Load Shifting, Interrupting or Both? Customer Portfolio Composition in Demand Side Management

Abstract

The share of renewable power sources in the electricity generation mix has seen enormous growth in recent years. Generation from fluctuating renewable energy sources (Wind, Solar) has to be considered stochastic and not (fully) controllable. To align demand with volatile supply, balancing and storage capacities have to be increased. To avoid high costs of storage investments, we suggest exploiting demand side flexibility instead. This can be operationalized through scheduling of electrical loads. Prior research typically assumes that both the set of customers, as well as the flexibility endowments of the scheduling problem, are exogenously given. However, the quality of the scheduling result highly depends on the composition of the customer portfolio. Therefore, it should be designed in an optimal fashion. This includes two decisions: which customers should be part of the portfolio and how much flexibility each customer should offer. Thus, future energy retailers face a complicated decision-making problem.We present a portfolio design optimization model which includes both selecting customers to be part of the portfolio and scheduling their flexibility. Furthermore, we present exemplary results from a scenario based on empirical load and generation data.

Appendix

With the parameters and decision variables described in Sect. 3 the portfolio design problem is formulated as follows. First, we describe the model constraints. We then define the objective function and its components. Constraint (1) ensures that each customer’s overall shiftable demand is covered over the optimization horizon.

$$\displaystyle{ \sum _{t\in T}D_{c,t}^{S} =\sum _{ t\in T}\sum _{s\in T}X_{c,t,s}^{S}\quad \forall c \in C }$$

(1)

Load shifted from t to s cannot exceed the gross shiftable load in t.

$$\displaystyle{ D_{c,t}^{S} \geq \sum _{ s\in T}X_{c,t,s}^{S}\quad \forall c \in C,\forall t \in T }$$

(2)

Similarly, dispatched interruptible load in t $X_{c,t}^{I}$ is bounded by the minimum dispatch amount and the gross interruptible load in t.

$$\displaystyle{ I^{P}D_{ c,t}^{I} \leq X_{ c,t}^{I} \leq D_{ c,t}^{I}\quad \forall c \in C,\forall t \in T }$$

(3)

Total load must equal the sum of available renewable supply and dispatched conventional generation:

$$\displaystyle{ G_{t} =\sum _{c\in C}\left (D_{c,t}^{B} + X_{ c,t}^{I} +\sum _{ s\in T}X_{c,t,s}^{S}\right ) - R_{ t}\quad \forall t \in T }$$

(4)

The supplier’s objective is to maximize profits which is given by revenues minus costs. We split the costs into two components, contracting costs and dispatching costs:

$$\displaystyle{ \max _{C^{B},C^{S},C^{I},X^{S},X^{I}}\mathop{\underbrace{ \sum _{t\in T}\sum _{c\in C}p\left (D_{c,t}^{B} + D_{c,t}^{S} + D_{c,t}^{I}\right )}}\limits _{\text{revenues}}-\mathop{\underbrace{F^{S} + F^{I}}}\limits _{\text{contracting costs}}-\mathop{\underbrace{C^{G} + C^{S}}}\limits _{\text{dispatching costs}} }$$

(5)

Contracting costs occur during the portfolio design phase and are driven by the discounts on the two flexibility types:

$$\displaystyle{ F^{S} =\sum _{ t\in T}\sum _{c\in C^{S}}p\delta ^{S}D_{ c,t}^{S}\qquad F^{I} =\sum _{ t\in T}\left (\sum _{c\in C^{I}}p(D_{c,t}^{I} - (1 -\delta ^{I})X_{ c,t}^{I})\right ) }$$

(6)

Dispatching costs reflect the usage of costly conventional generation and shifting distance penalties from shifting execution:

$$\displaystyle{ C^{G} = c^{G}\sum _{ t\in T}(G_{t})^{2}\qquad C^{S} = c^{S}\sum _{ c\in C}\sum _{t\in T}\Big(\mathop{\underbrace{\sum _{s=0}^{t-1}(t - s)^{2}X_{ c,t,s}^{S}}}\limits _{ \text{loads shifted forward}}+\mathop{\underbrace{\sum _{s=t+1}^{T}(s - t)^{2}X_{ c,t,s}^{S}}}\limits _{ \text{loads shifted backward}}\Big) }$$

(7)