Fig 2 - uploaded by Avik Ghosh
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Temporal schematic example for a 48 h prediction horizon together with a 48 h reference horizon, both starting at time t, which falls on day n of a month M with N days. The set of time points for the month M is denoted by Tt, with T NC,t and T OP,t defining the subsets corresponding to NC and OP demand charge periods, respectively. The final time points for these periods are represented as τ NC,t and τ OP,t . The set T OP,t is the union of the daily subset of OP demand charge time points T OP,t,n . Starting from t, the set of all time points in the reference horizon of length T R are defined in T R,t , with its final time point called τ R,t andˆτandˆ andˆτ R,t marking the time point at which the 50% SOC low threshold is placed. Similarly, the prediction horizon starting at the time point t, with length T MPC , is represented by T MPC,t . The final time point in this horizon is τ MPC,t , andˆτandˆ andˆτ MPC,t identifies the time point at which the 50% SOC low threshold is placed. Bold and unbold time parameters T MPC,t , T R,t ,T MPC , T R , τ MPC,t , τ R,t , ˆ τ MPC,t , andˆτandˆ andˆτ R,t designate rolling and shrinking horizons, respectively.
Source publication
Monthly demand charges form a significant portion of the electric bill for microgrids with variable renewable energy generation. A battery energy storage system (BESS) is commonly used to manage these demand charges. Economic model predictive control (EMPC) with a reference trajectory can be used to dispatch the BESS to optimize the microgrid opera...
Contexts in source publication
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... T be the set of time points as shown in Fig. 2, where t ∈ T is a time point. Since the demand charge horizon is equal to the entire month, for a given t, T t is defined as the set of all time points in the month that t belongs to. This work considers two demand charge peaks: (i) the monthly noncoincident (NC) peak demand, which is the highest average power demand in any 15-minute ...
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... and (ii) the on-peak (OP) peak demand, which is the highest average power demand of a 15-minute interval during 16:00 h to 21:00 h of the month. T NC,t and T OP,t are defined as subsets of T t containing all time points corresponding to NC and OP demand charge periods for the entire month. Note that T OP,t is a disconnected set, as shown in Fig. 2. The time points corresponding to the prediction horizon at the current MPC step t are collected in T MPC,t and T MPC is the prediction horizon length. Similarly, the time points corresponding to the reference trajectory horizon (called reference horizon) are collected in T R,t and T R is the reference horizon length. The time points τ ...
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... k is used to denote the prediction horizon T MPC,t = {t, ..., τ MPC,t }. Fig. 2 shows the corresponding prediction horizon temporal scheme. The objective function (6a) minimizes the total energy cost and the demand charges assessed over the prediction horizon of length T MPC . The constraint (6b) is the state update equation for the SOC x, where BESS en is the BESS energy capacity. Constraint (6c) is the load ...
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... to incorporate both demand charges (NC and OP) and the online reference trajectory. First, the system model is augmented with two auxiliary state variables, y NC and y OP , to track the two demand charge peaks within the prediction horizon T MPC,t starting at time t and denoted using k. The temporal scheme of the prediction horizon is shown in Fig. 2. The variables y NC and y OP are defined ...
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... Reference Trajectory without Peak Demand Tracking (Reference Stage): The reference trajectory z r (k ′ ) is computed at the reference stage of the proposed EMPC. Its temporal alignment is shown in Fig. 2. The reference trajectory is an input to the MPC stage and is used as a basis for measuring the economic performance of the system. The reference trajectory without peak demand tracking is the sequence {(x r (k ′ ), u r1 (k ′ ), u r2 (k ′ ))} k ′ ∈TR,t that solves the following optimization problem over the reference horizon T R,t ...
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... T be the set of time points as shown in Fig. 2, where t ∈ T is a time point. Since the demand charge horizon is equal to the entire month, for a given t, T t is defined as the set of all time points in the month that t belongs to. This work considers two demand charge peaks: (i) the monthly noncoincident (NC) peak demand, which is the highest average power demand in any 15-minute ...
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... and (ii) the on-peak (OP) peak demand, which is the highest average power demand of a 15-minute interval during 16:00 h to 21:00 h of the month. T NC,t and T OP,t are defined as subsets of T t containing all time points corresponding to NC and OP demand charge periods for the entire month. Note that T OP,t is a disconnected set, as shown in Fig. 2. The time points corresponding to the prediction horizon at the current MPC step t are collected in T MPC,t and T MPC is the prediction horizon length. Similarly, the time points corresponding to the reference trajectory horizon (called reference horizon) are collected in T R,t and T R is the reference horizon length. The time points τ ...
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... k is used to denote the prediction horizon T MPC,t = {t, ..., τ MPC,t }. Fig. 2 shows the corresponding prediction horizon temporal scheme. The objective function (6a) minimizes the total energy cost and the demand charges assessed over the prediction horizon of length T MPC . The constraint (6b) is the state update equation for the SOC x, where BESS en is the BESS energy capacity. Constraint (6c) is the load ...
Context 9
... to incorporate both demand charges (NC and OP) and the online reference trajectory. First, the system model is augmented with two auxiliary state variables, y NC and y OP , to track the two demand charge peaks within the prediction horizon T MPC,t starting at time t and denoted using k. The temporal scheme of the prediction horizon is shown in Fig. 2. The variables y NC and y OP are defined ...
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... Reference Trajectory without Peak Demand Tracking (Reference Stage): The reference trajectory z r (k ′ ) is computed at the reference stage of the proposed EMPC. Its temporal alignment is shown in Fig. 2. The reference trajectory is an input to the MPC stage and is used as a basis for measuring the economic performance of the system. The reference trajectory without peak demand tracking is the sequence {(x r (k ′ ), u r1 (k ′ ), u r2 (k ′ ))} k ′ ∈TR,t that solves the following optimization problem over the reference horizon T R,t ...
