Long-term Solar PV Planning in High-Density Urban Systems

Future resilience systems. His research focuses on black box and robust optimization, clustering in complex networks and information retrieval. His presentation today is titled Long Term Solar PV Planning in High density urban systems. Dr. Alberto, please.

Thank you. So it's another presentation about solar energy in Singapore, only that this time the focus is more on the optimization and modeling. So some of these reasons for why we are doing this research has been shared previously. But Singapore has very ambitious solar pv target. By 2025 they would like to achieve 1.5 gigawatt and by 2032 gigawatt. And the main source that we analyze in this study is the rooftop and facade. What is the challenge here is that the space is scarce and there is also competition for the space. For example, in the rooftop you may want to put panels, but you may want to have some green area. So there is competition on that. And how can we achieve, or rather how can the government and agencies achieve these targets knowing that there are these challenges? This is what we are trying to answer with this study. The approach we use is robust optimization. So we develop a robust optimization model to kind of Forecast in the 2020-2050 the amount of capacity that Singapore can install. And to do that, what is the idea? We build a model, we calibrate with past data, existing data that we can find, and then we determine also something interesting from the analysis of the model. If we cannot get to the targets, what are the incentives that we need to give to people in order to achieve such targets? Here you can see something that has been shared already. The fact that from 2014 to 2019, this picture show you the residential and non residential solar capacity has been increasing a lot. So what are the assumptions of our model? Of course there is the objective, what is the driving objective? And here we look at the economic surplus principle. That basically means there are buyers and sellers of these solar PV systems and we want to maximize the total benefit for them. So the sellers may have a selling price, a minimum selling price in mind, the buyer, they also have a buying price and the transaction price will give a benefit to both. We want to maximize that. We look, as I said at Singapore in the 2020-2050 time frame and we know that the space for rooftop and facade is limited. We also consider the consumers as risk averse and this will be important later because we have to take into account uncertainty. And as I said, we have some parameter that we calibrate with past data. And the objective is to meet the targets by the agencies and government. So the optimization model that we Build, As I say, the objective is to maximize this economic benefit for the stakeholders in the system. The constraints are the space availability. We cannot exceed the available space for rooftop and facade. And also of course an equilibrium between the amount of capacity that is sold and bought. When we have that, we can derive what is called robust counterparts. So we move from a robust optimization model to a model that we can solve with existing software and then we can forecast this capacity in the period 2020-2050. And finally we can analyze the solution to derive these incentives that we need to achieve the targets specified by agencies. Don't be scared about that. This is just to let you know what is the kind of optimization model we are talking about. And just this is the constraint where we want to satisfy the target. So we just quickly changed that. But just for you to know that there is an optimization modeling behind. Now the background is Singapore. We use it because I shared before, there is a very good potential for the solar. And then we look this facade and rooftop. For the rooftop we consider the five region in Singapore and three consumer type, residential, commercial and industrial. For the facade, because we don't have enough past data for the calibration, we consider a single profile. Data are taken mostly from the EMA and the Solar Energy Research Institute of Singapore. They published two reports in 2014, 2020 with information like available space projection for the price of panels and so on. Now the first step, as I said, is calibrating the model. So what we did, we took the data from 2014 to 2018 and and we run our model fixing the parameters that we don't know in such a way that the prediction of our model that are the blue lines are as close as possible to the real data. That is the red line. As close as possible in the residual minimization terms, if you are familiar. But basically means the line should be as close as possible. These here represent the non residential consumers. And then we use the 2019 just to see if the model was good enough. I mentioned that we have uncertainty. So in this slide I will just quickly show you why that is important. Because if we don't have uncertainty, what happens is that the buyers will decide to buy everything. So use all the space at the most convenient time period. That in this case is 2020. The top figure means install everything at the beginning and then nothing else. But when you have uncertainty, the prediction of the model on the bottom are more realistic. So there is an adoption that is increasing. That is what we would expect. Okay, what are the results? Can we achieve the Targets? No. So this is what the model is telling us. If we just run the model with the data that we have. You see this picture, the two dots, the two purple dots are the targets I mentioned earlier in 2025, 2030. And the blue line is the capacity that is predicted or forecasted by our model. So we cannot achieve that. How can we achieve that? Well, we analyze the solution and we derive the incentive. So Singapore dollar for kilowatt installed that we need to give to consumer so that is more convenient for them to install more. And if we do that, then yes, we can achieve the targets. Here you can see the amount of money. We have three scenarios if we want to achieve the 2025, the 2030 or both of them. And you see the amount of money again. This is Singapore dollar for kilowatt we need to give for each year. Another interesting thing I want to mention is this. We notice some relationship between these results and resilience. So look at this picture. The green line is basically the business as usual, what the model predicts. And then we say, well, what will happen if there is a sudden increase in the selling price, a shock, for example, you know, with the commodity price increase after the war, this could happen. And we are talking about 30 years, many things can happen. So if there is in our simulation a 50% increase, you see that the solar adoption, the capacity installed is going down and then it's picking up again. But if there is an 80%, then it's basically collapsing. And this is similar to what you see when you analyze resilience. When after a shock you can have a decrease and then you go back to normal. Or if the shock is too big, you can have a collapsing behavior. So this means that potentially there can be a study where we try to understand better this model using concept taken from resilience. To summarize, we derive a model based on robust optimization. Space constraints are included, risk aversion of consumer as well for forecasting the solar adoption in Singapore in the medium to long term. And this model, we are not saying that take this and trust this. No, is just a decision support tool that agencies can use and complement with other requirements. Like for example the budget that we say is necessary. Maybe it's not available, so they need to check with other things. But this can give another perspective on this problem. We have a paper recently published on that. If you want more information, all the details, the model is there. And if it's not enough, just write me and I will be happy to answer. Thank you.

Thank you very much. Dr. Alberto for your presentation on solar PV planning the.