Multimodal AI for Online Micro-Grid Distribution and Monitoring with Equity Assurance

As mentioned in Section 1, zero-shot and few-shot predictive models are of tremendous importance in determining the placement and configuration of micro-grids, and in learning equitable energy distribution policies. To train the models, we assume that historical data is available from $n$ sites, which might be very diverse geographically and socioeconomically. Let $A_{i}$ be the characteristics of site $i$ – information about the weather, topology, demographics, socioeconomic indicators – serviced by a micro-grid characterized by specifications $M_{i}$. Furthermore, the area $A_{i}$ encompasses $n_{i}$ units, which could range from individual homes to apartment complexes, or other entities with detailed energy consumption and supply data. $X_{i}\in\mathbb{R}^{n_{i}\times T\times d}$ represents the spatiotemporal information available for the unit, typically a multivariate time series, accompanied by maps, charts, or satellite imagery. The information about the unit typically includes specifics about the electrical installation, including alternative electrical supplies, as well as the number of inhabitants, meter readings, size of the house, number of bedrooms, bathrooms, electrical vehicles, and other indicators relevant to energy consumption. We use the notation $C_{i}\in\mathbb{R}^{n_{i}\times T}$ to refer to the energy consumption at all units in area $A_{i}$ over time. We will train predictive models for the energy consumption at each individual unit, as well as models that predict the production of existing micro-grids or candidate micro-grids. The former can be expressed as $\displaystyle\hat{C}_{i}=\xi(A_{i},X_{i})$, while the latter can be expressed as $\hat{P}_{i}=\psi(M_{i},A_{i})$, where $\xi$, $\psi$ are the predictive models. To train $\xi$ and $\psi$, we propose to combine and extend several of our contributions on multivariate time series prediction, specifically MultiWave deznabi2023multiwave, our deep architecture that captures multiresolution signals through wavelet decomposition, CALM-Net shaw2019personalized, our technique for personalization, and our zero-shot predictive model deznabi2023zero that uses a fully connected layer to transform the embeddings associated with source locations into those corresponding to the target location. We have shown that our zero-shot method surpasses conventional weather forecasting techniques in predicting microclimate variables by leveraging knowledge extracted from other geographic locations, which is a problem that involves signals with similar characteristics to those needed for the task of predicting energy production and consumption.

We also aim to instrument micro-grids to ensure equity in energy distribution. Equity assurance begins with the appropriate placement and configuration of the micro-grid, as argued in Section 1. Thus, our first objective is to learn the placement and configuration for a micro-grid $M_{\text{new}}$ to be placed in area $A_{\text{new}}$ based on data from locations $A_{1}\dots A_{n}$. Our zero-shot personalized predictive models in Section 2.1 ensure that we will be able to predict consumption at all units in the new area as $\hat{C}_{\text{new}}=\xi(A_{\text{new}},X_{\text{new}})$ by leveraging data from other areas. We need to learn the optimal placement of the micro-grid $\tilde{M}_{\text{new}}$. To ensure equity, we analyze a specific set of features $U_{i}\in\mathbb{R}^{n_{i}\times T\times d_{u}}$ for each area $A_{i}$, which represent the levels of underprivilege across all units in that area. This dataset may include variables such as socioeconomic records, household income, the current status of supply, and access to alternative suppliers. Additionally, we denote the electrical supply from the micro-grid to all $n_{i}$ units in the area as $S_{i}\in\mathbb{R}^{n_{i}\times T}$. This supply is influenced by $M_{i}$ (the characteristics of the micro-grid), other relevant data about the area, and the implemented distribution policy.

To pose the selection of the best micro-grid configuration $\tilde{M}_{\text{new}}$ as an optimization problem separate from determining the energy distribution policy that will eventually be used in area $A_{\text{new}}$, we make the assumption that, given a fixed placement and configuration of the micro-grid, distribution will occur in a similar fashion to that of other areas. In other words, we assume we can learn to estimate $S_{\text{new}}$ by training a model on historical data from the other areas: $\displaystyle\hat{S}_{i}=\hat{\delta}(A_{i},X_{i},U_{i},M_{i},C_{i})$. Once $\hat{\delta}$ is trained, for area $A_{\text{new}}$, we will have $\displaystyle\hat{S}_{\text{new}}=\hat{\delta}(A_{\text{new}},X_{\text{new}},U_{\text{new}},\tilde{M}_{\text{new}},\hat{C}_{\text{new}})$, where $A_{\text{new}}$, $X_{\text{new}}$, $U_{\text{new}}$ are known, $\tilde{M}_{\text{new}}$ is the micro-grid configuration we are trying to learn, and $\hat{C}_{\text{new}}$ is the predicted consumption, a known quantity once we apply our predictive model. Thus, as $\tilde{M}_{\text{new}}$ is the only remaining variable in $\hat{S}_{\text{new}}$ , for simplicity, we write $\hat{S}_{\text{new}}(\tilde{M}_{\text{new}})$. We’d ideally like to select $\tilde{M}_{\text{new}}$ such that the supply is as close as possible to the demand, that is, to minimize some distance, such as $\displaystyle\min_{\tilde{M}_{\text{new}}}||\hat{S}_{\text{new}}(\tilde{M}_{\text{new}})-\hat{C}_{\text{new}}||_{2}^{2}$.

However, this objective does not ensure that the micro-grid is configured to fit the needs of the under-served units. To address this, we devise a metric that quantifies how under-served a location is. We start by considering historical records from other areas and learn a mapping $\nu$ from $A_{i}$, $X_{i}$ and $U_{i}$ to the supply deficits $C_{i}-S_{i}$. The higher the supply deficits at a location, the less well-served it is. For the new location, we have the estimated supply deficit as $\nu(A_{\text{new}},X_{\text{new}},U_{\text{new}})$. We also must adjust our assessment using domain knowledge that generalizes across areas, such as adjustments due to extremely low income. This can be expressed through a multiplier $\beta(U_{i})$. Also, area-specific factors must be considered, such as frequent power outages from an existing supplier in certain locations. This can be expressed through a multiplier $\alpha(X_{i})$. Thus, we’ll have the measure of under-service as $\displaystyle\mu(A_{\text{new}},X_{\text{new}},U_{\text{new}})=\nu(A_{\text{new}},X_{\text{new}},U_{\text{new}})\beta(U_{\text{new}})\alpha(X_{\text{new}})$.

The new objective is $\displaystyle\min_{\tilde{M}_{\text{new}}}||\mu_{\text{new}}^{T}\Big{(}\hat{S}_{\text{new}}(\tilde{M}_{\text{new}})-\hat{C}_{\text{new}}\Big{)}||_{2}^{2}$, with $\mu_{\text{new}}\stackrel{{\scriptstyle def}}{{=}}\displaystyle\mu(A_{\text{new}},X_{\text{new}},U_{\text{new}})$ used to up-weight the importance of the under-served units.

Once micro-grids $M_{1}\dots M_{n},M_{\text{new}}$ exist, what remains to be solved is the power distribution policy. We’ll need to learn a function $\delta_{i}$ that supplies $\tilde{S}_{i}=\delta_{i}(A_{i},X_{i},U_{i},M_{i},\bar{C}_{i})$, where $\bar{C}_{i}$ is partly observed and partly predicted. The objective is matching the supply to the demand while ensuring service in underserved areas, that is $\displaystyle\min_{\delta_{i}}||\mu_{i}^{T}\Big{(}\delta_{i}(A_{i},X_{i},U_{i},M_{i},\bar{C}_{i})-\bar{C}_{i}\Big{)}||_{2}^{2}$. We propose the introduction of additional constraints such that a minimal supply is provided, depending on the unit’s needs. This is, that $\delta_{i}\geq\mu_{i}\kappa$, where $\kappa$ is a multiplier dependent on minimal household needs and the cost of living. As the data, objective, and constraints will vary, we will research efficient algorithms able to learn offline policies for dynamic deployments, such as our Constrained Offline Policy Optimization (COPO)polosky2022constrained, which explicitly accounted for distributional shifts, outperforming the s.o.t.a. on control problems.

The online AI systems powering micro-grids will be faced with large volumes of continuously incoming data that need to be processed in real-time. Further, the incoming data stream changes constantly, in ways that are not typically handled by current online learning methods. These meta-level changes include (i) the introduction of new modalities, for instance when new equipment becomes available for data collection; (ii) modifications of the settings or context of a modality, such as changes in the data collection protocol, or when a more precise sensor becomes available; (iii) changes in the interdependence between modalities, for instance after heavy snowfall, the amount of energy produced might not increase proportionally to sunlight. Computational and time constraints make it difficult, even impossible, to consider a wide variety of architectures to account for all the variability, creating a high demand for methods capable of quickly testing the different aspects of fusion. In our lab, we seek to address these key questions that must be answered to achieve fast, adaptive, and efficient multimodal fusion, enabling the creation of flexible online AI systems.