Cesena, Eduardo A. Martinez

Churkin, Andrey

Mancarella, Pierluigi

English

A widespread approach to characterise the aggregated flexibility of active distribution networks (ADNs) is to estimate the boundary of the feasible network operating areas using convex polygons in the P-Q space. However, such approximations can be inaccurate under realistic conditions where, for example, the nonlinear nature of the network is captured, and the behaviour of flexible units is constrained. This letter demonstrates, using a small ADN example with four flexible units and considering only nonlinearities from the network, that reaching the full P-Q flexibility areas would require perfect coordination of units and high ramping rates. Without these requirements, the P-Q areas become nonconvex. Thus, if the effects of nonlinearities and nonconvexities are ignored, existing approaches in the literature can result in overestimation of ADN flexibility and give rise to impractical solutions, hampering coordination between transmission and distribution system operators

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The University of Manchester ResearchAssessing Active Distribution Network Flexibility: On theEffects of Nonlinearities and NonconvexitiesLink to publication record in Manchester Research ExplorerCitation for published version (APA):Churkin, A., Mancarella, P., & Cesena, E. A. M. (2022). Assessing Active Distribution Network Flexibility: On theEffects of Nonlinearities and Nonconvexities.Citing this paperPlease note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscriptor Proof version this may differ from the final Published version. If citing, it is advised that you check and use thepublisher's definitive version.General rightsCopyright and moral rights for the publications made accessible in the Research Explorer are retained by theauthors and/or other copyright owners and it is a condition of accessing publications that users recognise andabide by the legal requirements associated with these rights.Takedown policyIf you believe that this document breaches copyright please refer to the University of Manchester’s TakedownProcedures [http://man.ac.uk/04Y6Bo] or contact uml.scholarlycommunications@manchester.ac.uk providingrelevant details, so we can investigate your claim.Download date:09. Jun. 2023IEEE PES LETTERS 1Assessing Active Distribution Network Flexibility:On the Effects of Nonlinearities and NonconvexitiesAndrey Churkin, Pierluigi Mancarella, Senior Member, IEEE, and Eduardo A. Martı́nez Ceseña, Member, IEEEAbstract—A widespread approach to characterise the aggre-gated flexibility of active distribution networks (ADNs) is toestimate the boundary of the feasible network operating areasusing convex polygons in the P-Q space. However, such approx-imations can be inaccurate under realistic conditions where,for example, the nonlinear nature of the network is captured,and the behaviour of flexible units is constrained. This letterdemonstrates, using a small ADN example with four flexibleunits and considering only nonlinearities from the network, thatreaching the full P-Q flexibility areas would require perfectcoordination of units and high ramping rates. Without theserequirements, the P-Q areas become nonconvex. Thus, if theeffects of nonlinearities and nonconvexities are ignored, existingapproaches in the literature can result in overestimation of ADNflexibility and give rise to impractical solutions, hampering coor-dination between transmission and distribution system operators.Index Terms—Active distribution network, network flexibility,distributed energy resources, flexible resources, nonlinearities,nonconvexities, TSO-DSO coordination.I. INTRODUCTIONRECENT advances in the integration of renewable anddistributed energy resources (DERs), information andcommunications technologies, and network automation haveled to the emergence of active distribution networks (ADNs).Such networks can aggregate and utilise the flexibility pro-vided by flexible units - resources with the technical ability tocontrol power exchange with the grid, e.g., controllable DERs,battery energy storage systems, prosumers, electric vehicles,etc. Recent studies, e.g., [1]–[3], have proposed characterisingthe flexibility of ADNs as a set of feasible network operatingpoints in the P-Q space. This approach enables estimating thelimits of aggregated flexible active and reactive power thatan ADN can provide. Different methods have been used inthe literature to approximate the boundary of the networkfeasibility area, including random sampling and optimal powerflow (OPF) methods [4], [5]. Such approximations are usu-ally considered as a tool for coordinating transmission anddistribution system operators (TSOs and DSOs) in flexibilityprocurement at the TSO/DSO interface.However, despite the rapidly evolving research on ADNflexibility, existing studies overlook nonlinearities and non-convexities of network flexibility models and do not considerThis work was carried out as a part of the ATTEST project (the Horizon2020 research and innovation programme, grant agreement No 864298).The authors are with the Department of Electrical and Electronic En-gineering, the University of Manchester, UK (e-mails: {andrey.churkin,p.mancarella, alex.martinezcesena}@manchester.ac.uk). P. Mancarella is alsowith the Department of Electrical and Electronic Engineering, the Universityof Melbourne, Australia. E. A. Martinez Cesena is also with the Tyndall Centrefor Climate Change Research, UK.related issues of ADN operation. This research gap arose dueto the use of flexibility estimation algorithms that approximatethe feasible network operating area in the P-Q space byconvex polygons. Some studies, e.g. [1], [3], do not questionthe correctness of this convexification. Other works, e.g. [4],deliberately use linearised and convexified OPF formulations.Moreover, the focus has been placed on estimating the bound-ary of the network feasibility area. It is usually implied, forexample in [6], that the larger this area approximated by theboundary, the more flexibility the network can provide, andthe more useful TSO-DSO coordination can be achieved. Byfocusing on the boundaries of the flexibility area, existingstudies inherently assume perfect DER coordination and activenetwork management with fast unit response. In practice, how-ever, such coordination will require incentives, informationexchange, high ramping requirements, and other factors thatmay not be in place. Therefore, existing approaches in theliterature can lead to overestimation of ADN flexibility andgive rise to impractical solutions.This letter aims to raise concerns about the nonlinearitiesand nonconvexities associated with ADN flexibility. The non-linear behavior of flexible power provision is illustrated bythe case study of a radial distribution network with four units.Only the nonlinearities of the network power flow modelare considered, while other parameters are assumed linear(individual P-Q capabilities of flexible units and their costfunctions) or omitted in the modelling (minimum stable levelof generation for units, ramping constraints, etc.). The resultsdemonstrate that flexible units perform active network man-agement to ensure the feasibility and cost-efficiency of certainoperating points. For example, some units can produce flexiblepower while others consume it. This power swap effect enablesalleviating voltage constraints to maximise the aggregatednetwork flexibility. The network feasibility set also containsareas where flexible units have to shift their power outputrapidly and precisely between close operating points. Sucheffects of nonlinearities and nonconvexities pose challenges tothe operation of ADNs and should be accurately consideredin future research on distribution network flexibility.II. SIMULATION RESULTS AND DISCUSSIONTo illustrate the nonlinearities and nonconvexities of ADNflexible power provision, a cost-minimising OPF model wasselected as a tool for network flexibility analysis. A generalisedformulation of this model is given by (1a)-(1d). The objectivefunction (1a) minimises the cost of upward and downwardregulation of flexible active and reactive power for flexiblearXiv:2209.03845v1  [eess.SY]  8 Sep 2022IEEE PES LETTERS 2MODEL Cost-minimising flexibility estimationminpl,ql,vk,p↑k,p↓k,q↑k,q↓k∑k∈KCfk (p↑k, p↓k, q↑k, q↓k) (1a)s.t.p↑k − p↓k = pk − p0k ∀k ∈ K (1b)q↑k − q↓k = qk − q0k ∀k ∈ K (1c)pk, qk ∈ F ={∆Sk : ∀k ∈ K (1d)vk ≤ vk ≤ vk ∀k ∈ Kpl2 + ql2 ≤ sl2 ∀l ∈ L}units located at each node of the system, k ∈ K. Equations(1b) and (1c) define the volume of regulations depending onthe initial flexible power output of units, p0k and q0k, and theoutput at the new operating point, pk and qk. The flexiblepower output of units is limited by the feasibility set F in (1d),where the output of each unit is bounded by its P-Q capability,∆Sk, and the network constraints are imposed depending onthe selected OPF model, e.g., power balance and voltage limitsfor each node, and power flow limits for each line l ∈ L. Inthis study, the analysis of network flexibility is based on thenonlinear DistFlow OPF formulation, which is an exact OPFmodel for radial distribution networks [7], [8].A popular case study, the IEEE 33-bus radial distributionnetwork [8], is selected to illustrate the effects of nonlinearitiesand nonconvexities. Four flexible units with identical P-Qcapabilities are placed in the network at buses 22, 25, 33, and18 (one at the end of each feeder). Parameters of the units arespecified in Table I. Note that the P-Q capability constraintsand the cost functions are assumed to be linear. Thus, theonly nonlinearities come from the network power flow model.The buses with flexible units have different voltages, whichimposes different constraints on the flexible power provisiondue to voltage limits. For example, units C and D operateat voltages close to the lower limit of 0.9 p.u. and thereforecannot increase their power consumption significantly. Model(1a)-(1d) was solved for multiple feasible operating points,both at the boundary of the feasible network operating area andwithin the boundary. Specifically, the model was solved 58,067times for the discretised operating area with a step of 16.66kVA. The results are displayed in Fig. 1, where the aggregatednetwork flexibility is shown from the perspective of flexiblepower regulation by different units. Since there are four unitsregulating P and Q components of flexible power, the figurehas a total of eight subplots. Moreover, the consumption andproduction of flexible power is differentiated using a red-blueheatmap. This visualisation enables a clear interpretation ofthe flexible unit actions at different feasible operating points.Since the operation of flexible units is limited by voltageconstraints, the units cannot achieve their maximum totalpower consumption, which is displayed as the reduced upperright part of the network flexibility area. Note that apply-ing the cost-minimising OPF model (1a)-(1d) for flexibilityanalysis results in solutions where cheaper flexible units getactivated first, subject to the network constraints. It can beobserved that units C and D (the cheaper ones) participatein the flexibility provision at operating points close to theinitial operating point. Units A and B (the more expensiveones) get activated later, at the operating points closer to thefeasibility boundary. However, the optimal operation of theflexible units exhibits highly nonlinear behavior. For example,at operating point 1©, flexible units B, C, and D consumeactive power and increase the total power consumption of thenetwork. Yet, unit D produces reactive flexible power. Thiscounterintuitive solution is justified by the fact that unit D islocated at the part of the network with a low voltage profileand cannot increase its power consumption further. Thus, unitD still produces reactive power, while unit B consumes it.This flexible power exchange (swap) enables units to alleviatethe voltage constraints and maximise the network feasibilityarea. But, perfect coordination of units is required to workat such operating points, which might not be the case inrealistic distribution networks. Without the flexible powerswap, the network feasible operating area reduces and becomesnonconvex, as shown by the dashed boundary.Another effect of the model’s nonlinearities is the rapidshifts in flexible power output of the units between closeoperating points. This can be demonstrated by comparingflexible reactive power management at operating points 2©and 3©. At point 3©, the cheapest unit D is activated toproduce reactive power. But, at the nearby point 2©, mostof the reactive power production is shifted to unit C. Thisshift is justified by the cost-minimising model that identifiesthe least-cost flexible power production, subject to networkconstraints. Other notable examples of rapid and nonlinearactive network management by flexible units are operatingpoints 4© and 5©. These points belong to the areas where unitsB, C, and D shift their active power consumption to reactivepower consumption. If adding ramp constraints or forbiddingsuch shifts, the feasible operating area will also reduce andbecome nonconvex.Ignoring these effects of nonlinearities and nonconvexitiescan lead to overestimating the aggregated network flexibilityand developing inaccurate models that are not applicable toreal case studies. As demonstrated by the simulations, feasiblenetwork operating areas can be nonlinear and nonconvex whennetwork constraints and additional limitations are imposed.Such effects can be noticed even in existing studies. Forexample, in [1], even though not discussed by the authors,the flexibility areas constrained by the maximum flexibilityTABLE IPARAMETERS OF FLEXIBLE UNITS PLACED IN THE NETWORKParameter Flexible unitA B C DBus # 22 25 33 18Initial bus voltage (p.u.) 0.991 0.970 0.917 0.913P regulation limits (kW) ±500 ±500 ±500 ±500Q regulation limits (kVAr) ±500 ±500 ±500 ±500P cost ($/kWh) 0.375 0.350 0.325 0.300Q cost ($/kVArh) 0.188 0.175 0.163 0.150IEEE PES LETTERS 31 2 3 4 5 6P,MW012345Q,MVArFlexible unit A(bus 22)Flexible unit B(bus 25)Flexible unit C(bus 33)Flexible unit D(bus 18)Flexible power of units, MW or MVAr1 2 3 4 5 6P,MW012345Q,MVAr1 2 3 4 5 6P,MW012345Q,MVAr1 2 3 4 5 6P,MW012345Q,MVAr-0.50Feasibility set without flexible power swap between the units -0.25 0 0.25 0.50Network feasibility set1 2 3 4 5 6P,MW012345Q,MVAr1 2 3 4 5 6P,MW012345Q,MVAr1 2 3 4 5 6P,MW012345Q,MVAr1 2 3 4 5 6P,MW012345Q,MVArFlexible active power management, MW:Flexible reactive power management, MVAr:(consumption) (production)Initial operating pointOperating points of interest12 34512 34512 34512 34512 34512 34512 34512 345Fig. 1. Flexible active and reactive power of the units for different flexibility requests defined by the cost-minimising OPF model, in MW and MVAr. Theconsumption and production of flexible power is differentiated using a red-blue heatmap. The areas characterise the aggregated network flexibility in the P-Qspace at the TSO/DSO interface. The cross-markers correspond to the initial operating point, while the coordinates represent the network’s power consumption.costs are nonconvex (Fig. 2 in [1]). It is important forfuture research to investigate the conditions under which theflexibility area remains convex. There is also a need to studypossible coordination issues related to the power swap betweenflexible units and the rapid nonlinear shifts in unit operation.III. CONCLUSIONThis letter raises concerns about the nonlinearities andnonconvexities associated with ADN flexibility. Estimation ofaggregated flexibility as a boundary of the feasible networkoperating area (or even approximating it by the Minkowskiaddition) overlooks the actions that units take to reach thisboundary. As demonstrated in this work, due to the nonlin-earity of the network power flow model, operation of flexibleunits exhibits highly nonlinear behavior, which requires perfectunit coordination and high ramping requirements. If theseeffects of nonlinearities and nonconvexities are ignored, ex-isting approaches in the literature can result in overestimationof ADN flexibility and give rise to impractical solutions.Future research on the flexibility of distribution networksshould accurately consider these effects when modelling andanalysing operating points both at the boundary of the networkfeasibility set and within the boundary.REFERENCES[1] J. Silva, J. Sumaili, R. J. Bessa, L. Seca, M. A. Matos, V. Miranda,M. Caujolle, B. Goncer, and M. Sebastian-Viana, “Estimating the Activeand Reactive Power Flexibility Area at the TSO-DSO Interface,” IEEETransactions on Power Systems, vol. 33, no. 5, 2018.[2] F. Capitanescu, “TSO–DSO interaction: Active distribution networkpower chart for TSO ancillary services provision,” Electr. Power Syst.Res., vol. 163, 2018.[3] S. Riaz and P. Mancarella, “Modelling and characterisation of flexibilityfrom distributed energy resources,” IEEE Transactions on Power Systems,vol. 37, no. 1, pp. 38–50, 2022.[4] M. Bolfek and T. Capuder, “An analysis of optimal power flow basedformulations regarding DSO-TSO flexibility provision,” Int. J. Electr.Power Syst., vol. 131, 2021.[5] D. A. Contreras and K. Rudion, “Computing the feasible operating regionof active distribution networks: Comparison and validation of randomsampling and optimal power flow based methods,” IET Generation,Transmission and Distribution, vol. 15, no. 10, 2021.[6] S. Stanković, L. Söder, Z. Hagemann, and C. Rehtanz, “Reactive PowerSupport Adequacy at the DSO/TSO Interface,” Electr. Power Syst. Res.,vol. 190, 2021.[7] M. E. Baran and F. F. Wu, “Optimal capacitor placement on radialdistribution systems,” IEEE Transactions on Power Delivery, vol. 4, no. 1,1989.[8] M. E. Baran and F. F. Wu, “Network reconfiguration in distributionsystems for loss reduction and load balancing,” IEEE Transactions onPower Delivery, vol. 4, no. 2, 1989.

Assessing Active Distribution Network Flexibility: On the Effects of Nonlinearities and Nonconvexities

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Assessing Active Distribution Network Flexibility: On the Effects of Nonlinearities and Nonconvexities

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