Decentralised peak energy demand minimisation in networks of buildings


 Simultaneous peaks in the energy demand from networks of buildings can decrease system stability and increase operational costs. However, reducing these peaks can require complicated centralised control schemes. 
Here, taking inspiration from biological systems, we investigate a decentralised, building-to-building load coordination schema that requires very little information and no human intervention. 
Using agent-based modelling, we investigate both the optimal system size and robustness of the results to changes in the system parameters.
It is found that substantial reductions are readily achieved through coordination between a small number of buildings, analogous to models of coordination between flocks of birds. Strikingly, the schema significantly outperforms existing techniques and is robust to varying network topology and the inclusion of large time-constrained thermal loads. These results imply that significant reductions in network peaks are achievable through simple low-cost controllers implemented at the building level; particularly important for developing countries with fragile networks.

plex biological system -with no knowledge of the overall system's state or properties -can result in highly 48 desirable "emergent" behaviour at system level [48,49]. Studies have shown that the number of coordinating applicability to the problem of peak demand has previously not been studied, so their efficacy is not known. 54 Thus, a simple schema was developed using an agent-based model (ABM) framework to study the extent 55 of peak load reduction that could be achieved through this type of decentralised load coordination between 56 groups of buildings in a network. Dwellings are used as the buildings in the model due to their higher demand 57 profile compared to non-dwellings and the fact they present a more significant coordination challenge due 58 to the distributed nature of loads. The coordination schema is based around loads that are "shiftable" in 59 time [55][56][57], as opposed to base loads (e.g., refrigerators) and on-demand loads (e.g., kettles). We also 60 distinguish less-constrained shiftable loads, such as dishwashers, from more-constrained thermal loads for 61 space heating or cooling requirements. This is an important distinction, often missing in the literature, 62 as time-constrained thermal loads are also larger than other loads, and their impact on network peaks is 63 therefore more pronounced. 64 A variety of simulations was used to determine which key parameters significantly influence the magnitude 65 of any observed peak reductions arising from the schema. The factors investigated were group size, network 66 topology, coordination time-scale and the size of load allowed to be redistributed in each time-step. Each 67 of these factors represents a significant unknown that could affect the overall robustness of the system: for 68 example large groups may prove harder to coordinate in practice, a single successful network topology could 69 be less flexible than a multitude of topologies and longer coordination time-scales might negatively affect 70 user-acceptance depending on the nature of the load. 71

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Our goal in this work is to discover the key factors influencing load coordination between buildings and if 73 they are likely to result in substantial peak reduction. Since the interaction of buildings will occur via the 74 links of the network connecting them, we examined a range of network topologies with a view to investigate 75 their impact on any resultant peak load reduction. Alongside this, we investigated the key parameters in a 76 simple load coordination schema that requires little data or human intervention, relying on only simple rules 77 and minimal interaction. The buildings or dwellings constitute the nodes on a network and are directly connected with others 80 (their network neighbours) via information links (the network edges). Several common network topologies 81 were investigated (described in §5.1). For the nodes to coordinate their demand, some information must 82 be exchanged between groups of directly-connected nodes, termed the neighbourhoods of the nodes. This 83 information is used to enable one of the following actions-if a suitable shiftable load has been requested for 84 either now or is offset into a "demand pool" for later: 85 i consume a shiftable load now, to fill spare capacity -either on-demand or from the deferred demand-pool; It is pertinent to observe that, while clear minima are identified at a particular load distribution limit, 143 the width of a given curve indicates the robustness of the different configurations. That is, the less steep the 144 trough of a curve, the more robust the given configuration to produce lower peak demand. values for each α, as can be seen by the relatively narrow coloured envelopes for each set in Figure 2. The 150 partition and ring lattice topologies are particularly close, and whilst the RMSEs from random network 151 topologies differ slightly from those of the partition and random WS(p = 0) topologies, these are not 152 significant and likely due to the variation in node degrees inherent in such random networks.

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The most interesting result here is the impact of average node-degree (see §5.1.1), i.e., number of neigh-154 bours, on peak demand reduction. While all node-degrees share similar RMSE minima, their gradients 155 increase more steeply with higher node-degree as α increases. The width of our curves can be compared 156 using the well-known full width half maximum (FWHM) bandwidth, which reveal that, for all network 157 topologies, RMSE curves for average node degree 2 are approximately twice the width of those with average 158 degrees 8 and 10. However, the FWHM widths for networks with average node degrees 8 and 10 do not show 159 any significant differences. This indicates that our peak coordination schema is most robust over a broad 160 range of the load redistribution limit α for networks with node degrees 2-4, but its effectiveness is limited 161 to a very narrow range of α values with higher node degrees.

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The overall impact of these results on peak demand reduction is significant. An analysis of all imple-163 mented scenarios shows that the largest reduction of peaks in electricity consumption (average 59%, standard 164 deviation 13% and maximum of 73%) can be achieved in the networks of node degree 4 and with α values 165 ranging between 5% to 25%. The reduction of peaks regardless of the choice of α, on average, is 31% with 166 standard deviation 21%. While this striking difference highlights the utility of choosing an optimal value 167 Figure 2. Impact of network topology on peak control and reduction illustrated for a 6 hour time shifting window selected due to Group 1 results ( §2.2.1). The RMSE (root mean square error) values show the deviation from a flat (average) demand profile, with zero being totally peak-free. Each network average degrees cluster comprises of shifted demands for the following four networks: partition, ring lattice (WS(p=0)), random config. model and random (WS(p=1)). FHWM bandwidth for node degrees 2, 4 and 8 are 0.58, 0.4 and 0.24 correspondingly.FHWM bandwidth for node degrees 8 and 10 are virtually identical and hence only 8 is shown. Note that RMSE values for networks with node degree greater than 8 increase at approximately the same rate as the ones for networks with node degree of 8.
for the load redistribution limit α, it also demonstrates that significant reductions can be robustly obtained 168 across a wide range of chosen values for α. Loads from heating and cooling systems are not only significantly larger than those from a typical large home 171 appliance modelled above, they are also time constrained through a combination of weather and lifestyle 172 and hence known to have a significant impact on network peaks. The overall success of a peak coordination 173 schema, such as that described here, will therefore largely depend on its ability to manage such loads. Hence, 174 we now investigate the impact of extending the ABM to include such large time-constrained loads.

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To run the extended ABM model, we choose the scenario group with optimised parameters (time window 176 of 6h and network average degree of 4) that, in our previous experiments in §2.2.1 and §2.2.2, guaranteed 177 the greatest peak demand flattening results (Table 2). We also expect that the time shifting window for our 178 heating loads will, in practice, be considerably smaller due to the lower flexibility in how much they can be 179 shifted compared to the loads considered earlier. For example, there would be little use in supplying heat to 180 a home six hours after it is usually needed, as is the case with our most optimal result in §2.2.1. On the other 181 hand, we can expect predictably stable demand during summers in cooling dominated climates and winters 182 in heating dominated climates, allowing thermal loads to be brought forward in addition to being delayed. 183 Hence, we constrain the time shifting windows for our heating loads to either one or two hours either side of 184 "scheduled" demand. In other words, the total window for heating operation is increased by two hours (split 185 one hour each side of scheduled demand) or four hours (split two hours each side). Hence, the extended 186 model is purposely loaded against peak flattening through the use of significantly larger loads that are also 187 highly constrained in how much they can be shifted, but counterbalanced by the choice of the most optimal 188 scenario group from the previous results. It is noteworthy that while the need to know heating or cooling 189 schedules increases the information needed to implement our system, it is a quantity readily obtained from 190 a modern domestic controller.

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Our extended model achieves the greatest peak electricity demand flattening when the load redistribution 192 limit α ≈ 10% and the time shifting window for heating loads is equal to 4 hours. Figure 3 illustrates the 193 typical load profile of a network with three neighbours with uncoordinated and coordinated loads. Our 194 findings show that while a two-hour time window of shifting heating operation results in a maximum 44% of 195 peak flattening, a four-hour time window in a maximum 61% reduction, consistent with the idea that greater 196 flexibility would result in greater flattening. Note that the minimum reduction for both scenarios is zero.

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Furthermore, the analysis of maximum ramp rates (kW/half hour) shows that reductions of 31% and 29% 198 can be achieved for four-hour and two-hour time windows correspondingly. These results, though lower than 199 for non-thermal loads, show substantial reductions and are consistent with the findings presented earlier.    Figure 4 suggests that the most common heating outage length is 15 minutes for the 208 two-hour window, while it is 105 minutes for the four-hour window. This is due to the fact that the system 209 is able to advantageously use the larger window of four hours to simply shift longer heating periods, whereas 210 it is "forced" to break this schedule up into smaller chunks in the two-hour window. Longer breaks are also 211 evident in the two-hour window, but are significantly less likely to occur. Further analysis shows that, on 212 average, a single building is expected to have two outage events per day for the four-hour shifting window,

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Our main result is that the greatest peak demand flattening occurs when the time shifting window is equal to 218 six hours, the network degree (i.e., number of neighbours) is four buildings and the load redistribution limit 219 α is between 10% and 25% of the neighbourhood's peak load. When α = 1 or α = 0 no peak reduction is seen 220 in the network. This is similar to game theoretic approaches-used to study the formation of networks- [60]. However, we find that even a poor choice of α, on average, results in a 31% reduction in peak demand.

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Hence, the range of possible reductions predicted by our approach (31% to 73%) are far greater than even 225 the predicted range of reductions in the DSM literature of between 13% to 50%. 226 Figure 5 illustrates the typical load profile of a network with just three neighbours with uncoordinated 227 (i.e. occurring near-simultaneously) and coordinated loads, the latter for both highly optimised (best case) 228 and non-optimised (worst case) parameters. The effect on ramp rates is also dramatic. That is, for the best 229 case peak reduction scenario (i.e. α = 0.15 the maximum ramp rate (kW/half hour) of schema-coordinated 230 load can be reduced by 65% of the maximum ramp rate of the original, uncoordinated, load. In contrast for 231 the worst case scenario when α = 0.95, the maximum ramp rate of schema-coordinated load is 8% higher 232 than the maximum ramp rate of the original uncoordinated load. Strikingly, our results demonstrate that 233 network topology does not significantly influence peak flattening. This suggests that it is the simple presence 234 of connections between dwellings that is important, rather than the manner of connection. However, there 235 is a limit to the utility of the number of connections, or average degree of the network. Not only does 236 increasing the average degree not improve the effectiveness of the peak coordination strategy, but it also 237 limits the effective range of α to a very small window. This is analogous to the social behaviour of animals 238 where it has been observed that, due to homogeneous interaction, animal social contact networks are not 239 scale-free (i.e., node degrees do not follow power-law degree distribution) [61]. A second notable similarity 240 with models of biological systems-such as flocking birds-is that the optimal number of neighbours is small.

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For example, birds are known to interact with a small number (six to seven) of neighbours to form a flock 242 ([51], [48]).

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The impact of the window within which behaviours can be shifted is observed to be optimal at 6 hours 244 (RMSE = 0.46), though substantial reductions in peak demand can also be observed at the other intervals, 245 with the 12-hour window being the "worst". In this case an RMSE of 0.65 is obtained, i.e., 19% worse than 246 the 6-hour window, but still 54% better than with no coordination (RMSE = 1.42).It is noteworthy that 247 the time window only specifies the range within which an energy consuming action can be deferred. In our 248 modelling, agents randomly distribute loads within this window, which is consistent with the behaviour of 249 an unmediated (i.e., automatic) controller. To what extent such behaviour can be expected from human-250 mediated action, were such mediation deemed useful, remains to be seen. Given that thermal loads, such as those from a heating or cooling system, tend to be large in absolute 252 terms and the key driver of peak loads, it is pertinent to ask whether such loads can be deferred for 3 to 12 253 hours. After all, the impulse to use heating and cooling is strongly dependent on external weather conditions, 254 and there may be little flexibility in the timing of these loads. However, unlike some appliances, such as 255 some washing machines whose individual cycles may be hard to interrupt once started, heating and cooling 256 systems are fundamentally interruptible. Hence, it is possible, in principle, for a heating or cooling system 257 to temporarily interrupt operation, with the possibility of restarting in the next 15 minute interval. This is 258 entirely within the remit of the schema propose here since there is no decision memory -the system makes 259 decisions independent of those made in previous intervals. Our tests of such loads using smaller shifting 260 windows of only two or four hours demonstrate the striking possibility that even with the flexibility of just 261 an hour before or after scheduled demand in the timing of these loads, it is possible to obtain a 44% reduction 262 in peak load demand. This widens to 61% in a ±2-hour window; both results being the maximum expected 263 savings. These reductions are associated with a 29% and 31% reduction in ramp rates for the two-hour 264 and four-hour cases, respectively (e.g., see Figure 6); and an average outage length of 38 and 66 minutes 265 respectively. The standard deviation for outage lengths for the four-hour case (42 minutes) is almost two 266 times higher than are the one for the two-hour case (23 minutes), indicating that households across the 267 sample experience much higher variability of outage lengths upon time window increase.  . 24-hour load profiles of a random dwelling for 2-hour (a) and 4-hour (b) load shifting time windows. Each graph shows: the peak load coordination schema achieving the most peak demand flattening, the peak load coordination schema achieving the least peak demand flattening, the profiles when no peak coordination schema is applied and constant average demand.
Naturally, the drift in indoor temperature caused by a cessation of the heating or cooling system is 269 strongly dependent on the thermal characteristics of the building envelope itself, as discussed in Section 1.

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Highly inefficient envelopes will cause a rapid drift away from comfortable temperatures, resulting in high 271 ramp rates on the network when the system is switched back on. Conversely, well insulated or thermally

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In this section we describe in detail the methodology used for the numerical results described in previous 285 sections. First, the different network topologies that were investigated are detailed. Next, we consider 286 possible modelling approaches to investigate the problem that can adequately represent our load sharing 287 schema. Finally, we describe our model set-up and the peak coordination algorithm and underlying data 288 assumptions.  • generate a grid with n nodes such that the nodes can be arranged in a regular lattice or ring;

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• connect each node in the ring to its k nearest neighbours (where k is an even number for symmetry);

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• "rewire" each link in the regular network with probability p -i.e., disconnect it from one of its neigh-318 bours and connect it with another node that is chosen uniformly at random from the other nodes (often 319 using pairwise swapping to preserve the degree of each node).  Here we describe the ABM employed to investigate the system-level emergent result of scheduling of 355 various shiftable appliances in different networks of dwellings for the purpose of optimal peak coordination.

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The effect of three key aspects on peak reduction were investigated, based on §5. time-frames is unlikely to affect our results given that either being longer or shorter merely affects the total 367 number of observations, but not the nature of the decisions, which is the central aspect of this model.

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Thus, after initialisation of the agents (Fig. 8(a)) and the network environment ( Fig. 8(b)), the ABM 369 runs in a cycle that can be described in three stages (Figure 8(c) neighbourhood's overall usage over the last 15 minutes but do not influence each others decisions directly.

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A simple controller in each dwelling can then use this information to make decisions which affect the output 373 of the model (Fig. 8(d)).   = 0)), random using the small world scheme WS(p = 1)) and the configuration model with fixed node degree (see Table 3 for details).
The average degree is the number of directly connected neighbours in the network. α is the load redistribution limit (Sec. 5.4) increased at intervals of 0.05 over the indicated range. Time window is the maximum interval of time that a load can be shifted within, with the actual length of shift being randomly determined.
In preliminary runs, windows of 15 and 30 minutes were also tested but the outcomes did not show any 384 significant reduction of peaks from that when no schema was applied.

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The following network topologies were generated using Python library NetworkX [92] and Java library • network connections (Fig. 8b) -described in Section 5.1 and listed in Table 3;

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• external factors -system parameters including total system size, threshold (τ ) for action, time-window 403 for shifting of appliances and each agent's neighbourhood's maximum demand level (see §5.4).

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Once the input data has been provided, the internal properties of the "dwelling" agents in the network 405 are initialised. Each dwelling is assigned a set of loads representing appliances according to appliance 406 ownership rates defined in [55]. For example, if the ownership rate for the appliance A is 80% then 80% 407 of the dwellings will be selected randomly and the appliance A added to the list of appliances they own.

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To guarantee variable and realistic appliance usage schedules, initial appliance time schedules are generated is taken, as follows. If electricity consumption in the closed neighbourhood is greater than or equal to τ , 430 the decision to decrease electricity demand at time step t will be made and a load that can be shifted will 431 be identified from the appliance list. The load is then shifted to a demand pool, to be rescheduled within 432 the defined shifting time window N . Otherwise, if the electricity consumption of the dwelling is below τ the 433 decision to increase electricity demand at time step t will be made and an appliance-load within the demand 434 pool will be identified. The electricity demand for the agent will then be updated for that time step. The 435 simulation then outputs the computed electricity loads for each dwelling in 15 minute intervals over one 436 week. This process is then repeated for each 15-minute interval for the whole computed week. The total 437 number of steps over one week is hence 672. The algorithm below illustrates the sequence of steps described above. Defining the set of all dwelling agent nodes D = {d 1 , d 2 , ..., d n }, the undirected network of agents is denoted as a graph G(D, C), connecting nodes D via links given by C = {(d i , d j )} where 1 ≤ [i, j] ≤ n and i = j. The neighbourhood of agent d i is given as: Further, the closed neighbourhood of d i is defined as the set containing both d i and its neighbourhood N (d i ), given by the union The electricity consumption of an agent d i at time step t is denoted e(d i , t), so the electricity consumption of agent d i 's closed neighbourhood at time t is thus given by: Similarly,ê(d i ) denotes the sequence of all demands for every 15 minute interval in 1 ≤ t ≤ 672 for agent d i over the whole week, and the sequence of electricity consumption values for d i 's closed neighbourhood is the sum over this and denotedÊ N [di] . Hence the peak electricity consumption of agent d i 's closed neighbourhood is defined as: The algorithm 5.1 shows workflow of the ABM in detail.

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Algorithm 5.1: Peak coordination algorithm Data: set of Dwellings D; network topology of connections; base load profiles; occupancy type; list of appliances (A), their unshifted schedules, cycle length and mean electricity demand; α load redistribution limit for peak electricity consumption in neighbourhoods of agents 0 < α ≤  [55]. This open source tool generates realistic, high resolution load profiles through simulation of occupant 447 behaviour, validated against measurements obtained in a field-test [55]. (c) Base and total load for a single, randomly selected, agent. Figure 9. Example base load profiles over a single weekday for (a) 100 individual agents (b) total base load for all agents and (c) base and total load for a single, randomly selected, agent. Note that the base load, while small, compared to total load is in itself "peaky".

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There exist a wide variety of domestic occupancy types depending on the number of people in a household, 451 their ages, employment status etc., [95]. For simplicity, we consider just two: "employed" and "unemployed" 452 (in a 70:30 distribution ratio) as it provides the two extremes of "intermittent" and "permanent" occupancy, 453 respectively. An advantage of this simplification is that it reflects the profiles used in the ALPG tool noted 454 above. The main difference between the two occupancy types is that a dwelling with "employed" occupants 455 will initially be scheduled to only use appliances in the mornings or in the evenings, whereas appliances are 456 scheduled randomly throughout the day for "unemployed" occupants.

Model Constraints
Since the focus of this paper is to investigate the impact of the network topology and average number of 459 neighbours on the peak coordination schema it was assumed that all shiftable appliances can be shifted by 460 the peak coordination algorithm (see §5.1), so factors such as appliance priority or appliance run-time factor 461 (the ratio of time for which a particular appliance was in the running state during the previous time slot) 462 are not included in the current scheme. However, given that thermal loads are usually the single largest load 463 type, and their demand is time-constrained, we investigate them separately, see below. kW, a sufficiently large capacity for most common heating loads, including heat pumps [97,98]. To ensure 477 variability and simulate the well-known "demand diversity factor", a heating schedule is generated for each 478 dwelling in the network by randomly sampling within fixed intervals in morning (05:00-08:00) and in the 479 evening (17:00-19:00).
480 Figure 10 illustrates the base and total load for a single, randomly selected, dwelling in our simulation.

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Compared to the load produced by the simple ABM model presented in Section 5 with no heating system 482 included (Fig. 9) the total load when a heating system is included is significantly higher, as expected.