In an electric grid one manages production variables (e.g. electricity generation) and corresponding time rates of change to meet net demand. But additionally, other variables internal to each plant may be subject to constraints. For each plant, such as nuclear reactor, gas turbine, thermal energy storage, industrial process, there are temperatures, pressures and flow rates whose transients need to be bounded so that equipment design limits are not exceeded. Otherwise components may be damaged, and performance will degrade while system availability may be affected. The task then is to minimize an electricity function subject to maintaining the conditions of the IES system components within the normal operation range.
Consider the integrated energy system represented in the figure. The system performance measure is cost of electricity which needs to be minimized at the same time the system is subject to an exogenous electricity demand that is variable and has a stochastic component. The optimization will force an increase in turbine (i.e. SES) inlet temperature to achieve maximum thermodynamic efficiency but there are also material temperature limits that must not be exceeded. These are hard constraints.
This problem has been solved using the Reference Governor (RG) control system approach that is shown in the figure. The RG algorithm acts as a supervisory control system layer. It ensures that the set-points issued to the low-level controllers (PID) will not lead to violations of constraints associated with the main process variables (thermo-mechanical stresses, power ramps, etc.)
The figure below depicts the process of iterating with the power dispatcher until an optimal and feasible solution is found. During every iteration, the power dispatcher will evaluate the optimal set-point trajectories over a certain time horizon (i.e., one day, one week, two weeks). The RG will assess that these values will not lead to the violation of the imposed constraints at any time step. At every time-step, the RG will return the admissible range of values that could have been assumed by the power set-points before they would lead to the violation of any of the imposed constraints. This piece of information will be used by the power dispatcher during the second iteration of the power set-point optimization, and a more consistent power set-point trajectory will be evaluated.
The system identification task involves sampling in real time the dynamic response of the state variables and the power set-point trajectories for the physical system. System dynamics matrices that represent the dynamic system in the figures are continuously updated and represent the most accurate approximation of the system for current operating conditions.
The system identification method uses the “rolling window” concept shown at right to maintain a current linear time variant (LTV) representation of the system dynamics. The LTV is then used to predict the evolution of process variables over the next few time steps.
The results for the problem above are shown in the plots. The balance of plant and turbine are successfully scheduled to produce minimum cost electricity subject to meeting the operating constraint on turbine firing temperature.
There are significant computational and scheduling challenges for performing real time optimization of plant operation to meet demand reliably and at the least cost. One must anticipate near-term demand and ensure that finite capacity storage devices are used in an optimal manner. There are also significant design challenges. The set of assets in an energy system will evolve with time as market forces change over the longer term. It will be a challenge to design in robustness so that the system is not moved significantly off the optimal capacity mix with time.