Deduction of Optimal Control Strategies for a Sector-Coupled District Energy System

We present a method to turn the results of model-based optimisations into resilient and comprehensible control strategies. Our approach is to define priority lists for all available technologies in a district energy system. Using linear discriminant analysis and the results of the optimisations, these are then assigned to discrete time steps using a set of possible steering parameters. In contrast to the model-based optimisations, the deduced control strategies do not need predictions or even perfect foresight but solely rely on data about the present. The case study using priority lists presents results in terms of emissions and prices that are only about 5% off the linear optimum. Considering that the priority lists only need information about the present, the results of the control strategies obtained using the proposed method can be considered competitive.


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In this section, we describe how our solution for optimal control strategies matters and one of the 12 main hypotheses we build on: Priority lists can describe optimal control strategies as well as linear To achieve the 1.5 • C [1, 21] goal of the Paris Agreement, immediate action is strongly advisable [2- In Equation (1), the steering parameters x get weights w and are converted to a value z. With 48 cut-off-values, each value for z represents a class and each class represents a priority list of the available 49 technologies. These priority lists can control the operation of the local energy supply system so 50 that emissions of and prices for the operation are comparable to the ones obtained with the linear 51 optimisation.

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With the proposed control strategies, data and computation intensity as well as the need for 53 prediction in operation are reduced. Also, priority lists as control strategies could reduce the need for 54 models and simulations and therefore make elaborate control strategies available for a wider range 55 of actors. This would become possible as soon as the control strategies are not deduced from linear 56 model optimisations. With our paper, we show that the control strategies perform almost as well as 57 model-based optimisations and thereby lay the foundation for further work in that direction.

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One important hypothesis for us is that priority lists can describe model-optimised control 59 strategies. In the following subsection 1.2, we argue why we think that this is actually the case.  • c e (t), the cost (in Units per Joule), • η e > 0, the transmission efficiency, and

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Now, a linear optimizer can be used to find argmin ∑ e c e (t) × P e (t), the optimal control strategy that minimises the cost.

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If there is just one sink and the graph is acyclic (loop-free), it is trivial that alternatively a list can 69 be created that orders all possible supply options (all paths connecting the sources and the sink) by 70 their cost. When starting from the cheapest option, this priority list also gives the optimal supply 71 solution.
by a priority list of paths connecting the sources and the sinks. As the P max,e (t) < ∞ and c e (t) > 0 are 79 determined by "technologies", this can be seen as a list of technologies.

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Also, there might be linked edges with P e (t) ∝ P e (t), e = e . In this case, the two paths count as 81 one technology in the priority list. These complicate the creation of the priority list, but do not render 82 the approach invalid: Consider the case of demand for heat and electricity, where electricity is for free 83 but heat is provided cheapest by a combined heat and power plant: In this case, the chp will have 84 priority. Also note that creating the priority list is typically not as easy as sorting by costs. To summarise, creating a priority list expressing the optimal control strategy is possible. However,

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it is not an easy task. Hence, we fall back to linear optimisation and create priority lists on that basis. In this section, we introduce our methodology. For our complete research, we use the methodology 100 shown in Figure 1. In this article, we focus on the presentation of our approach of deducing optimal 101 control strategies which is the second step in the figure. Therefore, we introduce our energy system 102 design and the linear model optimisation in subsection 2. In Figure 2, the local energy supply system is shown. The yearly demand for electricity is supplies to the local demand for a given time step. For pv, the capacity is a time series depending on 128 the irradiation. If there is no irradiation, the capacity for pv is set to a very high number in order to 129 identify these special circumstances. For chp, the capacity is a fixed value in terms of installed capacity.

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For the grid, the capacity is equal to the demand.

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Priority Number (1 is highest priority) per Technology (Electricity) Observed Hour pv chp grid 09-10 1 2 3 10-11 1 2 3 11-12 1 2 3 12-13 1 3 2 13-14 1 3 2 These capacity shares help to identify which of the technologies is prioritised by the optimisation 132 in each hour. For our example, the resulting priority numbers with 1 being the highest priority for each technology and hour are shown in Table 1. In this example, pv has the highest priority in each hour.

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The second highest priority has chp for the first three hours and the grid for the last two hours. In the 135 following, we explain how we assign different situations in the energy system in terms of different 136 capacity shares of the different technologies to technology-specific priority numbers.

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Class Definitions (Electricity) Class pv chp grid class 1 1 2 3 class 2 1 3 2 class 3 2 1 3 class 4 3 1 2 class 5 2 3 1 class 6 3 2 1 we already reduce the numbers of classes at this stage. For the given example, the classes 5 and 6 do 140 not need to exist both as if the grid is preferred, it can supply the full demand -the second and third 141 priority do not matter. So, we already reduce the classes before assigning certain conditions of the 142 energy system to them.

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Having this set of classes, we assign a class to each time step via conditions. A condition is a 144 certain set of capacity share combinations. In Table 3, two of these conditions are shown as an example 145 for the electricity supply. The first example is full-load supply of the chp plant, part-load supply of 146 the pv plant and no supply from the grid. Part-load of the pv plant refers to some of its energy being 147 exported to the grid. The priorities and thereby class can, for this condition, intuitively be assigned. In 148 case of both technologies in full-load-operation, it is harder to assign a class. To assign classes to these Share pv Share chp Share grid Class pv-full-and chp-part-load x = 1 0 < y < 1 1 pv-and chp-full-load x = 1 y = 1 1 Table 3. example: assignment of classes with conditions of capacity share combinations (shares of pv (x), chp (y) and grid (z) more difficult cases, we assign the classes to the easy-to-assign conditions first. Then, we evaluate 150 the relative frequency of each of the classes. And based on these relative frequencies, we assign the 151 difficult-to-assign conditions. In our example of pv and chp in full-load operation, the most occurring 152 class with the easy-to-assign conditions for the emissions-optimisation is class 1 and therefore we 153 assign this condition to class 1 with pv prioritised over chp. We assign conditions to classes until all 154 data points are assigned to one of the defined classes.  Table 5 for emissions (subsection 3.1) and Table 6 for prices 177 (subsection 3.2). In order to only have one priority list, we combine the deduced optimal control strategies for 183 electricity and heat. In our case, the two priority lists are linked through the chp plant. For a validation of our approach, we have the two time series of priority lists shown in Table 4 191 with which we control the supply of our local energy system. We have one time series for each, the 192 optimisation on emissions and the optimisation on prices.
In our validation, we compare the results in terms of emissions for the emissions-optimisation and 194 in terms of prices for the price-optimisation. To validate the deduced optimal control strategies, we use 195 our energy system model in oemof again but replace the costs in terms of emissions or prices by costs 196 for our priorities. We implement this for the heat technologies with ten to the power of the priority 197 number in the heat priority list. For electricity, we use higher costs in order to prioritise electricity 198 over heat. Thus, the costs for electricity for these technologies are ten to the power of four plus the 199 priority number yielding ten to the power of five, six or seven depending on the priority number of 200 the technology for a specific time step. Note that we choose this way to directly compare the methods 201 within the same energy system model. In principle, the deduced energy system does not rely on the 202 linear optimisation. 203 We compare the results of the model-optimisation to the results that we obtain with the deduced 204 optimal control strategies. We validate both, the class-definition-based and the classification-based

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We want to give an overview about our research boundaries. We have a look on a sector-coupled 216 local energy supply system but exclude mobility demands. We do not validate our control strategies in 217 a real case but implement our control strategies in our oemof-model and solve it using the Cbc-solver 218 on an energy balance level with a time step size of 1 hour. For the steering parameters, we only consider 219 available time series data. These could be reduced to the number of relevant steering parameters.

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Also, derived steering parameters like the residual electrical load as the electrical demand minus the 221 pv-supply could be used. Last but not least, we simplify the deduction by deducing electricity-and 222 heat-specific priority lists and then prioritise electricity over heat.

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After presenting our methodology and the most important input data, we now want to present 224 our results.

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With this reduction, we want to find out how many priority numbers are significant for the results and 237 the three columns are thus the results for our sensitivity analysis.

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In terms of emissions, the class-definition-based priority lists lead to 5.5 % higher emissions. This    In terms of prices, we obtain similar results to those in terms of emissions. The prices in Table 6 250 are negative as we yield a revenue from selling the energy. Thus, the lower the values are, the better is   for optimisation could be included. An example for another goal for optimisation is the regional use 280 of energy and thereby the added value to the regional economy -if the power plants are owned and 281 operated by regional actors.