Renewable energy curtailment: A case study on today's and tomorrow's congestion management

Energy Policy 112 (2018) 427–436

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Renewable energy curtailment: A case study on today's and tomorrow's congestion management

MARK

⁎

Hans Schermeyera, , Claudio Vergarab, Wolf Fichtnera a b

Chair of Energy Economics, Karlsruhe Institute of Technology (KIT), Hertzstrasse 16, 76187 Karlsruhe, Germany MIT Energy Initiative, Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue E19-307, Cambridge, MA, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Curtailment Optimization Renewable energy Congestion management Optimal power flow

This work aims at contributing to the development of congestion management in power systems facing a strong expansion of renewable electricity generation. We address a comparatively new but increasingly important challenge to electricity markets with a uniform price zone: Renewable curtailment due to grid constraints. Our goal is to provide a model framework suitable to investigate the impact of expanding the grid operator's flexibility under varying congestion management regimes. We aim to expose the limitations of the current regime and to present a favorable alternative. For our analysis, we develop an optimal power flow program to replicate the current congestion management regime for distribution grids with high penetration of distributed generation in Germany. Furthermore, we introduce district heating as additional flexibility option and investigate the impact under different approaches to congestion management. Our results suggest that introducing additional flexibility, while keeping the current congestion management regime, bears significant risk to increase the cost of congestion management. Adjusting the regime to take into account economic criteria, as outlined in this work, eliminates this risk and grants direct control on the trade-off between curtailment and cost.

1. Introduction Numerous countries in Europe and around the world are in the process of transforming their power systems to generate more electricity from renewable energy sources. The large-scale employment of distributed electricity generation from renewable energy sources (DG) is associated with increasing grid congestion and, hence, DG curtailment in many of the affected power systems. In the context of this work, curtailment refers to the reduction of renewable generation due to grid constraints in contrast to a market-driven reduction due to, for instance, negative prices. Geographically, we concentrate our analysis on Germany. In 2015, about 4.7 TWh of potential DG were curtailed within the feed-in management scheme in Germany, causing an estimated 478 million euros of compensation payments (BNetzA, 2016). Furthermore, the amount of curtailed energy strongly increased over the recent years and tripled in 2014 and 2015 (Fig. 1). This suggests that the amount of future curtailment and compensation might further increase. With regard to grid reinforcement, there has been significant activity for several years aiming to alleviate congestion and the associated cost in the medium and long terms (BNetzA, 2015a). Despite these efforts, curtailment amounts rose to their historic peak in 2015. Less

⁎

activity could be observed with regard to improving the congestion management algorithm. Regulators and policy makers are called upon to increase the efficiency of existing congestion management approaches and the coordination between grid operators (50Hertz GmbH et al., 2017; BDEW, 2015; Ecofys and Fraunhofer IWES, 2017; ENTSOEE, 2016; Gerard et al., 2016; VDE, 2014). To contribute to the development of future congestion management and to shed light on the causation of renewable curtailment in Germany, we develop a model of the real-world 110 kV distribution grid system in Schleswig-Holstein, including all interconnectors to the transmission grid. We select this case study because the vast majority, roughly 70%, of Germany's total curtailment occurs within this distribution grid (Fig. 1). According to the relevant German regulations, grid operators facing congestion caused by DG are to apply a congestion management algorithm that minimizes the amount of curtailed energy (Deutscher Bundestag, 2017a). However, since there are no exact details provided on how congestion management is carried out, there is a high uncertainty among market participants and scientists with regard to the resulting curtailment. Nevertheless, very concrete plans are on the way to expand the flexibility options available to grid operators when managing congestion: For example, the installation of up to 2000 MW power-to-heat capacity at district heating systems to grant

Corresponding author. E-mail addresses: [email protected] (H. Schermeyer), [email protected] (C. Vergara), wolf.fi[email protected] (W. Fichtner).

http://dx.doi.org/10.1016/j.enpol.2017.10.037 Received 13 March 2017; Received in revised form 16 October 2017; Accepted 19 October 2017 0301-4215/ © 2017 Elsevier Ltd. All rights reserved.

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Fig. 1. Curtailment of power generation from renewable energy sources in Germany over time. For each year the share of curtailed wind power and curtailment within the distribution grid of the grid operator Schleswig-Holstein Netz AG are shown as well. (BNetzA, 2012, 2013, 2014, 2015b; MELUR, 2016a).

2017a), and “adjustment measures” regulated via the German Energy Act. Adjustment measures allow the grid operator to adjust any feed-in, feed-out or the transit of power in order to guarantee the safety and reliability of the power system. They may only be applied if redispatch measures do not suffice. The amount of energy affected by adjustment measures is two orders of magnitude smaller than that affected by both other instruments and is therefore ignored in the following. The impact of redispatch measured in energy and estimated cost was 16 TWh and 412 million euros in 2015 (BNetzA, 2016). Redispatching largely affects conventional power plants and is exclusively driven by transmission grid constraints. It is also omitted for this work. Our analysis will focus on the DG curtailment resulting from feed-in management. To the present, the German Renewable Energy Act allows for curtailment only in the course of a congestion management approach that minimizes the amount of curtailment (Deutscher Bundestag, 2017a, p. 16). Even though the legislator recently passed a very concrete scheme to support the installation of power-to-heat units if they “efficiently” alleviate congestion (Deutscher Bundestag, 2017b), it remains unclear how such flexible and additional demand becomes part of the congestion management algorithm.

combined heat and power (CHP) plants more flexibility, incentivized by the revised Energy Act 2017. Our contribution consists of a model framework suitable to investigate the impact of expanding the range of flexibilities to the grid operator and to compare the performance of different congestion management scenarios. Besides modeling the current congestion management regime, we develop two concrete future scenarios: Whereas the first is inspired by the current state of regulation and still minimizes renewable curtailment, the second breaks with precedence and takes economic factors into account. The sections below are structured as follows: In Section 2, we provide an overview of the background of our study and the relevant literature. Section 3 presents the model implementation consisting of the full representation of the three optimization programs, the input data of our real-world case study in Northern Germany and the interface to the wholesale market. Section 4 summarizes the results of applying the different model derivatives and closes with a critical review of our modeling approach. In Section 5, we outline the implications of our results and derive concrete policy recommendations. 2. Background The approaches to design power markets around the world are diverse and the resulting regulation complex. Therefore, we focus our summary of the regulatory background of congestion management and the resulting DG curtailment on Germany. Subsequently, we present a brief overview of existing work from literature investigating with a similar angle.

2.2. Literature review The existing literature on power systems analysis with grid constraints is abundant. To point out where we intend our contribution, we narrow our review down to literature dealing with congestion management challenges arising from an increasing renewables penetration in a power market like Germany. We choose to cluster the relevant literature we identified into qualitative and quantitative work on how to improve congestion management, starting with the latter: Kunz (2013) reproduces re-dispatching of transmission grid operators (TSO) in Germany and predicts a significant increase in congestion and associated cost for the future. He argues for a strong need to improve the congestion management approach currently in place. Trepper et al. (2015) similarly argue for the importance of an improved congestion management. They analyze whether and how much splitting the German price zone on transmission grid level can contribute to reducing the need for re-dispatching and increasing welfare. Egerer et al. (2016) focus on a scenario with two and four price zones to analyze the effect on congestion within the German transmission grid and conclude for a need of different approaches to regional pricing to deal with network constraints. The mentioned studies provide excellent examples for the increasing occurrence of congestion and the need to improve congestion management addressed in this work. However, the existing studies focus on transmission grid constraints and investigate the corresponding tools: Splitting the uniform price zone, changing the

2.1. Congestion management and renewable curtailment in Germany In Germany, DG, in accordance with the German Renewable Energy Act (Deutscher Bundestag, 2017a), enjoys priority access to the grid infrastructure. This generally means that congestion has to be relieved by means of conventional power plants, and DG remains only as a last resort.1 As electricity in Germany is traded within a single price zone, congestion is unlikely to be prevented by the price signals of the market. Therefore, grid operators often have to intervene to alleviate congestion. Aside from transmission switching and network topology optimization, intervention is based on three legal instruments: “Redispatching” regulated via the German Energy Act (Deutscher Bundestag, 2017b), “feed-in management” regulated via both the German Energy Act and the German Renewable Energy Act (Deutscher Bundestag, 1 There are exceptions, for example for combined heat and power plants serving a heat demand. More details on how curtailment is to be executed are given in the latest curtailment guidelines by BNetzA (2017) that are currently being discussed.

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3.1. Base Case

network topology or expanding it. We aim to address the relatively new but increasingly important challenge of congestion on distribution grid level that can hardly be resolved by measures on transmission grid level. While we identified a lack of studies dealing quantitatively with the growing decentralization of grid congestion, there exist a few qualitative surveys: VDE (2014) and BDEW (2015) both present a qualitative framework for decentralized markets as a tool to coordinate flexible generation and demand for congestion management below the transmission grid on the regional and local level. The studies of Gerard et al. (2016) and Ecofys and Fraunhofer IWES (2017) conduct a helpful survey on examples from practice and existing literature dealing with the coordination between TSO and DSO in the European context. The authors identify congestion management across grid operators as a major challenge and describe various schemes for future coordination. Altogether, these studies provide helpful design approaches and a general background to improving congestion management. Nevertheless, they lack concrete algorithms to implement these improvements and to verify the effects quantitatively. The goal of our study is to provide a quantitative framework that is adequate for giving decision support to policy makers in the prevailing discussion about curtailment and congestion management on distribution grid level.

For modeling the status quo of congestion management in distribution grids, we apply current legislation: The German Renewable Energy Act obliges grid operators to implement a congestion management that minimizes the necessary curtailment of power generation from renewable energy sources and CHP (Deutscher Bundestag, 2017a). For the renewables, we assume that only generators based on wind, solar and bio energy may be curtailed.2 This yields our objective function for modeling the current decision making in congestion management of distribution grid system operators (DSO): “Minimize curtailment” bio min ∑ ∑ ⎛Δpi,wnd + Δpisol t , t + Δpi, t − t∈T i∈I

wind power curtailment at node i in time step t [MW] solar power curtailment [MW] biomass (& biofuel, biogas) power curtailment [MW] change of CHP power dispatch, negative values correspond to curtailment [MW] grid node iterator i I set of all nodes within the modeled grid infrastructure t time step iterator T set of all time steps n CHP plant iterator set of CHP plants connected to the district heating system at Ni grid node i The following paragraphs present the constraints that are accounted for by the optimization program. Electrical energy balance per node (Kirchhoff's first law): The total electric energy consumed equals the generated and transported energy to/from the system boundaries of the modeled electricity grid at all times and at every grid node.

In this section, we present an approach to congestion management on distribution grid level through the formulation and computation of a (mixed integer) linear optimization program, generally known as an optimal power flow (OPF) problem. We formulate three different optimization programs, representing the current state of regulation and two future scenarios. Please refer to Table 1 for an overview of the three scenarios and the main differences across the modeling approaches. In the Base Case scenario, we design an objective function that is meant to represent the current state of congestion management as described in the German Renewable Energy Act (Deutscher Bundestag, 2017a). For the second scenario we develop a hierarchical, multi-criteria optimization program that fully utilizes the flexibility of changing the CHP dispatch but limits its change when it does not help curtailment via a secondary objective function. As the third scenario, we modify the objective function to represent a cost-based approach to congestion management. In all the scenarios, the optimization problem includes constraints representing a linearized (DC) power flow approximation. Our congestion management approach is based on established methods of operations research for solving the OPF problem (Momoh, 2008). We implemented our modeling framework in Java, using the API and linear solver of Gurobi for optimization. The temporal horizon of one optimization problem spans 24 h and is motivated by the format of the day-ahead auction of power on most European markets taking place on a daily basis. The temporal increment is one hour.

sol bio bio rst giwnd − Δpiwnd + gisol ,t ,t , t − Δpi, t + gi, t − Δpi, t + gi, t +

Change of chp dispatch

Base Case

(Obj. 1) minimize curtailment (renewables & chp) multi-criteria optimization: (Obj. 2.a) minimize renewable curtailment (Obj. 2.b) minimize chp change (Obj. 3) minimize the cost of congestion management

Δpnchp, el ∈ ≤ 0

Heatflex - min (curt)

Heatflex - min (cost)

∑

pnchp, el

n ∈ Ni

−

∑ pij,t j∈I

+

∑ pji,t j∈I

− piwhl − d i, t = 0 | ∀ i ∈ I , ∀ t ∈ T ,t

(1)

giwnd ,t gisol ,t gibio ,t girst ,t

wind power generation potential [MW] solar power generation potential [MW] biomass (& biofuel, biogas) power generation potential [MW] other power generation (run-of-river, pit & sewer gas, conventional without heating) [MW] pnchp, el CHP power output of plant n [MW] pij, t power import to node i from node j (i←j) over line “ij” [MW] pji, t power export from node i to node j (i→j) over line “ji” [MW] piwhl power exchange across the DSO's boundaries via wholesale ,t market [MW] power demand [MW] d i, t Active power flow (Kirchhoff's second law): The active power flow from node i to node j according to Kirchhoff equals a function of voltage level, phase angle of the voltage, and reactance. We approximate the physical laws determining this relationship by applying a set of simplifications that linearize the non-linear power flow laws (compare e.g. Momoh, 2008). This approach is generally known as a direct current (DC) power flow.

Table 1 Overview of the congestion management scenarios and their modeling differences. Objective function

(Obj.1)

Δpiwnd ,t Δpisol ,t bio Δpi, t , el Δpnchp ,t

3. Model description

Scenario

⎝

, el ⎞ ∑ Δpnchp ,t ⎠

n €Ni

Δpnchp, el ∈ 

2 Other renewables are also eligible for curtailment but very rarely used: Curtailment of wind, solar and bio power generation represents more than 99,8% of the yearly curtailment in Germany (BNetzA, 2016). Consequently, we assume for other renewables to be non-dispatchable.

Δpnchp, el ∈ 

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pij, t =

U 2 × (θi, t − θj, t ) x ij

| ∀ ij ∈ B, ∀ t ∈ T

In the course of congestion management, the dispatch of CHP and heating plants may be adjusted compared to pre-optimization per district heating system. In the Base Case the adjustment of CHP electricity may only be negative (decreasing).

(2)

voltage level [V] phase angle of node voltages [rad] reactance of line “ij” [Ω] set of all power lines within the modeled grid infrastructure Thermal limits on the flow between nodes (line capacity): The active power flow per electrical line is limited due to the increase in line temperature with increasing power flow.

U θi, t x ij B

− pij ≤ pij, t ≤ pij | ∀ ij ∈ B, ∀ t ∈ T

, el , el , el Δpnchp = pnchp − gnchp | ∀ n ∈ Ni , ∀ i ∈ I , ∀ t ∈ T ,t ,t ,t , el Δpnchp ≤0 ,t

Δpmth, t = pmth, t − gmth, t | ∀ m ∈ Mi , ∀ i ∈ I , ∀ t ∈ T

gnchp, el

power output of CHP plant n resulting from microeconomic optimization per district heating system prior to congestion management [MW] ∆pnchp, el change of the CHP dispatch due to congestion management [MW] gmth, t heat output of heating plant m resulting from microeconomic optimization per district heating system prior to congestion management [MW] ∆pmth, t change of the heating plant dispatch due to congestion management [MW] Change of power exchange with wholesale market: The total change of power exchange corresponds to the sum of dispatch changes due to congestion management of all generating units across the DSO's boundaries.

active power limit of line “ij” [MW] calculated as: 1 thermal limit [A] × voltage level [V ] × 3 × 6 = pij 10 Renewable curtailment limits: Curtailment of a generation unit is bounded to be less or equal the maximum generation potential. (4)

Thermal energy balance of district heating: The thermal demand of a node's district heating system has to be served by the sum of available heat supply. , th (pnchp )+ ,t

∑ n ∈ Ni

∑

(pmth, t ) − d ith ,t = 0 | ∀ i ∈ I , ∀ t ∈ T

m ∈ Mi

(5)

, th pnchp ,t pmth, t Mi

thermal output of CHP plant n [MW] thermal output of heating plant m [MW] set of heating plants connected to the district heating system at grid node i dith thermal demand [MW] ,t Combined heat and power supply: CHP plants may supply both their output products in combination. Depending on the technology the rate between the outputs may vary. For this analysis, we assume an individual heat to power ratio per CHP unit and keep this ratio constant. , el pnchp ,t

μnel

=

, th pnchp ,t

μnth

| ∀ n ∈ Ni , ∀ i ∈ I , ∀ t ∈ T

Δptwhl =

⎛

∑ ⎜∑ i∈I

This section outlines the two scenarios for a future congestion management developed in this study. The Heatflex-min(curt) scenario that uses the same setting as the Base Case except for three small adaptations and the Heatflex-min(cost) scenario that uses a completely different objective function.

(6)

3.2.1. Heatflex–min(curt) Removing the CHP dispatch change from the objective function yields the new, primary objective function: “Minimize renewable curtailment” (primary objective) bio min ∑ ∑ (Δpi,wnd + Δpisol t , t + Δpi, t )

(Obj.2.a)

t∈T i∈I

To achieve that the heat serving dispatch of CHP and heating plants, which is pre-scheduled based on microeconomic cost minimization per district heating system, remains unchanged if it has no impact on renewable curtailment, we expand the problem for a secondary objective function, that minimizes the absolute value of the change of CHP and heating plant dispatch: “Minimize changing the pre-scheduled CHP and heating plant dispatch” (secondary objective)

(7)

minimum power output of CHP unit n [MW] maximum power output of CHP unit n [MW] binary variable determining if unit n is running or shut down [-] Minimum and maximum generation level of thermal peaker units: We assume for peaker units to be able to operate free between zero and maximum capacity:

min

⎛

, el |+ ∑ ∑ ∑ ⎜∑ |Δpnchp ,t

t∈T i∈I

pmth

(11)

3.2. Future congestion management

pnel pnel bn

pmth, t ≤ pmth | ∀ m ∈ Mi , ∀ i ∈ I , ∀ t ∈ T

⎝ n ∈ Ni

, el bio ⎞ (Δpnchp ) − ∆piwnd − ∆pisol ,t ,t , t − ∆pi, t ⎟ | ∀ t ∈ T ⎠

Non-negativity: All variables determining thermal and electrical supply or demand and curtailment at any location and time are constrained to positive real numbers.

, el power output of CHP plant n [MW] pnchp ,t el μn electrical efficiency of CHP plant n [-] thermal efficiency of CHP plant n [-] μnth Minimum and maximum generation level of CHP plants: assume for all CHP plants to have a minimum generation level. They can only generate at or above the minimum level or remain shut down. We model this with the help of a binary variable via the following formulation which expands our problem complexity from linear programming (LP) to mixed integer linear programming (MILP).

, el pnel × bn ≤ pnchp ≤ pnel × bn | ∀ n ∈ Ni , ∀ i ∈ I , ∀ t ∈ T ,t

(10)

Δpmth, t ∈

(3)

pij

sol bio bio ∆piwnd ≤ giwnd ;∆pisol ,t , t ≤ gi, t ;∆pi, t ≤ gi, t | ∀ i ∈ I , ∀ t ∈ T ,t

(9)

(8)

⎝

n €Ni

m €Mi

|Δpmth, t |

⎞ ⎟ ⎠

(Obj.2.b)

Change of CHP dispatch In extension of the base case, the congestion manager may both decrease and increase CHP output in pursuit of his objective to minimize renewable curtailment:

maximum output of heating plant m [MW] Prescheduling and change of CHP and heating plant dispatch: 430

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means of standard load profiles (E.dis, 2016) in combination with the grid operators publications on vertical grid load and census data, e.g. number of residents or employees within a commercial sector (Genesis, 2016). To create a grid model, we extract the locations of substations and interconnecting lines from the OpenStreetMap contributors (OSM, 2016) followed by an extensive survey and completion check. For the technical parameters of the 110 kV distribution grid lines and the transformers interconnecting distribution and transmission grid we assume generalized values provided by Brakelmann (2004), Oswald and Krämer (2006) and Oeding and Oswald (2016). We incorporate security constraints in a simplified way and limit all active power flow capacities to 70% of the rated capacity following Deutsche EnergieAgentur (2010), and IFHT (2015). However, we assume the capacity of transformers connecting distribution and transmission grid to be fully backed up and thus make 100% of their capacity available to the model. Finally, the textbook assumptions on line and transformer capacity are calibrated such that the capacity suffices to serve the load without any electricity generation throughout the grid. We account for various kinds of DG fed into our modeled distribution grid, namely, wind onshore, photovoltaics, biomass, biogas, water, sewage gas, and geothermal. Wind power is the most important renewable energy source in our distribution grid, with roughly 70% of installed capacity and 64% of supplied renewable energy in 2014, followed by generation from biomass-based fuels and photovoltaics with 21% and 11%, respectively (MELUR, 2016a). Details on the modeling of regionalized DG generation profiles, including a physical solar and physical wind model, can be found in Ringler et al. (2016). For modeling district heating systems we mainly resort to the following two publications: To calculate a thermal load profile per district heating system we apply the procedure described by BDEW et al. (2015) to calculate natural gas utilization for heating purposes in an apartment block (code 2D4). The profile is further depending on ambient temperature and scaled with the total heat demand per year. For details on where to allocate district heating systems, their yearly heat demand and their associated CHP and heating plants, we rely on data from AGFW (2016). We are able to match a total of 3.4 TWh heat demand, 1070 MW heating plant capacity and 326 MW electrical capacity of CHP plants (806 MW thermal capacity). Based on AGFW (2016), we derive individual data for every plant on efficiency, fuel type (coal or natural gas) and heat to power ratio where applicable. We assume a minimum electricity generation level of 30% for CHP plants. Coal prices are obtained via the monthly futures of the API#2 index published by the European Energy Exchange (EEX). For gas prices we average the daily reference price of the market areas GPL and NCG, published by the PEGAS gas exchange. The distribution of the 12 district heating systems within the grid infrastructure and their relative size, measured in total heat demand per year, is presented in Fig. 2. To obtain a startdispatch of all CHP and heating plant units prior to congestion management, we formulate a simple optimization program for each district heating system, serving thermal load under the individual constraints of the CHP and heating plants. The objective is to minimize fuel cost and CHP electricity output may generate negative cost via the wholesale market.

(12)

Absolute value of CHP dispatch change (electrical) To allow for a symmetric penalty of positive and negative changes of the CHP dispatch, we use the following auxiliary variables and , el , el, + , el, − = Δpnchp + Δpnchp constraints. Together they imply Δpnchp ,t ,t ,t , el , el, + , el, − Δpnchp = Δpnchp − Δpnchp | ∀ n ∈ Ni , ∀ i ∈ I , ∀ t ∈ T ,t ,t ,t

(13)

, el, + 0≤Δpnchp ,t , el, − 0≤Δpnchp ,t

, el, + auxiliary variable representing an increase of the electrical Δpnchp ,t CHP dispatch [MW] , el, − auxiliary variable representing a decrease of the electrical Δpnchp ,t CHP dispatch [MW]

3.2.2. Heatflex–min(cost) In the third scenario, we change the optimization program to take into account economic factors. The setting corresponds to the Heatflex–min(curt) scenario apart from a fundamentally altered objective function. This approach implies that any net increase or decrease of power generation will be exchanged via the wholesale market through transfer capacities across the DSO's boundaries at the wholesale market price. We assume for the DG that are available for curtailment to have zero marginal cost. Consequently, we define the cost of congestion management to be dependent of the changes the congestion management causes in the power exchange across the DSO's borders and the dispatch of heat serving plants: “Minimize the cost of congestion management”

min

⎛

∑ ⎜c (Δptwhl , rt ) + ∑ ∑

t∈T

⎝

c (∙)

rt cn, t cm, t μmth

i ∈ I n ∈ Ni

, el ∆pnchp × ,t

cn, t μnel

+

∑ ∑ i ∈ I m ∈ Mi

cm, t ⎞ μmth ⎟ ⎠ (Obj.3)

∆pmth, t ×

cost function of power exchange with the wholesale market [€] residual load of the wholesale market area prior to congestion management [MW] cost of the fuel used in CHP plant n [€/MWh] cost of the fuel used in heating plant m [€/MWh] thermal efficiency of heating plant m [-]

3.3. Data We apply the two alternative optimization problems formulated in the previous sections to a real-world distribution grid system in Germany. Our case study covers the 110 kV distribution grid of the federal state of Schleswig-Holstein which is operated by the SchleswigHolstein Netz AG (SH Netz AG) and includes the transformers interconnecting to the transmission grid level that are operated by the TSO (Fig. 2). We select this distribution grid for its relevance with regard to curtailment: Roughly 70% of Germany-wide curtailment is executed within this distribution grid by the distribution grid operator (Fig. 1). Moreover, the chosen distribution grid has no electrical connection to another distribution grid (except via the transmission grid level), which allows for a better isolation of the analyzed effects. Additionally, the federal state of Schleswig-Holstein has a very high penetration of DG, with 5200 MW wind and 1455 MW photovoltaic capacity at the end of 2014 (DGS, 2015) and thus serves as a proxy for a future power system dominated by DG. There are roughly 2.8 million people living in the modeled area, and yearly electricity consumption amounts to around 14 TWh (SN, 2016). We break the yearly electricity demand down in space and time by

3.4. Cost of power exchange Major part of the cost of congestion management is the cost for substituting curtailment by an alternative generation capacity. The matter of who has to substitute the curtailed energy to balance the system is under discussion. A concrete curtailment guideline, published by Germany's federal grid agency, is being discussed at the time of writing this paper (BNetzA, 2017). Basically, two options are being discussed: Either the grid operator executing curtailment directly contracts a power plant to balance the curtailed energy or informs the plant operator before the curtailment event who is then responsible for 431

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Fig. 2. Overview of the modeled distribution grid. The district heating symbols are sized proportionally to their yearly heat demand.

balancing via the short-term market. We implement the first option in this study and assume that the entity executing the congestion management is obliged to balance the curtailment via the wholesale market. We assume the day-ahead auction results of the joint bidding zone Germany/Austria/Luxembourg (PHELIX), published by the EPEX SPOT, as representative indicator for the cost to acquire the substituting power generation. To take into account that the wholesale market price might be influenced from large scale interventions in the power plant dispatch in the course of congestion management, we model the wholesale market price as a function of residual load. This reduces the complexity of the underlying power market, which is driven by numerous factors as for example the marginal cost of generators that are available or the current electricity demand. The approach is inspired by the established concept to estimate a mathematical relationship between power prices and residual load (Burger et al., 2004; Keles et al., 2013; Wozabal et al., 2016). In our case, residual load is defined as the total electricity demand across the above mentioned joint bidding zone DE/AT/LU reduced by the electricity generation from renewable energy sources. We obtain the necessary data from the Transparency Platform of the European Network of Transmission System Operators for Electricity (ENTSOE-E, 2017). A third degree polynomial regression between residual load and wholesale market price yields the price function presented in Fig. 3. We use its integral to represent the cost that occur when congestion management alters the power exchange with the wholesale market and thus the overall residual load. As expected, the cost for power exchange is monotonically increasing when the price is positive and vice versa. The cost shall be zero in the case that the congestion management does not change the power exchange. Thus, the integral is separately solved in each time step based on the respective residual load rt before congestion management takes place: c (Δptwhl = 0,rt ) = 0 . We linearize the cost function for changing power exchange c (Δptwhl , rt ) which is a polynomial of the fourth degree.

Fig. 3. Regression of residual load vs. wholesale market price of the DE/AT/LU bidding zone in 2015 (dashed line) and its integral solved for c (Δptwhl , rt = 0) = F (0) = 0 (solid line) representing the cost to change residual load.

with data on past curtailment events published by the DSO. In the third subsection 4.3 we present the results of adding the flexibility of CHP plants under the two developed congestion management scenarios developed in this study. We close this section by reviewing potential improvements of our modeling approach that we identified. 4.1. DC simplification The DC simplifications we apply may lead to different power flow results compared to a more sophisticated alternating current (AC) power flow approach and might affect the amount of curtailment and system cost. To quantify the order of magnitude of these differences, we compare the resulting power flow of the DC OPF to an AC power flow of the same dispatch (AC power flow calculated using the MATPOWER application developed by Zimmerman et al. (2011)). It turns out that during all times, the difference in active power flow between DC and AC is less than 3% of the respective line's capacity throughout the grid. It should be noted that we do not model the supply or consumption of

4. Results Our results are structured in four sections: First, we briefly comment on a few tests we ran to review the simplifications of our DC linearization. Then, we compare the resulting curtailment of the Base Case 432

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reactive power by generation or demand units. Thus, this should not be considered a complete comparison of AC and DC power flow analysis but rather to provide an error estimator for future researchers to decide whether to apply AC or DC constraints in a similar context. Additionally, we verified whether the resulting phase angle differences of the voltage between two nodes are small, as this is a major assumption of the DC linearization. The results show that the absolute difference stays well below 0.2 rad during all time steps.

Table 2 Comparison between the estimator for the historical curtailment and the model results of the Base Case in 2015. Published yearly curtailment based on (MELUR, 2016b).

4.2. Base Case evaluation

be used to analyze the implications of adjusting the congestion management approach.

Linear correlation Curtailment per year Maximum 0.95-quantile

To evaluate our model and data framework we compare the Base Case curtailment decisions with historical curtailment decisions published by grid operators. However, there are no publications available that provide historical curtailment straightforward as a time series. We generate a basis of comparison by the following two steps: First, we download data on past curtailment events from the distribution grid covered by our case study via the distribution grid operator's website (SHN, 2016). These data contain information on the feed-in limit per time for each DG plant and are available for current and past events starting in 2014. Combining these data with a register of renewable plants in Germany (DGS, 2015) reveals the plant's generation type and allows us to combine the curtailment data with a time series of the plant's potential power generation level. We extract the per-plant generation time series from our renewable generation model outlined in Section 3.2 as generation potential. The amount of curtailment at a node is calculated as the difference between potential generation of all affected generators at this node and their generation limit specified by curtailment events, when the latter is smaller. Such an evaluation for all curtailment events of the year 2015 generates a time series of historical curtailment. An illustrative excerpt of the time series covering a few hundred hours in 2015 is presented in Fig. 4. A comparison reveals some differences between our Base Case model results and the published values, as the yearly sum of modeled curtailment is lower and amounts to roughly 86% of the published amount (Table 2). We largely attribute these differences to the fact that our grid model is limited to the 110 kV voltage level of the distribution grid and the transformers that interconnect to the transmission grid level. Hence, we do not account for congestion that occurs within the transmission grid, which in practice leads to curtailment requests from the TSO to the DSO and significantly impacts the power flows. This interpretation was supported during our meetings with the distribution grid operator SH Netz AG. Overall, the modeling results reasonably approximate the curtailment pattern, with a positive correlation of 93% between model output and historical data. We conclude from the comparison that our model reproduces curtailment on distribution grid level realistically enough to

– [GWh] [MW] [MW]

Historical curtailment

Model (Base Case)

93% 3097 2495 1857

2672 2070 1760

4.3. Adjusting congestion management In this section we compare the performance of the two alternative approaches to congestion management outlined in Section 3.2 against the Base Case with regard to total curtailment and the cost of congestion management. The cost consists of the three components presented in objective function (Obj. 3): Cost for changing the net power exchange with the wholesale market and the fuel cost or savings for changing the dispatch of CHP and heating plants. Even though cost does not affect decision making in the Base Case and Heatflex-min(curt) scenarios, the variables are used to enable cost-based comparisons. Please refer Figs. 7 and 8 for a detailed comparison of the changes in energy outputs and cost across the three scenarios. The results of the Heatflex–min(curt) scenario suggest that including the flexibility of heat serving units of district heating systems has the potential to alleviate congestion and thus to reduce curtailment (Fig. 7). However, the effect on curtailment is limited (−2.8%). On the one hand due to the relatively low electrical capacity of CHP (326 MW) working against substantially larger curtailment peaks (Table 2) and suboptimal location of some of the capacity on the other hand. Furthermore, the yearly cost of congestion management experience a threefold relative increase of 10.9%. The cause behind this super proportional gain lies in the objective function that minimizes curtailment, regardless of the economic impact. Having access to the flexibility of CHP plants, the congestion manager consistently chooses heating plants over CHP plants for heat supply, if curtailment may be reduced. Any flexibility available with even the least effect on curtailment is bound to be dispatched at any cost, regardless of the economic and ecological impact. Fig. 5 demonstrates this effect: The reduction of renewable curtailment always coincides with a higher reduction of CHP electricity output. This leads to a drop of CHP utilization of roughly 22%, substituted by heating plants. The fuel savings of CHP plants are countered by additional fuel cost in heating plants and the expenses to buy back the reduced electricity output from CHP plants via the wholesale market. To limit the cost increases, we developed a multi-criteria Fig. 4. Illustrative excerpt of the reproduced historical curtailment and the modeled curtailment in the Base Case scenario for the modeled distribution grid in 2015.

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Fig. 7. Selected results of the three congestion management scenarios with regard to energy (totalled over the modeled distribution grid and for 2015).

Fig. 5. Change of curtailment or CHP denominates the difference between the results of the Base Case and the Heatflex-min(curt) scenario (simulation year 2015). It is calculated as Base Case – Heatflex-min(curt), thus negative values correspond to the Base Case result being higher and vice versa.

optimization program for this scenario that successfully avoids the solution space where CHP dispatch changes do not affect curtailment. Summarized, the congestion management algorithm of the Heatflexmin(curt)-scenario reduces curtailment of renewables by 76 GWh at yearly cost of about 7.4 million Euro. Thus, curtailment is reduced at average cost of 97 €/MWh. By means of the Heatflex–min(cost) scenario we explore the potential of applying a congestion management approach that takes economic criteria into account. While grid congestion still has to be alleviated in this scenario, the congestion manager balances the various options with regard to cost efficiency. Altering the cost efficient dispatch of CHP and heating plants found by each district heating system beforehand to reduce curtailment is weighted against the cost or savings for changing the net power exchange. From our modeling results we derive a low economic potential for CHP plants in alleviating congestion. Changing the dispatch of CHP and heating plants serving thermal load of district heating systems rarely proves beneficial and is utilized to a very low extent. The resulting curtailment remains close to unchanged. Aside from the few occasions with negative prices when the cost based congestion manager curtails as much renewable generation as is available until the price is driven to be non-negative (Fig. 6). Consequently, the congestion management approach of the Heatflexmin(cost) scenario avoids the substantial cost premium of the previous scenario when integrating additional flexibility options (Fig. 7). Compared to the Base Case, the resulting cost decreases by 0.4% while

Fig. 8. Selected results of the three congestion management scenarios with regard to cost (totalled over the modeled distribution grid and for 2015).

curtailment slightly increases by 2%, both mainly due to higher curtailment during periods with negative prices. On average the additional curtailment reduces cost by 5 €/MWh (Fig. 8). 4.4. Discussion and outlook We assume the marginal cost of electricity generation from renewables to be zero. While this seems reasonable in the case of wind and solar, biomass generation may possess fuel cost or the opportunity to shift generation, making it more attractive for curtailment. As the cost based congestion management approach in the Heatflex-min(cost) scenario can take advantage of this we expect such an extension of the model to strengthen its case. In the Heatflex-min(cost) scenario the congestion management approach decreases cost by curtailing renewable generators during times of negative prices. As we do not take into account that a high share of renewable generation is traded via the direct marketing scheme of the German Renewable Energy Act and thus may be curtailed at negative prices independently of congestion, we are likely to overestimate curtailment across all scenarios. However, the direct marketing scheme still implies an incentive to keep generating at moderate negative prices Fig. 6. Change of curtailment or resulting price denominates the difference between the results of the Base Case and the Heatflexmin(cost) scenario (simulation year 2015). The change in curtailment is calculated as Base Case – Heatflex-min(cost), thus positive values correspond to the Base Case curtailment being lower and vice versa.

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interconnecting to the transmission grid, roughly 86% of the reported yearly curtailment amount is necessary to alleviate congestion in distribution. This result is consistent with the feedback we received in our communication with the respective grid operator SH Netz AG but surprising when comparing to the allocation of curtailment to a grid level by BNetzA (2016). Derived from the liability for compensation payments, the federal grid agency attributes only 11% of curtailment to have its cause in the distribution grid. Based on our results, we conclude that it is of great importance to take into account the layout of the 110 kV distribution grid, including the transformers interconnecting to the transmission grid, when working to improve congestion management. The ongoing efforts to implement a joint planning for congestion management between transmission and distribution grid (ENTSOE-E, 2016) represent a good example for this. In contrast, the process to decide on dimension and location of future power-to-heat capacities incentivized by the German Energy Act 2017 exclusively addresses transmission grid operators and their constraints (Deutscher Bundestag, 2017b). Our results suggest that investing in additional flexibility options under the current congestion management scheme is likely to reduce curtailment but also to increase the total cost of congestion management super proportionally. The cost increase of 11% in the Heatflex–min(curt) scenario results from including the flexibility of 326 MW of electrical CHP capacity only, compared to several thousand MW of curtailment necessary at times. Moreover, the mentioned CHP plants likely run at low capacity during times of high curtailment (as the corresponding high renewable feed-in drives down power prices), further limiting the impact of those CHP units. We expect that adding 2000 MW of power-to-heat capacity, which is currently under discussion, and maintaining the existing approach to congestion management will lead to a much higher increase.4 We urge policy makers to accompany the expansion of flexibility options with the adoption of a cost-based congestion management mechanism. The major contribution of this study is the formulation and assessment of the effectiveness of a cost-based congestion management mechanism. We find that such mechanism is able to accommodate additional flexibility options while reducing the risk of substantially increasing cost. We aim it to serve as a blueprint for regulators to encourage grid operators to improve the efficiency of congestion management with explicit opportunities for different agents to generate and capture systemic value. Furthermore, the proposed cost-based congestion management scheme enables policy makers to exercise direct influence on the tradeoff between cost and curtailment: Compared to the Base Case, the Heatflex-min(curt) scenario reduces renewable curtailment at an average cost of 97 €/MWh. The Heatflex-min(cost) scenario increases curtailment, saving 5 €/MWh on average. DG feed-in tariffs lie the same order of magnitude as the cost/saving, thus policy makers might be willing to accept increasing cost for less curtailment or vice versa. To account for this, the objective function of the presented cost based congestion management regime may easily be extended by adding a penalty on curtailment reflecting the willingness to pay for additional renewable feed-in.

above an individual threshold and occurrences of negative prices are rare.3 Therefore, we do not expect this to affect our results strongly and less so our conclusions. While we presented the model's ability to reproduce historical curtailment in a realistic way, a considerable level of uncertainty remains in our input data, especially with regard to grid parameters and topology. To assess the impact of this uncertainty on our results, we conducted a sensitivity analysis comparing the influences of various input parameters. We found that our results are less influenced by the highly uncertain grid parameters than by e.g. the results of the wind power generation model, whose uncertainty is smaller. Moreover, we assume that all demand and supply within our modeled region is connected to 110 kV substations and neglect those parts of the grid with a lower voltage level (aggregation). We also omit modeling the transmission grid beyond the interconnections at various substations and reduce it to a single slack node (abstraction). We acknowledge that in reality, the power system outside of our chosen system boundaries has a significant influence on decision making within our modeled case study of the 110 kV distribution grid system of the Schleswig-Holstein Netz AG. While we consider aggregation to be of minor relevance to our results, we expect simplification of the transmission grid to notably affect our results. We presume that a large part of the difference between historical curtailment and the curtailment decisions resulting from our modeling is due to this simplification (compare Section 4.2). We expect that integrating transmission grid constraints would yield even larger differences for curtailment and cost between the two future scenarios for congestion management we presented and thus to support our conclusions. The results of this work encourage to evaluate the value of additional flexibility options under the cost-based congestion management scheme, foremost power-to-heat capacity in combination with district heating systems. Coupling the power and heat sector on smaller and more decentralized scales, such as residential and commercial buildings for space or water heating, also appears to be promising, as does the integration of additional and flexible demands by a future electric vehicle fleet. Another important extension for the future would be to take relevant transmission grid constraints into account, towards proposals for a better coordination between distribution and transmission system operation.

5. Conclusion and policy implications The main issue we address in this paper is to develop a future congestion management on distribution grid level with a method which takes advantage of flexibility options alternative or complement to DG curtailment. Motivated by recent regulatory activity, we focus our analysis on the potential of CHP and heating plants serving district heating loads. Our analysis yields three major findings which are relevant for policy-makers. First, distribution grid constraints may be more relevant than the current discussion suggests. Second, maintaining the existing approach to congestion management will not allow to take advantage of emerging flexibility options such as thermal loads without the risk to substantially increase cost. Third, the cost based congestion management approach developed in this work is able to accommodate additional flexibility options granting full control on the trade-off between cost and curtailment. In the following we elaborate on each of these findings: Comparing the model results for curtailment to the observed, historical curtailment reveals a surprising outcome: Even though we neglect congestion in the greater transmission grid, limiting our power flow analysis to the 110 kV distribution grid and the transformers

Acknowledgments Part of the work presented here is the result of a research stay (April - August 2016) of Hans Schermeyer at the MIT Energy Initiative, which was financed partly by the Karlsruhe House of Young Scientists (KHYS).

4 The revised Energy Act 2017 incentivizes to build up to 2000 MW of power-to-heat capacity in combination with district heating systems until 2020. The additional flexibility may solely be utilized for congestion management and is limited to certain regions, including the one from this study.

3

In 2015 the day ahead auction of the DE/AT/LU bidding zone (PHELIX index of the EPEX SPOT) produced negative prices in 126 h of the year. Only 5 of the occurred negative prices were below −40 €/MWh.

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