Transactive Energy System for Distribution Network Management: Procuring Residential Flexibility Services Under Dynamic Pricing

The formulation of dynamic pricing is one of the emerging solutions to guide residential demand for the benefits of the bulk power system. However, the schedule of residential demand in response to time-differentiated energy prices could cause congestions in distribution networks at both the lowest-price and highest-price time intervals. To enable the adoption of dynamic pricing, this work presents a novel framework to manage the constraints of distribution networks based on the concept of Transactive Energy System (TES). The TES-based framework produces incentives during network issues to unlock customers’ flexibility services to reschedule controllable assets (e.g., batteries). By running Home Energy Management Systems (HEMS), the flexibility of customers to modify schedules are quantified against predefined set of incentives. For each incentive, the amounts of net-demand change per customer are aggregated and submitted through aggregators to the Distribution System Operator (DSO) in the forms of both generation offers (reducing demand) and demand offers (increasing demand). The latter are crucial to cater for generation-driven network issues. The resulting aggregators’ staircase bidding curves are embedded to an advanced Optimal Power Flow (OPF) model to identify the successful offers to manage network constraints whilst minimizing incentives paid to aggregators. This allows defining incentives and quantities directly without extensive iterations between DSO and aggregators. The application of the framework to an urban 11kV feeder shows its effectiveness to manage congestions. Further, the highly variations in dynamic prices increase the amounts of incentives particularly when flexibility services are requested at evening and night time intervals.


I. INTRODUCTION
The transition towards advanced residential electricity pric-21 ing schemes plays an important role to support the operation 22 of power systems particularly with the wide-scale adoption 23 of residential low-carbon technologies [1], [2], [3]. In partic-24 ular, the formulation of residential time-differentiated pricing 25 instead of the traditional flat retail tariff is considered as 26 one of the potential emerging solutions to guide power con-27 sumption of residential customers for the benefits of power 28 The associate editor coordinating the review of this manuscript and approving it for publication was Miadreza Shafie-Khah . system operators [4]. This dynamic pricing scheme may also 29 support the uptake of residential batteries and Home Energy 30 Management Systems (HEMS) to reduce customers' electric-31 ity payments [5]. However, the management of residential 32 demand in response to a dynamic price signals defined by the 33 System Operator (SO) may lead to adverse technical impacts 34 on local distribution networks [6]. Most of customers' power 35 consumption could be scheduled towards the lowest-price 36 time intervals to reduce electricity bills. Thus, the diversity of 37 load will be affected resulting in new local peak demand [7]. 38 During the highest-price time intervals, reverse power flows 39 could also be created when residential customers maximize 40 VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ energy export to increase revenues. Therefore, the adop-41 tion of residential dynamic pricing may overload distribu-42 tion networks (lines and transformers) and/or cause voltage 43 issues [8]. 44 To limit the aforementioned technical impacts on distribu-45 tion networks, it is important that Distribution System Oper-46 ators (DSOs) enhance their new roles to manage transactions of power flows across congested networks [9], [10]. Future Power Flow (OPF) [26], [27], [28], [29], [30] as the decision-97 making algorithm. For instance, the price-based OPF pre-98 sented in [26] aims to solve congestions through the provision 99 of incentive signals to customers in return of controlling their 100 power consumption for the benefits of distribution networks. 101 The above studies assumed that DSOs/aggregators have the 102 ability to directly control customers' assets to solve network 103 issues. This might not be implementable in practice. The 104 aggregators may not have access to the full data of distri-105 bution networks to manage network constraints. In contrast, 106 DSOs with unbundling regulation rules do not have direct link 107 with customers' meters. Further, the adoption of OPF to man-108 age large numbers of controllable variables may significantly 109 increase the computational burden of the optimization engine. 110 Thus, the scalability of the TES algorithm will be limited.

111
A few models in the literature realistically model the inter-112 actions between customers, aggregators and DSOs [27], [28], 113 [29], [30]. Although iterative optimization-based approaches 114 were adopted to define the successful bids, extensive iter-115 ations between the DSO and aggregators were required to 116 agree on quantities and prices. Furthermore, the proposed 117 algorithms are limited to solve demand-driven network issues 118 (at the low-price). All the previous mentioned studies do not 119 cater for network issues resulting from reverse power flows 120 when energy export of residential customers is increased to 121 sell energy at high prices. 122 Based on the above, Table 1 provides a summary of the 123 gaps in the literature. To bridge the gaps from previous stud-124 ies, this work presents a framework to manage the constraints 125 of distribution networks under residential dynamic energy 126 pricing using the concept of transactive energy system. The 127 TES-based framework produces incentive-based price signals 128 during network issues to procure flexibility from residential 129 customers to reschedule their controllable assets. By run-130 ning HEMS, the maximum flexibility to modify schedules 131 are assessed per residential customer against the predefined 132 set of incentives. The resulting amounts of potential net-133 demand changes are aggregated and submitted through aggre-134 gators to the DSO in the form of generation offers (reducing 135 demand) and demand offers (increasing demand). Each offer 136 determines the quantity of potential net-demand change and 137 the corresponding price. The successful offers are identified 138 using an optimal power flow model formulated to minimize 139 the allocated incentives to aggregators (in return of net-140 demand adjustment) whilst respecting network constraints.

141
The contributions of this work compared to previous stud-142 ies could be summarized via the following bullet points: • The modelling of a novel approach to determine the 153 quantities and prices of aggregate flexibility services 154 (net-demand adjustment) that could be unlocked from 155 residential customers to support distribution networks.

156
• The provision of both generation offers (reducing prices (£/MWh). The TES aims to procure flexibility services 189 from residential customers to reschedule their controllable 190 elements for the benefits of distribution networks. For this 191 purpose, incentive-based price signals (£/MW) are produced 192 during time intervals of network issues to remunerate res-193 idential customers who are contributing to managing net-194 work constraints. The framework also assumes the presence 195 of spatially-distributed aggregators (e.g., an aggregator at 196 each distribution substation) across distribution networks to 197 interact with residential customers, the DSO and SO. The 198 existence of aggregators is important particularly in countries 199 with regulatory rules that do not allow DSOs to have direct 200 access to the individual customers' meters. The proposed 201 framework provides clear roles of residential customers, 202 aggregators and DSOs. The details are explained as follows. 203 In response to the electricity energy market prices defined 204 by the SO, each customer aims to minimize the daily energy 205 payment through the optimal management of controllable 206 flexible assets. For this purpose, the HEMS described in [7] 207 and [31] is adopted to define the optimal daily schedule of 208 EVs and batteries. The resulting customers' net-demand pro-209 files are then aggregated and sent to the DSO through aggre-210 gators. The response of customers to the energy prices may 211 result in the violations of network constraints. Thus, a dis-212 tribution Network Management System (NMS) is introduced 213 to check for the violations of network constraints. Based on 214 the net-demand profiles submitted by aggregators, an AC 215 power flow is run at each time step in the operational plan-216 ning (e.g., one day) to calculate network voltages and power 217 flows throughout lines and transformers. For any time step 218 with congestion or voltages issues, the TES is triggered to 219 procure flexibility services from aggregators to maintain net-220 work constraints within limits. The DSO requests offers from 221 aggregators to modify their power schedules. In response 222 to the DSO's request, each aggregator is connected to the 223 TES platform to submit a set of offers to either reduce 224 or increase the net-demand from the customers. Each offer 225  the usage of batteries to solve demand-driven network issues 258 in the early morning (e.g., voltage drop issues) may reduce 259 the volume of stored energy and increase import during night 260 periods that are mostly associated with high electricity market 261 prices. Thus, the offers placed by the aggregators are defined 262 to compensate the adverse impacts on customers' bills. At a 263 particular offer's price, the HEMS is run per residential cus-264 tomer to determine the maximum net-demand change that 265 each customer could deliver without affecting the desired 266 daily electricity payment. To define adequately the flexibility 267 per aggregator, the offers' prices are also gradually increased 268 between their minimum and maximum values in small steps. 269 The customers' response at each offer's price are aggregated 270 to define the offer's quantity.

271
Once all the aggregators submit their offers to the DSO, 272 an AC OPF-based optimization engine at the DSO's network 273 management system identifies (selects) the successful gen-274 eration and demand offers (single offer could be selected at 275 most from an aggregator). Since the DSO will pay the cost 276 of net-demand adjustments, the AC OPF is formulated to 277 minimize the amounts of payments to the aggregators whilst 278 respecting thermal and voltage constraints. The outcomes 279 of the OPF are then notified to the aggregators to deliver 280 the quantities of the successful offers. Then, the prices of 281 successful offers are sent to individual customers (incentive-282 based price signal) to achieve the committed power.

284
This section presents the modeling of the transactive energy 285 system including the decision-making algorithm, the process 286 to define aggregators' generation and demand offers as well 287 as the HEMS.   (2) 329 is formulated. It is worth to highlight that it is possible that 330 the DSO may not procure offers from an aggregator (e.g.,

331
offers with high prices). Therefore, the modelling considers 332 the inclusion of an offer per aggregator whose quantities and 333 prices are set to zero (i.e., no adjustment of net-demand). gator can be identified as given in (3) and (4); respectively.

339
The aggregators are notified with the successful offers. Each 340 aggregator is committed to adjust its initial net-demand at the 341 time step t * (p a,t=t * ) according to the quantities of accepted 342 generation and demand offers. Therefore, the committed 343 active power of each aggregator (p a,t=t * ) is formulated in (5). 344 The applied incentives (π g * a , π d * a ) in return of delivering the 348 quantities in the accepted generation and demand offers are 349 given in (6) and (7), respectively (i.e., prices defined by the 350 aggregators in the accepted offers).
The optimization problem is also subject to the traditional 354 Kirchhoff's voltage and current laws (KVL and KCL) as well 355 as to thermal and voltage constraints which are modelled to 356 keep both power flows throughout the network branches (set 357 L indexed by l) and network voltages all within limits.

358
At each bus (set B indexed by b), the balance of active 359 and reactive power are given in the constraints (8) and (9), 360 respectively.
where ρ u denotes the bus (b) to which each network element 366 is connected (u ⊂ {a, d, l}). The modelling considers the 367 active and reactive power of non-controllable loads (p d , q d ) 368 and the committed active power of aggregators (p a,t=t * ) as 369 well as power flows from the upstream grid (p x , q x ). Further, 370 the reactive power of aggregators is considered assuming 371 a fixed power factor (φ a ). The KVL equations in [32] are 372 used to calculate the active and the reactive power injections 373 (f for each branch at the start and end 374 bus (represented by 1 and 2, respectively). The voltage and 375 thermal constraints (applied at the start and the end of each 376 network branch l) are given in (10) and (11), respectively. bility of the residential customer to provide generation offer.

413
The quantity of the generation offer ( G offer h,i g ) per residential 414 customer is calculated in (12) as the difference between the 415 initial residential power at t = t * (p h,t=t * ) and the new 416 adjusted power (p h,i g ,t=t * ) that is obtained from the HEMS 417 at a generation offer's price. Since HEMS might be triggered multiple times in the day 436 (in response to the DSO requests to solve network issues), it is 437 important to preserve power consumption before the current 438 time step (t * ), as formulated in (15).
The delivery of generation offers at t = t * may increase 441 demand in the subsequent time steps (t > t * ) to satisfy cus-442 tomers' energy needs. However, this may increase electricity 443 payments particularly when power consumption is moved to 444 time intervals with higher energy prices. For this purpose, the 445 constraint in (16)  The daily electricity payment consists of three parts. The 454 first part is related to the cost of electricity up to the current 455 time step (Cost t<t * h ). Its value is calculated according to the 456 previous power consumptions (p h,t ) and the energy market 457 prices (π M t ) as well as the revenues received from previous 458 applied incentives, as given in (17).
where t is the time step (in hour), G * h,t and π g * h,t are the 462 quantities and prices of previously accepted generation offers, 463 respectively. In contrast, D * h,t and π d * h,t are the quantities and 464 the prices of previously accepted demand offers, respectively. 465 The second and third part of electricity payment are the cost 466 at the current time step (Cost t=t * h,i g ) and the cost in the next time 467 steps (Cost t>t * h,i g ), as given in (18)  The HEMS at each residential customer is also run for dif- where p M h,t is power consumption responding to energy prices.

505
The objectives of HEMS to provide generation and demand 506 offers in (14) and (21) where η ch and η dis are the charging and discharging efficien-531 cies, respectively.

532
The HEMS also manages the charging actions of EV to 533 achieve the required energy level E ev,h between the arrival 534 and the departure time step The proposed TES framework is applied to a UK urban 11kV 547 feeder with 2700 residential customers. The single-line repre-548 sentation of the network is given in Fig. 2 [34]. The residential 549 load profiles are produced using the tool developed by the 550 Centre for Renewable Energy Systems Technology (CREST) 551 considering half-hourly resolution [35]. It is considered that 552 each customer has a 14kWh battery with round trip efficiency 553 of 90% and power rating of 3.6kW [36]. Further, it is assumed 554 that 50% of the residential customers have EVs. The charg-555 ing profiles of EVs are produced according to the statistics 556 provided in [7]. This includes the users' driven distances, 557 arrival times and departure times. For demonstration pur-558 poses, a price signal from the UK electricity market is adopted 559 from [37] and provided in Fig. 3. It is also assumed the exis-560 tence of a single aggregator per distribution transformer to 561 facilitate the interactions between the downstream residential 562 customers and the TES. The modeling language AIMMS 563 [38] is used to formulate the HEMS and the decision-making 564 algorithm at the TES. The HEMS is formulated as a Mixed 565 Integer Linear Programming (MILP) optimization problem 566 and it is solved using the CPLEX solver [39]. In contrast, the 567 CONOPT solver [40] is utilized to determine the decision-   revenues for residential customers by injecting power back to 609 the grid. This can be clearly seen in the aggregate profiles of 610 batteries presented in Fig. 4.    incentive. However, this depends on the constraints of con-686 trollable appliances.

687
The DSO collects generation offers from the aggregators.

688
The submitted offers depend on the number of residential are not enough to compensate the adverse impacts on the 696 customers' energy bills. Also, the amount of generation offers 697 increases with the adoption of higher incentives. The max-698 imum generation offer that could be achieved is 18 MW. 699 However, the marginal increase in generation offers becomes 700 smaller after an incentive of 125£/MW. This staircase curve 701 demonstrates the importance of defining the proper value of 702 incentive to trigger the required amount of generation offers 703 from aggregators. For instance, it is not possible to increase 704 the total amount of generation offers when the applied incen-705 tive is above 25£/MW and smaller than 50£/MW.

706
To determine the accepted offers and incentives, the DSO 707 runs the proposed TES algorithm. At 4:00 a.m., it is possible 708 to decide the proper amount of incentive graphically. It can 709 be seen that the cross between the excess loading of 2.9MW 710 and the generation offers' curve is going to be the incentive 711 required to solve congestions. Therefore, an incentive value 712 of 25£/MW is the minimum one to maintain power flows 713 at the head of the feeder below its limit. By using the OPF, 714 it is found that the total amount of accepted offers is 3.7MW 715 which makes about 59% of the available generation offers 716 (6.3MW). This shows the effectiveness of the OPF to identify 717 the successful offers to manage network constraints whilst 718 minimizing the incentives paid by the DSO to the aggregators. 719 The above process is repeated at each time step with 720 overloads due to excess demand (4:30 a.m.-7:00 a.m.). 721 Fig. 8 presents a summary of the total generation offers. 722 The accepted offers and the resulting incentives are given 723 in Table 2. It can be noticed that the maximum amount of 724 generation offers (19.4MW) is almost the same throughout 725 the time steps (see Fig. 8). However, the incentive to release 726 this maximum gradually increases from a time step to the 727 next one. For instance, an incentive of 25£/MW is able to 728 trigger generation offer at 4:00 a.m. compared to 100£/MW 729    Table 2 ). Since the accepted offers are selected from dis-

753
For illustration purposes, Fig, 10 (a) presents the profile 754 of an aggregator with 300 customers with only respond-755 ing to the energy market prices. This aggregator maximizes 756 energy exports back to the grid to maximize its revenues 757 from the sold energy to the system operator at high prices 758 of 240£/MWh. The maximum export reaches 0.94MW. With 759 an incentive of 100£/MW applied at 4:30 p.m. (blue line), the 760 aggregator is encouraged to reduce export to deliver demand 761 offer. This is done by rescheduling the control actions of 762 batteries from the last schedule (black line). It can be seen in 763 Fig. 10 (b) that batteries go into idling mode at 4:30 p.m. with 764 zero output power (i.e., discharging is stopped). This enables 765 the provision of demand offer of 1.1MW. To compensate 766 revenues' losses, the volume of discharged power is increased 767 in the subsequent time steps. To cope with any network issues 768 resulting from rescheduling, the TES algorithm continues 769 monitoring network' operating conditions and defines the 770 proper amount of incentives. The results are summarized in 771 Fig. 11 and Table 3. Different from generation offers, there 772 are variations in the energy market prices when demand offers 773 are requested. This in turn affects the response of aggregators 774 VOLUME 10, 2022 to the adopted incentives. In particular, the allocated incen-  [24], [25] to mitigate the impacts on distribution networks 806 is adopted. The approach considers managing the response 807 of residential demand to the market prices below predefined 808 export and import power limits. The approach is applied to 809 the UK urban 11kV feeder in Fig. 2 with 2700 residential cus- For demonstration purposes, Fig.13 shows the daily energy 814 cost of an aggregator with 300 customers (each customer 815 with EV and battery) for different power limits starting from 816 0.5 kW to 4.5 kW per residential customer (in steps of 817 0.5 kW). From the aggregators' perspectives, the adoption of 818 a large value of power limit allows customers to almost freely 819 exchange power from/to the distribution network to minimize 820 their energy bills. The figure shows a significant reduction 821 in the daily energy cost with large values of power limits. 822 In particular, the energy cost at a power limit of 4.5 kW is 823 75% smaller than the one obtained at a conservative limit 824 of 0.5 kW. However, the adoption of a large power limit 825 results in network issues (shaded area in red). The results 826 show that the selection of a power limit larger than 1.5 kW 827 is not feasible from the perspective of distribution networks. 828 Thus, deciding the most-adequate value of power limit to 829 manage network constraints effectively (i.e., below 1.5 kW 830 per residential customer) is at the expense of minimizing 831 energy cost. In contrast, the TES-based framework provides 832 better performance for both the customers and the distribution 833 networks. The TES-framework allows customers to minimize 834 their bills whilst managing network constraints effectively. 835 In particular, it is found that the energy cost with TES equals 836 the minimum possible energy cost that could be achieved by 837 using large power limit (4.5 kW per residential customer). 838 Also, the power flows of lines and transformers as well as 839 network voltages by using TES are all managed effectively 840 (see Fig. 12).

842
For the benefits of the readers, the key remarks resulting 843 from the application of the proposed TES framework are 844 summarized as follows: system. By controlling residential demand to minimize elec-906 tricity payments, the natural diversity of customers' net-907 demand is affected. In particular, the results show that most of 908 customers' power consumption is moved towards the lowest-909 price time intervals whilst increasing energy export at the 910 highest-price to maximize revenues from selling energy. For 911 the studied feeder, the resulting significant import and reverse 912 power flows cause congestions.

913
Further, it is found that the TES-based framework enables 914 managing effectively network constraints by procuring gen-915 eration and demand offers. From customers' perspective, the 916 allocated incentives maintain desired electricity payments 917 and compensate adverse financial impacts due to reschedul-918 ing. The results also demonstrate that the allocated incentives 919 are influenced by energy prices. In particular, larger amounts 920 of incentives are required at the highest-price to trigger flex-921 ibility to deliver demand offers. The results also demonstrate 922 that customers' flexibility is progressively reduced through-923 out the day. This in turn leads to higher amounts of incentives. 924 It is important to highlight that the implementation of the 925 TES-framework in practice requires addressing information-926 related challenges such as communication issues (e.g., syn-927 chronization), measurement errors and privacy of customers 928 as well as customers' commitment to the accepted offers.