PAYMENT MINIMIZATION IN A COMBINED MARKET OF ENERGY

AND RESERVE CONSIDERING UNCERTAIN

GENERATION AVAILABILITY

Taísa de Almeida Felix, Universidade de Brasília ,Phone : +55 61 84824485,E-mail:

Pablo Eduardo Cuervo Franco, Universidade de Brasília, Phone: +55 61 31075579, e-mail:

Overview

As a rule, in the short term market clearing process most of the power system markets operate considering the bid cost minimization (BCM) approach. Prices of energy and services are obtained in a straight forward manner and reflect the cost of supplying an additional MW. Nevertheless, this procedure has inconsistency because the total bid cost minimization is different from the total load payment. Because of this, several models have been suggested looking for directly minimize the loads payments. In the BCM approach a unit commitment is solved for clearing the market. In the payment minimization (PM) approach, models need a more complex formulation that requires the interaction with a unit commitment. New formulations and procedures are necessary to improve simplicity and performance of the PM approach. Besides this economic need, power systems require a safe operation to supply loads at any moment. This required reliability is also essential for market purposes. Because of this, it is important for the system to have reserve ancillary services to hedge against frequency deviations and energy unbalances. These additional important services should be procured in an appropriate market based on lower bid costs. Some systems use a separate market of ancillary reserve services independent from the short term energy market. Others on the contrary, integrate both short term markets and co-optimize the energy and reserve procurement in order to better observe the natural intrinsic relationship between allocated levels of services and obtained prices of these services [1].

Two types of uncertainty are normally presented in power systems: one of them is the load uncertainty whichproduces load forecast errors and therefore unexpected unbalances in the system. The other uncertainty is theavailability of equipment due to unexpected outages. Several studies have modeled uncertainty in their formulations. Some of them use Monte Carlo simulation techniques and others stochastic programming. Both approaches have advantages and disadvantages. In the disadvantage side, Monte Carlo simulation requires an elaborated previous procedure in the generation of appropriate samples to be used. The stochastic programming has the adverse exponential increase of variables when considering several possible scenarios [2].

Methods

In the context of short term operation, the proposed model here considers a PM approach with the cooptimizationof energy and reserve services taking into account the uncertainty of capacity availability of generationunits in a multi-period horizon. Start up payments and ramps of generators units are part of the model. Generatorsunits are classified in two groups: slow generators that supply the base of the load profile and fast generators that areable to quickly change their dispatch as required by the upper part of the load profile. In the reserve market, slowgenerators can supply for instance non spinning reserve for the purpose alleviate energy unbalances and fastgenerators can provide regulation up and down as well as spinning reserves for alleviating frequency unbalances. Financial adequacy of generators is enforced in each period of the horizon. In order to simplify the analysis thetransmission constraints are not considered and the only stochastic variable is the capacity availability of generatorsunits.

The methodology is based on the formulation of the PM optimization problem as a bilevel linear model. Thisformulation allows transforming the whole problem into one mixed integer optimization problem which can besolved by standard solvers. Moreover, it makes possible to establish a common framework for comparing with theBCM approach which is normally formulated as a mixed integer optimization problem. The stochastic multi-periodproblem is solved by using a hybrid strategy with two stages. The first one is based on the definition of few possiblescenarios of the capacity availability with associated probabilities. The second stage uses a Monte Carlo simulationin each scenario to capture a larger spectrum of uncertainty. In the first stage a stochastic bilevel linear model issolved considering both slow and fast units for obtaining the unit commitment, allocated levels and prices of servicesgiven a required system reserve level. In the second stage a bilevel linear problem is solved considering only fastunits (with the information of the generators status given by the stochastic problem solution) and the possibility ofhaving load shedding. Expected payments of services are obtained as a function of the system required levels ofsecurity in the multi-period horizon. Expected portfolios of generators revenues showing their participation in thejoint market can be obtained.

Results

The suggested model is tested with the IEEE 30-Bus system data. Generators 1, 3, 4, 5 and 6 are slow units. Onlygenerators 2, 3 and 7 have start up cost different from zero. The horizon of study is composed by three periods oftime with load levels of 250 MW, 350 MW and 500 MW. Three scenarios are considered: scenario 0 (withprobability of 0.8) is related to the case of no loss of any unit, and scenarios 1 (with probability of 0.1) and 2 (withprobability of 0.1) are the cases with the loss of the largest and second largest units, respectively. The additionalMonte Carlo simulations include samples of units malfunction during the periods of the horizon without consideringthe possibility of returning to operation due to repair. The total expected payment is obtained as the sum of theproducts of the scenarios probabilities times the average payments obtained in the Monte Carlo Simulation.

Figure 1 – Expected Payment as a function of the Reserve Requeriment

As can be observed in Figure 1, in both approaches (BCM and PM) the expected payment increses when thesystem required reserve level increases (for ensuring more security to the system). It can also be observed that total expected payments are always lower under PM. Moreover, the difference between expected payments obtained by both approaches increases as far as the required level of reserve increases.

Conclusions

The suggested model incorporates the uncertainty involved with the capacity availability of generators units inthe payment minimization approach in the context of power systems operating with combined markets of energy and reserve ancillary services. The PM model is formulated as a stochastic bilevel linear mixed model including possible operation scenarios of the stochastic variable. In order to cover a broader spectrum of uncertainty (not considered by the scenario definition) a hybrid technique is used in conjunction with a Monte Carlo simulation. Results show that the expected payments of loads are always lower under PM than the expected payments obtained under BCM. This difference is increased as far as the system requires more security by increasing the expected level of the total system reserve. Furthermore the expected payment under PM model is more stable to variations in the reserve requirements than the payment in BCM model.

The procedure is efficient in the sense that the hybrid stochastic problem reduces the number of scenarios to beexplored but at the same time covers a larger spectrum of uncertainty through the use of the Monte Carlo simulation in each scenary. The identification of slow and fast generators contributes to the reduction of the complexity of the problem.

References

  1. Alayawan, Ziad, Papalexopoulos, Alex D., Rothleder, Mark e Wu, Tong. “Pricing Energy and Ancillary Services in Integrated Market Systems by an Optimal Power Flow”, IEEE Trans. Power Systems, July 2002.
  2. Ruiz, P., Philbrick, R., Zak,E., Cheung, K., Sauer, P., “Uncertainty Management in the Unit Commitment Problem”, IEEE Trans. Power Systems, May 2009.