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Receding‐horizon OPF for real‐time management of distribution networks

2018; Institution of Engineering and Technology; Volume: 12; Issue: 9 Linguagem: Inglês

10.1049/iet-gtd.2016.1939

1751-8695

James Robertson, Gareth Harrison, Robin Wallace,

Microgrid Control and Optimization

IET Generation, Transmission & DistributionVolume 12, Issue 9 p. 2124-2131 Research ArticleOpen Access Receding-horizon OPF for real-time management of distribution networks James Robertson, Corresponding Author James Robertson j.robertson@ed.ac.uk School of Engineering, University of Edinburgh, King's Buildings, Edinburgh, UKSearch for more papers by this authorGareth Harrison, Gareth Harrison School of Engineering, University of Edinburgh, King's Buildings, Edinburgh, UKSearch for more papers by this authorRobin Wallace, Robin Wallace School of Engineering, University of Edinburgh, King's Buildings, Edinburgh, UKSearch for more papers by this author James Robertson, Corresponding Author James Robertson j.robertson@ed.ac.uk School of Engineering, University of Edinburgh, King's Buildings, Edinburgh, UKSearch for more papers by this authorGareth Harrison, Gareth Harrison School of Engineering, University of Edinburgh, King's Buildings, Edinburgh, UKSearch for more papers by this authorRobin Wallace, Robin Wallace School of Engineering, University of Edinburgh, King's Buildings, Edinburgh, UKSearch for more papers by this author First published: 14 March 2018 https://doi.org/10.1049/iet-gtd.2016.1939AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study presents a new formulation for real-time active network management (ANM) control of distribution networks to maximise energy yield from distributed generation (DG). Coordinated scheduling of renewable DG and distribution network control assets can limit DG curtailment and significantly increase energy yield and economic performance of DG in weak or congested networks. Optimal power flow (OPF) has been employed in the literature for this purpose. However, single time frame snapshot formulations are limited by their narrow interpretation of temporal constraints. Here a formulation is presented for a new receding-horizon OPF technique to better control real-time ANM in distribution networks with high levels of temporally and spatially variable renewable DG. It is shown to improve the coordination between time sequences of system dispatch and improve voltage performance. Nomenclature Indices and sets g distributed generator index b bus index l line and transformer index x grid supply point index k current time index j control cycle index Decision variables CVC voltage target DG real power curtailment ϕg (j) DG power factor angle State variables voltage magnitude δb (j) voltage angle active and reactive power flows (p, q)x (j) GSP active/reactive power exchange Parameters pg DG real power capacity peak real and reactive power demands ωg (j) generation normalised resource level η (j) demand normalised loading level upper/lower voltage bounds upper/lower on load tap charging (OLTC) voltage bounds sl thermal rating of lines and transformers GSP exchange limit t0 control cycle timing reference δt measurement delay time Δt implementation delay time 1 Introduction Distribution networks are undergoing an unprecedented period of change. Increasing levels of renewable distributed generation (DG) [1], evolution to a distribution system operator (DSO) [2], as well as new technologies, such as electric vehicles [3], are increasing operational complexity and creating planning challenges. Active network management (ANM) [4] is expected to be deployed to handle future operation. Several projects have pursued ANM and flexible connection contracts in order to access 'spare' distribution network capacity. These have involved use of DG curtailment, thermal constraint management [5], voltage control [6–8], dynamic line ratings [9] and demand side management [10]. Each scheme takes on either a 'decentralised' or a 'centralised' form. The control actions or dispatch of decentralised schemes is determined based on local measurements and intelligence. Centralised ANM typically see the DNO using data measurement (or state estimation) to determine the network power flow conditions in real-time across a wider network area, and defining set-points for network and third-party assets (including DG) to maintain safe operation. In line with the unbundled regulatory environment, the dispatch is 'technical' rather than 'economic' in nature. Embedding localised control practices in distribution networks with bi-directional power flows has the potential to create operational conflict between new control practices, as well as established means. For example, simultaneous switching of voltage regulators (VRs) can lead to over-correction, or step voltage violations. Non-simultaneous switching may incur a coarse form of hunting between control actuators. To avoid this, authors in [11] propose a hierarchal approach for voltage control, using a decentralised scheme with temporal grading to prioritise local DG control practices over OLTCs. Authors in [12] present a centralised logic-based priority scheme for voltage control between DGs based on sensitivity and electrical distance. The first generation of ANM controllers determined control set-points based on the assumption that measured power flow conditions will persist to the next control cycle. 'Persistence forecasting' can be susceptible to short-lived fluctuations in network conditions and fails to take into account how new control actions will impact the power flow regime in the next control cycle. Receding-horizon (RH) approaches offer a potential solution and have been used in optimisation strategies in real-time control environments [13]. The RH approach determines a rolling sequence of system set-points over an upcoming time period (control horizon), which are re-evaluated at defined intervening stages (control cycles) using updated system and forecast data. As such, they are better able to handle active control strategies, determining set-points that meet instantaneous and evolving system needs. RH control has therefore been applied in power systems applications. Authors in [14] propose a multi-agent RH control framework for local area voltage control in a transmission network in response to emerging voltage instability events; at each control cycle agents update and improve their response via neighbour-to-neighbour communication. Authors in [15] use a multi-period optimal power flow (OPF) with an RH to schedule voltage controllers and restore non-viable or unstable transmission voltages to a 'target-state'. Authors in [16] use RH to prevent violation of ramp rate constraints between discrete runs of a multi-period, finite-horizon economic dispatch of generation. Authors in [17] use a rolling multi-period optimisation to manage voltages and overloading by scheduling electric vehicle charging in (radial) low voltage (LV) networks. The results of RH algorithms depend on, and are sensitive to, the formation of the system forecasts. Authors in [16, 17] utilise random number generators to disturb the time-series of power demands but assume a perfect forecast over the initial control interval. Authors in [18] developed a risk-based ANM approach to cater for wind power uncertainty: the risk level was based on output variance as determined from statistical analysis of historical data. This was used to inform the decision making in an optimisation-based network management system and was shown to reduce the frequency and severity of network thermal and voltage violations. Authors in [19] used deterministic and stochastic RH controllers to dispatch energy storage in LV networks; the formulation involves demand forecasts generated by a scenario tree derived from a priori demand knowledge. Authors in [20, 21] use an OPF and a two-stage relaxation process to optimise hourly day-ahead economic dispatch of a radial distribution system with renewables and energy storage; authors in [21] demonstrate this on a real-time digital simulator. Authors in [22] use an RH OPF for day-ahead hourly scheduling of energy storage with forecast variable generation; it uses a separate power systems estimator to 'close' the control loop at an hourly operational time step. The authors' earlier work [23] employed 5-min time-sequential OPF to actively dispatch a distribution network. This employed a pseudo 'real-time' network simulator [24] which mimics the rolling operation of a real system on a short-time step (5 s). The separation of dispatch decisions and their implementation allowed a more realistic view of performance as the operation of individual controls is explicitly captured (e.g. transformer tap delay, voltage deadbands). The approach reduced the frequency and magnitude of voltage and thermal violations whilst minimising DG curtailment. However, the use of fast cycles of measurement and dispatch, and limitations with the use of persistence forecasting for near-term estimation of generation and demand suggested alternative approaches may provide value. With this in mind, and building on an early outline of the idea [25], this paper substantially extends [23] to provide a new framework for RH control for centralised and coordinated ANM. The approach uses a rolling cycle of 30-min generation and demand forecasts to produce a series of dynamic horizon forecasts from which network control set points are determined; these are simulated at a high time resolution in pseudo real-time. Furthermore, it incorporates a new time-indexed constraint within the OPF to minimise unnecessary changes in reactive power controls; this desensitises the system to large step changes in voltages. The application to multiple network constraints, data-streams and control time-frames, implemented on a coupled dispatch and real-time simulation architecture, makes the work unique in the literature. This paper is structured as follows: Section 3 summarises the simulation environment and presents the formulation of the real-time RH OPF (RHOPF), detailing the forecasting application. Section 4 evaluates the RHOPF technique on a generic model of the UK medium-voltage distribution network. Sections 5 and 6 discuss and draw conclusions. 2 Problem formulation 2.1 Framework for real-time simulation A framework performing time-sequential power flow analysis simulating 'real-time' network operation across successive steady-state intervals was presented in [23, 24]. The framework, shown in Fig. 1a, has two interfaced elements: (i) a distribution management system (DMS) within which a range of network management approaches can be articulated and (ii) a distribution network simulator (DNS) that translates commands within specific infrastructure in the 'proxy' distribution network. A dedicated distribution dispatch system forms part of the distribution management system and is capable of hosting bespoke dispatch algorithms such as OPF or other formulations. Fig. 1Open in figure viewerPowerPoint Simulation framework (a) Simulation architecture, (b) Receding-horizon application and control interval, (c) Control interval and DG control practice This system provides the opportunity to programme and interpret new formulations for active management without acting directly on the control settings in the power flow. In addition, it allows the active regulation of individual DG and network asset controllers to be modelled explicitly in the power flow solution so that the control interactions and network response under ANM strategies can be observed. Variable power flow conditions are modelled by time series profiles of generation and demand. The time-series input data are fed exclusively to the power flow solutions of the 'proxy' distribution network. Sampling of 'real-time' load and generation values, as well as prevailing network conditions, is carried out by the distribution management system and input into the dispatch system. This mimics operation of a realistic system. Here, the approach has been updated to facilitate the input and management of forecast data in the new RH formulation. The OPF is formulated in the AIMMS optimisation modelling environment using the CONOPT 3.14A non-linear solver. Plug-and-play of the OPF into the software environment via the COM interface allows the OPF to be implemented online. OpenDSS is the power flow engine used to simulate the 'proxy' distribution network. 2.2 Receding-horizon formulation The control scheme works as a time sequential feedback loop. For each time step, the control scheme will: measure the prevailing network conditions and gather 'forecast' data; using a multi-period AC OPF determine a sequence of upcoming control set-points to manage voltage and thermal constraints within system boundaries; pass these new system control set-points to be implemented for the first control cycle. The RH application is the continual automation of this process, as illustrated in Fig. 1b. In this manner, the control horizon is continually receding and the network set-points are actively tracking optimal network configuration. The methodology is applicable to a timescale best chosen to suit the unique circumstances of its application. The 'proxy' distribution network is simulated using steady-state power flow at 5-s time intervals, sufficient to show the network response to the implementation of new network control settings. The RH formulation operates on two distinct time intervals of network management, in the form of a control horizon, and control cycles. Here, the time horizon is 30-min within which there are a series of six sequential, 5-min control cycles, as shown in Fig. 1b. Further information on the cycles is presented below. 2.2.1 Control cycle Within each control cycle a sequence of events simulates the real-time operation and network actions. These are illustrated in Fig. 1c with the timing of actions expressed relative to the availability of new set-points from the dispatch algorithm, t0. Communication, analysis and implementation time delays are illustrative but representative of real settings. The sequence of events is as follows: 'Measurement', time t0 – δt : Measurements include the network state, prevailing resource availability and demand level. The delay, δt, is assumed to be 90-s. 'Dispatch', time t0 : Measurements are input to the DDS which produces new network and DG operating set-points for each of six consecutive 5-min control cycles. Execution time is short compared to operational timescales. 'Instruction', time t0 + Δt : The set-points are passed by the DMS to the 'proxy' network for implementation. The communications delay, Δt, is assumed to be 30-s. The DDS prescribes individual target set-points for local control assets; these then invoke changes in local infrastructure as opposed to enacting direct control of local controllers. 'Completion', time, t0 + 2Δt : Once the transition from the existing state is initiated, the control actions of each network component vary according to their own control practices. All actions are complete by this time. For DG active power output, the ramp to newly prescribed control setting occurs linearly across the interval Δt. Changes to DG reactive power dispatch occurs in tandem with the active power dispatch. Should the voltage set-point require it, tap-changing transformers (OLTCs) follow standard operating practice with a (typical) 30-s delay prior to the tapping action. 2.2.2 Control horizon Each control horizon is a multi-period sequence of control cycles. In each instance, the operating set-points for each control cycle are determined by an RH 'forecast', which is created by linear interpolation between two sets of data: (i) 'real-time' network measurement as per the periodic control cycle and (ii) forecast data. For the purpose of illustrating the RH approach an (imperfect) 'forecast' is synthesised. This uses a central moving average smoothing process using a 15-min interval of the real-time data for each generation resource and demand levels. A sample of the 'forecast' and the data on which it is based is illustrated for wind in Fig. 2. Fig. 2Open in figure viewerPowerPoint Illustration of wind power forecast data The RH forecast, that is the projected temporal variation for each DG resource and demand in each successive control horizon, is a linear interpolation from the measured prevailing resource level to the forward 15- and 30-min forecast level. This process moves on with every 5-min control cycle as illustrated in Fig. 3. Therefore, in each successive control horizon the point forecast value for the first control cycle, from which new network control set-points will be actioned, is close to the persistence value but transitioning towards the expected future conditions. Fig. 3Open in figure viewerPowerPoint Illustration of the RH forecasting for wind 2.3 Distribution dispatch: RH OPF formulation The dispatch of the network and DG set-points is carried out by a bespoke Receding Horizon OPF formulation. This is based on an earlier AC OPF [23] that has been substantially altered to handle multiple consecutive time frames and time-dependent control limits. It is designed to operate on a rolling basis, using a combination of data on generation output and demand loading levels 'sampled' from the network, and suitably generated forecast data. In the RH approach, the time series of network power flows are evaluated consecutively over a control horizon composed of j discrete control cycles leading from the current time k. The algorithm returns projected solutions for each control cycle, subject to initial network conditions k (k + j|k). Warm start conditions across the horizon for each successive RHOPF solution are inferred from the last converged solution. As DNOs do not currently perform economic dispatch of DG within their networks, dispatch is purely technical. The objective function therefore maximises the DG energy yield over time by minimising the curtailment of DG active power over each horizon control cycle: (1) where pgcurt is the active power curtailment of DG g (set G). The objective is subject to the range of normal power flow constraints, further enhancements of ANM control variables and special temporal network dispatch conditions to reduce network 'nuisance' switching. The standard equations of network power flow include: the active and reactive nodal power balance (2) and (3); voltage (4) and thermal loading constraints (5) and (6). For brevity, the control horizon index (k + j|k) has been reduced to (j) (2) (3) (4) (5) (6) Here pg is installed DG capacity; db(P,Q) denotes peak active and reactive demand at bus b (set B), (p, q)x are grid supply point (GSP) flows, (p, q)l1,2 are the active and reactive power injections at the ends of each branch (denoted 1 and 2); and ϕg is the DG power factor angle. Across each control horizon, ωg (j) and η (j) denote the per-unit resource and demand level, relative to installed capacity and peak load, respectively. The complex power injections at the ends of each branch are determined in terms of voltage magnitudes Vb (j) and angles δb (j) by the standard Kirchhoff's voltage law formula. In the case of transformers, the primary voltage (Vi) must be divided by the transformer tap ratio, τl. For active management of the OLTCS and VRs the tap ratio is constrained within the limits of each transformer: (7) As small short-term overloading of network assets was considered acceptable, power flow thresholds were set at rated capacity. However, a more conservative voltage envelope of ±5.5% nominal, rather than the regulatory ±6% was considered in the DMS formulation. This narrower range was employed to reduce the impact of real-time residual voltage variation within the proxy network due to, for example the effect of discrete bandwidth on transformer taps. ANM assumes that DNOs are capable of controlling existing network assets, such as tap changing transformers, and centrally dispatching DG active and reactive power output. Three control techniques are included in the OPF scheme: curtailment (8); variable power factor control (PFC) (9) and (10) and coordinated voltage control (CVC) (11) (8) (9) (10) (11) Power curtailment is modelled as a simple reduction of production. The set-point issued to DGs is a per-unit reduction of the maximum resource-dependent power output and is therefore proportional to the forecasted resource levels, not DG capacity. This has the disadvantage of making it slightly more susceptible to forecast errors. All DG is assumed capable of providing variable PFC by actively adjusting the DG power factor angle to absorb or inject reactive power as necessary. To reduce the potential circulation of reactive power, generation and absorption of reactive power by the DG was restricted to 0.98 leading and lagging. This was adopted to reflect the pre-existing ratio of local loading patterns. Due to the complex and differentiated relationship between independent control variables, additional governance is required to avoid unnecessary systematic switching: an additional constraint (9) limits the shifting of power factor control between control cycles. PFC can still be utilised to its full extent but requires a prior commitment. This constraint reduces instantaneous voltage spikes caused by the time differences between actions of each control element. CVC allows dynamic control of regulated voltage levels of tap-changing transformers; in the optimisation it is modelled by relaxing the limits of the voltage at transformer regulated buses (11). 3 Case study The case study demonstrates the operation and effectiveness of the RH formulation in the UK Generic Distribution System EHV1 [26] network, shown in Fig. 4a. The system is a section of weakly meshed network of parallel feeders supplied by two 30-MVA 132/33-kV transformers. A subsea cable between buses 318 and 304 connects the 'mainland' to an 'island' section. Voltage levels in the network are maintained by the substation OLTC, a VR between buses 304 and 321 and OLTCs at the 33/11-kV distribution transformers. The network also contains a 15-MVA rated interconnector, which is treated as a PV bus with a target voltage of 1 p.u. Fig. 4Open in figure viewerPowerPoint Case study (a) UK GDS EHV1 network [27], (b) 24-h renewable energy resource generation and demand profiles (p.u. of nominal capacity and peak demand) Six DG locations and two renewable energy technologies were considered. Three wind farm developments at buses 1105, 1106, and 1108 and three tidal generation sites are connected at buses 1113, 1114, and 1115. The maximum headroom for DG at these locations was evaluated for two connection strategies in [27], as Table 1 shows. Under a 'fit-and-forget' philosophy, maximum DG capacity was limited to 20.5 MW, 55% of total system peak demand (38.2 MW); the binding constraint was voltage rise. With adoption of the ANM control strategies DG capacity increased to 52 MW; sections of the network consequently experience widespread reverse power flows and the active constraint on further DG capacity is a combination of voltage rise and the thermal limits on the 33/11-kV transformers, depending on the supply and demand conditions. Table 1. DG Installed Capacities Location Resource 'fit-and-forget' ANM Capacity, MW Capacity, MW 1105 wind 2.5 10 1106 wind 10 15 1108 wind 3 5 1113 tidal — 2 1114 tidal 5 10 1115 tidal — 10 total 20.5 52 High-resolution simulations were run for a 24-h period. Fig. 4b shows the demand pattern and generation profiles for wind and tidal generation. These are based on 1-s data from individual devices that have been aggregated and smoothed to reflect the pattern from medium sized farms. While the sequences of wind and tidal data are not concurrent their independence makes their use of value. The generation time series has been synchronised into 30-s intervals while the demand pattern was taken at 30-min intervals. The data was synchronised to run concurrently and linearly interpolated between data points to very high-resolution time steps in OpenDSS for use in the power flow simulations. To examine the value of the RH formulation, the analysis is compared with the 'fit-and-forget' connection capacity, unconstrained operation and dispatch using a sequential OPF operating at 5-min intervals using a persistence forecasting routine, as in [23]. The latter two and the RHOPF employ the full 52 MW installed DG capacity. Reflecting standard UK practice the voltage levels in the 'proxy' distribution network results were assessed against the ±6% statutory limits, not the ±5.5% levels of the optimisation algorithms. In keeping with earlier work, a number of key metrics measure quality and effectiveness of the real-time controller: (i) volume of curtailment; (ii) total voltage excursion measured as instantaneous peak and 10-min averages to assess compliance with EN 50160 [28] (which permits short-term overvoltages <5% of time); (iii) exceedance of branch flow limits measured as instantaneous peak relative to rated capacity and as percentage total instantaneous overload over the 24-hour test case; (iv) frequency of OLTC taps; and (v) the reactive power demand at the GSP (the transmission interface) which may indicate challenges for the transmission system to deliver this [29]. A summary of the simulation results is given in Table 2. Table 2. Full EHV1 results summary 'fit-and- Unconst rained Snapshot OPF RHOPF forget' DG capacity, MW 20.5 52 52 52 DG production, MWh 265.56 620.79 585.56 578.79 DG net reactive output, MVArh 53.92 126.06 −24.75 −5.83 DG energy curtailed, MWh 0.00 0.00 34.72 41.39 DG energy curtailed, % 0.0% 0.0% 5.6% 6.7% DG capacity factor 54.0% 49.7% 46.9% 46.4% GSP, MWh −334.99 −25.59 −0.86 5.59 GSP, MVArh −182.93 −116.96 −210.83 −176.54 GSP power factor 0.878 0.214 0.004 −0.032 network losses, MWh 14.3 29.2 24.4 20.0 Network charge, MVArh 22.1 52.7 47.9 41.5 minimum voltage 0.9760 0.9751 0.9547 0.9535 maximum voltage 1.0532 1.2445 1.0929 1.0809 undervoltage excursiona 0.00% 0.00% 0.00% 0.00% overvoltage excursiona 0.00% 51.39% 5.56% 3.47% max. thermal loading, % 75.14% 171.03% 130.96% 127.68% total overloading 0.0% 22.7% 10.1% 13.5% total tap changes 291 810 676 812 a Measured in 10-min averages. (i) Energy yield : Energy yield increases with the connected capacity and in comparison to the fit-and-forget case, energy yield in the ANM schemes was increased by 121 and 118% in the snapshot OPF and RHOPF, respectively. Relative to the unconstrained case, both OPF and RHOPF mandate modest curtailment of available active power of 5.6 and 6.7%. (ii) Voltage compliance : By definition, the fit-and-forget case experiences no voltage excursions but the unconstrained case sees frequent and extreme episodes. Both the snapshot and RHOPF ANM schemes vastly improved the voltage levels, bringing them predominantly within statutory and regulatory limits. Observations of the voltage control measures indicated that the OPF and RHOPF formulations achieved voltage regulation via differing control means. In the snapshot OPF formulation, the optimisation favours voltage compliance primarily through the switching of the OLTC and VR tap-changing transformers, enforcing 'global' control strategies. In the RHOPF formulation, more localised control measures are deployed, with a preference for DG power-factor control and coordinated switching of local tap-changing transformers. The differing preferences in the optimisation formulations have implications for the observed voltage compliance. The snapshot OPF formulation had a maximum instantaneous peak voltage level of 1.0929 p.u. and a total 10-min average overvoltage excursion of 5.56%. The instantaneous peak is likely to cause tripping of overvoltage protection relays and the total overvoltage excursion does not comply with the 5% EN50160 limit. With the RHOPF formulation, the total overvoltage excursion was 3.47%, well below the EN50160 limit. Although lower than for the snapshot OPF, the maximum observed voltage level may still be problematic if sustained. Sustained voltage excursion was almost exclusively concentrated on the primary winding of the 326–1115 transformer. Here the accumulation of residual overvoltage variation at high output from all island-connected DGs increases the voltage supply above statutory limits on the unregulated primary winding. This residual variation is dampened to the extent that voltage levels on the upstream VR transformer are within operational bandwidth resulting in no upstream voltage correction. Analysing the network on a complex moving time-frame in the RHOPF case facilitated greater visibility of the fluctuating power flows caused by the renewable DG and significantly improves on the real-time performance of deterministic OPF snapshot solutions. Two examples of improved voltage compliance with the RHOPF case are illustrated in Figs. 5–7. Fig. 5Open in figure viewerPowerPoint Time-series trace of real-time tidal power forecast in the snapshot OPF and RHOPF Fig. 6Open in figure viewerPowerPoint Time-series traces of (top) tidal generator 1115 active power set-point and (bottom) bus 326 voltage profile Fig. 7Open in figure viewerPowerPoint Time-ser