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Paper accepted for presentation at the 2011 IEEE Trondheim PowerTech 1 Coordination of Active and Reactive Distributed Resources in a Smart Grid Marco Bronzini, Member, IEEE, Sergio Bruno, Member, IEEE, and Massimo La Scala, Fellow, IEEE, and Roberto Sbrizzai Member, IEEE, Abstract—The authors present a methodology for assessing centralized control of active and reactive distributed resources in a smart distribution grid. The methodology is based on threephase optimal power flow and is able to deal properly with unbalanced conditions and both single-phase and three-phase control resources. Single-phase resources that can be exploited by means of this approach are domestic loads, photovoltaic and distributed micro-generation. The methodology is developed on an open-source simulating environment and tested on the IEEE 123-bus Radial Distribution Feeder test case. Index Terms-- Smart Grids, Optimal Power Flow, Distribution Management System, Automatic Meter Reading. D I. INTRODUCTION ESIGNING the future of transmission and distribution grids is a current issue of the power system community. According to general opinion, the modernization of power systems should move around the concept of smart or intelligent grids. Even though the debate about the definition of a smart grid is still open, some of the main principles have already been established: resiliency, flexible and self-healing infrastructures, enhanced power quality standards, high penetration of ICT technologies, integration of distributed generation and power storage, advanced metering infrastructures, availability of new power customer services [1]-[4]. The actual impact that this new fashionable concept will have on power systems can be hardly predicted, but the necessity of renovating electric power networks is indisputable. More prudently it can be asserted that, in the years to come, power systems will be characterized by an increasing penetration of ICT, sensors and computation that will allow to implement advanced monitoring and control functions [5]. In this call for modernization, distribution systems must surely face the greatest challenge. Distribution systems are traditionally passive networks, built with a straightforward radial (or multi-radial) configuration and minimal ability of monitoring and controlling power flows [3]. Differently from The present study was funded under the grant PST #44 “Smart-Grids: Advanced Technologies for utilities and energy”, received by the Regione Puglia as Strategic Project in the Framework Program Agreement on the scientific research sector in the Apulian region. M. Bronzini, S. Bruno, M. La Scala, R. Sbrizzai are with the Electrical and Electronic Department (DEE) of the Polytechnic School of Bari (Politecnico di Bari), Bari, 70125, Italy. (e-mail: [email protected], [email protected]). 978-1-4244-8417-1/11/$26.00 ©2011 transmission systems where the innovation follows an evolutionary course [6], in distribution systems the implementation of smart grid principles requires a revolutionary transition whose major driving forces are given by increasing penetration of distributed energy resources (DERs) and request for more sophisticated customer-sided energy market services. This revolution has partly begun, also thanks to the diffusion of advanced digital meters, distribution automation, building automation, low-cost cabled and wireless communication systems [1] and to the setting up of specific plans for the modernization of distribution systems. In Europe, for example, the European Commission has promulgated several directives for the development of smart grids and smart metering systems [7]-[8]. The most recent Directive 2009/72/EC encourages the modernization of distribution networks through the introduction of smart grids and intelligent metering systems, setting targets for the penetration of advanced metering systems and aiming at reaching the 80% in 2020 [8]. In Italy, the energy regulator (Autorità per l’energia elettrica ed il Gas) with the Decision ARG/elt39/10 introduced incentives for distribution companies promoting investments and research activity for smart grid pilot projects through a specific financial support plan [9]. In North America [1], major research projects are oriented in the same direction, including results of the Department of Energy (DOE) and EPRI. In this scenario, it is foreseeable that in a next future control centers, and Distribution Network Operators (DNOs) in the case of distribution systems, will be able to develop advanced functions for monitoring and control of distribution systems [10]. In particular, due to the increasing penetration of dispatchable resources, control equipments, real time monitoring architectures and two-ways communication systems, DNOs will be able to dispatch active and reactive distributed resources in order to respond to technical and economical requirements. In a distribution network, centralized control is a function that can be developed within the extended real-time operative framework of what has been defined advanced Distribution Management System (DMS) [11]. Originally, DMS was developed as an extension of Supervisory Control And Data Acquisition (SCADA), scaling SCADA methodologies and technologies from transmission system down to distribution [11]. In a smart grid, advanced DMS will be responsible for elaborating all available data (on-line or historical) and perform several management applications [11] that can be 2 performed in extended real-time for system operation (load curtailment/shedding, voltage regulation, line switching, etc.) or in the medium-long term for planning (optimal network configuration, optimal placement of capacitors, protection relay coordination, short-circuit analysis, etc.). The tools that will be adopted by DNOs in advanced DMS framework can be conceived similarly to the ones adopted for operation and control of transmission systems (topology processor, state estimator, load modelling, load flow and optimal power flow-OPF), but they must be suitably adapted to the specific characteristics of distribution systems and to the new operative requirements. For example load flow and OPF, that are traditionally the most commonly adopted tools for power system analysis, operation and planning, must be able to deal properly with radial networks, three-phase (or multi-phase) circuits and unbalanced conditions [11]-[13]. In [11], the authors present a methodology for solving a three-phase distribution OPF, that is based on the conversion of a mixed-integer non-linear programming (MINLP) problem into a non-linear programming problem. In this paper, the authors present a methodology, based on [13], for solving unbalanced Three-phase Optimal Power Flow (TOPF). The proposed methodology is based on a quasiNewton method and is implemented in an open-source simulation environment for distribution systems. In this paper, the authors propose the use of TOPF in an extended real-time framework, and explore some possible coordinated control strategies for active and reactive control of distribution grids. Test results are presented on the IEEE 123-bus Radial Distribution Feeder test case. II. ACTIVE AND REACTIVE CONTROL IN A DMS FRAMEWORK The main assumption of this paper is that in a near future DNOs will have at their disposal suitable pieces of information about main electrical parameters that can be collected and elaborated at the distribution control centre for performing on-line centralized control of the network in extended real-time framework (approximately every 15-30 minutes). Together with more conventional functions related to distribution system operation such as optimal network reconfiguration, reactive power compensation, operation under fault conditions, DNOs will be called to perform some advanced centralized control functions that might involve voltage regulation, demand side management and control, demand or generation peak shaving, distributed generation redispatch, optimization of storage charge and discharge cycles. Currently, in distribution systems, voltage regulation and reactive power compensation are usually performed by means of on-load tap changers and switching capacitors that are manually operated or can automatically adapt their settings on the basis of local measurements [12]. In an advanced DMS framework, set-points of such devices might be remotely controlled on the basis of real-time measurements and according to specific operational requirements or new control strategies. For example tap changers, that are usually adopted for boosting voltage levels up along the radial back-bone of the distribution system and guaranteeing that every node is above nominal voltage, can be controlled for performing what has been defined conservative voltage regulation (CVR) [14]. CVR working principle is far from usual voltage regulation since it aims at keeping voltage profiles close to functional bottom limits, reducing overall load demand. In order to be effective, CVR must be applied to loads that are voltage responsive and that can be modelled close to a fixed impedance (residential and tertiary areas are therefore preferred to industrial ones where motors are the bulk component of load demand). Clearly, tap changer control can be integrated by dispatch of reactive distributed resources for what is defined Volt/VAr optimization (VVO). This can be aimed to improve voltage profiles across feeders, sustain voltage, reduce losses, improving energy efficiency or achieve better performances in conservative voltage regulation. Reactive resources can be ensured by remotely controlled switching capacity [12] [14], static voltage compensators [3], but also by distributed micro-generation or any power controllable device at residential level. In [15], the authors suggest that reactive resources in the grid can be found in any location where electric machines or converters are installed, being either part of load or generations equipments (voltage control is then operated by means of a sensitivity analysis that detects nodes and devices that have highest potentials in controlling voltage globally or locally). The more straightforward idea of employing the inverters of distributed photovoltaic (PV) generators for centralized [16]-[18] voltage regulation of smart grids is also a current issue, even though some issues about control structure (control schemes for local or generalized control) and ancillary services remuneration (PV inverters participating at voltage regulation must be oversized and therefore are more expensive than the ones operating at a fixed power factor) should still be overcome. This hypothesis is not unrealistic since certain system operators (SOs) are already settings the minimal reactive regulating capacity that any installed DER must provide to the system. As an example the Grid code of the Italian TSO recently introduced specific requirements for non programmable renewable resources in order to guarantee active and reactive control [19]. In smart distribution grids active power could be a further control resource. Mostly it is foreseeable that DNOs will be able to dispatch distributed generation or manage power storage charge/discharge cycles (as with pluggable hybrid electric vehicles - PHEVs), not very differently from how a system operator would dispatch generation on transmission level [10], [15]. An alternative control architecture can be based on energy hubs that can manage multiple energy resources on the basis of market or dispatching signals provided by the utilities [20]-[21]. More original active power control strategies can be based 3 on demand side control. It is foreseeable, for example, that in the presence of violation of security limits (for a example a sudden overload on the HV/MV interface) or as a response to particular energy market signals, the DNO would be able to control certain specific loads that, in return of electricity tariff discounts, are available to load shedding or curtailment. AMR devices can be easily employed as actuators of load curtailment control actions (AMR devices already receive a signal that can limit load capacity, as done for example for insolvent customers). Cleary, all above mentioned techniques can be implemented only if an extensive set of real-time measurements is available to control centre. For example, CVR can work successfully if the voltage at each node of the network is known (or at least at those nodes that, independently from actual network configuration, are characterized by lowest voltages). At this stage of development DNOs have scarce details about the state of the network. Distribution systems might lack completely of SCADA infrastructure or have monitored only few electric quantities and switches. Nevertheless, previous assumptions are credible having considered that part of the investments necessary for developing such control architecture have already been made or scheduled. In countries like Italy or Sweden the replacement of energy meters with smart Automatic Metering Reading (AMR) devices will be close to 100% very soon. First implementations of AMR showed how basic functions of energy metering can be easily overcome, transforming AMR devices into smart terminal units and gateways for many functions and multiple services, able to guarantee a real-time bidirectional communication between customers and utilities (what is usually defined as an Advanced Metering Infrastructure – AMI). A bottleneck to the implementation of such devices in smart grid framework is the time response which is still quite far from real-time requirements. However, improvements in the communication technology and computer architectures will make these concepts implementable in the very near future. III. PROPOSED METHODOLOGY A. Three Phase Optimal Power Flow For Smart Grids Most of proposed control functions must be performed at control centre level by means of suitable analysis and decision-making tools. Optimal Power Flow, that is undoubtedly the most commonly adopted tool for operation and planning of power systems, will have for sure a part in this but, as already remarked, it must be suitably adapted to the operative requirements of smart distribution systems. In the past years, many studies have been devoted to reformulate OPF, or Distribution Optimal Power Flow (DOPF), equations in order to face the new challenges introduced by Distributed Generation (DG) in terms of voltage control, losses reduction and power flow management. Most of them, being based on multi-object or multiperiod OPF, are referred to system planning and very few studies are able do deal properly with unbalanced conditions and three-phase representation of load flow equations [12], [22]. Distribution systems are unbalanced because of unequal three-phase loads, untransposed lines, conductor bundlings [22]. Moreover, in the last few years, the spreading of singlephase DG plants (domestic solar and micro wind generators) contributes heavily to produce further imbalance, whose extent is very difficult to forecast due to randomness of intermittent energy sources. The proposed TOPF methodology is aimed at optimizing active and reactive control resources in the presence of unbalanced conditions and in the extended real-time framework. Moreover, being based on a full multi-phase representation of load flow equations, the methodology is able to treat single-phase components (i.e. load or micro-generator installed at LV levels) and unbalanced electric variables. B. Mathematical Formulation The proposed formulation for TOPF is similar to the classical single-phase OPF, with main differences limited to the representation of the steady-state grid equations. Singlephase OPF is commonly based on the use of the sole positive sequence component model, whereas TOPF can adopt both sequence and multi-phase models. In general a TOPF problem can be formulated as a min Cobj ( x ,u ) (1) u subject to f ( x ,u ) = 0 (2) g( x , u ) ≤ 0 (3) and where Cobj is the objective function, x is the n-dimension state variable vector, u is the m-dimension control variable vector, f is the set of load flow equations, g is the set of inequality constraints that keep into account thermal or capacity limits, acceptable voltage profiles, maximum injected reactive power and other functional constraints. According to the proposed approach, the function f represents load flow equations with a full multi-phase model, whereas the control variable vector u is given by active and reactive power at any device whose power reference is remotely controlled via the ICT layer of the smart grid. Different formulations are possible for the representation of load flow equations in both sequence and phase components. The proposed method is sufficiently general to consider both full multi-phase and sequence models. The OPF problem can be expressed in terms of an unconstrained minimization problem, by applying the penalty factor methods. This means that inequality constraints (3) are treated as soft inequality constraints and formulated as penalty functions, leading to the following formulation: min C ( x , u) (4) u subject to f ( x ,u ) = 0 with (5) C( x , u ) = Cobj ( x , u ) + ¦ C ip ( x , u ) i and where C is an objective function, Cpi is the ith penalty 4 function. In addition, the feasibility domain for control variables can be defined by the following hard limits: umin ≤ u ≤ umax (6) Through the Implicit Function Theorem [23], [13], whose conditions are often satisfied for a large set of practical cases, it is possible to assume that around the solution of the load flow equations ( x , u ) it exist a unique function Ȗ ( u ) = x that permits to reformulate the constrained problem (4)-(5) as an unconstrained problem: min C( Ȗ ( u ), u ) (7) u whose minimum can be obtained by imposing the conditions: dC( Ȗ ( u ), u ) F( u ) = =0. (8) du By applying the Newton method, equation (8) can be solved iteratively considering the rule u k +1 d Fk =u − du Fk (9) k dC( Ȗ ( u ), u ) =0. du k The evaluation of the second order term in (9) can be characterized by a heavy computational burden. In order to speed-up convergence and avoid time consuming calculations the proposed methodology, based on Quasi-Newton method, solves equation (8) with the approximate formula: u k +1 = u k + ȁk F k (10) Fk = k where k is the iteration number, and ȁ is an m×m matrix which can assume different structures (scalar, diagonal, full) as largely discussed in [24]. Among all structures of ȁk matrix, the simplest one is given by: ȁk = Ȝ k ⋅ I (11) where λk is a scalar suitably chosen on the basis of computational and convergence properties and I is the m×m identity matrix. Different formulations have been proposed for the evaluation of λk [24]. A suitable choice, according to the method proposed by Barzilai and Borwein [25]-[26], is given by: T Ȝk = three-phase load flow (OpenDSS) evaluate C0 (u0 ) and F 0 set initial guess Ȝ0 u1 = u 0 + Ȝ 0 ⋅ I ⋅ F 0 k= k+ 1 three-phase load flow (OpenDSS) evaluate Ck(uk) Numerical evaluation of gradient Fk for i = 1, … , m fix a small deviation İik u'ik = u ik + İ ik Fik = C' ik − C k İ ik three-phase load flow (OpenDSS) evaluate Cƍ ik(uƍ ik) evaluate Ȝ k through eqn. (12) k where k k=0 u=u0 −1 k k evaluation of first order derivatives of F is required. ΔF k −1 ⋅ Δu k −1 (12) T ΔF k −1 ⋅ ΔF k −1 where Δ denotes the forward difference operator defined usually as Δa i = a i +1 − a i . C. Solving Algorithm The solving algorithm, whose structure is presented in Fig. 1, finds a solution through eqns. (10-12). According to the Implicit Function Theorem, sensitivities Fk are obtained evaluating numerical derivatives of C on the basis of small deviations of control variables u around the solution of a three-phase Distribution Load Flow (DLF). No analytical control variables update u k +1 = u k + Ȝ k ⋅ I ⋅ F k no Δu k < İ yes STOP Fig. 1 Flow-chart of the proposed algorithm The advantage of this structure is that, for solving DLF, any software (research or industrial grade) can be exploited, provided that is fast, reliable and has an easy data exchange interface. In this paper, the algorithm was implemented on a MatlabOpenDSS platform and relies on two-way data exchange between a Matlab code, that evaluates sensitivities and assesses control variable variations, and the OpenDSS simulation engine that performs DLF and implements control variable variations on the network model. This data exchange is performed by means of a COM (Component Object Model) interface. OpenDSS is a open source software that is developed by EPRI in an on-going project [27]. This software is specifically designed for solving distribution circuits (it represents unbalanced conditions, stochastic processes and load models, detailed distribution equipment models) and was chosen under multiple rationales. OpenDSS is specifically optimized and compiled for solving rapidly DLF of large distribution networks. OpenDSS is freeware and open-source and, given that distribution systems lack of software standards, it has good chances in becoming a standard software framework in the near future. The proposed methodology can be implemented through any other DLF software (research or industrial grade), provided to be fast and reliable, and have an easy data exchange interface. 5 IV. TEST RESULTS The proposed methodology was tested on the IEEE 123-bus Radial Distribution Feeder case [27]-[28], represented in Fig. 2, suitably adapted for testing the proposed methodology. It was assumed that active control resources (curtailable loads) and reactive control resources (micro-generators and controlled capacitor banks) were available at selected nodes and circuits. load reactive power is not a control variable since it was assumed that loads have a constant power factor at nominal voltage. Thermal ratings at the HV/MV interface are taken into account through the penalty function: 2 2 §I −I · + α pc ¨¨ c max ¸¸ © I max ¹ α pa = 0 if I a < I max with Fig. 2 Scheme of the IEEE 123-bus Radial Distribution Feeder A. Test A In this test the grid was supposed to be affected by a 35% uniformly distributed load increase, causing an overcurrent on the HV/MV interface. The feeder is connected to the subtransmission network by means of a 115kV/4.16kV transformer. Considering the rate of the HV/MV transformer [28], it was supposed that the thermal rate of the MV line at the supply-side of the feeder (in Fig. 2 the line between buses #149 and #1) is 650A for each phase. In this test, loads are modeled, according to the original base case in [27], with the following models: constant P and Q, constant impedance, constant P and quadratic Q, linear P and quadratic Q. Three test cases were developed in order to assess the potentiality of the approach. Further strategies can be implemented for controlling active and reactive resources (generation redispatch, energy storage management, etc.). In the three cases the objective function is aimed at minimizing the control effort: 2 § ui − u 0 · ¸ (13) Cobj = ¦ α o ,i ¨ ¨ u0 ¸ i © ¹ where the index 0 refers to the initial conditions, Įo,i is a weighting factor, ui is the ith control variable. The control variable vector u is given by active power at each load (case A1), or reactive power at generators and switching capacities (case A2). The case A3 was solved considering the availability of both active and reactive control variables adopted in case A1 and case A2. Please note that i i 2 §I −I · §I −I · C p = α pa ¨¨ a max ¸¸ + α pb ¨¨ b max ¸¸ + © I max ¹ © I max ¹ α pb = 0 if I b < I max α pc = 0 if I c < I max (14) and where Ia, Ib and Ic are the phase-currents on the interconnection line, Imax is the thermal rate (650A). Please note that due to the three-phase formulation of the optimization problem and, in particular, of eqn. (14) the algorithm is able to evaluate sensitivities of any load, generator or capacitor (being either single phase, two-phase or three phase) with respect to the actual currents flowing in each phase of the congested interconnection line. Results are summarized in Table I. The first row of the table shows the values of currents at the substation supply-side in the base case (i.e. system state before optimization). Id , Ia , Ib , and Ic , are respectively the positive current component and the physical currents at phases a, b and c. TABLE I TEST RESULTS Case Base A1 A2 A3 Id [A] 707.1 680.7 649.2 605.8 Ia [A] 867.7 650.1 806.3 650.5 Ib [A] 560.2 557.9 522.9 521.7 Ic [A] 693.9 650.1 650.5 645.4 ¨PL [kW] 0 -545.9 0 -383.6 ¨QG [kVAr] 0 0 352.2 285.0 In the test A1, where the sole control of active resources is performed, the congestion is removed curtailing loads in such way that all phase currents are brought below the threshold limit of maximum current protections (650 A). The total curtailment is about 546 kW (about 11.6% of the overall active demand) and is distributed among loads as showed in Fig. 3. The requested curtailment is averagely 2530% for single phase loads on phase a, null for single phase loads on phase b, and 3-7% for single phase loads on phase c. Two- and three-phase loads are out of this average statistic as showed in Fig. 3 for loads #24, #33-34, #50-52, #61-63. In case A2, reactive control is not able to remove the congestion. Reactive control can just mitigate currents by increasing power factor and hence minimizing the reactive component of Ia , Ib , and Ic. The third case A3 is referred to a combined active/reactive redispatch. Results for case A3 are obtained by solving the TOPF considering the concurrent availability of active and reactive resources. 6 variable vector is given by dispatchable reactive power and tap ratio of transformers at the substation and at bus #160 (see Fig. 2). Voltages were constrained by the penalty function: 35 load curtailement [%] 30 25 § Vi − Vlim ¨¨ ¦ σi i =1 © Cv = α v nbus nbus 20 15 10 · ¸¸ ¹ 2 (15) where 5 Vlim 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 load number Fig. 3 Test case A1, expected load curtailment. As clearly showed in table I, the combined exploitation of active and reactive resources allows to remove the congestion, reducing the overall amount of expected curtailed active power (384 kW, about 8.1% with respect to the total). The distribution of curtailment is represented in Fig. 4. Differently from the previous case, loads which needed small adjustments on phase c do not experience any active power curtailment thanks to reactive compensation. 35 Vi M if Vi > Vi M ° = ®Vi m if Vi < Vi m °V otherwise ¯ i and 1 ¯Vi m Vi m < Vi < Vi M if σi = ® otherwise M In this test, Vi and Vi were set at each node respectively at 0.95 and 1.0, assuming that 0.95 represents for all loads the minimum acceptable voltage. Figure 5 represents voltage profile before and after optimization. Tap changers and reactive power outputs were regulated in such way that all voltages were constrained in the interval 0.95-1.00 p.u. The voltage regulation resulted in an overall active power decrease of about 10% (from 3710 kW to 3330 kW). Elapsed time was about 43 seconds. 30 ] 25 [% t n e m20 e il a rt 15 u c d a 10 lo 1,2 5 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 load number voltage magnitude [p.u] 1,1 1 0,9 no CVR after CVR Fig. 4 Test case A3, expected load curtailment Elapsed time on a HP Compaq 8000 Elite CMT PC, with Intel Core 2 Quad CPU Q 9650 3.00 GHz and 4.00 GB RAM for Cases A, B and C was 2.3s, 11.2s, 23.1s respectively. B. Test B This second test was aimed at implementing the CVR/VVO strategy described in the previous section. In order to show the potentials of this approach the base case was modified representing all loads with a constant impedance model. The TOPF problem was formulated considering an objective function aimed at minimizing the exchange of active power at the HV/MV interconnection: 2 where Psup § Psup · Cobj = α o ¨ 0 ¸ (14) ¨ Psup ¸ © ¹ is the active power supplied at the feeder at the substation and the index 0 refers to the base case. The control 0,8 1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 bus number Fig. 5 Voltage profiles before and after CVR V. CONCLUSIONS Centralized control of a large set of control variables is one of the possible functions to be developed in smart distribution grids. Having assumed the availability of a centralized monitoring and control architecture, control can be assessed in both extended real-time or daily system operation by means of classical power system analysis and optimization methodologies such as power flow and optimal power flow. These methodologies, already well-known and fully developed, should be re-adapted to specific requirements and properties of distribution systems and to the availability of new control resources and innovative smart control strategies. 7 The authors have proposed a three-phase OPF methodology for assessing centralized control of active and reactive distributed resources in a smart distribution grid. The methodology is based on quasi-Newton method and was implemented on an open source load-flow code for distribution systems. The proposed methodology is general enough to solve several optimization problems during operation of distribution networks and can be easily implemented on any other distribution load flow software. The approach was tested for congestion management and conservative voltage regulation applications, showing good convergence performances in the presence of different sets of objective functions and control resources. Computational performances appear to be compatible with extended real-time framework. [19] [20] [21] [22] [23] [24] [25] [26] REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] R.E. Brown, “Impact of Smart Grid on distribution system design”, Proc. of IEEE PES General Meeting 2008, Pittsburgh, July 20-24, 2008. J. A. 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