This paper proposes a zero placement technique-based design of virtual inertia controller for a DC microgrid. Small-signal models for the system with the proposed controller designed using zero placement were developed to analyze the stability and the effect of parameter variation for optimal performance. Next, the application of the proposed design methodology is extended to a system employing two battery energy storage system units for analyzing parallel operation. Finally, the effectiveness of the controller designed using the zero placement technique was verified under different loading conditions through MATLAB/Simulink simulations and experiments carried out on the developed laboratory prototype.

Impact of Dynamic Thermal Rating on optimal siting and sizing of energy storage systems under Renewable Portfolio Standards requirements

Renewable Portfolio Standards (RPS), enforced as part of environmental regulations, are taking precedence worldwide to promote investments in renewable energy sources (RES). From the grid perspective, one of the bottle-neck factors that limits large-scale RES integration is the transmission network congestion. Dynamic Thermal Rating (DTR) is a smart grid technology that utilizes line condition and real-time weather conditions to alleviate network congestion by exploiting the transmission network inherent flexibility. Due to the intermittency of the RES, energy storage systems (ESS) have emerged as an essential component of power system that stores the excess generated energy by RES and pumps it back into the network at peak hours. However, despite the benefits of these technologies, the coordination of these two technologies with RPS regulations are not studied together. This paper presents a co-optimized model to evaluate the role of DTR in optimal siting and sizing of ESS units in connection with RPS requirements. The modeling framework co-optimizes bulk ESS expansion and DTR investment planning subject to constraints on RPS regulations and is formulated as a two-stage stochastic mixed integer linear programming (MILP) optimization problem. The model utilizes DTR to overcome the problem of network congestion and ESS to mitigate RES curtailment by saving the extra generated energy in non-peak hours. The efficacy of the proposed model in realizing impact of the DTR on ESS (location, energy capacity and power rating) in achieving high RPS targets is investigated on the modified IEEE 24-Bus system. Results demonstrate that DTR complements ESS under different RPS constraints by reducing the total system cost and ESS size significantly.

Mathematical Model of a Local Grid with Small Modular Reactor NPPs

The technical and economic processes of the Local Grid, regional electricity system comprising small modular reactor nuclear power plants, renewable electricity generators, and electricity storage systems are investigated. Smart grid technologies are used in the management of such a system. In relation to the electricity system, the Local Grid acts as a consumer or producer of electricity depending on the price situation in the wholesale market and its own ability to balance the volume of electricity generation-consumption.
 The Local Grid market is considered to be perfect, otherwise the wholesale electricity market is characterized by imperfect competition. The mathematical model of the Local Grid is offered. The presented model adequately reproduces the characteristics of the interaction between the local market and the wholesale market. The mathematical model is generated in the form of the commitment problem for small modular reactors and electricity storage systems. The model reflects the technological limitations for the loading modes of small modular reactors and units of the energy storage system, which operate in the modes of direct and reverse energy conversion. In particular, the model reflects the shunting modes and start-shutdown modes of small modular reactors and charge-discharge modes of energy storage system units, which together determine flexibility of the operation modes for the entire power system. The commitment problem of small modular reactors of a nuclear power plant, units of the electricity storage system, and transmission lines connecting the Local Grid with the power system is a mixed integer programming problem with an objective function of minimized system costs.
 Cluster integer functions are used to reduce the dimensionality of the problems of mathematical modeling the loading modes of the Local Grid in the descriptions for the sets of the same type small modular reactors, as well as the same type energy storage units. The Local Grid model reproduces the modes of its disconnection from the system operator's network to increase nuclear safety in the event of a natural disaster or hostilities. The results of computational experiments on modeling the commitment modes of the local electrical grid are presented.
 The experiments used standard data on the volume of electricity consumption and its production from renewable energy sources. The results of the computational experiment confirm the adequacy of the suggested mathematical model for the Local Grid. The presented model is suitable for the use both independently – to analyze Local Grid functioning - and in combination with the models of electric power industry - to determine the impact of the Local Grids on the electricity system.
 The article is developed based on the results of the research carried out under target program “Support of State-Priority Research and Scientific and Technical (Experimental) Solutions of the Department of Physical and Technical Problems of Energy of the NAS of Ukraine for 2022 – 2023” with program expenditure classification code 6541230 (applied research).

Optimization strategy of secondary frequency modulation based on dynamic loss model of the energy storage unit

When the Energy Storage System (ESS) participates in the secondary frequency regulation, the traditional control strategy generally adopts the simplified first-order inertia model, and the power allocated to each energy storage unit follows the principle of equal distribution. Therefore, it is impossible to consider the inconsistency of each internal unit for a long time, increasing capacity loss of the energy storage system, and the difficulty in improving the frequency regulation effect. This paper proposes an optimal control strategy based on the ESS unit loss and dynamic model. Firstly, we established the dynamic variable-parameter model of lithium batteries and gave the capacity loss of the Li-cell model. And then on this basis, we deduced the capacity loss of each unit to apply in the power system. Secondly, the requirements of Automatic Generation Control (AGC) signals to the differences between generator unit and ESS units are analyzed, and the output constraints of generator units and ESS are given, and the weight coefficients are determined by using the fuzzy control theory. Finally, a double-level control strategy considering frequency deviation rate and the capacity loss rate is formed, and the implementation process is given. The capacity loss of each ESS unit is 16.19% lower than that of the traditional method, and the frequency deviation of the regional power grid is effectively improved by more than 23.07%. The control strategy of this paper is of great significance for the design of a large-scale ESS control system.

Smart deployment of energy storage and renewable energy sources for improving distribution system efficacy

<abstract><p>Climate change, global warming, the depletion of fossil fuels, and rising energy demand are the main forces behind the increase in renewable energy sources. However, the unpredictability of power output from these renewable energy sources presents distribution system integration issues such as limited feeder capacity, unstable voltage, and network power loss. This study analyses the African vulture optimisation algorithm to determine the best allocation of distribution generators, with an emphasis on reducing the ageing of distribution transformers and delaying investment in feeders. The optimization technique provides faster global convergence and outperforms existing bio-inspired algorithms verified with benchmark uni-modal functions as a result of a larger crossover between the exploration and exploitation phases. The key aim is to decrease active power loss while simultaneously enhancing security margin and voltage stability. The IEEE 69-bus RDS system is utilised to validate the case studies for appropriate allocation of photovoltaic, wind turbine generation, and battery energy storage systems units, as well as offering the ideal energy management approach. During simulation, uncertainty on the characteristics of renewable energy source is accounted for. The results demonstrate the efficacy of the proposed algorithm with a substantial improvement in voltage profile, the benefit of lower CO2 emissions, an increase in security margin of up to 143%, and the advantage of extending the feeder investment deferral period by more than 50 years. In addition, the distribution transformer ageing acceleration factor improves significantly in the case of an increase in load demand.</p></abstract>

Distributed energy storage planning method considering multi-point aggregation effect

ABSTRACT The economic performance and utilization rate have become the key factors limiting the development of energy storage systems (ESS). From the perspective of the aggregation effect manifested by multi-point ESS, an inspired concept of “aggregation configuration, decentralized location” is proposed. Based on this concept, this paper proposes a planning method using two-stage optimization including sizing, siting and operational optimization for distributed energy storage (DES). The first-stage optimization aims to maximize the net present value (NPV) of aggregate ESS, while the second stage aims to mitigate the voltage fluctuation after the integration of distributed PV generation. In addition, the operational optimization for both the aggregate ESS and individual DES units are considered to better achieve the objectives of the two-stage optimization, and the particle swarm optimization (PSO) algorithm is employed to solve the planning problem. Case studies show that the proposed method helps to ensure the global NPV over the lifespan of aggregate ESS by considering operational optimization and depth of charge (DOD). Compared with the centralized ESS solution, the proposed multi-point DES solution can improve the overall voltage fluctuation mitigation capability by more than 40%. With the PV capacity penetration rate varying from 0 ~ 210%, sensitivity analysis reveals that when the penetration rate is close to 100%, the aggregate ESS has better economic performance and voltage fluctuation mitigation capability.

Nearly optimal demand side management for energy, thermal, EV and storage loads: An Approximate Dynamic Programming approach for smarter buildings

This paper proposes a distributed feedback-based optimization method, based on the principles of approximate dynamic programming, aiming for the optimal management and energy efficient operation of grid connected buildings. Modern building management faces multiple challenges, aiming for, energy efficiency, RES integration, EV operation, cost reduction and of course user comfort. Therefore, this paper adopts a multi-criterion cost objective, where minimum energy costs are required without sacrificing user preferences and satisfaction. Different type of loads are presented, including both thermostatically controllable loads (simulated and modelled in Energy Plus), and controllable electric vehicles (EV) and energy storage systems (ESS). Extensive simulations showcase the effectiveness of the proposed method introducing comparisons with different strategies by exploiting renewable energy integration, varying pricing tariffs and the stored energy of EVs and ESS units. A robustness evaluation of the proposed method is presented, validating the performance under different conditions. Finally, the paper demonstrates that the proposed strategy can be utilized for the management of real-world problems and buildings.

Lithium battery loss model and economic optimal control strategy for secondary frequency regulation in power system

Lithium battery energy storage system (ESS) has fast response speed, but it is in service for a long time. Therefore, in the research of secondary frequency regulation, it is necessary to establish a battery model that can reflect the short-term polarization and estimate SOC accurately under long-term service. Therefore, we propose a method of variable parameter loss model of lithium battery suitable for secondary frequency modulation of power system and optimize its control strategy based on the relationship between the independent variable SOC and the internal electrical parameters of the battery. Firstly, we discretize the state equation of single cell to obtain the PNGV model with variable parameters. Then the SOC estimation method is improved by using the modified extended Kalman filter method. Finally, we did an analysis about the economy of the ESS participating in secondary frequency regulation by using the loss model, and the optimal control strategy is designed. The HPPC experiment of the ESS unit is designed by Simulink, and the accuracy of the simulation and experimental curves has been analyzed. Finally, the economic differences between the traditional control strategy and the optimal control strategy considering loss are compared. The results show that the error of the variable parameter model in the fitting experiment is no more than 0.41%, and the accuracy of SOC estimation is 12.96% higher than that of the traditional estimation. The economy of the optimized control strategy is 15.38% higher than that of the traditional control strategy.

Decentralized Control of DC Microgrid Based on Droop and Voltage Controls with Electricity Price Consideration

In this paper, a power flow control strategy (PFCS) for the decentralized control of DC microgrids (DCMGs) is proposed to enhance the flexibility and scalability of the microgrid power system. The proposed scheme is achieved by combining the droop control and DC-link voltage control with the consideration of the electricity price condition. Generally, the droop control method can be used effectively in decentralized DCMGs to achieve power-sharing without additional communication links. However, the deviation of the DC-link voltage caused by the droop control affects the amount of power delivered to the load. As an alternative, the DC-link voltage control can be used to prevent such a deviation. To combine both control schemes in this study, the utility grid (UG) unit uses the DC-link voltage control to exchange the power between the DC-link and a UG in the grid-connected mode, while a distributed generator (DG) and energy storage system (ESS) units use the droop control method in the islanded mode. The operating modes of the UG, DG, ESS, and load units are determined by the deviation values of the DC-link voltage to maintain DCMG power balance. The overall PFCS is also developed for a decentralized DCMG system by taking into consideration several uncertainties such as DG power variation, battery state of charge (SOC) level, load demand, and grid availability. The proposed PFCS also considers electricity price conditions to adaptively change the DC-link voltage level for the purpose of minimizing the utility cost. When the DC-link voltage level is reduced due to the high electricity price condition, the proposed droop controller is designed such that the ESS unit operates with a discharging mode, which leads to the required minimum power support from the UG. The effectiveness of the proposed PFCS is demonstrated by comprehensive simulation and experimental results under various conditions. Those test results clearly confirm the control flexibility and overall performance of the proposed PFCS for a decentralized DCMG system.

Research on Multi-objective Optimization of Capacity Allocation for Marine Hybrid Energy Storage System

The hybrid energy storage system’s allocation problem is a multi-target and multi-direction optimization problem. Single-objective allocation for the Marine Hybrid Energy Storage System (MHESS) cannot help the hybrid energy storage system unit give play to its optimal effect. A diesel-electric hybrid ship is used as the object. In this paper, a mathematical model of a hybrid energy storage device is established, and multi-objective optimization allocation is performed on the model based on the NSGA-II. Finally, the optimized model is applied to a ship, and eleven kinds of batteries and six supercapacitors are selected for simulation. The simulation results show the relationship between the objective functions.

배전계통의 신뢰도 향상을 위한 전력회사 관점에서의 경제성 평가

Economic evaluation from the perspective of electric utility is performed about the reliability improvement of distribution system. The benefit from the perspective of the electric utility for improving the reliability of distribution system is the reduction of interruption cost, and the cost is assumed to be investment in distribution facilities. Therefore, the reduction in the cost of interruption for the case where SAIDI improves in a virtual distribution system is quantified. The total investment cost of automatic switch and Energy Storage System (ESS) invested to improve reliability of distribution system is calculated. The result of economic evaluation is presented as Benefit-Cost Ratio(B/C Ratio) by comparing the calculated benefit and cost. The sensitivity analysis on ESS capacity and unit price of interruption cost is conducted to reflect the uncertainty of future cost.