Improving Microgrid Performance by Cooperative ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

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Improving Microgrid Performance by Cooperative Control of Distributed Energy Sources Tommaso Caldognetto, Student Member, IEEE, Paolo Tenti, Fellow, IEEE, Alessandro Costabeber, Member, IEEE, and Paolo Mattavelli, Senior Member, IEEE

Abstract—This paper proposes a simple and effective approach to control the distributed energy resources (DERs) in a low-voltage microgrid, to increase energy efficiency and hosting capacity of the microgrid itself, with the only requirement of narrow-band communication among distributed loads and generators. More specifically, the control aims at taking full advantage of the power control capability allowed by distributed renewable sources and energy storage units, to optimize energy efficiency and voltage stability. The resulting distributed control architecture is scalable, ensures prompt response to power transients, and provides proper power sharing even if some DERs saturate their power capacity. Index Terms—Distributed power generation, energy efficiency, microgrids, reactive power control.

I. I NTRODUCTION

S

MART microgrids offer a potentially huge application domain for information and communication technology (ICT) and power electronics. In fact, they are increasingly populated by distributed energy resources (DERs), which are interfaced with the grid by means of electronic power processors (EPPs). The control flexibility of EPPs, in conjunction with their communication capability, enables distributed control of the active and reactive currents flowing in the power lines, with potential improvement of the grid performance in terms of distribution efficiency, hosting capacity, stability, demand response, and exploitation of DERs [1], [2]. In general, these goals can be achieved only if EPPs are driven cooperatively [3]–[6], either by centralized [7]–[10] or distributed control systems [11], [12]. Centralized control is impractical for wide networks populated by a high number of DERs, but can easily

Manuscript received October 24, 2013; revised February 13, 2014; accepted March 5, 2014. Date of publication March 25, 2014; date of current version November 18, 2014. Paper 2013-IPCC-778.R1, presented at the 2013 IEEE Energy Conversion Congress and Exposition, Denver, CO, USA, September 16–20, and approved for publication in the IEEE T RANSACTIONS ON I NDUS TRY A PPLICATIONS by the Industrial Power Converter Committee of the IEEE Industry Applications Society. T. Caldognetto and P. Tenti are with the Department of Information Engineering, University of Padova, 35131 Padova, Italy (e-mail: [email protected]; [email protected]). A. Costabeber is with the Department of Electrical and Electronic Engineering, University of Nottingham, Nottingham, NG7 2RD, U.K. (e-mail: [email protected]). P. Mattavelli is with the Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2014.2313648

be implemented in smart microgrids, which insist over limited areas, include a limited number of DERs, and can easily be equipped with point-to-point bidirectional communication either via power line or wireless [13]. This paper presents a cooperative control approach where each unit (either load or DER) communicates at low rate with the other units and/or the central controller, exchanging data in the form of active and reactive power. Based on this data flow, the distributed EPPs are driven toward an operating condition of quasi-minimum power loss in the entire microgrid. The proposed control requires the knowledge of the distances among nodes, which can be determined online by ranging techniques on the power line [14] or can be derived by an a priori knowledge of the microgrid, and implements a saturation management algorithm that tracks the minimum loss condition even if one or more DERs saturate their power capability. To validate the cooperative control performance, an experimental testbed has been built, implementing the proposed control in a laboratory-scale microgrid, including two DERs with total power of 3 kW. II. O PTIMUM C ONTROL P RINCIPLE Before introducing the cooperative control principle, we first determine the active and reactive currents, which are fed by the EPPs into the grid nodes, which theoretically minimize the distribution and conversion losses in the microgrid. This also implies minimization of the active and reactive currents flowing in the distribution lines, thus resulting in minimum voltage drop across the line impedances and stabilization of the voltage profiles [15], [16]. The result is a global increase of the power quality in the microgrid. The optimum control technique was extensively discussed in [17]. Here, we only recall the basic relations required to estimate the theoretical total loss, including both the conversion loss in the EPPs [18] and the distribution loss in the cables. We assume that the microgrid is fed by the utility at the point of common coupling (PCC), which acts as an ideal voltage source of large power capacity and is the slack node of the microgrid (node 0). A. Conversion Loss Fig. 1 shows the efficiency of three commercial photovoltaic (PV) inverters as a function of output power (dashed, dotted, and dash–dot lines) extracted by the corresponding datasheets. The corresponding power loss can be represented, with good

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In case of meshed grids, the incidence matrix is not invertible, but (3b) still holds with a different structure of matrix Rd , as shown in [17]. In all cases, the following considerations remain valid. C. Total Loss The total power loss can be expressed as a function of the node currents by adding terms (1) and (3b), i.e., T ∗ T ∗ Pt = Pc + Pd = I˙g Rc I˙g + I˙ Rd I˙ .

(4a)

D. Minimum Loss Condition Fig. 1. Inverter efficiency curves.

accuracy, by a constant term (no-load loss) plus a term proportional to the square of the output current (pseudoresistive loss). The accuracy of this estimation is quite good, as shown by the solid line, which refers to the considered model applied to the inverter by Power-one. In this case, the two model parameters, i.e., the equivalent loss resistance and the no-load loss, were calculated on the basis of the declared efficiency at 20% and at 100% of the rated output power (4.2 kW at 230 Veﬀ ). With the aim to find the minimum loss condition, we may therefore represent the inverter loss as a pure resistive contribution. Let Rc be the diagonal matrix of EPP resistances and I˙g be the currents fed by EPPs into active grid nodes (generated currents), which are expressed in the form of phasors for sinusoidal operation; the conversion losses can be estimated as Pc =

T ∗ I˙g Rc I˙g

(1)

where index (T ) means transpose, and (∗ ) means complex conjugate. B. Distribution Loss In case of a tree-shaped grid, number N of grid nodes, excluding node 0, is equal to number L of distribution line paths (grid branches). Thus, the incidence matrix A of the network is square and invertible. Let J˙ be the vector of branch currents and I˙ be the vector of currents injected into the grid nodes (both active and passive); the current balance at the grid nodes can be expressed as ˙ I˙ = AT J˙ ⇒ J˙ = (AT )−1 I.

(2)

The distribution losses in the microgrid are given by T ∗ Pd = J˙ Rb J˙

(3a)

where Rb is the diagonal matrix of branch resistances. Owing to (2), the distribution losses can be also expressed as a function of the node currents in the form T ∗ Pd = I˙ Rd I˙

(3b)

where Rd is a symmetrical matrix given by Rd = A−1 Rb (A−1 )T .

(3c)

Let I˙a be the phasors of the currents injected into active nodes (generated currents minus load currents at active nodes) and I˙p be the phasors of the currents absorbed at passive nodes; (4a) can be rewritten and partitioned as ∗ T Ra,p −I˙a T R Pt = −I˙a I˙p a,a ∗ Rp,a Rp,p I˙p T ∗ T ∗ T ∗ = I˙a Ra,a I˙a − 2 I˙a Ra,p I˙p + I˙p Rp,p I˙p (4b) where means real part, and for symmetry, Ra,p = Rp,a . The optimum node currents, which minimize the total power losses, occur if (∂Pt /∂ I˙a ) = 0, which gives ˙ I˙aopt = R−1 a,a Ra,p Ip .

(5)

The optimization procedure can be extended to include the constraints corresponding to the saturation of EPP power capacity. In general, we observe the following. • Computing optimum currents (5) requires the knowledge of both network topology and line parameters, which is reasonable for medium-voltage distribution grids but may be difficult for low-voltage residential microgrids. Moreover, a centralized controller is needed to dispatch the current references to the EPPs. • In case of renewable sources, the active components of the generated currents are constrained by the generated active power and cannot be regulated. Nevertheless, (5) shows that, even in this case, the power loss can be reduced by acting on the reactive current, i.e., the imaginary part of (5), which is only constrained by EPP current ratings. • Depending on the optimization objective, the control action can minimize total loss, thus maximizing the global efficiency, or distribution loss only, to increase hosting capacity and voltage stability of the microgrid. III. D ISTRIBUTED C OOPERATIVE C ONTROL The control technique proposed in this paper approaches the optimization problem from a simplified and more intuitive perspective, with the goal of minimizing the distribution loss while avoiding overloading of EPPs. Observe first that the distribution losses tend to decrease if each EPP feeds the active and reactive power demanded by the loads nearby. A control method can therefore be devised in which, during each control interval, the loads split their power

CALDOGNETTO et al.: IMPROVING MICROGRID PERFORMANCE BY CONTROL OF DISTRIBUTED ENERGY SOURCES

demand among the different sources in inverse proportion of the distance. This approach, which only requires the knowledge of node-to-node distances and applies both to tree-shaped and meshed grids, leads to an operating condition very close to optimum. In order to implement the distributed cooperative control, a bidirectional communication link is needed, either power line communication (PLC) or wireless, between loads and generators. In addition, a non-time-critical synchronization system (e.g., based on Global Positioning System signals) is required within the microgrid, to ensure that control units share a common time reference. A. Distance-Based Criterion The basic principle of distributed cooperative control is the following. Let S˙ m be the complex power absorbed at passive grid node m (m = 1, . . . , M ) and S˙ n be the complex power fed by the EPP at the active node n (n = 1, . . . , N ). Thus S˙ m = Pm + jQm , S˙ n = Pn + jQn ,

m = 1, . . . , M n = 1, . . . , N.

(6)

Therefore, each active node n receives M power requests by the loads connected at passive nodes, for a total amount S˙ n =

n S˙ m .

by small generators, according to (7), most of the load power would be demanded to these generators, which cannot fulfill the request, thus failing the original target of the technique. Algorithm (7a) is therefore reformulated in (8) in a way that takes into account the actual power capacity of active nodes, i.e., n n = Pm + jQnm S˙ m N −1 N −1 βnP βnP βnQ βnQ = Pm n + jQm n (8) dm n=0 dnm dm n=0 dnm

where coefficients βnP and βnQ account for the residual active and reactive power available at active node n. In the beginning, coefficients β are set to 1, resulting in the distance-based criterion (7a). Then, at each computation step k, which is defined as the instant when all loads update the local measurements of their power demands, coefficients β are adjusted to suit the residual power capability of the EPPs, which is defined, for each of them, by the quantities αnP (k) = PnS /Pn (k − 1)

In the first instance, the control system shares the power demand S˙ m of each passive node among all active nodes (including the utility at PCC) in inverse proportion of their distances dnm from node m. Accordingly, the complex power n S˙ m requested from passive node m to active node n is N −1 1 1 n S˙ m = S˙ m n . (7a) dm n=1 dnm

M

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(7b)

m=1

Note that, in order to implement control algorithms (7), the knowledge of node-to-node distances is required. While the meaning of node-to-node distance is clear and unique in tree-shaped networks, it may be ambiguous in meshed grids, where multiple paths can connect any pair of nodes. In practice, this ambiguity can be overcome if we define the node-to-node distance as the length of the shortest path connecting two nodes. This is the information that we obtain by PLC ranging techniques, e.g., based on time-of-arrival (TOA) measurements [14], [19].

αnQ (k) = QSn /Qn (k − 1).

(9a)

In (9a), terms PnS and QSn are the maximum active and reactive power that the EPP at node n can actually deliver, respectively; whereas Pn (k − 1) and Qn (k − 1) are the total active and reactive power demanded to node n at step k − 1, respectively. Thus, coefficients αnP and αnQ are as high as the power capability of node n exceeds the demanded power. Coefficients β are then computed by βnP (k) = βnP (k − 1) · αnP (k) βnQ (k) = βnQ (k − 1) · αnQ (k).

(9b)

This is a recursive formula by which coefficients β are updated, at each computation step, according to the excess of power available at each active node in the previous step, by simply increasing in (8) the weight of those generators that still can provide power. This algorithm provides a fast adaptation of the power sharing criterion to any variations of the generated and consumed power. As will be shown later, it also prevents limit cycles to occur when one or more EPPs saturate their power capability, thus increasing control robustness and avoiding instability even for severe dynamic conditions. Note that, in order to apply (8) and (9), the loads must collect from EPPs data on the power demands occurring at previous step k − 1, along with actual active and reactive power capability. Obviously, this implies an additional communication burden to properly manage EPP saturation. In practice, coefficients β are constrained by

B. Power-Based Correction

βnP,min ≤ βnP ≤ βmax

In the absence of specific provisions, power request (7b) can exceed the power capability of the EPP at node n. Thus, the pure distance-based sharing criterion (7a) must be modified to account for the actual power capability of active nodes. This is a necessary provision; otherwise, the distance-based approach might lead to nonoptimum behaviors of the control. For example, in the simple case of a large load closely surrounded

βnQ,min ≤ βnQ ≤ βmax .

(9c)

The upper limit βmax is usually set to 1 to ensure that the pure distance-based criterion (7a) is applied in the absence of EPP saturation. Instead, lower limits βnP,min and βnQ,min are kept slightly greater than 0 to avoid that an EPP drops in the idle state (β = 0), which would keep stable according to algorithm (9b).

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As concerns the PCC (node 0), it is usually capable to satisfy the whole load demand; thus, its coefficient βmax is stuck to 1. Nevertheless, if there are limitations on active and reactive power exchange with the utility, which are dictated by other control rules, the PCC coefficients can be set as it was an EPP. With the preceding provisions, power sharing criterion (8) ensures dynamic saturation management, which means that load power demand is properly shared among the various EPPs according to their distance until their power limits are reached, and if the power demanded by the loads cannot be provided by the generators nearby, the demands are automatically moved to EPPs located farther but with residual power capacity. C. Effect of Current Harmonics While optimum control is formulated in terms of phasor quantities and is therefore valid for purely sinusoidal currents and voltages, the distributed control is less demanding in terms of waveform purity. In fact, it relies on average power computations (active and reactive power terms), which can be applied even in case of distorted currents. The only requirement is that the power terms are additive across the microgrid, i.e., that they are conservative quantities. Hence, we assume that active and reactive power terms are computed according to the Conservative Power Theory definitions given in [20], which are easily evaluated in the time domain. D. Effect of Communication Errors The proposed control technique is very robust against communication errors or delays. In fact, the control quantities are updated at every cycle or half-cycle of the line voltage, and this gives time to implement redundant communication algorithms, security procedures, and repetition of data transmission. Moreover, even if a data packet is entirely lost and update of β coefficients is not possible, the EPPs keep the same control parameters of the previous cycle. This causes a control delay, which is, however, noncritical because the utility ensures the power balance. IV. S ATURATION M ANAGEMENT A NALYSIS Note that (8) and (9) implement a saturation management algorithm that is nonlinear, due to the time-varying property of load power terms Pm and Qm and EPP power capacities PnS and QSn . Thus, stability and dynamic properties cannot be derived in a simple form, despite the intuitive control principle. In the following, we propose a simplified approach to analyze the behavior of the control algorithm under dynamic conditions. Although approximated, such analysis provides interesting considerations on the actual system operation. A. Simplified Analysis Based on the Equivalent Load Approach The stability of algorithm (9) is analyzed under the assumption that the computational speed of the algorithm is much faster than the evolution time of power terms, both absorbed

and generated. In this instance, we may run (8) and (9) to show the evolution of coefficients α and β from an initial steady-state condition to another stationary condition. Observe first that, in the steady state, all coefficients β converge to unity if the power demand to active nodes does not exceed their capability. In this situation, in fact, according to (9), coefficients α are always greater than 1, and coefficients β progressively increase until they reach upper limit βmax = 1. This means that, in the stationary regime, in the absence of saturation of EPP power capabilities, algorithm (8) converges to the same results of (7), i.e., the pure distance-based power sharing algorithm. Moreover, if we observe the dynamic evolution of the system from a steady-state condition to another steady-state condition, we will see coefficients β starting from unity, then evolving, and, finally, stabilizing again to unity. Such evolution gives a first indication on the stability and convergence property of the algorithm. As a second remark, we observe that, in a stationary condition, we can establish a correspondence between the actual network with M loads and an equivalent network with a single load, taking entire load power PLtot , whose distances from active nodes are selected to cause the same power request to all EPPs. In the first instance, we may analyze the stability of the algorithm with reference to this equivalent load, which guarantees the same initial condition and a similar evolution of coefficients α and β, which are mainly determined by the behavior of the power terms. Applying (8) and (9) to the case of a single load, we describe the evolution of coefficients β with the following equation, where, for brevity, only coefficients βnP related to active power terms are reported: ⎤ ⎡ ⎡ ⎤ ⎡ P S d1P ⎤ P1S d1P 1 β1P (k) β1P (k + 1) · · · tot d tot d PL P 1P NP L ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ .. .. ⎥·⎢ ⎢ ⎥=⎢ ⎥. .. . . ⎦ ⎣ ⎣ ⎦ ⎣ ⎦ .. .. . . . S S PN dN P PN dN P · · · tot tot βN P (k + 1) βN P (k) P d PL dN P L 1P FP

(10) In (10), terms d1P , . . . , dN P are the distances from the equivalent load to active nodes, which are derived from (8). It is possible to show that state matrix FP can be transformed through diagonalization in the form O12 O11 S (11) FP D = P1S +P2S +···+PN O21 P tot L

(M −1)×(N −1)

where submatrices O11 ∈ R , O12 ∈ R(M −1)×1 , 1×(N −1) are null matrices. and O21 ∈ R The diagonal form of (11) shows that the only nonzero element is the pole (P1S + P2S + · · · + PNS )/PLtot . This single eigenvalue lies out of the unity circle if the aggregated power capability of distributed generators exceeds load power demand. In this case, in fact, coefficients β would diverge, unless they are limited by (9c). Instead, the eigenvalue remains within the unity circle if the aggregated power capability of EPPs cannot fulfill the load power demand, and coefficients β tend to drop below unity. In both cases, limits (9c) prevent coefficients β to divergence or stabilize to zero, which would be a no-return condition.


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Fig. 2. β equilibrium points in the P1S , P2S plane.

Note also that, if one or more EPPs saturate their power capability, the order of system (10) reduces, since some β coefficients are, in fact, stuck at a constant value. Even in this case, however, the form of state matrix (11) remains the same, showing a single eigenvalue. The dynamic properties of the system do not change, and the stability of the algorithm is again ensured by limits (9c). Taking into account the limitation of β coefficients defined by (9c), the dynamic model can be extended, for the generic βnP in (10), in the form sat βnP (k + 1) = σi (βnP (k + 1))

where σn : R → R is the saturation function defined as βnP,min , x ≤ βnP,min σn (x) = βmax , x ≥ βmax x, otherwise.

(12)

(13)

The preceding equations set the basis for the determination of equilibrium points and dynamics of β coefficients in the general condition accounting for saturations. The analysis can be repeated for reactive power, too, by simply taking the imaginary part in (11) instead of the real part. In practice, all the coefficients β can be locally determined at each passive node, provided that each generator communicates its power capability (PnS , QSn ), each load communicates its power absorption (Pm , Qm ), and the node-to-node distances (dnm ) are known. Moreover, in order to apply (8), all loads need to share coefficients βnP and βnQ . This calls for a wideband communication channel to allow fast collection of the data needed to compute coefficients α and β. If the available data rate is not fast enough, an alternative solution is to share the information of the node-to-node distances among the passive nodes only once and to store them in local memory devices. In fact, while load power and generator capabilities must be updated at each iteration k, distance information remains valid until a new load or generator is connected to the grid. This second solution increases the information exchanged among the nodes; however, it is more feasible, since node-to-node distances are constant quantities, except in case of new connec-

tions or disconnections of generators and loads in the microgrid. Therefore, after an initial training phase, the additional communication burden during normal operation becomes limited. B. Case Study: N = 2, M = 1 (Two EPPs, One Load) This subsection briefly investigates the behavior of cooperative control in the simple case of two EPPs acting in a microgrid with a single load, in the same configuration that will be later used for the experimental results. By using (13), we can determine the relevant equilibrium points of the system. Rewriting (10) for this specific scenario, we have S ⎧ d1P 1 ⎨ β1P (k + 1) = σ1 Ptot β (k) + β (k) 1P 2P d2P PLS (14) d2P 2 ⎩ β2P (k + 1) = σ2 Ptot . d1P β1P (k) + β2P (k) P L

By imposing the equilibrium condition on (14), i.e., βi (k + 1) = βi (k), the picture in Fig. 2 can be drawn, where all possible operating conditions are represented in the plane (P1S , P2S ). Observe first that the plane is split in two subplanes by the diagonal straight line P1S + P2S = PLtot : On the right side of this line, the power capability at active nodes exceeds load power, whereas on the left side, the load power demand cannot be met. The plan is further divided in zones, which correspond to a different behavior of coefficients β. For each zone, the pair (β1P , β2P ) of equilibrium coefficients is explicitly given as a function of grid parameters (load-to-EPP distances and load power), EPPs’ parameters (power capability), and control parameters (minimum value of beta coefficients). The zones have the following meaning: In zone 1, both EPPs can accomplish the ideal power sharing (7); in zones 2 and 7, EPP1 is saturated, whereas EPP2 provides, within its power limits, the power resulting from (8); similarly, in zones 3 and 8, EPP2 saturates, and EPP1 meets the distance-based criterion (8); in zones 4 and 6, both EPPs saturate; thus, their power references are set to the maximum power capacity. Fig. 2 refers to active power terms only, but a similar picture can be drawn for reactive power, too.

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V. C ONTROL I MPLEMENTATION A. General Considerations In order to implement algorithm (12), at each computation step k, every EPP broadcasts the information on its power ratings PnS , QSn to all passive nodes. Given the node-to-node distances, which are measured at start-up and then updated only if a new EPP or load is connected to the microgrid, each load can calculate the evolution of all β coefficients by (12). When (12) reaches the steady state, the correct sharing coefficients are known by all loads. They can therefore apply (8) and send their power requests to the EPPs. This control approach obviously requires bidirectional communication, measurement, and data processing at every grid node, either active or passive. In fact, the same control principle can be implemented by a centralized controller, which collects the data on load power, EPP ratings, and distances and dispatches the active and reactive power references to each EPP. B. Network Response The actual response time of control at microgrid level is limited by the load power calculation time, i.e., the line voltage period. Moreover, the execution time of the power commands depends on the control methods implemented in the EPPs (voltage control or current control) and is also affected by network parameters and communication delays of the ICT infrastructure. It is, however, remarkable that the requested communication speed is limited and can be met by commercial PLC standards and protocols [13], e.g., PoweRline Intelligent Metering Evolution technology with orthogonal frequency-division multiplexing modulation. The distances between grid nodes, which are needed to implement algorithm (8), can seldom be obtained by the distribution system operator (DSO). However, they can be estimated online by applying ranging techniques on the power lines, based, for example, on TOA measurement techniques [14], as explained below.

of propagation of the signal over the medium, node A can determine the distance of node B. Although effective, this approach requires a precise time synchronization between the two nodes, which may be difficult to achieve. Alternatively, node A can measure the round-trip time, without requiring a common time reference. For this purpose, at time to , node A broadcasts a packet with its ID in the electrical line. Each node that receives the packet transmits back, on the same line, a response packet (including its ID) after a fixed time T . Therefore, node A receives a number of response packets equal to the number of nodes that heard its initial broadcast on the electrical line. It may happen that the response packets overlap, and unless suitable provisions are taken, this can be seen as interference and may result in a reception failure. This can be avoided by implementing a code division multiple access, which ensures that the response packets are orthogonal and do not interfere with each other. Let us consider a single response packet coming from node B. Node B receives the message at time τB , waits a fixed time T , and then replies to node A, which receives the packet at time τA = 2τB + T . Time τB is related to the distance dAB between nodes A and B by the relation τB = dAB /c, with c being the speed of light. Thus, dAB can be derived as dAB =

c(τA − T ) . 2

(15)

In order to compute the distance, it is therefore necessary that node A measures the round-trip time τA . This approach has been successfully applied on ultrawideband systems, demonstrating ranging accuracy of some 30 cm with a communication bandwidth of 500 MHz. Of course, the measurement accuracy reduces for a lower bandwidth, but today’s commercial PLC ensure ranging accuracy of a few meters, which is adequate for our application. With this ranging approach, each node sends a query packet, and all nodes that receive it (corresponding nodes) reply with a response packet. Therefore, after the ranging procedure has been completed, each node owns a list of corresponding nodes and their distances. Note finally that the preceding distance measurement approach holds both for radial and meshed grids.

C. Node-to-Node Distance Measurement The node-to-node distance measurement technique is explained in detail in [14] and is summarized here for completeness. The distance measurement can be done by using ranging techniques via PLC. Indeed, PLC may be the best choice for ranging techniques, as it exploits the electrical connections among grid nodes and does not require a separate communication network. Ranging over PLC can be implemented with various techniques, the main approach being the measurement of the TOA. TOA measurement is very robust against channel impairments typical of PLC, such as multipath propagation [19]. With this technique, node A measures the distance with respect to node B by letting B transmit a packet to A containing a time stamp, i.e., an indication of the time when the packet was sent. If the two nodes have a common time reference, by comparing the time at which the packet is received with the time when it was transmitted, as well as knowing the speed

VI. E XPERIMENTAL R ESULTS The description of the experimental testbed employed to validate the proposed cooperative control technique and the acquired results are presented here. A. Testbed Description The system is a low-voltage microgrid composed of two current-controlled inverters (EPPs) and a parallel R−C load. Fig. 3 shows the considered grid topology and the organization of the experimental setup. For simplicity, only the centralized version of the proposed cooperative control technique has been implemented, and the active and reactive power exchanged with the main grid through the PCC has been set to zero. With these hypotheses, the


Fig. 3.

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Experimental setup organization. TABLE I B RANCHES PARAMETERS

TABLE II S ETUP PARAMETERS

operation of the cooperative control can be appreciated by only observing the power references sent to the two EPPs. Interconnecting lines are made of distribution cables with useful sections listed in Table I. The parameters of the microgrid, the EPPs, and the load are detailed in Table II. The

communication between the various components of the setup is achieved via a dedicated Ethernet network, by which power references are transmitted from the central controller to EPPs, while the central controller receives from each EPP its actual active and reactive power capacity and its maximum power rating and from the load its total power absorption. The exchanged variables and the internal state of the cooperative controller are recorded by the supervision and data-log unit for monitoring and postprocessing purposes. The Ethernet link has been used for simplicity, and the distances are known from the knowledge of the topology. The flexibility of the setup will allow the future integration of PLC and distance measurement techniques. The central controller iterates the β update routine, based on (14), at a cycle time equal to 10 ms. Simultaneously, at a rate equal to 5 s per iteration, the central controller dispatches the calculated power references to EPPs and, subsequently, acquires the power absorption measured locally at the load and the power ratings of the EPPs. In the following, the first cycle is called “beta update cycle,” and the latter cycle is called “power update cycle.” It is worth noting that choosing different execution rates for the two cycles prevents the dynamics of β coefficients to affect the dynamics of EPPs’ power references. For practical reasons in the data-logging and observation time, in the considered case, the ratio between the rates was chosen to cause minor changes in beta coefficients after the first iteration. In the following, the experimental results with regard to the response of the system to the connection and disconnection of

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Fig. 4. Behavior of beta coefficients.

Fig. 5. Active power at testbed nodes.

Fig. 6. Reactive power at testbed nodes.

the parallel resistive/capacitive load specified in Table II are reported. B. Testbed Results The experimental results are reported in Figs. 4–7. In particular, Fig. 4 shows beta coefficient dynamics; Figs. 5 and 6 show the active and reactive power at various nodes, respectively; and Fig. 7 shows the power exchange with the PCC. The experiment is arranged to begin with the load disconnected, the two EPPs injecting zero current, and the beta

Fig. 7.

Power exchanged with the PCC.

coefficients set to one. The load is connected after instant (a) in Figs. 4–7. At the connection of the load, the total absorbed power is equal to (2900 W, −890 VA). This is the power initially acquired at instant (b) in Figs. 5 and 6 by the cooperative controller, which, on the basis of the pure distancebased criterion of (7), would produce ideal power sharing between the EPPs of about (1.9 kW, 1 kW). This power level exceeds EPP2 power capacity P2S , which is equal to 500 W (see Table II). Hence, (14) comes into play, making beta coefficient β2P to decrease until P2S constraint is satisfied. The resulting active power sharing then becomes (2.4 kW, 0.5 kW), and the residual power capability of the two EPPs becomes (1.2 kVA, 2.6 kVA). On the other hand, the ideal reactive power sharing, corresponding to (−570 VA, −320 VA), remains within the power capability of both EPPs, and the corresponding βQ coefficients remain stuck at one. In fact, the maximum reactive power QSn of the nth EPP is determined on the basis of its rated power Sn,nom and the requested active power Pn,ref . Referring to the representation in Fig. 2, the two EPPs are operating in region 3 for active power and in region 1 for reactive power. The EPP power references are dispatched at instant (c). The voltage support effect corresponding to the distributed current injection causes the power absorption of the load to increase to (3.11 kW, −1 kVA). The change in the load absorption is then acquired at instant (d). Being EPP2 already saturated, the additional active power demand is in charge of EPP1 , although it can satisfy the additional active power request only with 200 W, then its maximum power capacity is reached. The corresponding EPP1 maximum reactive power, i.e., QS1 , becomes 512 VA, whereas the needed amount would be 640 VA. This leads EPP1 into saturation for both the active and reactive power, as shown in Fig. 4, where, after instant (d), β1P and β1Q start to decrease toward their steady-state values. As reported in Fig. 4, the steady-state values for β coefficients establish in the interval [30 s, 40 s], to values that are in accordance with Fig. 2. EPPs are now operating in region 5 for active power and in region 2 for reactive power. Finally, at load disconnection, the system returns to the original state: the no-load condition is acquired at instant (h), then β coefficients move up and reach the upper saturation bound, and the resulting zero power references to EPPs are dispatched at instant (i).


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Finally, Fig. 9 shows the actual experimental setup. The design process of the setup took advantage of hardware-in-theloop and rapid prototyping approaches [21] to speed up the development of the adopted controllers.

VII. C ONCLUSION A distributed cooperative control technique has been proposed to drive the inverters interfacing the distributed energy sources in smart microgrids. The control aims at optimizing different aspects of microgrid operation, i.e., distribution and conversion efficiency, voltage stabilization, hosting capacity, and dynamic response to load and source transients. The control algorithm was devised to perform properly even in case of saturation of the current capability of the inverters, and its stability was analyzed to assess control robustness for whichever operating condition. To test the actual performance, the proposed cooperative control was implemented in an experimental microgrid, showing good correspondence with theoretical expectations in improving energy efficiency and voltage stability of the microgrid.

R EFERENCES Fig. 8. Waveforms of node quantities. (a) Before activating cooperative control. (b) Transients at the first update of inverters’ current references after activation of cooperative control. (c) Steady-state behavior with cooperative control.

Fig. 9.

Setup of the experimental testbed.

Figs. 5 and 6 show the behavior of the active and reactive power at the various nodes of the microgrid in the various phases of the operation described above, whereas Fig. 7 shows the power exchanged at PCC. As a result of the power flow control accomplished by the proposed cooperative control technique, the total loss in the distribution lines significantly decreases when EPPs are driven by the cooperative controller according to the requested load power. Note from Fig. 5 that the power loss drops by nearly 50% during cooperative control regime. Fig. 8 shows the voltage and current waveforms at load terminals, together with EPP currents, during the various phases of operation.

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Tommaso Caldognetto (S’10) received the M.S. degree (with honors) in electronic engineering from the University of Padova, Padova, Italy, in 2012. He is currently working toward the Ph.D. degree in the Graduate School of Information Engineering, Department of Information Engineering, University of Padova. His research interests include real-time simulation for power electronics, design of controllers for microgrid applications, and power electronic architectures for distributed energy sources.

Paolo Tenti (M’85–SM’90–F’99) received the Laurea degree (cum laude) in electrical engineering from the University of Padova, Padova, Italy, in 1975. He is currently a Professor of electronics with the Department of Information Engineering, University of Padova, where he was a Department Director and the Chairman of the Board of Directors from 2002 to 2008. His main research interests are industrial and power electronics and electromagnetic compatibility. His current research interests include the application of modern control methods to power electronics, electromagnetic compatibility analysis of electronic equipment, and cooperative control of distributed electronic power processors in smart grids. Prof. Tenti is the President of CREIVen, an industrial consortium for research in industrial electronics with special emphasis on electromagnetic compatibility. From 1991 to 2000, he was as a member of the Executive Board of the IEEE Industry Applications Society (IAS) and chaired various society committees. In 1997, he served as the President of the IEEE IAS. In 2000, he chaired the IEEE World Conference on Industrial Applications of Electrical Energy in Rome, Italy. For the years 2000 and 2001, he was appointed as a Distinguished Lecturer on “electromagnetic compatibility in industrial equipment” of the IEEE IAS.

Alessandro Costabeber (S’09–M’13) received the M.S. degree (with honors) in electronic engineering and the Ph.D. degree, on energy-efficient architectures and control techniques for the development of future residential microgrids, from the University of Padova, Padova, Italy, in 2008 and in 2012, respectively. In 2012, he started a two-year research fellowship with the University of Padova. In the same year, he visited the Automation and Integrated Systems Group (GASI), São Paulo State University (UNESP), São Paulo, Brazil. In 2014, he joined, as a Lecturer in power electronics, the Power Electronics, Machines and Control Group, Department of Electrical and Electronic Engineering, The University of Nottingham, Nottingham, U.K., where was a Visiting Researcher in 2011. His current research interests include control solutions and stability analysis of ac and dc microgrids, control and modeling of power converters, power electronics and control for distributed and renewable energy sources, and high-voltage dc converters. Dr. Costabeber was a recipient of the IEEE Joseph John Suozzi INTELEC Fellowship Award in Power Electronics in 2011.

Paolo Mattavelli (S’95–A’96–M’00–SM’10) received the Ph.D. degree (with honors) in electrical engineering from the University of Padova, Padova, Italy, in 1995. From 1995 to 2001, he was a Researcher with the University of Padova. From 2001 to 2005, he was an Associate Professor with the University of Udine, Udine, Italy, where he led the Power Electronics Laboratory. In 2005, he joined the University of Padova in Vicenza with the same duties. From 2010 to 2012, he was a Professor and a member of the Center for Power Electronics Systems (CPES) with Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA, USA. He is currently with the University of Padova, with an adjunct position with CPES. His major fields of interest include analysis, modeling, and analog and digital control of power converters and grid-connected converters for renewable energy systems and microgrids and high-temperature and high-power density power electronics. In these research fields, he has been leading several industrial and government projects. Prof. Mattavelli was the Industrial Power Converter Committee Technical Review Chair of the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS from 2005 to 2010. For terms 2003–2006 and 2006–2009, he was also a Member-at-Large of the IEEE Power Electronics Society Administrative Committee. He served as an Associate Editor of the IEEE TRANSACTIONS ON P OWER E LECTRONICS from 2003 to 2012. He was a recipient of Prize Paper Awards from the IEEE TRANSACTIONS ON POWER ELECTRONICS in 2005, 2006, and 2011 and the Second Prize Paper Award at the IEEE Industry Applications Society Annual Meeting in 2007.