High Taxes on Cloudy Days: Dynamic State-Induced Price Components in Power Markets.

AuthorGoke, Leonard

    Compliance with international climate objectives requires a major expansion of variable, meaning weather-dependent, renewables (VRE) like wind and solar (European Commission, 2011, 50). Large-scale integration of these technologies relies on a flexible power system that no longer just adapts to fluctuations of demand, but to demand minus variable generation, also referred to as residual load. Apart from technical options to address this problem, like energy storage or interconnection, a regulatory measure often proposed is passing on wholesale prices to consumers in order to create more favorable demand patterns, usually referred to as real-time pricing (RTP) (Pahle et al., 2017; Mills and Wiser, 2015; Sioshansi and Short, 2009). One intended result could be, for example, that demand from electric car batteries is shifted towards periods with excess power generation from VRE. In this paper, we aim to take the idea of RTP one step further and analyze how not only charging the power price at time-variant rates, but state-induced price components as well can benefit the integration of VRE and help to efficiently achieve the overarching goal of decarbonizing the energy system.

    This concept, hereafter referred to as "dynamization", is illustrated in Figure 1. (1) In case (a), electricity prices are independent of time, as is usual for most consumers today, and in case (b) under RTP only wholesale prices are passed on. Now, as soon as dynamization is introduced, state-induced price components are assumed to be set proportionally to wholesale prices, as displayed in (c). This measure further expands the range of consumer prices and, since price and demand are inversely related, has an opposed effect on the residual load, which facilitates the integration of VRE: Lower prices at negative residual loads increase demand in order to avoid curtailment and, vice versa, higher prices at high residual loads decrease demand in order to reduce the need for thermal backup-capacities. However, there are also well-founded arguments for adverse effects: First, deadweight losses in the market could rise and, second, the use of emission intensive mid-load technologies could increase, in contradiction to the overarching objective of decarbonization. In addition, the severe shift of consumer prices induced by dynamization, displayed in Figure 1, can be expected to cause strong distributional effects among consumers depending on their demand profile and their ability to adjust it.

    According to Hirth et al. (2016), costs of integrating VRE are a result of energy from thermal power plants and energy from solar panels or wind turbines not being perfect substitutes. Although physically they all provide electrical energy, thermal power plants are able to produce at any desired point in time, while production from VRE sources such as wind and solar is dependent on the weather. This incurs costs that go beyond the direct investment costs of VRE and can be interpreted as opportunity costs, for example, due to curtailment or the constant need for thermal backup capacities. Ueckerdt et al. (2013, 65) consistently define integration costs as "[...] all additional system costs induced by VRE that are not directly related to their generation costs" and, building on this, provide a formula to compute integration costs from the results of a power market simulation, on which we will pick up further below.

    While integration costs are found to rise steeply with the share of VRE, they can be reduced by various instruments, collectively termed "integration options". Well-studied examples include energy storage, interconnection, demand-side management (DSM) and flexible thermal power plants (Hirth, 2015; Lund et al., 2015; Mills and Wiser, 2015). Dynamization of state-induced price components as a regulatory measure to integrate VRE has been politically proposed (see Perner and Zahringer, 2017, among others), but not scientifically examined yet, unlike RTP, being a closely related measure, which has already been analyzed in this context by Mills and Wiser (2015).

    Schweppe (1988) was the first to propose time-variant pricing of electricity as a measure to achieve efficient markets, explicitly not limiting his proposal to wholesale prices and RTP, but including other price components as well; the following research focused on this issue.

    Borenstein (2005) finds efficiency gains from introducing RTP to be substantial even at low demand elasticities, and introduces a framework for quantitative research on RTP in competitive markets, which most of the research listed hereafter refers back to. For example, Holland and Mansur (2006) analyze the impact of RTP on the market outcome in more detail and conclude that RTP causes an increase in the overall demand largely covered by mid-load power plants. The one drawing on empirical load patterns of residential and the latter of industrial consumers, both Borenstein (2007) and Horowitz (2014) find that the adoption of RTP leads to substantial welfare transfers. These transfers mostly depend on the demand profiles concerned and are offset, but not entirely compensated, if higher demand elasticities are assumed.

    Gambardella and Pahle (2018) extend research on RTP by focusing on power systems characterized by VRE instead of conventional power plants. Results suggest that VRE cause a mitigation of distributional effects from RTP adoption, since increased variable generation reduces the covariance between prices and demand.

    In Pahle et al. (2017) this approach is extended to analyze the impact of RTP on different subsidy schemes for renewables. They focus on comparing an energy- and capacity-based subsidy and allow negative prices, while varying the exogenously set share of VRE and consumers subjected to RTP. In all cases considered, they find a subsidy on energy to be preferable, mostly because under RTP a premium on energy increases the utilization of VRE, thus reducing the capacity required to meet a certain share of VRE. However, they note that since they "neglect other flexibility options such as dispatchable renewable electricity sources, electricity storage, and international trade", their model is likely to overestimate benefits from price incentives for consumers (Pahle et al., 2017, 166). For the analysis of dynamization in this paper, a model capable to cover these aspects is introduced and applied.

    The remainder of the paper is organized as follows. Section 2 describes the general modeling approach and how it differs from previous work. Next, the case study that the model is applied to and its underlying data are introduced in section 3. In section 4, detailed results from the case study are presented and discussed for a base-case scenario, and summarized for a broad range of sensitivities. Finally, section 5 concludes.


    Like the previous work on RTP and VRE cited above, we apply a long-term partial equilibrium model of a perfectly competitive wholesale market. While capacities of renewable energy and storage technologies are set exogenously, the level of subsidies to finance them and capacities of thermal power plants are determined endogenously. Except for the comprehensive introduction of RTP and dynamization, the assumed regulatory framework corresponds to the framework currently installed in Germany. The targeted expansion of renewables is achieved through a technology-specific premium on energy, which is financed by a levy on the consumption of electricity. To analyze effects of dynamization, this levy is charged proportionally to wholesale prices. The wholesale market is designed as an energy-only market with zonal and scarcity pricing.

    In contrast to earlier work, the model includes a broad range of integration options. While analysis in Pahle et al. (2017) is limited to RTP, we additionally introduce dynamization and DSM technologies like electric vehicles. To achieve an accurate representation of DSM technologies, cross-price-elastic demand is introduced. Within technical restrictions, this demand can be shifted between periods and is therefore sensitive to all prices within these periods. As a result, it is of particular interest when analyzing pricing mechanisms for consumers. In addition, the model does include storage as well as export and import of electricity. Although these integration options are not directly affected by consumer prices, omitting them would overestimate benefits from dynamization.

    Including DSM creates a notable amount of demand that is highly sensitive to wholesale prices. In addition, imports provide an additional source of peak-load supply. Therefore, these integration options do not help to integrate renewables, but also mitigate market power. In addition, zonal pricing generally reduces market power. Therefore, assuming a perfectly competitive market and consequently neglecting market power seems acceptable.

    The following subsection 2.1 introduces the model's general approach. Afterwards, subsection 2.2 details how demand is modeled. A particular focus is on the representation of DSM as cross-price-elastic demand. To complete the model description, the energy balance and storage equations are presented in section 2.3. Extending the model to account for additional integration options prevents formulation as a mixed complementarity problem. Consequently, solution methods used in previous research cannot be applied anymore and are replaced by a novel solution algorithm introduced in subsection 2.4. Some additional model description is provided as Supplementary Material.

    2.1 General approach

    Since a perfectly competitive market is assumed, the objective function of the model's underlying optimization problem maximizes social welfare and is displayed in eq. (1). To facilitate understanding, lower case letters indicate model parameters, while variables are denoted with capital initials.

    [Please download the PDF to view the formula] (1)


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