In my last post some background and previous concepts about National Electricity Markets and grid-tied Photovoltaic Plants were introduced. Now, it’s time to go deeper in the issue under consideration by applying that knowledge. In this second part a management strategy based on a Model Predictive Control (MPC) is proposed in order to increase the competitiveness of gried-tied PV Plants when it comes to National Electricity Markets participation and their daily operation.
First of all, let’s remember the last question we were discussing: Do we really need to supply the whole production every hour?
Nowadays, the correct answer would be: NO, as long as the PV Plant is equipped with Energy Storage Systems. From my point of view, this is the key condition to make PV Plants more competitive in the electricity markets. I know that one could think that the idea is not really original, and it is undeniable that this same concept has been used in the past in other Power Plants, such as the Hydroelectric ones. Nevertheless, the simplicity of an idea should never be considered as a drawback.
An intuitive approach could be summarised as follows:
“Imagine that our Plant is supposed to generate, according to the predictions available, 5 MWh during 8 am and 9 am and 7 MWh from 9 am to 10 am. Assuming that the Market Price of the second time slot is higher than the first one, why don’t we store those 5 MWh and supply 12 MWh from 9 am to 10 am?”
Although it sounds really easy, the proposal that I would like to make in this article is a little bit more complex. It is important to say that it could only be applied over a PV Plant with Energy Storage Systems (ESS). By the way, with ESS one should imagine a farm full of modules like the one shown below.
The mentioned proposal could be divided into two phases. The first phase is the one that we will call Scheduler and the second phase will be a real-time controller. The Scheduler is a program whose main results, in short, consist of the bids to the market participation, which are calculated by optimizing a linear cost function using market price predictions and weather forecasts. And the Second Phase will be responsible for controlling the real-time delivery and operating the Storage System, with the aim of accomplishing the hourly electric energy levels committed the day before.
For example, charging or discharging the Storage our Plant could supply approximately constant power signals during every time slot. In addition, this second phase is thought to be based on a Model Predictive Controller (MPC), by means of a relatively easy model of the managing plan. A simple diagram of our proposal is shown below:
Mathematically, Pcharge > 0 and Pdischarge < 0, notice that it can be automatically deduced the following relations:
It is pretty straight forward that the control variables during the operating day will be the charging an discharging powers, through which the Predictive Controller will try to make the Plant follow the references given by the Phase 1 (which are legal commitments with a National Electricity Market). The MPC will use short-term radiation predictions as well as a battery model and some simple equations in order to model the electric delivery. The models under consideration can be as complex as the author considers, but a correct balance should be found between their accuracy and the simplicity of the formulation.
One of the main drawbacks of MPC Controllers is the high calculation load, what could make the algorithm too slow to be implemented in real time. The calculation procedure of the control variables by means of a quadratic optimization problem extended to a prediction horizon is a noteworthy advantage. Notice that the function to be optimized can be customized in order to improve the Plant performance, as well as the weights (importance into the optimization problem) given to each controlled output (i.e. power supply, stored energy) and also the prediction horizon can be modified, taking into account that the higher it is, the slower and tougher it becomes to solve the problem and obtain the control actions.
The most typical function is:
Which basically considers the quadratic deviations in the real-time tracking of the references given by the Phase 1 and what we call in the Automation field control effort, which could represent the cost of charging and discharging the Storage. Both terms are extended to the prediction horizon and weighted by the weights mentioned before.
This proposal has been developed in the School of Engineering of Seville, in the Department of Systems Engineering and Automation. The project has been led by Dr. D. Carlos Bordons Alba (current Head of the Department) and Dr. D. M. Ángel Ridao Carlini, both professors of the mentioned department. The results achieved in different simulations have been proved to be satisfactory.
To sum up, with the proposed strategy a PV Plant is able to optimally perform during the operating day, by means of a Scheduler which establishes an optimal set of energy levels (from an economic point of view) committed with the Electricity Market and a real-time predictive controller that operates the Energy Storage in order to avoid financial penalties. Notice that these penalties could severely damage the revenue of the company responsible for the PV Plant operation, in case they don’t get to meet their energy commitments at any hour of the day. To conclude, a diagram of the two-phase system is shown below.
In the third and final part of my debut article, some results will be provided and analysed in order to easily prove the effects of the proposed strategy in different situations, such as unexpected cloudy periods of time! Don’t miss it!