Marginal Electricity Prices Research Articles

Scheduling and Pricing of Load Flexibility in Power Systems

This paper proposes a fundamental approach for scheduling and pricing of load flexibility in power systems operation. An optimal control model is proposed to co-optimize the continuous-time flexibility of loads with the operation of generating units to supply the flexibility requirements of the net-load, while satisfying delay-based and deadline-based service quality constraints of the flexible loads. A function space-based solution method is developed to solve the continuous-time problem, which is based on reducing the dimensionality of the continuous-time decision and parameter trajectories by modeling them in a finite-order function space formed by Bernstein polynomials. The proposed method converts the continuous-time problem into a mixed-integer linear programming problem with the Bernstein coordinates of the trajectories as the decision variables. The proposed method not only allows for full exploitation of the load flexibility through higher order solution spaces, but also includes the traditional discrete-time solution as a special case. This paper proves that the Lagrange multiplier associated with the continuous-time power balance constraint is the continuous-time marginal price of electricity in the presence of flexible loads. The marginal price is calculated in a closed from, which demonstrates the dependence of the price on the incremental cost rates of generating units, on parameters of the flexible loads, as well as on ramping limitations of generating units and flexible loads. Numerical results, provided for the IEEE Reliability Test System, demonstrate the effectiveness of the proposed model in deploying load flexibility to reduce operation cost and ramping requirement of the system, as well as smoothing the load and marginal price trajectories of the system.

The costs of charging Plug-in Electric Vehicles (PEVs): Within day variation in emissions and electricity prices

The social costs of charging plug-in electrical vehicles (PEVs) that vary by times of day and by levels of emissions in electricity production are investigated. Using data available for the Sacramento area in the United States for 2013, we estimate marginal emission rates of electricity and marginal price of electricity provided for charging PEVs at different times of the day. As the marginal emission rates and wholesale electricity price have different daily patterns, there is a trade-off between emission and charging cost. Moreover, the estimates in the literature of the social costs for the most important emission, CO2, vary substantially, implying that the social cost of charging PEVs vary with the assumed cost. Simulations show that the charging time of lowest social costs for PEVs is found to be at midnight if the social cost of CO2 is not very high (<$90/ton), however, we find this pattern changes with an increase in the social cost of CO2. A high price of CO2 tends to shift the time of lowest social costs of charging to other times of day, thus, charging at workplaces during the daytime rather than at home overnight can reduce the social cost of charging PEVs.

Continuous-Time Marginal Pricing of Electricity

The current practice of discrete-time electricity pricing starts to fall short in providing an accurate economic signal reflecting the continuous-time variations of load and generation schedule in power systems. This paper introduces the fundamental mathematical theory of continuous-time marginal electricity pricing. We first formulate the continuous-time unit commitment problem as a constrained variational problem, and subsequently define the continuous-time economic dispatch (ED) problem where the binary commitment variables are fixed to their optimal values. We then prove that the continuous-time marginal electricity price equals to the Lagrange multiplier of the variational power balance constraint in the continuous-time ED problem. The proposed continuous-time marginal price is not only dependent to the incremental generation cost rate, but also to the incremental ramping cost rate of the units, thus embedding the ramping costs in calculation of the marginal electricity price. The numerical results demonstrate that the continuous-time marginal price manifests the behavior of the constantly varying load and generation schedule in power systems.

Providing frequency regulation reserve services using demand response scheduling

During power grid contingencies, frequency regulation is a primary concern. Historically, frequency regulation during contingency events has been the sole responsibility of the power utility. We present a practical method of using distributed demand response scheduling to provide frequency regulation during contingency events. This paper discusses the implementation of a control system model for the use of distributed energy storage systems such as battery banks and electric water heaters as a source of ancillary services. We present an algorithm which handles the optimization of demand response scheduling for normal operation and during contingency events. We use dynamic programming as an optimization tool. A price signal is developed using optimal power flow calculations to determine the locational marginal price of electricity, while sensor data for water usage is also collected. Using these inputs to dynamic programming, the optimal control signals are given as output. We assume a market model in which distributed demand response resources are sold as a commodity on the open market and profits from demand response aggregators as brokers of distributed demand response resources can be calculated. In considering control decisions for regulation of transient changes in frequency, we focus on IEEE standard 1547 in order to prevent the safety shut-off of inverter-based generation and further exacerbation of frequency droop. This method is applied to IEEE case 118 as a demonstration of the method in practice.

Two-Stage Economic Operation of Microgrid-Like Electric Vehicle Parking Deck

This paper addresses a two-stage framework for the economic operation of a microgrid-like electric vehicle (EV) parking deck with on-site renewable energy generation (roof-top photovoltaic panel). This microgrid-like EV parking deck is a localized grouping of distributed generation (solar), energy storage (EV batteries), and load (EV charging load). Although EV parking decks can enable greater adoption of renewable energy sources by scheduling charging loads to coincide with periods of strong sun, the inherent intermittency of renewable energy resources and variable EV parking behaviors complicates the economic operation. In this paper, the proposed first stage of this framework provides the parking deck operators with a stochastic approach for dealing with the uncertainty of solar energy so as to make an optimal price decision (marginal electricity sale price and parking fee rebate) at the day-ahead time scale. The second stage introduces a model predictive control-based operation strategy of EV charging dealing with the uncertainty of parking behaviors within the real-time operation. Case studies demonstrate the better performance of the proposed framework, offering an effective day-ahead marginal electricity price for tomorrow’s operation and increasing the microgrid-like EV parking deck’s revenue during the real-time operation.

Innovations-based Neural Network Seasonal Day-ahead Marginal Price Forecasting

Successful bidding and operational strategies of electric power generators (GENCO) depend highly on the availability of accurate and timely load and price forecasts. Several techniques have been proposed and applied over the past few years to predict the marginal price of electricity in deregulated markets. To improve accuracy, these techniques apply time-consuming, complex, and hybrid methods requiring multiple inputs and large databases. This article introduces the first application of the method of “innovations” and a single artificial neural network to provide accurate forecasting results with mean absolute percentage error comparable to more complex and hybrid artificial neural network forecasting methods. The proposed model is applied to data of two seasons of Spain's power market operator (OMEL) marginal price data. The technique provided average accuracy improvement of 26% with overall mean absolute percentage error of 6.5%, which is reasonable considering the number of inputs and the simplicity of this model compared to other proposed models.

Towards Optimal Electric Demand Management for Internet Data Centers

Electricity cost is becoming a major portion of Internet data center (IDC)'s operation cost and large-scale IDCs are becoming important consumers of regional electricity markets. IDC's energy efficiency is gaining more attention by data center operators and electricity market operators. Effective IDC electric demand management solutions are eagerly sought by all stakeholders. In this paper, a mixed-integer programming model based IDC electric demand management solution is proposed, which integrates both the impacts of locational marginal electricity prices and power management capability of IDC itself. Dynamic voltage/frequency scaling of individual server, cluster server ON/OFF scheduling, and dynamic workload dispatching are optimized while complying with all the IDC system-wide and individual heterogeneous servers' operation constraints according to the IDC applications' temporal variant workload. Reduced electricity cost can be achieved together with guaranteed QoS requirement and reliability consideration by using the proposed model. World Cup '98 data is utilized to evaluate the effectiveness of the proposed solution. According to the experimental evaluation, electricity cost could be cut by more than 20% in a peak workload period and by more than 80% in a light workload period. Besides, more than 6% electricity cost could be cut by considering the impact of electricity price difference. Experimental results also reveal that higher QoS requirement and reliability consideration could result in higher electricity cost.

The Importance of Marginal Cost Electricity Pricing to the Success of Greenhouse Gas Reduction Programs

This paper identifies a previously unnoticed problem important for the efficient reduction of GHG emissions: the pricing of off-peak electricity. There may be many opportunities to reduce emissions by substituting relatively clean and inexpensive off-peak electricity in place of a more GHG-intensive fuel, with the most important example being vehicle electrification. However, off-peak electricity for residential consumers is currently priced at 331% above its marginal cost in the United States as a whole. Even for the 1.3% of residences that are on some form of time-of-use rate schedule, the off-peak rate is still almost three times higher than the marginal cost. A primary barrier to the increased use of marginal-cost based TOU rates is that less than 5% of U.S. households have the “smart” meters in place that can measure and record the time of consumption. A FERC report estimates the deployment rate of these meters for residences by 2019 will reach only 40%; policies should be put in place so that this deployment rate nears 100% by that time. Another important barrier is TOU rate design. I describe two TOU rate designs (baseline and two-part tariff) that utilize marginal-cost based rates, ensure appropriate cost recovery, and minimize bill changes from current rate structures. A final barrier is to get residences on to these rates. I consider whether a marginal-cost based TOU rate design should remain as an alternative for which residences could “opt-in,” or become the default choice, or become mandatory. I conclude that it should become mandatory. Time-invariant rates are a historical anachronism that subsidize very costly peak-period consumption and penalize off-peak usage to our environmental detriment. There is no reason for such a system to continue. This paper is the earlier working paper version of the final paper published in Energy Policy

Estimating the value of wind energy using electricity locational marginal price

There is an increasing interest in adding renewables such as wind to electricity generation portfolios in larger amounts as one response to concern about atmospheric carbon emissions from our energy system and the resulting climate change. Most policies with the aim of promoting renewables (e.g., RPS, FIT) do not explicitly address siting issues, which for wind energy are currently approached as the intersection of wind resource, land control, and transmission factors. This work proposes the use of locational marginal price (LMP), the location and time specific cost of electricity on the wholesale market, to signal locations where generation can address electricity system insufficiency. After an examination of the spatial and temporal behavior of LMP in Michigan over the first two years of wholesale market operation, this work combines LMP with wind speed data to generate a value metric. High value sites in Michigan tend to be sites with higher wind speeds, with the bulk of value accruing in the fall and winter seasons.

Supply amount and marginal price of renewable electricity under the renewables portfolio standard in Japan

The Renewables Portfolio Standard (RPS) in Japan requires that approximately 1.35% of each retail supplier's electricity sales in FY2010 come from renewable energy sources (RES), for example, photovoltaics, wind, biomass, geothermal, and small hydropower. To help retail suppliers and renewable generators develop effective strategies, this study provides a quantitative analysis of the impact of this measure. We assume the supply conditions for electricity generation from renewable energy sources (RES-E) based on regional resource endowments, and we derive the cost-effective compositions of renewable portfolios, RES-E certificate prices, and additional costs to retail suppliers. The future prospects of RES-E are assessed based on technology, region, and year up to FY2010. The analysis reveals that wind power and biomass power generated from municipal waste will provide the majority of the total supply of RES-E under the RPS. It also indicates that the marginal price of RES-E certificates will be approximately 5.8 JPY/kWh (5.2 USc/kWh) in FY2010, in the case wherein the marginal price of electricity is assumed to be 4 JPY/kWh (3.6 USc/kWh). In order to elaborate on this further, sensitivity analyses for some parameters of RES and the price of electricity are provided. The dynamic supply curves of RES-E certificates are also indicated.

Constrained optimal power dispatch for electricity and ancillary services auctions

This paper proposes a constrained optimal power dispatch algorithm (COPD) for electricity and ancillary services auctions. The problem is decomposed into social welfare maximization subproblem which is solved by the mixed integer linear programming (MILP) and real power loss minimization subproblem which is solved by the quadratic programming (QP). The proposed COPD is tested on the modified IEEE 30 bus system with six generator companies (GenCos) bidding to sell the electricity and ancillary services. The social welfare of the proposed competitive electricity and ancillary services price scheme is higher than the competitive electricity price scheme and the constrained down payment (CDP) scheme adopted by the future Thailand power pool, thereby leading to a lower average electricity price. With the spot price including the marginal electricity price and marginal ancillary services prices, the correct price signal could be sent to all market participants. In addition, using the proposed scheme, the individual generator congestion gaming is not effective.

Prediction of system marginal price of electricity using wavelet transform analysis : Kim, C. et al. Energy Conversion and Management, 2002, 43, (14), 1839–1851

Prediction of system marginal price of electricity using wavelet transform analysis : Kim, C. et al. Energy Conversion and Management, 2002, 43, (14), 1839–1851

Prediction of system marginal price of electricity using wavelet transform analysis

This paper proposes a novel wavelet transform based technique for prediction of the system marginal price (SMP) of electricity. Daubechies D1(Haar), D2 and D4 wavelet transforms are adopted, and the numerical results reveal that certain wavelet components can effectively be used to identify the SMP characteristics with relation to the system demand in electric power systems. The wavelet coefficients associated with certain frequency and time localization are adjusted using the conventional multiple regression method and then reconstructed in order to predict the SMP for the next scheduling day through a five scale synthesis technique. The outcome of the study clearly indicates that the proposed wavelet transform approach can be used as an attractive and effective means for SMP forecasting.

Wholesale marginal prices in competitive generation markets

Wholesale marginal electricity prices are being used in several actual competitive generation markets worldwide, both to remunerate generators and to charge consumption. These prices must account not only for energy, but also for guarantee of supply in the long and the short term. This paper: (a) provides a sound conceptual and quantitative foundation for wholesale pricing based on generation services, where any existing restrictions in operation or planning in real power markets are accounted for; (b) clearly establishes the relationship between short term marginal costs, long term marginal costs and optimal wholesale electricity prices; and (c) identifies the reasons for mismatches in cost recovery with marginal generation prices. The theoretical results are verified with a detailed realistic power system model.

The relation between marginal product and price in US energy markets: Implications for climate change policy

This paper reports an empirical test of the axioms that describe the relationship between the marginal product and price of factor inputs in US energy markets. To do so, I estimate a reduced form of a production function that represents the amounts of various energy types that are required to produce a given level of output. The partial derivative of this production function is used to calculate the change in output that is generated by a marginal change in the use of coal, oil, natural gas or electricity. A partial adjustment model is used to estimate the relation between the marginal product and price of coal, oil, natural gas and electricity. The results indicate that rational agents manipulate their use of coal, oil, natural gas and electricity so that the marginal product of these energies adjust to changes in the relative prices of these energies. Because the marginal products of oil and natural gas are greater than coal, less than one heat unit of oil or natural gas is needed to substitute for one unit of coal and this increases the quantity of carbon emissions that can be abated by interfuel substitution. The time required to achieve these reductions may be longer than thought previously because of the slow rate at which the relative marginal product adjusts to relative price.

The Economics of Utility Residential Energy Conservation Programs: A Pacific Northwest Example

The bottom line for any utility conservation program is its overall worth: whether program costs are justified by the value of the electricity savings. That is, are these programs worthwhile investments to utility customers that participate in the programs, customers that do not participate, the utility system, and society as a whole? How sensitive are estimates of program worth to the input parameters (program-induced energy savings, discount rates, future average and marginal electricity prices)? This paper discusses our assessment of program benefits and costs for the Bonneville Power Administration (BPA) Residential Weatherization Pilot Program. Unlike other assessments, the present work is based on a detailed empirical evaluation of the program. We collected enough data from both program participants and nonparticipants to analyze the actual energy savings that could be attributed to the BPA program. We also obtained information on actual program costs. This information was used to compute the Net Present Worth (NPW) of the program from the perspectives of program participants, the BPA power system, and the Pacific Northwest region as a whole.

Notes - Two-Part Tariffs and the "Spiral of Impossibility" in the Market for Electricity

The author argues against the ''spiral of impossibility'' theory that utilities might not be able to raise adequate revenues on the grounds that utilities have other ways to raise money than the marginal price of electricity. A two-part tariff which raises customer prices will work better than raising the marginal price because users place a high value on access to electric power. He cites the Washington Public Power Supply System situation to illustrate that the public would pay higher costs with little change to their consumption habits. 1 figure.

Residential demand for electricity

Short- and long-run responses by households to changes in the price of electricity are estimated using data which permit measurement of the marginal price of electricity, the infra-marginal demand charge, and estimates of household appliance stocks. The price elasticities of high- and low-level users of electricity are compared. The theoretical bias in price elasticity estimates resulting from neglect of the infra-marginal demand charge is shown to be empirically insignificant.

Econometric estimation of peak electricity demands

The majority of existing econometric studies of the demand for eiectricity estimate models of kilowatt-hour usage as a function of prices, income and other economic variables.’ Estimates of kilowatt-hour demand equations, or elasticities of demand for total usage, are only partially useful for utility planning purposes and for analyzing policy alternatives in the electric utility industry. Capacity is built to meet system and monthly peak demands. Utilities are interested not only in kilowatt-hour output, but annual peaks, monthly peaks and the load duration curve.’ In this paper we estimate as econometric model of peak electric demands using time series data for one utility, Virginia Electric Power Company. The estimated econometric model relates system megawatt peaks to marginal electricity prices, temperature, income, and industrial activity. The model is estimated using monthly VEPCO data for the period 1960-1973 for the four summer months, June, July, August and September.