Perfect Foresight Research Articles

Optimization of Energy Storage System Economics and Controls by Incorporating Battery Degradation Costs in REopt®

The use of stationary electrochemical energy storage systems utilizing lithium-ion batteries has increased rapidly as the production scale has grown and price for lithium-ion batteries has decreased. These energy storage systems are crucial for maintaining grid resiliency, especially for grids operating with high penetration of renewable energy generation assets or with a variety of distributed energy generation and storage systems. One challenging factor for the adoption of battery energy storage systems is estimating the proper sizing, in terms of both power and energy, that minimizes total cost; properly sizing energy storage systems is difficult in simple cases, where a battery is costed independently of any other systems, but is extremely challenging when building loads and electrical generation by photovoltaic resources are also considered. REopt® is a techoeconomic optimization tool developed by NREL to address these challenges. Previously, battery degradation has been priced by simply assuming a 10-year replacement schedule for battery systems. However, this does not account for varying degradation trends observed across real-world batteries, or inform degradation-aware control strategies to optimize battery dispatch and extend lifetime.This work incorporates a battery life model into REopt. The battery life model is linearized so that it may be solvable within the constrains of a mixed-integer linear optimization problem. To achieve the best possible accuracy for lifetime estimates given these constraints, parameters for the battery life model in REopt are estimated by fitting 20-year simulations of battery life after identifying a state-space battery degradation model from accelerated aging data. Comparisons of battery life predicted in REopt and from the state-space battery degradation model are made to ensure validity of lifetime estimates made by REopt.Battery life impacts system cost through three decision variables: battery sizing, daily state-of-charge, and daily energy-throughput. The cost of battery degradation as a function of these control variables is then estimated assuming two possible maintenance strategies: replacement, where the entire battery system is replaced if cells reach an end-of-life capacity threshold; and augmentation, which establishes a fund to pay for continual purchase of new batteries to maintain the initial energy capacity of the system. These two strategies offer conservative (for replacement) and optimistic (for augmentation) bounds for total system cost. The degradation cost incurred by these strategies is then used to inform battery dispatch decisions, operating the battery in a degradation-aware manner that maximizes battery lifetime while also providing energy when economically favorable. Because the mixed-integer linear program has perfect foresight of future energy needs, batteries are often operated using ‘just-in-time’ charging, which is unrealistic, as no energy is left in the storage system to perform other energy services or to serve as emergency back-up power. To combat this, an inequality constraint on the average annual state-of-charge is imposed, and the sensitivity of system cost to average stored energy, e.g., the cost of system resiliency, can be quantified. Analysis of results has several conclusions, for instance, increasing battery capacity to provide more flexibility for dispatch, enabling the extension of useful life beyond 10 years and resulting in greater avoided utility costs per unit for energy storage while providing more energy storage for grid resiliency.

Developing and Evaluating Sector Rotation Strategy for Indian Equity Markets

This study examines the effectiveness of rotating in and out of a sector based on the stage of a business cycle. Here, we assume that business cycles exist, are part of nature, and neither repeat at a regular intervals nor their intensity or duration are constant. However, we assume that with a perfect set of high-frequency indicators, an investor can perfectly time the business cycle phases. This study divides India's real GDP growth into High, Moderate, Low, and Minuscule growth. GDP Growth is used as an indication of a start/end of a business cycle. In an investor were to create four different portfolios, optimized for each of the business cycle phases, will he/she be able to outperform the SENSEX returns of the buy-and-hold strategy? Here, an attempt to create such four models has been done using Python based on Markowitz Efficient Frontier and Modern Portfolio Theory. Once developed using historical data from September 2005 to March 2020, the study tries to estimate its performance in out-of-sample data, i.e., June 2021-April 2023. Can an investor make higher absolute (not alpha) returns with perfect foresight? We try to evaluate such in this study. Some obvious drawbacks of this model are inapplicability for large investors, mutual funds, etc. However, an investor with small capital and access to data can have an accurate foresight, thus, applying the model in practice can earn higher absolute returns. Even with a tax consideration of moving in and out of sectors, an investor can make a higher absolute return compared to a buy-and-hold strategy.

Evaluation of sector-coupled energy systems using different foresight horizons

Energy system models are increasingly being used in politics, industry and science. At the same time, model complexity continues to increase. Different possibilities of computing time reduction are in use, for example rolling horizons and incremental optimisation with reduced foresight. However, the combination of using strongly sector-coupled models with different foresight variants, in particular, has not been investigated thoroughly yet. This study aims to evaluate different model foresights by using a mathematical model of the German energy system, which includes electricity and heat supply as well as the supply of basic chemicals and mobility. Three scenarios of this model are used to evaluate the influences of changing foresights. The considered foresight variants are perfect foresight, myopia incremental, and myopia with foresight. Carbon budget models are shown to be more suitable than the price drop and CO2 price variants with the aim to minimise deviations from the least-cost energy system transformation. Moreover, this study demonstrates the importance of the chosen model foresight. If the goal of the optimisation is to simulate unforeseen events or shocks, the foresight of the model should be chosen to have a rather small value to depict a realistic reaction of the model. If the goal is rather to simulate long-lasting consequences of decisions taken at the beginning of the simulation, the foresight horizons should be chosen to be rather long while also considering the computational costs that scale with increasing foresight.

Trade-offs between aggregated and turbine-level representations of hydropower in optimization models

To model a future power system with high shares of variable renewables, it is essential to capture the flexibility of dispatchable technologies such as hydropower. However, the representation of hydropower is often oversimplified in energy system investment models, such that the flexibility of hydropower is significantly exaggerated. This suggests the need for improved representations of hydropower that capture physical river dynamics but are computationally efficient to maintain the tractability of large models. Here, we develop a series of hydropower optimization models for a single river with various levels of techno-physical detail to evaluate options for hydropower representations in energy system investment models. All models operate hourly over a full year with perfect foresight. We explore trade-offs between accuracy and computational time involved in including features such as the river network, head-dependent power production, and discharge-dependent turbine efficiencies. We find that the level of detail significantly affects the optimal production and confirm that a simplistic hydropower representation similar to those often used in investment models significantly overestimates the flexibility of hydropower. The most detailed nonconvex model includes a full river network, head-dependency, and turbine efficiencies and is solved in just one hour on a modern desktop computer. Furthermore, we linearize this detailed model, thereby reducing computation time to one minute while featuring production dynamics substantially more similar to the full nonconvex model than a naive linear network model. These contributions pave the way for improving hydropower representations in investment models to avoid overestimating the flexibility that hydropower may provide.

The rationality of adaptive decision-making and the feasibility of optimal growth planning

Rationality, the premise of economics, is an ideal behavioral norm. In the real world, however, intertemporal decision-making is based on adaptive behavioral principles from companies to individual households. It bases on managerial accounting procedures, whereby action plans are formulated and implemented, differences from actual results are recognized, and revisions accumulate over time. We take the intertemporal decision-making problem of households’ consumption/saving (investment) planning in this paper. And we compare the validity of rationality and adaptability as decision-making principles. First, rational decision-making in the optimal growth model leads to a unique path. However, optimal growth planning is practically unstable on the saddle-point path and can only realize if it assumes rationality leading to perfect foresight. On the other hand, the growth paths guided by budget-controlled adaptive decision-making are diverse and distributed in the myriad around the optimal growth path. This redundancy creates stability in the management and operation of the plan. Because through the trial-and-error process of planning and actual comparison, we can implement a more advantageous plan while allowing for multiple next-best goals, including the optimal growth path. Moreover, the numerical results show that the sequentially adaptive consumption/investment planning is comparable to the optimal growth plan on a social welfare basis calculated by accumulating consumption utility and is practically manageable. For example, paths that exceed 0.9 as a ratio to the optimal growth plan are reachable from the initial planning stage at a ratio of 0.58. Based on the above results, we can now analyze intertemporal economic problems with this realistic, practical, and simple method, replacing dynamic optimization ones.

Optimal dispatch of a multi-energy system microgrid under uncertainty: A renewable energy community in Austria

Microgrids can integrate variable renewable energy sources into the energy system by controlling flexible assets locally. However, as the energy system is dynamic, an effective microgrid controller must be able to receive feedback from the system in real-time, plan ahead and take into account the active electricity tariff, to maximize the benefits to the operator. These requirements motivate the use of optimization-based control methods, such as Model Predictive Control to optimally dispatch flexible assets in microgrids. However, the major bottleneck to achieve maximum benefits with these methods is their predictive accuracy. This paper addresses this bottleneck by developing a novel multi-step forecasting method for a Model Predictive Control framework. The presented methods are applied to a real test-bed of a renewable energy community in Austria, where its operational costs and CO2 emissions are benchmarked with those of a rule-based control strategy for Flat, Time-of-Use, Demand Charge and variable energy price tariffs. In addition, the impact of forecast errors and electric battery capacity on energy community operational savings are examined. The key results indicate that the proposed controller can outperform a rule-based dispatch strategy by 24.7% in operational costs and by 8.4% in CO2 emissions through optimal operation of flexibilities if it has perfect foresight. However, if the controller is deployed in a realistic environment, where forecasts for electrical load and PV generation are required, the same savings are reduced to 3.3% for cost and 7.3% for CO2, respectively. In such environments, the proposed controller performs best in highly dynamic tariffs such as Time-of-Use and Real-time pricing rates, achieving real cost savings of up to 6.3%. These results show that the profitability of optimization-based control of microgrids is threatened by forecast errors. This motivates future research on control strategies that compensate for forecast errors in real-world operation and more accurate forecasting methods.

Multi-period design optimization for a 5th generation district heating and cooling network

In the planning phase of district energy systems, optimization models based on mathematical programming are a widely used approach. Most optimization models determine the optimal energy system design based on a single representative year. However, this approach is unable to consider changing economic and technological boundary conditions over the system’s lifetime. As a result, these one-period models fall short for districts with 5th generation district heating and cooling (5GDHC) networks, which are typically developed over long time periods and are built in multiple construction phases. In this paper, we present two multi-period optimization approaches for designing 5GDHC districts: The first approach is a forward-looking model which determines the optimal investment pathway by using a perfect foresight of future parameter developments. In the second approach, a one-period model is solved repeatedly for every investment period without knowledge of future parameter developments. Both approaches are compared to a one-period model for a real-world 5GDHC district in Germany. In comparison with a one-period design approach, the forward-looking method leads to total cost savings of up to 17% and the sequential method of up to 11%. By using a forward-looking model, gas-fired technologies are sized smaller while the capacity of electricity-driven technologies in the energy hub as well as photovoltaic modules and thermal energy storages in buildings increases compared to a one-period model. The case study shows that a multi-period modeling approach is an important addition to design optimization models for 5GDHC networks and can have a significant impact on the optimal design.

Применение MIDAS-моделей с марковским переключением для наукастинга ВВП и его компонентов

The paper investigates the application of Markov‐Switching MIDAS (Mixed Data Sampling) models to nowcasting of Russian GDP and its components. Different methods to get the resulting nowcast based on nowcasts under different regimes are proposed: weighted by regime probabilities, most probable regime, and perfectly predicted regime nowcasts. The model obtained is compared with standard econometric nowcasting models. Among all the models tested, Markov‐Switching MIDAS model with perfectly predicted regime yields the best results for most of the series analyzed. MS MIDAS models without perfect regime foresight also perform better than standard MIDAS models and MFBVAR models for most of the series analyzed.

Heterogeneous expectations and equilibria selection in an evolutionary overlapping generations model

The way agents form their expectations, and which equilibria are consequently selected, are issues that come over macroeconomic growth models that study the transition between states characterized by different levels of capital. Existing theoretical works in this area have been mostly dominated by perfect foresight models although alternative expectations schemes have been proposed in the last decades. In the present paper we propose an OLG model with capital accumulation assuming that agents employ simple yet heterogeneous rules to forecast the future course of the interest rate and the real wage. The forecasting rules are selected according to an evolutionary mechanism that, on the basis of a fitness measure, evaluates the performance of the heuristics agents are currently adopting. We analytically show that, in the heterogeneous setting we consider, multiple equilibria are possible, but the evolutionary heuristic switching allows for a decrease in the number of possible steady states, drives their selection, and reduces the actual possibility that the economy might be locked into a poverty trap.

Expectation formation and learning in the labour market with on-the-job search and Nash bargaining

This paper develops a search and matching model with heterogeneous firms, on-the-job search by workers, Nash bargaining over wages and adaptive learning. We assume that workers are boundedly rational in the sense that they do not have perfect foresight about future bargaining outcomes. Instead workers rely on a recursive OLS learning mechanism and base their forecasts on a linear wage regression. We apply adaptive learning to a setting with generalized Nash bargaining and show analytically that the bargaining solution is unique. We use this solution to simulate the model and provide a numerical characterization of the Restricted Perceptions Equilibrium. We show that some job-to-job transitions are socially inefficient since workers can move to less productive employers. Output losses from these transitions decrease with workers’ bargaining power due to a more efficient allocation of workers to jobs. Finally, we find that bounded rationality taking form of adaptive learning can reduce wage inequality among heterogeneous worker groups if workers’ expectations are based on pooled statistical information.

Decentralizability of efficient allocations with heterogeneous forecasts

Do price forecasts of rational economic agents need to coincide in intertemporal perfectly competitive complete markets in order for markets to allocate resources efficiently? To address this question, we define an efficient temporary equilibrium (ETE) within the framework of a two period economy. Although an ETE allocation is intertemporally efficient and is obtained by perfect competition, it can arise without the agents' forecasts being coordinated on a perfect foresight price. With time-separable utilities, we show that there is a one dimensional set of ETE allocations for generic endowments. Moreover, these efficient allocations can be supported by forecasts that disagree up to one degree of freedom. Thus, strong as efficiency and perfect competition may appear, they do not imply perfect foresight, but they do add explanatory power to temporary equilibrium, since they select a small subset out of the Pareto efficient allocations, which generally have higher dimension.

Energy Storage Investment and Operation in Efficient Electric Power Systems

We consider welfare-optimal investment in and operation of electric power systems with constant returns to scale in multiple available generation and storage technologies under perfect foresight. We extend a number of classic results on generation, derive conditions for investment and operations of storage technologies described by seven cost/performance parameters, and develop insights on power systems with multiple storage technologies. Simulation of a deeply decarbonized “Texas-like” power system with two available storage technologies shows both the non-existence of simple “merit-order” rules for storage operation and the value of frequency domain analysis to describe efficient operation. Our analysis points to the critical role of the capital cost of energy storage capacity in influencing efficient storage investment and operation.

Does Market Timing Beat Dollar Cost Averaging?

This paper explores several methods for investing a series of monthly cash contributions in an equity index, such as the S&P 500 or the Nikkei 225. The dollar cost averaging (DCA), three variations of market timing (MT1, MT2, and MT3), and 12-month perfect foresight (PF) are examined, and they are built on the same assumptions, such as monthly cash inflows, no borrowing of cash, and no selling of equity. The PF outcomes, unachievable by human beings, serve as the optimal boundaries. Our results show that in both the U.S. and Japanese markets, the PF dominates the DCA, while the MTs tend to deliver similar results as the DCA. Thus, the DCA seems an effective investment method.

Impact of imperfect foresight on the optimal DER deployment, remuneration and policy

This paper proposes a decision-making framework to optimize electricity tariffs and remuneration policy for renewable energy sources operating in transmission- and distribution-level (T&D) marketplaces. We develop perfect and imperfect foresight models with a multi-level structure to investigate the effects of the inability of actors to correctly predict future remuneration on the efficiency of the decisions made by policymakers. The important advantage of the proposed models is that while they are capturing conflicting interests and different information availability of stakeholders involved, they also account for techno-economic constraints on operations of generation, transmission and distribution assets. The presented models can accommodate net metering, value stack, and distribution locational marginal price (DLMP)-based remuneration policies, which allows for their numerical comparison in terms of the effect on the optimal roll-out of distributed energy resources (DERs). The case study carried out for the NYISO and Manhattan T&D networks reveals that inaccurate foresight on the DER remuneration diminishes the social welfare under all DER remuneration policies, with the maximum loss of 1.6% across all considered scenarios.

Inter-temporal decisions, optimal taxation and non-compliant behaviors in groundwater management

A sizable part of the water extracted is unauthorized. This phenomenon may contribute to exacerbate the problem of groundwater over-exploitation. To consider both issues, we study the interaction between the water agency and farmers through a leader–follower differential game in which both agents are perfect foresight. Since the farmers have to pay a tax on individual withdrawals imposed by the water agency to manage the groundwater, illegal behaviors may arise to save this cost. However, if discovered, the farmers are punished with an administrative sanction. The game is solved using feedback Stackelberg solution. Moreover, to enrich the model’s policy suggestions, we also consider an alternative context in which farmers can adopt a trigger strategy. Finally, we perform numerical simulations based on the western La Mancha (Spain) aquifer data to better understand both the analytical results and the effects of the sanction mechanism on non-compliant behaviors.

Efficient solution and computation of models with occasionally binding constraints

Structural estimation of macroeconomic models and new HANK-type models with extremely high dimensionality require fast and robust methods to efficiently deal with occasionally binding constraints (OBCs). This paper proposes a novel algorithm that solves for the perfect foresight path of piecewise-linear dynamic models. In terms of computation speed, the method outperforms its competitors by more than three orders of magnitude. I develop a closed-form solution for the full trajectory given the expected duration of the constraint. This allows to quickly iterate and validate guesses on the expected duration until a perfect-foresight equilibrium is found. A toolbox, featuring an efficient implementation, a model parser and various econometric tools, is provided in the Python programming language. Benchmarking results show that for medium-scale models with an occasionally binding interest rate lower bound, more than 150,000 periods can be simulated per second. Even simulating large HANK-type models with almost 1000 endogenous variables requires only 0.2 milliseconds per period.

Financial Risk Management and Transmission Mechanism of Monetary Policy: An Empirical Evidence from Pakistan

Monetary policy plays a vital role in achieving development for any country. This study attempts to analyze the impact of the monetary transmission mechanism on unhedged interest rate exposure in the case of Pakistan. The study used time series data from 1980 to 2020 and applied the ARDL model to check the short-run and long run association between all the variables. First, URE (Unhedged interest rate exposure) was calculated and then estimated the factors affecting it. The study also used the perfect foresight model for addressing household behavior. The outcomes indicated that all exchange rates, interest rates, and money supply positively impact unhedged interest rate exposure, and they are significant both in the short and long-run. The interest rate substantially affects unhedged rate exposure more than the money supply. Development expenditures and money supply are negatively associated with income inequality; unhedged interest rate exposure is positively associated with income inequality.

Estimation of Internal Rate of Return for Battery Storage Systems with Parallel Revenue Streams: Cycle-Cost vs. Multi-Objective Optimisation Approach

This paper assesses the profitability of battery storage systems (BSS) by focusing on the internal rate of return (IRR) as a profitability measure which offers advantages over other frequently used measures, most notably the net present value (NPV). Furthermore, this study proposes a multi-objective optimisation (MOO) approach to IRR estimation instead of relying on the simple linear optimisation and compares the results to the popular linear optimisation with battery cycle-cost penalty. The analysis is conducted under perfect foresight conditions by considering multiple revenue streams: arbitrage trading in the day-ahead and intraday markets, peak shaving, participating in the primary reserves market, and from photovoltaic (PV) power-generation unit. Data are collected for the German power market for 2017 and 2021. The results show that MOO approach yields similar IRR estimates to the cycle-cost model in 2017. However, higher market volatility and increased electricity prices in 2021 resulted in tangible differences. The analysis shows that, if such conditions are coupled with a low battery capacity price, the MOO method significantly outperforms the cycle-cost model. The effects of battery calendar lifetime and state of charge which decrease profitability are also considered. Nevertheless, a noticeable rise in profitability in 2021 relative to 2017 could provide enough compensation to address the issue of relatively poor viability track record.

An analysis of the competitiveness of hydrogen storage and Li-ion batteries based on price arbitrage in the day-ahead market

Acceleration of the hydrogen economy is being observed on a global scale. It is considered to be a potential solution to the problems with high-carbon energy, industry, and transport systems. The potential of production, cost-competitiveness, and opportunities are currently being investigated to provide insights to policymakers, researchers, and industry. In this context, this study makes a quantitative assessment of the competitiveness of hydrogen storage compared to Li-ion batteries based on price arbitrage in the day-ahead market. Two scenarios that form the boundaries of rational decision-making regarding the charging and discharging of energy storage are considered. The first one assumes the charging and discharging of energy storage facilities over the same hours throughout the entire year. The selection of these hours is based on historical electricity prices. The second scenario assumes charge and discharge during historical daily minimum and maximum prices. The results show that NPV is below zero for both technologies when current values of investment expenditure are assumed. The outcomes of sensitivity analysis indicate that only a substantial reduction of investment expenditure could improve the financial results of the Li-ion batteries (NPV>0). The investigation also shows that even simplified charge and discharge over the same hours allows one to achieve 47% (hydrogen) and 70% (Li-ion batteries) of the maximum operating profit when the perfect foresight of prices is applied. In each case, NPV for Li-ion technology is significantly higher than for hydrogen; for example, for a 1 MWh and 1 MWout storage system, NPV is EUR -4.85 million in the case of hydrogen and with Li-ion NPV is EUR -0.23 million. Consequently, the application of expensive decision support systems in small systems may be unprofitable. The increase in profits may not cover the cost of developing and introducing such a system.

Capacity planning with uncertain endogenous technology learning

Optimal capacity expansion requires complex decision-making, often influenced by technology learning, which represents the reduction in expansion cost due to factors such as cumulative installed capacity. However, having perfect foresight over the technology cost reduction is highly unlikely. In this work, we develop a multistage stochastic programming framework to model capacity planning problems with endogenous uncertainty in technology learning. To assess the benefit of the proposed framework over deterministic optimization, we apply a shrinking-horizon approach to compute the value of stochastic solution. Further, a decomposition scheme based on column generation is developed to solve large instances. Results from our computational experiments indicate substantial potential cost savings and the effectiveness of the proposed decomposition algorithm in solving instances with large numbers of scenarios. Lastly, a power capacity planning case study is presented, highlighting the stochastic optimization’s ability to anticipate significantly different expansion and production decisions in low- and high-learning scenarios.