Operating in a carbon-constrained world has added a new dimension to competitive power markets. New modeling techniques can allow operators to combine the dynamic use of assets with emissions trading to maximize net cash margins.

Richard B. Jones, Ph.D. and Rodney W. Patefield, P.E., Solomon Associates, Dallas, Texas, USA

The phased schedule for greenhouse gas (GHG) emission reductions in the European Union has generated mandated limitations and resulted in new business opportunities. The current carbon dioxide (CO2) emission allocations for the approximately 12 000 identified industrial installations give those companies who expect to exceed their allocations the flexibility to install emission reduction technology, buy carbon emission credits, invest in emission reduction, or pay the regulatory penalties. The Emission Trading Scheme (ETS) has generated new trading markets for CO2 emission credit buyers and sellers; this scheme has also generated new sources of capital for project developers.

Power generation companies operating a diversified fleet of generation have an additional option. Given a required annual production level, fleet load management can be shifted from carbon-intensive power facilities to other units with lower carbon-equivalent emissions. The specific amount of load shift would depend on the market price of CO2 emission credits, unit capacities, unit availabilities, and other factors. The market price of CO2 emission credits can influence corporate strategies employed for generation load planning. For example, if CO2 emission credit prices are low, a company may plan to run their fleet without constraints on CO2 emissions and then purchase the needed credits to be in compliance with CO2 allocations. At the other extreme, if emission credit prices are sufficiently high, then actual credit creation may maximize net cash margin (NCM) and generation loads can be shifted to units where emission credit generation offsets the decrease in generation supply operational profitability.

Maximizing NCM in a carbon-constrained business environment requires that load planning analysis consider the economic cost of emission credits and apply more precision in measuring expenses related to unit operations at various load factors. Recent modeling advances – designed by Solomon Associates – can help maximize fleet NCM through refinements to fixed and variable unit operating expenses, CO2 emission reduction requirements, and emission credit prices.

Fleet analysis

To illustrate the application of these advanced techniques, consider a power generation fleet containing a mixture of coal and combined cycle units located in Europe (see Table 1). While the data values reflect currently operating generation units, they have been adjusted to maintain client confidentiality.

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The NCM optimization analysis is developed for this fleet under the following conditions:

Time period: the unit load allocation schedule for each plant is computed on a monthly time interval. At this level of detail, the model provides a load-planning, decision-support platform to analyse NCM effects resulting from various economic scenarios. Smaller time divisions are feasible for more detailed analyses.

Load: we set the load requirements for the fleet to operate at an overall annual capacity factor of 69 per cent, producing 19 000 GWh of electricity. The load requirements are further restricted to meet a monthly demand consistent with typical load demand cycles.

Load limitations: all units can operate at a capacity factor range of 0-100 per cent. We assumed no other minimum/maximum load factor requirements.

Availability: the units shown in Table 1 are assumed to be 100 per cent available for the planning year. In an actual application, unit unavailability would be incorporated as a constraint in NCM optimization.

Revenue: the units have monthly variable revenue values expressed as €/MWh, representative of average pricing in the regional markets they supply.

Fuel costs: fuel prices vary by month, representative of actual operations, with the major cost differences being for fuel type (i.e., coal vs gas).

Refined approach

NCM is defined as follows:

NCM = revenue – [fuel cost + operating expenses]±CO2 emissions

Each factor in the equation contains terms that vary with the MWh production of unit operation. Revenue (and fuel costs) follow similar forms as the product of the electricity price (fuel costs) per MWh and the amount of MWh generated. Operating expenses (OPEX) are derived from Solomon’s proprietary models that compute unit annual OPEX as a function of fixed and MWh-variable components.

The OPEX models are an application of Solomon’s comparative performance benchmarking database and proprietary, patent-pending performance measurement methodology, which manifest into a unique metric called Equivalent Generation Complexity (EGC). The EGC methodology enables quantitative unit performance comparisons of diverse operating facilities. Consistent with other industry applications of this patent-pending methodology, each unit’s particular EGC equation provides additional insights into the facility’s operating characteristics. One example of these insights is the observation that fixed costs vary according to the unit’s technical complexity, and non-fuel MWh-driven operating costs increase with unit operating and maintenance activities. Based on these observations, Solomon has restructured the EGC-based unit OPEX model into two major components: terms that relate to fixed costs and terms that vary with production. This proprietary OPEX model provides a quantitative approximation of the structure that a unit’s operating costs have between these two properties, and serves as a refinement to the standard ‘spark spread’ approach to modeling fleet generation optimization.

The emissions term in the NCM equation can be positive or negative, depending on whether credits are purchased or sold, and has the following form:

CO2 emissions revenue = (TA-TG)xP


  • TG = actual generated tons of CO2 (tCO2)
  • TA = regulatory allocation (tCO2)
  • P = market price of CO2 credits (g/tCO2)

NCM is computed on a unit basis for each month over the course of the year. The total annual NCM for the fleet is the sum of the monthly values for all units over all months. The primary independent variable is the MWh produced monthly by each unit. Fleet NCM is maximized subject to the constraints associated with fleet operations assumptions and subject to emission requirements.

Emission standards

While the EU’s ETS provides approved procedures to calculate historical emissions, facility emissions must be modeled for the purpose of analysing future emissions under different load and economic scenarios. Solomon’s research has developed emission and energy consumption benchmarking metrics designed for the refining, petrochemical, and power generation industries. This methodology follows a procedure similar to that applied to its operating expense activities (i.e., EGC).

To supplement research in the power generation industry, Solomon developed an emissions-related metric – Carbon Emission Index (CEI) – that contrasts the CO2 production efficiency of individual units. CEI is defined as the ratio of actual tonnes of CO2 emitted divided by the Solomon standard predicted tons of CO2.

The CEI standard enables facilities that have proactively reduced their CO2 emissions to have a lower CEI than similar units that have not taken proactive actions, regardless of fuel type or generation technology. Figure 1 illustrates the effectiveness of Solomon’s performance prediction compared with actual data for coal, oil, gas, and combined cycle units. For the four primary generation technologies, the plot depicts the variation in actual versus predicted CO2 emissions required for standards development.

Figure 1. Annual CO2 emissions – actual vs predicted. (Solomon Performance Database 2001-2003)
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The model describes how the emissions from each unit shown in Table 1 vary with MWh. For each unit, the CO2 emission model is normalized to scale the equation to go through the known MWh emissions data point for a given operational year, which allows the emissions values to reflect historical performance and contain the variation required to describe changes in CO2 emissions as a function of a unit’s production.

Modeling value

EGC, OPEX and CEI serve as the basis for estimating an optimal NCM for the example fleet previously described. The following two scenarios show the value of utilizing this modeling technique for developing information to assist asset managers with managing their generating fleets in this new environment.

Scenario I – fleet optimization without credit valuation: The first scenario quantifies the effect on fleet NCM caused by increasing CO2 emissions restrictions without emission credit trading valuation. The baseline – nominal point – is the optimum NCM, without any restrictions on CO2 emissions, for the calculated fleet unit loadings. Solomon’s models computed the baseline annual CO2 emissions to be 17 080 532 t. A 5-25 per cent emissions reduction requirement is applied, and the changes in fleet-wide NCM and unit capacity factors are plotted. All coal and combined cycle units loads are grouped by generation type, to show how the load distribution changes under different emission requirements. All emission reductions are achieved by allocating production among these units. No changes in emission technologies, engineering re-designs, or fuel quality are considered.

Figure 2. Fleet NCM vs CO2 emission reduction requirements
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The emission baseline under nominal operating conditions produces a fleet-wide optimum NCM of €222 million ($260 million), with coal units at 92 per cent capacity and combined cycle units at 18 per cent capacity. Figure 2 shows how the NCM decreases as emission restrictions are increased. It also provides information on the marginal cost of emissions. Notice that the slope of the curve becomes steeper as the emission reduction increases. Results will vary by fleet composition; however, in this case, a 20 per cent reduction in CO2 emissions results in a 30 per cent decrease in NCM. An emission reduction of an additional 5 percentage points (to 25 per cent) yields an overall 50 per cent decrease in NCM without including emission credit trading in the NCM equation. The scenario quantifies the cost of emission reductions in a scenario where no financial emission trading alternatives exist.

Figure 3. Operation capacity factors vs CO2 emission reduction requirements
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Figure 3 shows how the load is shifted from the more profitable, but higher CO2-emitting coal plants to the less profitable, but cleaner gas units as the emission reduction requirement increases.

Scenario II – fleet optimization with credit valuation: Using the same fleet data as that used in Scenario I, we introduce the emission credit trading valuation term in the NCM equation, which serves as the basis for the second scenario. The fleet generation requirement is maintained at 19 000 GWh. As the ETS allows pooling of emissions between installations, we combine all unit emissions and consider an annual pooled emission allowance that is ten per cent below nominal emissions. This corresponds to a pooled allowance of 15 372 479 tCO2.

The financial optimization load analysis now includes the option to trade emission credits to compensate for emission production in excess of the pooled allowance, to modify unit load capacity factors to produce lower emission levels, or both activities in some combination. The key variable we now add to the analysis is the cost of emission credits. A range of emission credit market values are considered here.

Figure 4. Fleet NCM vs CO2 emission credit costs/prices
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Figures 4 and 5 show the financial and load distribution effects of incorporating emission credit valuation into the fleet NCM equation. In Figure 4, as the cost of emission credits increases, the optimization model suggests that the fleet operates at emission levels greater than the allocation and maintain regulatory compliance through a combination of reduced actual emissions and emission credit purchases. As the price of emission credits increases, fleet NCM decreases, due to the cost of purchasing more credits. This trend continues until the allocation threshold is achieved. In this example, the threshold occurs when the cost of emission credits is in the €20-25/tCO2 range. As the cost becomes greater than this value, fleet NCM can be increased by credit creation from operating at a reduced emission capacity and load configuration.

Dynamic opportunities

Without carbon credit trading, a 10 per cent reduction in emissions from unrestricted operations results in a €17 million decrease in fleet NCM. The only available alternative in Scenario I is to re-allocate unit production levels to achieve regulatory compliance. However, in Scenario II, the same emissions restrictions produce opportunities to achieve financial results better than the pure load management approach, by purchasing or selling credits. This analysis suggests that emission credit trading can produce fleet-wide NCM results above the no-trading alternative levels in most cases, except in the regime of the critical price, as shown by the minimum in Figure 4.

Figure 5. Operational capacity factors vs CO2 emission credit cost (or market price)
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Technical solutions to reduce emissions can be capital-intensive and require long lead times before savings can be realized. The ETS provides the opportunity to dynamically utilize assets to maximize generation profitably. The ETS provides an effective mechanism to give power generation asset managers alternatives, allowing them to maximize fleet NCM under regulatory CO2 emission constraints.