(682f) Towards Optimal Production of Industrial Gases with Uncertain Energy Prices
In this work we consider air separation processes where the cost of energy changes hourly. The plant is assumed to participate in multiple energy markets for production: Day-ahead markets and Spot/Imbalance markets. In the day-ahead market, blocks of energy are nominated at an hourly level for the next day and are bought on a daily auction. The prices of energy are known after the auction closes, sometime around noon on the day before delivery. For a weekly time horizon, e.g. Monday to Sunday, the price and amount of power at every hour is known for Monday, whereas from Tuesday to Sunday neither the price nor the amount of power is known. However, forecasts are available for the day-ahead market for the next days. On the other hand, power is non-contracted in the imbalance market. It is the result of the imbalances in the physical power grid, and the attempt of the operators to match supply and demand. Prices of energy are known 15 minutes after the power is consumed. The challenge is to predict how long the price will remain profitable so the plant has time to react or even to forecast the spikes and valleys.
Therefore, we propose an efficient predictive and reactive solution strategy for real-world industrial scale problems to optimize participation in electricity markets under uncertainty in the operation of power-intensive air separation processes. A solution approach is developed based on a discrete-time scheduling formulation that allows modeling and optimizing operating decisions either in a fixed or a rolling horizon scheme. The objective is to compare both approaches in terms of computational efficiency and potential economical benefits. Accordingly, a deterministic MILP model is proposed to optimal production planning of continuous power-intensive air-separation processes to efficiently adjust production operation according to time-dependent electricity pricing. The main goal of this contribution is to find an optimal hourly schedule for next week, that minimizes total energy consumption cost while satisfying all operational constraints.
The model takes into account minimum and maximum production rates based on the plant state, storage capacity of the plant and minimum final tank level constraints, considering that minimum final tank levels must be fulfilled depending on the day of the week of last time period of the scheduling horizon. At the same time, detailed power consumption is taken into account for the different operating modes, which follows linear correlation. Expected daily demand and hourly electricity prices are used to generate and assess different scenarios.
An important aspect in this scheduling problem is to explicitly consider that there is an operational constraint on the minimum amount of time the plant should be running in the same operation mode. The plant has transition states to set-up and shut-down of equipment (ramp-up and ramp-down times) with minimum duration of 1 hour, and others states with minimum duration of 3 hours: uptime, standby time and downtime. Therefore, we propose an explicit modeling approach of feasible plant operational transitions and a systematic way of representing transition states.
A novel process state transition network is developed to model specific problem features. States with minimum duration of 3 hours are decomposed in 3 sub-states of 1 hour each and are called initial sequential transition states, Intermediate transition states, and critical transition states, respectively. The process state transition network model assigns states to time periods using proper binary variables denoting that process is operated at a given state at every time and ensuring that all operating constraints are satisfied. The model satisfies the start-up and shut-down restrictions, and also the constraints that concern the power consumption according to time-dependent electricity pricing schemes.
The proposed model was tested with real-world electricity price and demand input data. Scenarios were defined to assess how the model faces different situations. Scenarios tested with new formulation combines the input data (hourly and shift demand, and fixed, shift and hourly energy cost). In some cases the results are fixed to evaluate them with other data and to perform a fair comparison. The results show optimal solutions for the proposed methodology with a modest computational effort considering a one-hour time grid and one-week time horizon. Based on the preliminary results achieved, it can be concluded that the predictive MILP-based scheduling approach looks very efficient and robust. The model is able to consider all problem features and easy to adapt to reactive scheduling (a rolling horizon approach). Therefore, the developed model is a promising solution scheduling for the application to real-world air separation industrial plants. The model is also easy to adapt to other plant configurations, including the identified additional features. It allows the evaluation of daily and hourly reactive decisions based on energy price changes (day ahead market and imbalance market).