We present our collaboration with the OCP Group, one of the world's largest producers of phosphate and phosphate-based products, to reduce OCP's carbon emissions significantly. We study the problem of decarbonizing OCP's electricity supply by installing a mixture of solar panels and batteries to minimize its time-discounted investment cost plus the cost of satisfying its remaining demand via the national grid. OCP is currently designing its renewable investment strategy, using insights gleaned from our optimization model, and has pledged to invest 130 billion MAD (approx. 13 billion USD) in a green initiative by 2027, a subset of which involves decarbonization. We immunize our model against deviations between forecast and realized solar generation output via a combination of robust and distributionally robust optimization. To account for variability in daily solar generation, we propose a data-driven robust optimization approach that prevents excessive conservatism by averaging across uncertainty sets. To protect against variability in seasonal weather patterns induced by climate change, we invoke distributionally robust optimization techniques. Under a 10 billion MAD investment by OCP, the proposed methodology reduces the carbon emissions which arise from OCP's energy needs by more than 70% while generating a net present value (NPV) of 5 billion MAD over twenty years. Moreover, a 20 billion MAD investment induces a 95% reduction in carbon emissions and generates an NPV of around 2 billion MAD. To fulfill the Paris climate agreement, rapidly decarbonizing the global economy in a financially sustainable fashion is imperative. Accordingly, this work develops a robust optimization methodology that enables OCP to decarbonize at a profit by purchasing solar panels and batteries. Moreover, the methodology could be applied to decarbonize other industrial consumers.
Preventing Overfitting: An important concept in machine learning
In this section, we immunize our model against overfitting the solar capacity factors provided by OCP, using ideas from DRO. This is an important practical step. Indeed, as mentioned in the introduction, sample average approximations of capacity expansion problems generally perform well in large sample settings, but overfit in the presence of small sample sizes. Moreover, Moroccan weather patterns may change due to changes in the climate induced by increasing levels of carbon in the atmosphere, making historical data unreliable. Therefore, overfitting could certainly occur in our problem setting, where we have access to capacity factors on an hourly basis for one year.
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