Modelling and evaluation of control schemes for enhancing load shift of electricity demand for cooling devices

Environmental Modelling & Software 24 (2009) 285–295

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Modelling and evaluation of control schemes for enhancing load shift of electricity demand for cooling devices Michael Stadler a, Wolfram Krause b, Michael Sonnenschein c, *, Ute Vogel c a

OFFIS Institute for Information Technology, Escherweg 2, D-26121 Oldenburg, Germany EWE AG, Tirpitzstr. 39, D-26122 Oldenburg, Germany c University of Oldenburg, Department of Computing Science, Uhlhornsweg 84, D-26111 Oldenburg, Germany b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 May 2008 Received in revised form 17 July 2008 Accepted 20 July 2008 Available online 2 September 2008

Load balancing in electricity grids becomes a more sophisticated problem by the increased availability of time-varying stochastic supply of electricity from conversion of renewable resources like wind or sunlight. Due to the fact that large quantities of electrical energy cannot be stored easily, demand side management by shifting electrical loads is one attempt to cope with this problem. In this paper we discuss and compare two types of control signals to use the thermal storage of electrical household appliances as balancing power. As the system of our research consists of a high number of controllable refrigerators with independent parameters and behaviour, we investigate the synergetic behaviour by a simulation model. For this objective we analyze a simulation model of controllable refrigerators with respect to their ability to shift their energy demand depending on parameterized external signals. We show that both types of control signals can be used for short term reserves with delivery within 15 min of time, but they differ in possible shapes of the resulting load curves and in the reaction time of the controlled system. In addition to the simulation model we develop a model of the synergetic behaviour of an ensemble of refrigerators’ reaction on control signals. This mathematical model predicts the electricity demand of ensembles of controlled appliances. As it reduces the simulation model’s complexity it could be used in a sophisticated control strategy, e.g. in a model predictive control approach. The general attempt to integrate the load shift potential of cooling devices into the control of an electricity grid can probably be transferred to other electrical appliances with thermal storage capacities.  2008 Elsevier Ltd. All rights reserved.

Keywords: Demand side management Load shift Load peaks Renewable energies Thermal energy Cooling devices’ control Approximation of stochastic models

1. Introduction to the problem to be solved Large scale usage of renewable energies for electricity production results in time-varying stochastic availability of electricity. The growing proportion of electricity from fluctuating energy sources like wind and solar radiation results in a number of problems for current systems of energy supply. Two of those are as follows. (1) Capacity problems for the power grid due to big amounts of electricity from renewable sources which are not consumed locally but have to be transmitted from their originating location. This problem could be addressed by building new power lines which is both, costly and often hindered by political circumstances. Another technical approach to solve this problem is the incorporation of purpose-built power storage * Corresponding author. Tel.: þ49 441 798 2750; fax: þ49 441 798 2756. E-mail addresses: [email protected] (M. Stadler), wolfram.krause@ ewe.de (W. Krause), [email protected] (M. Sonnenschein), [email protected] (U. Vogel). 1364-8152/$ – see front matter  2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.envsoft.2008.07.003

systems into the grid. However, these systems are often inefficient and expensive, both in acquisition and maintenance terms. (2) The stable and secure operation of power grids requires a balance of electricity generation and consumption at all times (ETSO, 2003). Stochastic fluctuations caused, for example by wind power production, need to be compensated either by purpose-built storage systems whose drawbacks have been noted above or by the remaining generation units. The latter solution requires power plants with short start up and adaptation times (e.g. gas turbines), which are expensive in terms of acquisition and operation. As long as these problems are not solved, renewable energy sources will be forced to be switched off or reduced in their efficiency during peak availability (problem 1), and expensive as well as inefficient electricity production or storage is used to bridge small time spans of lacking energy supply (problem 2). In order to avoid such situations, further methods for coping with fluctuating energy sources should be envisioned.

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A well-known additional method to balance production and consumption of electrical energy is demand side management (DSM) (Gellings and Chamberlin, 1988). The general term DSM means all ‘‘utility activities that influence use on the customer’s side of the meter’’. As a major focus in DSM is on energy conservation or energy efficiency (Clinch et al., 2001), by relocating loads from periods of low availability of electricity to periods of peak availability (load shifting) both mentioned problems can be addressed (Brauner et al., 2006; Klobasa and Ragwitz, 2006). Whenever consumers use more power at periods of peak availability and reduce their consumption at periods of low availability, that power will not have to be transmitted or stored by means of the utility. Particularly if customers shift their load to periods of high availability of environmentally friendly produced electricity (e.g. by wind energy converters), they may contribute to reduce the CO2 emissions of conventional power plants that had to run in the periods of lower availability of environmentally friendly produced electricity (Friends of the Earth, 2006), and they contribute to avoid lossy and expensive storage of the electricity produced at supply peaks. This is particularly interesting in a scenario, where 20% of the total electricity supply is generated by wind energy converters as planned for the year 2020 in Germany. Klobasa and Ragwitz (2006) calculate additional CO2 emissions of 350,000 t/a for balancing energy in this scenario. These emissions should be reduced by an appropriate demand side management. There are several types of appliances suitable to be used for load shifting. Studies on load shifting by adaptive control of the air conditioning of buildings are known for a long time (Constantopoulos et al., 1991; Braun, 2003). Also refrigerated warehouses have been studied in its ability to support load shifting (Altwies, 1998). In principle this approach uses the thermal mass of buildings as energy storage. In 2004 German households consumed about 140 TWh of electrical energy. This is about 27% of the entire consumption of electrical energy in Germany (VDEW, 2006). In contrast to customers from industry that often have special contracts with their utility, residential customers currently have very simple contracts for their electricity supply: besides a fixed base price for metering, etc., residential customers pay a constant price for each kWh of electrical energy they consume. Control of household appliances is affected only by the customers. Billing of electricity consumption is done usually one-time per year. Consequently, currently there are no potentials for load shifting of residential consumers. This paper discusses a method to overcome this problem for a specific type of household appliances. A preliminary, abridged version of this paper has been published in Stadler et al. (2007). 2. Control of household appliances Within a project financed by a regional electricity utility in northern Germany, EWE AG, we analyze potential load-shifting effects of residential consumers that can be obtained via dynamic pricing of electricity and other control mechanisms. On one hand, there is a potential for shifting electrical load by encouraging people through incentives, i.e. financial benefits for shifting loads. An introduction to dynamic pricing programs, where electricity prices vary depending on current production costs can be found in Borenstein et al. (2002). In households this load shifting potential primarily involves devices such as washing machines, dish washers, or dryers. Extensive field studies on the load shifting potential of such household appliances triggered by real-time pricing have been carried out, e.g. in Morovic et al. (2007). Detailed scenarios of load shifting caused by dynamic prices can be modelled and simulated with our agent based framework (Sonnenschein et al., 2006). This tool could in principle be used to model

the scenarios of this paper, but for large numbers of devices (>2000) a more efficient modelling and simulation attempt turned out to be necessary. Modelling and simulation tools for the integrated consideration of supply by renewable energy converters (PV, wind turbines) and managed demand also exist (Born, 2001), but again they are too complex to analyze large, but quite uniform ensembles of devices. In this paper we will focus specifically on the load shifting potential originating from devices that serve the purpose of keeping temperatures within given bounds. These are among others, refrigerators, water heaters, night storage heaters, air conditioners, and heat pumps. Devices of this type have in common, that their load shifting potential is enabled by a thermal storage system. With other words they allow to store electrical energy after conversion to thermal energy. In principle this is a conversion of a higher order type of energy to a lower order type, but for cooling devices this is the only common method. The situation is different for night storage heaters. Buildings can more efficiently heated by directly using primary energy sources like gas, or by using heat pumps. Consequently, night storage heaters although they also could be used for load shifting, are currently phased-out in Germany by law. Hence, the following considerations focus mainly on cooling devices. In order to exploit their load shifting potential, no human interaction is necessary, given that the devices are equipped with suitable controllers. A detailed analysis of the principle potential of such devices for load shifting can be found in Stadler (2005). We will focus in this paper on different types of control signals for such devices and their potential effects. As an example of such a household device we will address a refrigerator. Refrigerators and freezers of residential consumers are responsible for a demand of about 16 TWh per year in Germany (Klobasa and Obersteiner, 2006). This exceeds the accumulated demand of washing, dish washing, and drying, and results in a load shift potential of up to 800 MW only for refrigerators, which is equivalent to the supply of a large power plant. In principal three different types of load shifting control for refrigerators are possible as follows. 1. The refrigerator senses the grid frequency that has the nominal value of 50 Hz in Europe. When demand exceeds supply, the frequency falls, when supply is over demand, the frequency rises. Depending on a measured difference from the nominal value of the frequency, the refrigerator can decide to precool by starting the compressor or to delay the activation of the compressor for a short-time. This control type is suggested, i.e. by Dynamic Demand (2005). Its advantage is a low price of the additional controller, because no communication between the utility and the device is necessary. On the other hand there is no way to integrate the devices into an intended schedule – the devices act completely autonomously. 2. Given a communication infrastructure between utilities and households, a refrigerator can be scheduled by a household controller integrated, i.e. into a set-top box, an Internet gateway, or a smart meter. The household controller computes a schedule for appropriate device’s activities in its specific household depending on dynamic price information given by the utility. This method allows to integrate the energy management of all household devices into one system and to retain the device’s control in the household, but its drawbacks are relatively complex control strategies and the fact that effects of sent tariff information to affect the load are not completely sure for the utility. 3. Given the mentioned communication infrastructure, utilities can send control signals to the refrigerators in order to raise or reduce the demand. This allows the utility a more direct control

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of the demand as the methods above, and to keep the controllers in the devices quite simple. In this paper, we will examine this alternative. To control refrigerators as distinguishable devices for its load shifting potential seems to be neither meaningful nor feasible due to the large number of devices and its low individual demand. Consequently the devices should be grouped to one or more ensembles in a control strategy. To become more concrete, we study in this paper the effect of two different schemes for sending control signals to exploiting the load shifting potential of an ensemble of refrigerators. An overall problem of using an ensemble of devices is the lack of a model of their aggregated behaviour. As the behaviour of single devices storing thermal energy is well-known, we use a simulation model that simulates each device and its reaction to control signals individually and aggregates the individual behaviours as systems reaction. Mathematically, each device represents an independent variable of the model, and hence increases the problem’s dimension. So, in a second step, we investigate how the system’s complexity can be reduced by aggregating subsets of devices and modelling their behaviour separately. This alternative model allows an evaluation of the simulation model and gives further insights to general aspects.

3. Modelling a single refrigerator Our model of a single refrigerator in an ensemble of devices is based on the model proposed in Constantopoulos et al. (1991) for air conditions or heating devices. The cooling compartment temperature T for an equidistant series of time steps is given by

 q Tiþ1 ¼ 3Ti þ ð1  3Þ T o  h i A

sA

with 3 ¼ emc

(1)

Ti is the cooling compartment inner temperature at the time ti, 3 is the system inertia depending upon the insulation A, the thermal mass mc (thermal storage capacity), and the time span s between the two time points ti and tiþ1. Parameter qi denotes the electrical power required during the last time interval depending on whether the cooling device was turned on or off, and h is the efficiency of the cooling device. To describes the ambient temperature, which is assumed to be constant. In general, the dynamics (1) leads to the behaviour illustrated in Fig. 1 for a cooling device controlled by a thermostat. The temperature increases until it reaches the set maximum temperature. Then the cooling device is activated and the energy demand is positive. In the ‘‘normal progression’’, the cooling device stays activated and the inner temperature decreases until the set lower bound is reached, and remains deactivated until the temperature

load

normal progression temperature modified progression τcooling

τwarming

control signal Fig. 1. Principles involved in load shifting by sending a control signal (solid line: normal progression of temperature and load, dashed line: modified progression after receiving a control signal for precooling).

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exceeds the upper temperature again. In the ‘‘modified progression’’, during this warming phase, a control signal to raise the energy demand is received, which leads to an immediate activation of the cooling device. In the following, we will denote the time span for cooling a given device under fixed parameters from the maximum to the minimum temperature as scooling, and the time span it needs to warm up again as swarming. Because of the high quantity and the unknown characteristics of the load shifting devices in a residential area, the available power shifting potential is not exactly predictable. Therefore, a probabilistic approach has to be used for modelling it. 4. Basic simulation settings We carried out discrete simulations assuming 5000 fridges all having the same appliance characteristics (same size, same thermal conductivity of 3.21, same rating of 70 W, same coefficient of performance of h ¼ 3.0), but with different contents resulting in thermal masses equally distributed between 7.9 kWh/ C and 32 kWh/ C. The values have been calculated by using thermal capacities of food (ThermCap, 2007) and construction materials. Using this value and assuming an allowed temperature range between 5  C and 8  C the model exhibited approximately the same behaviour as fridges measured in five different households for validating the model of a single device. The assumption of equally distributed thermal masses and the range of distribution is a guess due to lack of more precise knowledge. To increase the load shifting potential, it was assumed throughout this paper that all fridges have the same allowed temperature range of 3–8  C resulting in average time spans scooling ¼ 30 min and swarming ¼ 103 min depending on their thermal masses and their insulation (Fig. 1). In reality, the minimal temperature is biased towards 5  C. The fridges’ temperatures at simulation begin were assumed to be equally distributed. Derived from the mean load after a simulated day, 22% of refrigeration aggregates were assumed to be active at simulation begin. The simulation’s time resolution was set to 1 min for reasons of efficiency and each simulation covered 30 h. The latter setting is the same as in Dynamic Demand (2005) and results from observations showing effects of single control interventions only for very few hours. The scenarios justifying this setting are explained in Section 5. 5. Explored scenarios For the investigations presented here, we simulated the effect of two basic types of control signals on an ensemble of refrigerators as follows. (1) Direct storage control by signals directing participating fridges to augment or reduce the amount of energy in their thermal storage. For this purpose, there are two control signals load thermal storage and unload thermal storage. By integrating a random number generator into the fridges’ control logic, the time of a control signal taking effect can be spread over an interval. This intends to smooth edges in influenced load curves. (2) Timed load reduction activated by issuing load reduction requests to participating fridges at a notification time (tnotify), asking them to reduce electrical load at a given point in time called activation time (tactive) for a given time span (sreduce). In order to respond to these more complex controls, fridges in this scenario need to reprogram their cooling device’s activity periods. As shown in the following, these approaches differ in the degree of exploitation of load shifting potentials. Furthermore, they

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require different levels of intelligence and processing capacity at the device level and at the signalling instance’s level. 6. Fridge controller logic and complexity Any fridge appliance controller has to keep its cooling compartment temperature between a minimum temperature Tmin and a maximum temperature Tmax. This basic temperature constraint has to be satisfied at all times regardless of external control signals. A simple controller as needed for direct storage control is based on the following logic: it receives a load thermal storage signal or an unload thermal storage signal with an associated time spread, which describes in which time span the refrigerator has to be activated or deactivated. The controller first has to randomly choose an activation time in the spread interval. At that point in time, the cooling device is either switched off (unload thermal storage) or on (load thermal storage), if this will not lead to a violation of the basic temperature constraint based on the controller’s knowledge of current compartment temperature and current system inertia. In order to perform this task and regularly poll the temperature sensors the controller must be equipped with a real-time clock. Furthermore it must have a communication interface. Computing whether to activate or deactivate the cooling device at a given time point while taking into account the above control signals involves only a few arithmetical operations and a table lookup for retrieving the fridge’s system inertia. Storage requirements are low. Altogether – except for the communication interface – a device controller for implementing such a control strategy can be very simple. Computational and storage requirements for implementing a fridge controller suitable for reacting to timed load reduction signals are noticeable higher. Upon receiving a load reduction request, a cooling program is calculated. Such a program defines when to switch on and off the cooling device and has to be based on the fridge state at activation time. Based on the assumption of constant outer temperature, system inertia, and insulation, the preload activation time can be sequentially calculated from the current temperature and cooling device state by a modification of Eq. (1) in advance. The sequence of cooling device states and temperatures traversed while calculating the fridge state at activation time (reference state) is stored as a base program. If, based on the reference state, the requested behaviour cannot be sustained during the control interval the controller has to modify the base program. To this end, the base program’s steps can be performed in reverse order. It first calculates the maximum allowed temperature at activation time, which allows switching off the cooling device during the control interval. Knowing this temperature, the base program can be modified, to ensure the required temperature at activation time. In the worst case, this computation affords to calculate 2(scooling þ sreduce)/timebase steps, where timebase designates the length of the controller’s single control step. So, the computational complexity increases linearly in (scooling þ swarming)/timebase. In addition, a controller suited for scenario 2 must provide storage for the cooling device program and for temperature time series. For implementing an embedded controller for real fridges a linear approximation of a fridge’s temperature development might be considered. We discuss the consequences of a simplified model based on a linear function in Section 9.

cooling device’s power consumption, which for the settings relevant to this study can be either on (70 W) or off (0). The latter time series corresponds to the program referred to in Section 6. At initialisation time the series’ first values are, respectively, set to a randomly chosen, equally distributed value from within the allowed temperature range and a randomly chosen power consumption reflecting the mean percentage of refrigeration aggregates active at any time. The subsequent time series values are then calculated using Eq. (1) with the thermal mass randomly chosen for the fridge at initialisation time, switching power consumption whenever the current consumption would result in violation of cooling compartment temperature constraints. Once initialised, the time series are modified by function calls corresponding to signals sent to a fridge controller. Arguments to those functions may include the notification time (simulation step), a participation ratio, a notification interval (number of simulation steps), a control interval (number of simulation steps), and a mode of control (direct storage control or timed load reduction) and an interval for defining a spread for activating control. Modification of time series of single devices follows the control algorithms sketched in Section 6 for the fridges controllers. For the purpose of this study the same function calls are applied to every fridge object defined for a simulation scenario. Simulation results are obtained by applying aggregation operations to the fridge ensemble’s time series values at common simulation times. 8. Simulation results Filling up thermal storages increases electrical load; emptying storages reduces electrical load. Fig. 2 gives an overview of the load characteristic resulting from the thermal storage manipulation. At a given point in time tnotify (not shown in the figure), a control signal is issued which instructs fridges to fill up their thermal storage either with the purpose of increasing electrical load or with the purpose of maximising load shifting potential for a later point in time. To achieve this, the refrigerators start to fill their thermal storage at latest at time tpreload. So a load thermal storage signal results in a load peak during period spreload. The preload period is followed by a period of load reduction denoted by sreduce. During this warming phase, cold storages are emptied. If the load is less than the average load in the undisturbed system, we denote this as load reduction. The length of the load reduction interval, the minimum load reduction, and the duration of load reduction depend on the control signals and their parameters. Note that a period of load reduction can occur even some time after a load thermal storage signal has been given. This can result in a periodic behaviour of the demand and its synchronisation due to the control signal. In the scenarios described here, the shifting of electrical load is achieved by synchronising the fridges’ thermal storages to reach either a maximum temperature or a minimum temperature during a given period of time or at a well-defined point in time. Thus, after a maximum time of load reduction, cooling devices have to be switched on. Without further control, the previously achieved synchronisation leads to an oscillating electrical load. sfirstosc denotes the duration of the first peak in electrical load following the load reduction. Fig. 2 shows the qualitative reaction to a direct load thermal storage signal. The notation, which is used throughout this paper, is summarized in Table 1.

7. Model implementation The simulation model has been implemented in Java. Evolution of a single fridge’s state over time is represented by two time series implemented as arrays. One of those time series holds the fridge’s cooling compartment temperature and the other series holds the

8.1. Observations from simulated scenarios using direct storage control First, we conducted 100 simulation runs with the load thermal storage signal and spreads of 0–60 min, each. The analysis of the

M. Stadler et al. / Environmental Modelling & Software 24 (2009) 285–295

289

load ppeak τreduce

τfirstosc

pfirstosc pavg τpreload preduced tpreload tloadpeak

tminreduce

tendreduce

toscpeak

tend

Fig. 2. Electrical load evolution of 5000 devices after either issuing the load thermal storage signal at tpreload or an unload thermal storage signal at tnotify (not in the diagram, located some time before tpreload).

simulations results shows load reductions of at least 50% for a time span of approximately 1 h. However, it is not possible to achieve a 100% load reduction using this signalling type. The earliest time of availability of load reduction depends upon the spread. Analogous experiments using the unload thermal storage signal allowed for an immediate load reduction to approximate 10% of pavg lasting for 15 min without any preload peak. 8.1.1. The spread parameter’s influence on load shifting We investigated the influence of the spread interval in with respect to load reduction and load increase that can be achieved by issuing a load thermal storage signal. Augmenting the spread interval by 10 min delays the beginning of sreduce by approximately 5 min and increases preduced by about 0.005pavg. The duration of sreduce is not influenced by the spread. However, spread influences the characteristic of load reduction that can be achieved as indicated in Table 2. Increasing the spread reduces the oscillation peak, slightly increases the start frequency of the oscillation, and reduces the peak power consumption ppeak. 8.2. Results of simulating timed load reduction In the timed load reduction scenarios, a load reduction request is sent at time tnotify to reduce the load in the control interval [tactive, tactive þ sreduce] as far as possible. In the simulated settings, the largest possible power reduction, preduced z 0, can be sustained for a period of 39 min given Table 1 Terms to describe load shifting characteristics tnotify tpreload

spreload tactive tloadpeak

sreduce tminreduce

scooling swarming sfirstosc toscpeak pfirstosc ppeak pavg preduced

Time of sending/receiving the signal Start time of the preload phase Duration of the preload phase Time of requested reaction Time of maximum power consumption during preloading Time span of reduced power consumption (compared to non-signal scenario) Time of lowest power consumption during load reduction Maximal duration for reloading the thermal storage of a fridge Maximal duration for unloading the thermal storage of a fridge First time span of increased power consumption during oscillation Time of first oscillation peak First oscillation peak load Maximum power consumption during preloading Average load during simulation run without influence of control signal Lowest power consumption during load reduction

a notification time of 10 min. By extending the lead time of 20 min, preduced z 0 can be sustained for the duration of 47 min. The maximum duration of perceivable load reduction is 123 min. This value can be obtained using a minimum notification time of 40 min and a requested reduction interval of at least 135 min. Table 3 gives more detailed information about achievable load reductions using the timed load reduction control signal with a control interval of 135 min. An earlier notification time causes an earlier beginning of the preload phase [tactive  spreload, tactive] due to a longer duration spreload. This only slightly influences the moment tloadpeak, when the load reaches its local maximum, and does not significantly influence the height ppeak of the maximum. However, lead times over 50 min cause that the peak at tloadpeak is almost immediately followed by the phase of reduced load. It also causes a significantly lower pfirstosc. Generally, longer notification times tend to stabilize the amplitude of the oscillation at toscpeak. A timed load reduction signal is annotated with the start time of requested reaction tactive and the duration of the requested reduction. Increasing the control interval, i.e. the duration sreduce of the requested reduction, leads to an earlier start of the preload phase. It also heightens ppeak (up to an activation of all fridges) and shifts it closer to activation time. Furthermore this increases pfirstosc, reduces the oscillation’s start frequency and also sfirstosc, which in turn leads to a longer overall oscillation period. Generally, longer control intervals lead to a later occurrence of toscpeak. Those late occurring oscillation peaks require shorter notification times for stabilisation than oscillation peaks resulting from shorter requested reduction intervals.

Table 2 Duration of load reduction levels for different spread interval with direct storage control Spread (min)

0 10 20 30 40 50 60

Load reduction levels in percent of the average load 100%

90%

75%

50%

25%

10%

0 0 0 0 0 0 0

11 10 3 0 0 0 0

23 23 23 21 16 3 0

61 60 59 57 55 53 48

97 97 96 94 93 90 87

111 112 112 112 110 109 107

For example for a spread interval of 20 min a load reduction of 50% of the average load can be achieved for 59 min. A longer spread period allows devices to delay their reaction to the signal, and so diminish the achievable reduction at a point in time less than the spread interval.

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Table 3 Simulation results for load reductions using timed load reduction Lead time (min)

10 20 30 40 50

Load reduction levels compared to average 100%

90%

75%

50%

25%

10%

>0

39 47 47 47 47

44 52 52 52 52

47 57 57 57 57

51 75 76 76 76

55 85 112 112 112

58 90 118 121 121

60 94 120 128 128

For example with a lead time of 30 min a load reduction of 50% compared to the average can be observed for 76 min.

Both peaks, ppreload and preduced, linearly depend on the participation ratio. Furthermore, the probability of observable oscillation increases with higher participation ratios. For participation ratios 0.4 the oscillation probability stays close to 1 and tfirstosc occurs slightly later for smaller participation ratios. However, in case of a specific reduction interval, participation ratios exhibit no influence on oscillation peak timing. 8.3. Conclusions from the simulation results Let us now state some conclusions from the observations illustrated above:  Both timed load reduction and direct storage control can be used as short term reserves with guaranteed 100%-delivery within 15 min time. The unload thermal storage signal of direct storage control can even be used for generating balancing energy with immediate availability.  Timed load reduction (timed load augmentation) has the drawback of needing more powerful and expensive controllers. However, it enables a more precise control of load shifting due to the controller’s possibility of computing a future fridge state.  Timed load reduction can be used in order to maximise load reduction both in level and duration. The participation ratio parameter allows an easy way to scaling the reduction level.  When reducing load with help of direct storage control signals, it seems sensible to use a spread of 30 min. This increases the time to maximal load reduction preduced by about 15 min compared to a scenario without spread. However, at the same time ppeak can be reduced to 1.62pavg compared to 3.48pavg in a scenario without spread.

TðtÞ ¼ Ti þ at; where a ¼ ac ¼ ðTmin  Tmax Þ=scooling < 0; a ¼ aw ¼ ðTmax  Tmin Þ=swarming > 0;

power rating of the compressor and coefficient of performance) are necessary. Refrigerators able to be controlled externally are in fact available (Miele, 2008) but uncommon. The model allows a general assessment of the devices’ ability on load shifting and therefore a decision for an investment in a potential field test. It gives insights in the synergetic behaviour of a large set of independent and very heterogeneous devices and allows the determination of statistical characteristics. Mathematically, each device’s state represents an independent variable of the system. So, the simulation model represents a complex, high dimensional model. In Section 9, we will construct a more formal, but simplified model of subsets of devices with homogeneous parameters. By combining diverse of these aggregated models, we obtain a model with heterogeneous parameters, which we used to validate the general results of the simulation model. Besides due to its less complexity, such a formal model is also better suited for a model predictive control approaches (Camacho and Bordons, 2007); this aspect is discussed a bit more in the outlook of the paper. Currently our models are not part of such a control strategy. 9. Aggregated model As an alternative to the iterative computation of the fridges’ response in the simulation model discussed above, the dynamics of each device and in particular the time stamps of state changes can be computed directly. We start with a simplified model of one fridge, which we will expand to the system dynamics’ description of an ensemble of fridges with same parameters but different, uniformly distributed states. We used this alternative model for evaluating the results of the simulation model as well as for deducing some general characteristics of an ensemble of devices. Besides, the approximation by a linear function has the following advantages: , The complexity of the device controller is reduced, as only simple arithmetic operations are needed for determining the next switching time. , Assuming a uniform distribution of the initial device states, assumptions about the distribution of the states at a given time or after a control signal has been received are simplified. The approximation of the model of the temperature development of a fridge in Eq. (1) by a linear function is shown in Eq. (2). Given the allowed temperature of a fridge in the interval [Tmin, Tmax], we approximate Eq. (1) by the linear function based on the device parameter swarming or scooling:

if the fridge is in state ‘‘cooling00 and if the fridge is in state ‘‘warming00

8.4. Evaluating the simulation model First, it is essential to discuss the validity and the remaining uncertainty of the simulation results (Jakeman et al., 2006). The results given above are deduced from a model of an ensemble of devices that is based on a validated model of single devices, but varies the thermal mass of the refrigerators artificially by a uniform distribution due to a lack of data from a major field study. For modelling a real ensemble of devices, measurements of the distribution of thermal mass as well as measurements on the distribution of the other model parameters (thermal conductivity,

(2)

Whenever the fridge’s inner temperature reaches Tmin or Tmax, it switches its state to state ‘‘warming’’ or state ‘‘cooling’’, respectively, and it stays in this state for a time span of length swarming or scooling, respectively. The deviation of this approximation in the given temperature range (Tmin ¼ 3  C and Tmax ¼ 8  C) is acceptable (standard error < 0.00023). So, the following sections are based on such a linear function. In a real device controller, the time spans swarming and scooling could be estimated from the history, e.g. by measured moving averages of former time spans. In our model, we used the transformation of Eq. (1) for computing the time span, which a given

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device needs to cool down from temperature Ti to a (lower) temperature Ta. It can be computed by s(Ti, Ta):

! Ta  T o þ hAq mc sðTi ; Ta Þ ¼ ln ; Ti  T o þ hAq A

Ti  Ta

(3)

s(Tmax, Tmin) calculates the parameter scooling, i.e. the time span for cooling down from the maximum to the minimum temperature. The longest possible deactivation time, i.e. swarming can be derived by

swarming ¼ ln

  Tmax  T o mc Tmin  T o A

(4)

9.1. Devices with identical parameter values In the following paragraph, we consider fridges with identical constant parameter values, i.e. same insulation, same environmental temperature, same power rating, same efficiency, and in particular, same thermal mass. The switching states (on and off) and the temperature are assumed to be uniformly distributed in the ensemble of appliances. We will focus to the question of the duration of total load reduction, i.e. sreduce denotes the maximal time span when all fridges are switched off, i.e. the overall energy demand is reduced to 0. 9.1.1. The preload phase The preload phase occurs with timed load reduction and allows the fridges to cool down and to bridge over a certain time interval without further activation. As a direct storage control signal demands for an immediate reaction, a preload phase has only to be considered for timed control signals. Due to the uniform distribution of the fridges’ states and temperatures and due to the linear evolution of the temperature, the fraction of active fridges, which are currently in state ‘‘cooling’’, can be estimated by the duration of the warming and cooling phases, i.e. it is given by scooling/(scooling þ swarming). If we assume the load to be normalized, scooling/(scooling þ scooling) also describes the average load pavg. If a control signal arrives at time tnotify  tactive  scooling, no fridge needs to react until time tactive  scooling, because within a lead time of length scooling even fridges with temperature Tmax can cool down to Tmin. Even if a control signal is received at time tnotify with scooling  tactive  tnotify ¼ spreload > 0, not all fridges have to be activated immediately. Fridges with a low temperature Tstart at time tnotify can compute the maximal delay before they have to be activated by



s Tstart ; spreload



Tmin þ ac spreload  Tstart ¼ aw þ ac

(5)

For spreload ¼ scooling, each fridge with temperature Tnotify at notification time has to activate its cooling device after a time span of s(Tnotify, scooling) in order to grant T(tactive) ¼ Tmin. Hence, the longest 1 1 delay time is acscooling/(aw þ ac) ¼ (s1 cooling þ swarming) . In the time span [tactive  scooling, tactive  scooling þ s(Tstart, scooling)], it can be deactivated. With this behaviour, all fridges can grant T(tactive) ¼ Tmin. So, a notification time span of scooling leads to a complete

( syncDmdðtÞ ¼

0;

synchronisation of all devices. All these fridges can reduce their energy demand to 0 for the time span swarming. If a control signal arrives at tnotify later than tactive  scooling, i.e. spreload < scooling, this will cause a partial synchronisation of the fridges: all fridges with s(Tnotify, spreload) < 0 can not grant T(tactive) ¼ Tmin and have to be activated immediately. Hence, their reduction potential depends on their temperature Tnotify. Using the specific preload-time spans for all devices causes a maximum load ppeak at time tactive, immediately followed by a zero consumption preduced ¼ 0 afterwards, as at time tactive each device is deactivated and starts its warming phase. The model can easily be expanded to timed reduction signals with control intervals: estimating the temperature Tmax  sreduceaw at time tactive, the preload delay time for a requested reduction time span sreduce < swarming can be calculated by a formula similar to Eq. (5):

Tmax  aw sreduced þ ac spreload  Tstart aw þ ac More refined strategies which damp the following oscillation of load are possible but have yet to be researched. 9.1.2. The reduction phase In the reduction phase, all devices switch their cooling device off as long as possible, i.e. the energy demand is set to 0. In the following, we focus to timed control signals with a lead time s as derived in Section 8.1.1. In case of direct control signals, the following considerations hold with a lead time of s ¼ 0. For a lead time s ¼ scooling, all fridges can guarantee temperature Tmin at time tactive. Consequently for the time span of reduced load sreduce the equation sreduce ¼ swarming holds in this case. For a shorter notification time span s < scooling only the fridges which can cool down to Tmin in this time span, i.e. all fridges with a temperature in the interval [Tmin, Tmin þ acs], can guarantee the maximum reduction time span swarming. This corresponds to a percentage of s/scooling of all devices. From this follows, that 1  s/ scooling percent of all devices have a temperature in the interval [Tmin, Tmax  acs] at time tactive and can disconnect their cooling device only for a time span in the interval [sswarming/scooling, swarming], i.e. sreduce ¼ sswarming/scooling. The preload phase causes a loss in the diversity of the states: since time tactive, all devices with the same temperature switch their cooling device simultaneously. A portion s/scooling of all devices is synchronized and will react like one device in the future, as we did not integrate individual stochastic influences to the devices. These devices contribute subsequently in oscillations of the system. 9.1.3. The reactivation phase In order to simplify the following formulas, we assume, that the activation time tactive is set to time 0 and that the signal was received with a lead time s  scooling. The reactivation times of devices depend on their parameters and their temperature at activation time. The previous section has shown that there are different cases to regard. , A fraction of s/scooling percent of all devices is synchronized: they have the minimum temperature at time tactive and so their dynamics is given by

h i t˛ kscycle ; kscycle þ scooling

s ; 1  scooling

291

else with k˛N; scycle ¼ swarming þ scooling

(6)

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, Due to the linear approximation, a uniform distribution of the inner temperature at time tactive can be assumed for the rest of the devices. The duration of total load reduction sreduce depends on the maximal temperature at tactive which is given by Tmax  acs. Hence, sreduce can be estimated by sreduce ¼ sac/ aw ¼ sswarming/scooling. Afterwards, in the time span of duration d ¼ swarming  sreduce all devices will gradually be switched on. The dynamics of this group of unsynchronized devices also repeats in a cycle of length scycle. It depends on the relation between scooling and d ¼ swarming  sreduce: B If d > scooling, the devices which have been reactivated at time sac/aw have already cooled down at time sac/aw þ scooling, while others have still to be activated. So, the first cycle of the periodic dynamics is given by unsynchDmdd>(t) in Eq. (7). Fig. 3 illustrates the case d > scooling.

8 0;  >  > > > > < s= scooling d ðt  sac =aw Þ;   unsyncDmdd> ðtÞ ¼ scooling  s=d > > >   >  > : s= ds t  swarming ; cooling

B

[swarming, scooling þ sac/aw] and the duration of this peak as well as the duration of total load reduction increase linear with s. 9.2. Devices with different thermal capacities For validating the first simulation model, we compared its behaviour to the behaviour of a set of aggregated models. The parameters swarming and scooling of the subsets of fridges have been calculated using the same parameters as in the simulation settings; the thermal mass has been chosen from 20 values, which are evenly spread over the same interval as in the simulation settings. The result of the computation of load profiles of fridges with diverse thermal capacities is shown in Fig. 5. The timed load reduction signal arrives with a lead time s of 42 min and causes a preload peak. At time 0 a total load reduction starts. In the given

t˛½0; i h sac =aw  t˛ sac =aw ; sac =aw þ scooling i h t˛ sac =aw þ scooling ; swarming i h t˛ swarming ; scycle

For d  scooling, all devices are activated before the first of them has cooled down. The first cycle of the resulting dynamics is described in Eq. (8). Fig. 4 illustrated this case.

unsyncDmd>d ðtÞ ¼

8 > 0; > > > t  sac =aw > > > ; > s < warming

> 1  s=scooling ; > > > > > t  sac =aw  scooling > > ; : 1  s=scooling 

swarming

(7)

scenario the minimal values for scooling and swarming are 14.7 min and 52 min, the maximal values are 58.7 min and 207.9 min, respectively. The average load pavg in this scenario is about 22% of

t˛½0; sac =aw   t˛ sac =aw ; swarming h i t˛ swarming ; sac =aw þ scooling h i t˛ sac =aw þ scooling ; scycle

With a lead time s  (swarming  scooling)scooling/swarming, the relation scooling  d holds and the total load reduction duration is given by sreduce ¼ sac/aw  swarming  scooling. The energy demand after load reduction reaches the maximum load in the interval

(8)

the maximum load. About 60% of the fridges have a scooling parameter less than 42 min and hence have an inner temperature of Tmin at tactive. Further 33% of all fridges can also guarantee a total load reduction of at least 52 min. As the minimal swarming value is

1 Unsynchronized Synchronized Preload

0.9 0.8 0.7

Load

0.6 0.5 0.4 0.3 0.2 0.1 493.0

471.0

449.0

427.0

405.0

383.0

361.0

339.0

317.0

295.0

273.0

251.0

229.0

207.0

185.0

163.0

141.0

97.0

119.0

75.0

53.0

9.0

31.0

-13.0

-35.0

0

Time Fig. 3. Dynamic behaviour of a set of devices with scooling < d. The devices, which can cool down to the minimum temperature in the preload phase, can reduce their energy demand to 0 for a time span of about 175 min, activate for about for about 50 min and switch synchronized in the following. The other devices start to activate their cooling devices at time 50.

M. Stadler et al. / Environmental Modelling & Software 24 (2009) 285–295

293

1 Unsynchronized Synchronized Preload

0.9 0.8 0.7

Load

0.6 0.5 0.4 0.3 0.2 0.1 478.0

454.0

430.0

406.0

382.0

358.0

334.0

310.0

286.0

262.0

238.0

214.0

190.0

166.0

142.0

94.0

118.0

70.0

46.0

-2.0

22.0

-26.0

-50.0

0

Time Fig. 4. Dynamic behaviour of a set of devices with scooling  d. In comparison to Fig. 3, the longer preload phase allows nearly all devices to cool down to Tmin at time 0 and hence to deactivate their cooling device for about swarming ¼ 175 min. This leads to a short-time span of peak energy demand, where all devices are activated.

52 min, the synchronized devices in Fig. 5 start to activate their cooling devices at time 52. The calculated load curve shows a good correspondence to the simulation results – the deviation in the preload phase is due to the differing preload strategy (overcooling effect in the simulation). This mathematical model already allows first insights in the general behaviour of a system consisting of devices with diverse parameters: , If only the thermal masses mc of the fridges are varied, the parameters scooling and swarming increase linearly with a constant ratio r ¼ swarming/scooling. , The duration of total load reduction using a lead time s can conservatively be estimated for all devices with s  scooling by

sreduce ¼ sswarming =scooling ¼ sr As the ratio r ¼ swarming/scooling is constant in the ensemble, the duration of total load reduction, sreduce does only depend on s and r.

For all devices with s > scooling, the duration of load reduction equals the parameter swarming. , The distribution of the parameters scooling inside the ensemble influences the height of the peaks: the parameters swarming and scooling depend linearly on the thermal mass of the device, which we assume to be uniformly distributed. Hence, at the time given by the minimum of sr and the given swarming values, the fridges start to reactivate their devices. So, for min(swarming) < sr, the load increases linearly beginning at time min(swarming). In the interval [min(swarming), sr], it is bounded by the maximum demand of all devices with scooling  s. This is a very conservative approximation, as not every device which is activated in the interval [min(swarming), sr] stays active till sr. The case min(swarming)  sr is more complex: due to a short lead time s there can be devices in any group that are not able to guarantee an inner temperature Tmin at time tactive. The results of the mathematical model reveal a better preload strategy. In the reduction phase, they confirm the overall

1 Unsynchronized

0.9

Synchronized devices Preload Simulation results

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0 -50 -30 -10 10 30 50 70 90 110 130 150 170 190 210 230 250 270 290 310 330 350 370 390 410 430 450 470 490 510 Fig. 5. Resulting load based on the mathematical model and simulation results.

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simulation results and allow a better understanding of the dynamics. It suggests methods for setting the timing of control signals as well as the relation between control intervals and effects. The modelling of heterogeneous ensembles of devices leads to piecewise defined dynamics formulations, which also are difficult to understand. An integration of the model into a model predictive control approach would be helpful to determine optimal signal sequences for treating timed control signals with given control interval as well as oscillation patterns which occur due to the partial synchronisation of devices. 10. Conclusion, open issues and further work As a general conclusion we can state, that under the given assumptions of our scenarios, the operating conditions of refrigerators result in a rather small and varying time span (30–60 min) for load shifting per device. But the thermal storage of large number of refrigerators is well suited for short-time balancing. For larger time spans we would have to consider electric boilers, off-peak storage heaters, or freezers. On the level of detail needed for the analysis on hand, the models of those devices differ from our refrigerator model only in terms of parameterisation. Reaction capability to single signals both in the models and in future devices can be realised with a minimum amount of computing power. Adaptive fridges could thus very likely be based on hardware controllers commonly used in some of today’s types of household appliances if these fridges become equipped with an interface, e.g. for power line communication. The control strategies at utility level in order to decide when to send signals to which households in order to achieve desired load shifting are subject of further work. The essential control method that could be used for this requirement is ‘model predictive control’ (Camacho and Bordons, 2007); it is based first of all on a predictive model of the controlled ensemble of devices. In this article we gave an approach for this model that has to be refined in our future work by providing for further parameters. For the control strategy it is essential to model the systems behaviour to control signals when devices are synchronized in part by prior control signals. This can also be achieved by the mathematical model, because it allows a prediction of the synchronisation of devices for every time step. The mentioned control strategy uses an optimizer to generate a control signal. The objective function of the optimization can be derived from a specified load curve that has to be approximated as well as possible. The required load curve can be compared to the predicted load curve of the devices to determine the best control action to be taken next. The constraints to be satisfied by this controlling attempt are integrated into the model of the devices’ reaction to control signals, because the controller of a single refrigerator does never exceed its temperature bounds. This attempt to load shifting is not limited to augment or decrease load during a given period of time. By grouping thermal storage devices and activating these groups using different control signals, it should be possible to exactly compose a desired load curve which could, e.g. be used to compensate the starting behaviour of smaller, dynamic power generation units and thereby use the presented approach for realising virtual power plants. A major problem of this control approach for demand side management remains in the fact that the electricity demand of the ensemble of devices cannot be observed undisturbed in the electricity grid due to many other active devices’ demand; i.e. it is quite difficult to estimate the parameters of the model from the global systems observation. Potentially this problem can be solved by statistical assumptions based on measurements performed by

high-resolution smart meters at representative devices in the ensemble, or additionally by registering devices with some static parameter values to become part of a controlled ensemble. The presented work is only a first attempt to analyze the balancing potential of cold and heat storage in the grid. While the simulations and calculations presented focus on refrigerators, they can quite easily be adapted to appropriate heating devices. For example, we calculated behaviour of under sink water heaters limited to a water storage capacity of 5 L to avoid the need of modelling aspects of thermal layering. An allowed stored water temperature range from 55  C to 65  C, and a Styrofoam insulation of 10 cm results in scooling z 300 min while swarming z 2 min assuming a heating element with a power consumption of 2000 W. However, the overall balancing potential contributed by such devices differs by time of day due to patterns of warm water usage in households. The control strategy of timed load reduction will lead to very high peaks for this type of devices, so that different control strategies have to be applied. Furthermore, while fridges are encountered in about 98% of German households, boilers come to use in at most 16% of those households (RWI, 2005), and under sink water heaters are only a fraction of those. Therefore the absolute load reduction for a given number of households by controlling under sink water heaters is not thought to be higher than the load reduction achievable by controlling fridges. However, time intervals that can be bridged are substantially longer in the case of water heaters. Besides work on modelling other types of appliances, our further work concerning load shifting potential of household appliances will most likely include the following aspects:  The state awareness of fridges in the scenario of timed load reduction should lead to energy savings compared to direct storage control due to the minimization of ‘overcooling’ in the preload phase of the simulation model. This can be corrected by adapting the strategy suggested in the mathematical model.  In order to keep the system controllable, it is desirable, to reduce both the height of the oscillation peak and its duration, this means oscillations after load reduction have to be damped. This could be achieved by sending subsequent control signals that influence swarming and scooling and has to be integrated into a control strategy as discussed above.

References Altwies, J.E., 1998. Electrical Demand Reduction in Refrigerated Warehouses. MSc thesis (Mechanical Engineering), University of Wisconsin, Madison. Braun, J.E., 2003. Load control using building thermal mass. Journal of Solar Energy Engineering 125, 292–301. Brauner, et al., 2006. Verbraucher als virtuelles Kraftwerk. Berichte aus Energieund Umweltforschung 44/2006. Bundesministerium fu¨r Verkehr, Innovation und Technologie, Vienna, Austria (in German). Borenstein, S., Jaske, M., Rosenfeld, A., 2002. Dynamic Pricing, Advanced Metering and Demand Response in Electricity Markets. CSEM Working Papers, California, USA. Born, F.J., 2001. Aiding Renewable Energy Integration through Complimentary Demand-supply Matching. PhD thesis, University of Strathclyde, UK, Energy Systems Research Unit. Camacho, E.F., Bordons, C., 2007. Model Predictive Control. Springer Verlag, Berlin. Clinch, J.P., Healy, J.D., King, C., 2001. Modelling improvements in domestic energy efficiency. Environmental Modelling & Software 16 (1), 87–106. Constantopoulos, P., Schweppe, F.C., Larson, R.C., 1991. ESTIA: a real-time consumer control scheme for space conditioning usage under spot electricity pricing. Computers and Operations Research 18 (8), 751–765. Dynamic Demand, 2005. A dynamically-controlled refrigerator. (accessed 04.01.08.). ETSO Balance Management Task Force, 2003. Current State of Balance Management in Europe. European Transmission Management Operators, Brussels, Belgium. Friends of the Earth, 2006. How to: get our climate-changing emissions under control. Energy Efficiency 57. Gellings, C.W., Chamberlin, J.H., 1988. Demand-side Management: Concepts and Methods. The Fairmont Press, Inc., Georgia, USA.

M. Stadler et al. / Environmental Modelling & Software 24 (2009) 285–295 Jakeman, A.J., Letcher, R.A., Norton, J.P., 2006. Ten iterative steps in development and evaluation of environmental models. Environmental Modelling & Software 21, 602–614. Klobasa, M., Obersteiner, C., 2006. Technical constraints on and efficient strategies for the integration of wind energy. Energy & Environment 17 (6), 885–906. Klobasa, M., Ragwitz, M., 2006. Demand response – a new option for wind integration? In: Proceedings of the European Wind Energy Conference (EWEC) 2006, Athens, Greece. Miele, 2008. (accessed 01.07.08.). Morovic, T., Pilhar, R., Mo¨hring-Hu¨ser, W., 2007. Dynamische Stromtarife und Lastmanagement – Erfahrungen und Perspektiven. Forschungsgesellschaft fu¨r umweltschonende Energieumwandlung und -nutzung mbH, Kiel, Germany (in German). RWI, 2005. Erhebung des Energieverbrauchs der privaten Haushalte fu¨r das Jahr 2003. Rheinisch Westfa¨lisches Institut fu¨r Wirtschaftsforschung, Essen, Germany. forsa – Gesellschaft fu¨r Sozialforschung und statistische Analysen mbH, Germany (in German).

295

Sonnenschein, M., Stadler, M., Rapp, B., Bremer, J., Brunhorn, St., 2006. A modelling and simulation environment for real-time pricing scenarios in energy markets. In: Tochtermann, K., Scharl, A. (Eds.), Informatics for Environmental Protection, Graz, Austria, pp. 153–160. Stadler, M., Krause, W., Sonnenschein, M., Vogel, U., 2007. The adaptive fridge – comparing different control schemes for enhancing load shifting of electricity demand. In: Hryniewicz, O., Studzinski, J., Romaniuk, M. (Eds.), 21st Conference on Informatics for Environmental Protection – Enviroinfo Warsaw 2007. Shaker Verlag, Aachen, Germany, pp. 199–206. Stadler, I., 2005. Nichtelektrische Speicher fu¨r Elektrizita¨tsversorgungssysteme mit hohem Anteil erneuerbarer Energien. Habilitation. University of Kassel, Germany (in German). ThermCap, 2007. Multimediale Lehr- und Lernumgebung Maschinenwesen. Technical University of Dresden, Germany. (accessed 04.01.08.). VDEW (Verband der Deutschen Elektrizita¨tswirtschaft), 2006. Endenergieverbrauch in Deutschland 2004. Energie Spezial, Berlin, Germany (in German).