How is the reward function defined for the DQN agent in the microgrid secondary control case study, and what is the agent's objective?

In the microgrid case study, the DQN agent's reward is r = -(delta-omega) - (delta-v), where delta-omega is the sum over the three DGs of (omega_ss - omega_i) and delta-v is the sum over the three DGs of (v_ss - v_i). The agent's objective is to maximize this reward, which equivalently minimizes each DG's frequency and voltage deviation from the steady-state reference values under stochastic conditions.

The source defines the reward as r = -Δω - Δv. The terms are Δω = Σ_{i=1}^{3}(ωss - ωi) and Δv = Σ_{i=1}^{3}(vss - vi), where ωss and vss are the steady-state frequency and voltage references. Because the reward takes the negative of these sums, larger deviations produce more negative reward. The DQN agent acts in the secondary control layer, observing a nine-element state containing each DG's frequency, voltage, and intrusion detection system outputs, and selecting one of the three secondary-control compute/communication action sets. Its stated goal is to maximize r, thereby minimizing the frequency and voltage deviation from their nominal steady state under stochastic conditions such as load changes, outages, and cyberattacks.