A hybrid central-distributed control applied to microgrids ... - IEEE Xplore

15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia

A hybrid central-distributed control applied to microgrids with droop characteristic based generators Pablo Arboleya∗ , Cristina Gonzalez-Moran† and Manuel Coto‡ ∗ Electrical

Engineering Departament, University of Oviedo, Gijon, Spain, Email: [email protected] Engineering Departament, University of Oviedo, Gijon, Spain, Email: [email protected] ‡ Electrical Engineering Departament, University of Oviedo, Gijon, Spain, Email: [email protected]

† Electrical

Abstract—Many authors have conducted power flow analysis as a tool to operate microgrids in a coordinate manner. Some of them have combined a central management with a back-up distributed control. In this paper, a management system based in this previous concept is studied. What we proposed is an optimum power flow method to be applied to microgrids in which the generators are connected through power converters with droop characteristic based control. In this kind of microgrids, the frequency is not constant and must be considered as a variable to correctly estimate the power flow. The central management is combined with distributed control to guaranty the stability in case of communication failures. Index Terms—Distributed generation, Microgrids, Droop Characteristic, Power flow

I. I NTRODUCTION HE level of penetration of Distributed Generation (DG) technologies into the distribution networks has suffered a rapid increase in recent years due to the effect that technological developments, as well as deregulation and privatization in power system industry, cause in cost reduction of this kind of generators [1]. Since the level of penetration is still low in most power systems, the effect of DG over the bulk system can be neglected nowadays. However, it should be studied the way to solve some issues related to stability and protection, and power losses reduction in order to make a correct planning for future distribution system with a high level of DG penetration [2]. With a correct coordination of the distributed generators, not only the negative effects could be avoided, but also positive effects could be achieved. Grouping a set of generators and loads in a cluster to be operated in a coordinated manner, is the most widely accepted way to increase the penetration level of DG, guarantying a higher quality level. This brand of association is known as microgrid [3]. A whole microgrid can be managed as a power plant from the grid point of view and can also be used as an ancillary services provider for voltage control, load regulation and spinning reserve [4]. There exist three main trends to manage a microgrid: • The first one is known as physical prime mover management, because a generator larger than the others is needed. The larger unit will absorb all transient active and reactive power imbalances to maintain the voltage magnitude and frequency. The concept is very similar to the one used

T

978-1-4673-1972-0/12/$31.00 ©2012 IEEE

in conventional centralized generation systems. The cost of the central unit and the loss of stability when a fault occurs in that unit, are the main problems. • The second one is called virtual prime mover management. In this case, a central control unit measures the microgrid state variables, and dispatches orders to micro sources using a fast telecommunication system. This control scheme avoids the high cost of a central physical prime mover but the communication system bandwidth limits the expansion of the microgrid and additionally, a back-up system is needed in case of communication failure. • The third approach is based on a distributed control. In this case, each unit responds automatically to variations in local state variables. This is the most extended trend because neither a communication system nor a large central unit is needed [3], [5]–[8]. So the above mentioned problems are prevented. Among the proposed methods to implement a distributed control management system, the droop characteristic control is the most used. It allows an automatic load sharing between generators connected to the grid through power converters. The droop characteristic control was first introduced in [9] for parallel connected inverters working in a standalone system. More recently, droop control has been extended to microgrid distributed control [3], [10]. A detailed analysis of the behavior of droop control based generators was presented in [11]. This self-acting load sharing presents the advantage of its robustness, because all generators cooperate together to succeed the stability without any communication among them. However, the main drawback is that the load sharing achieved could not always be the optimal. To overcome this inconvenient, some authors have combined a distributed control with some class of communication between the microsources [12]–[14]. In those cases, the microgrid primary control is distributed, but the secondary control loops are based on telecommunications. This control improves power quality and economic efficiency. When a telecommunication fault occurs, the primary controller acts as a back-up system. In recent years, some authors propose the use of power flow testing, as a tool for microgrid management [15], [16].

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,

However, when applied to microgrids, the power flow problem with generators including grid connected converters, presents some problems that must be overcome. First, not all nodes can be processed as Active / Reactive Power (P Q), Active Power /Voltege (P V ) or Voltage / frequency (V f ) nodes [17], so traditional power flow statement must be avoided. Secondly, and most important, with droop characteristic control, the frequency is neither invariant nor initially known, when the microgrid is working in island mode. The frequency depends on active power demand level, implying one more unknown variable in the power flow problem. This means that traditional equations used in power flow, when the frequency is supposed to be known and constant, can not be applied. Related to microgrid adapted power flow calculations, in [18] a central coordination is used to avoid reverse power flows in microgrids with a high level penetration of photovoltaic generators. In [16] an optimal power flow based tool is used to reduce the enviromental cost of a microgrid, but a possible variation in frequency is not considered. In this work, we propose a power flow based tool to optimally reduce the power losses in a microgrid. The method considers generators connected to the grid through power converters, working with droop characteristic control. This method allows frequency variations, derived from the droop based behaviour. This paper continues and completes the preliminary research presented by the authors in [6], in which the control of the converters, and its transients in terms of stability, have been described. The structure of this paper is as follows. In the next section, a short review of the adopted control will be done. In section III, modeling issues as well as the power flow problem will be stated. Section IV will show obtained results for several study cases. Finally, conclusions will be presented in section V. II. P OWER CONVERTERS CONTROL STRATEGIES This section presents a short review of the power converter control that the authors formerly developed in [6]. Converters can operate in island or grid connected modes. In the island mode the frequency will be kept by the main grid as a constant value, so the power flow issue is similar to a conventional one. In the other hand, in island mode of operation, the frequency depends on the droop charatecristics and the active power demand level. So frequency is an unknown variable in this case. That is the reason why the proposed power flow analysis will be focused in the isolated mode. Each converter has three different working submodes when working in island mode: 1) Power quality mode, which adapts the droops to provide the voltage magnitude and frequency nominal values. In this case, the frequency is known and the power flow problem is similar to a conventional one. 2) Sync mode, in which the droop characteristics are changed while the phase and voltage magnitude of the microgrid at the connection node are synchronized with the grid. This mode is a transient mode so it is beyond the power flow statement problem and it will not be considered in this work.

,

,

3) Conventional droop mode, in which a conventional droop characteristic control is used. The frequency depends on active power. This mode of operation is the most suitable to be used in the proposed power flow method. Id_bias

Ud_ref

+

+

+

PI

dq

 Id



Ud

Uq_ref

PI

+

PI

Iq  +

PWM

PI

+



abc

Uq Iq_bias

f_ref

Fig. 1: Main control scheme. In Fig.1 the block diagram of the main control loop is presented. It is the same for the three different modes of operation. Udref and Uqref are the voltage references, Ud and Uq are the measured voltages after the connection filter, and Id and Iq are the measured currents before the connection filter. It can be observed that this control loop is based on a traditional droop characteristic control, augmented with the introduction of feed forward bias currents Id bias and Iq bias . This feed forward is used in grid connected mode, so Id bias and Iq bias are always disabled and set to zero in island mode. It should be noted that the voltage reference of the q-axis, Uqref , is set to zero in both situations, while the way in which voltage reference Udref and frequency reference fref are calculated depending on the working mode as it will be described next. A. Island mode Conventional-droop and Power-quality are the two possible modes of operation when the microgrid is isolated from the main grid. Both of them are roughly described in this section. In either situation it is necessary to calculate the voltage ( Eq. (1)) and frequency ( Eq. (2)) references, for each generator at its point of connection to the microgrid. Udref and ff ref are the same as in Fig. 1, P and Q are the measured active and reactive power respectively, P0 and Q0 are the rated active and reactive power, and finally U0∗ and f0∗ are the modified rated voltage and the frequency that depends on the selected mode of operation. Udref = U0∗ − Kp (Q − Q0 ) fref =

f0∗

− Kq (P − P0 )

(1) (2)

The droop characteristic constants, Kp and Kq , are calculated using Eq. (3) and (4), where fmax and Umax are the maximum permitted frequency and voltage in island mode,

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and Pmax and Qmax are the maximum active and reactive power that can be supplied by the converter. fmax − f0 Pmax − P0 Umax − U0 Kd = Qmax − Q0 Kp =

(3) (4)

1) Conventional droop mode: This control strategy allows the inverter to work in a classical droop mode where the values of voltage and frequency are fixed according to Eq.(6) and (5). U0∗ f0∗

=

U0 ≡ rated voltage

(5)

=

f0 ≡ rated frequency

(6)

2) Power quality mode: The Power-quality mode changes the position of the droop characteristic in order to recover the rated frequency and voltage when a change in the load occurs. As can be observed in Fig. 2, when the conventional droop mode is activated and the reactive power demanded from the converter is reduced from Q0 to Q2 , the operating point is moved from A to B, increasing the voltage of the microgrid to U2 . If the Power quality mode is activated at that point, the droop characteristic is modified and the voltage reference in the inverter changes to U0 . The same behavior can be observed in the frequency when the active load varies. In this mode the voltage, U0∗ , and frequency, f0∗ , are calculated using Eq. (7) and (8) respectively.

should be noted that any other optimization criteria could be implemented. What is important in this case is that the central manager will use the power flow tool to constantly correct the references achieved by the distributed controls implemented in the generators. If a communication failure occurs, the distributed control of each generation unit will guarantee the network stability. Under these assumptions the power flow must be stated as an optimal power flow problem:

min subject to

xmin pmin ≤ p ≤ pmax Where: •

•

•

B

U2

A

Uo C

•

Q2

Qo

Fig. 2: Power-Quality mode.

Kiq )(Ud − U0 ) (7) s Kip )(f − f0 ) (8) f0∗ = f0 − (Kpp + s where f is the measured frequency, Ud is the measured voltage, Kpq and Kiq are respectively the proportional and integral gain of a reactive power PI regulator, s is the Laplace operator, and Kpp and Kip are the proportional and integral gain of the active power PI regulator respectively . U0∗ = U0 − (Kpq +

III. P ROBLEM S TATEMENT As we above-mentioned, the power flow calculation proposed in this paper is used as a tool to reach a local optimum working point in the microgrid. In this case the optimum will be defined in terms of power losses minimization. It

g(x, p) f (x, p) = 0 ≤ x ≤ xmax

x is a vector of unknowns including node voltages, branch currents, active and reactive powers and network frequency. This vector has lower and upper limits, xmin and xmax respectively. p is a vector of unknowns that defines operating parameters of the power converter based distributed generators. In this case all Kp and Kq are included in this vector for all generators. Initial values of this parameters are obtained using expressions (3) and (4). Then, during the minimization process, these values will be modified to achieve the optimal solution. This vector has also a lower and upper limits (pmin and pmax ) g(x, p) is a scalar function modeling all power losses in the microgrid lines and also in generators. Generators are connected to the network using a LCL filter. The second inductance is known as coupling inductance and losses in generators are computed as the sum of the looses in all coupling inductances f (x, p) is a vector function with all load flow equations including droop models.

For modeling the whole power system, the lines have been considered as RL branches. The complex vector theory has been used. The voltage drop in a synchronous reference frame (vdq ) in an RL circuit can be dynamically expressed using this theory as follows:   d vdq = R idq + + jω L idq (9) dt where: vdq

=

vd + jvq

idq

=

id + jiq

idq ω

is the current through the RL element is the frequency of the synchronous reference

Expression (9) is generic; it serves either for transient or steady-state analysis and it gives us the insight to proceed to decoupling the system into dq components. The system will be analyzed in steady state, so the derivative term is null and equation (9) in steady state can be written as follows:

LS7a.5-3

Δvd Δvq

=

Rid − ωLiq

(10)

=

Riq + ωLid

(11)

Using the p.u. system, equations (10) and (11) can also be applied to branches including power transformers. The whole problem has been formulated using the Incidence Matrix (Γ) notation developed in [19], permitting us to express such equations in a vector form. Γ(vN d )T = RB (iBd )T − ωLB (iBq )T Γ(vN q )T = RB (iBq )T + ωLB (iBd )T

(12) (13)

where: • Γ is element node incidence matrix. • RB and LB are the resistance and inductance matrices respectively, representing the impedance between nodes. They are diagonal matrices where rii and lii represent respectively the resistance and inductance of branch i or the short circuit resistance and inductance of the transformer placed in the branch. • vN d and vN q are the node voltage vectors in components d and q respectively. • iBd and iBq are the branch current vectors in components d and q respectively. Extending the formulation for modeling the line capacitances we obtain: I(vN d )T = −(1/ωCB )(iCq )T I(vN q )T = +(1/ωCB )(iCd )T

Above-mentioned vector x can be constructed as follows x = [z, ω]. All loads are modeled as RL loads following eq (9). The main idea is the next: first the network reaches a stable point of operation by means of the distributed control. At this point the load sharing has been done without any need of communication. All measured voltages and currents will be sent to the central manager to run the optimum power flow. The results of this optimum power flow will be the new values of Kp and Kq to obtain the optimum working point of the network reducing the sum of all power losses. A more complex scalar function could be designed including other parameters, as for example operating costs. What we propose here is the main method of combining distributed control with central control and optimum power flow to operate the microgrid. IV. C ASE OF S TUDY For this case of study, the authors chose the IEEE 13 node test feeder topology depicted in Fig. 3. In this case all lines are considered as three-phase lines. This assumption is needed because all calculations are made considering balanced three-phase systems. Further works will consider the effect of unbalanced systems over three-phase converters with a droop characteristic based control.

(14) (15)

where • (1/ωCB ) is a vector representing the inverse of the capacitance between a node and earth times ω. • iCd and iCq are vectors representing the current flowing from nodes to earth through the parasite capacitances. • I is the identity matrix. The use of Γ can be also applied to the formulation of the Kirchhoff’s Current Law (KCL) at each node of the system. Obtaining: (Γ)T (iBd )T = I(iCd )T + I(iN d )T (Γ)T (iBq )T = I(iCq )T + I(iN q )T

(16)

where: • iN d and iN q are the injected currents in components d and q in the nodes. Using this formulation, all above-mentioned linear equations can be expressed in a compact form as follows: MzT = 0

(18)

where z is the vector representing voltage and current magnitudes that is constructed in the following form: z=

Fig. 3: IEEE 13 Node test feeder

(17)

[ iBd iBq iCd iCq iN d iN q vN d vN q ] (19)

The construction of M is represented in expression (20).

In Table I, the considered resistance and inductance for all lines in Ω/mile are shown. The lengths of all lines are the same as the specified in the IEEE Standard. As it can be observed, nodes 633 and 634 are connected by a power transformer. The parameters of this transformer are exactly the same as the ones described in the IEEE Standard network. In addition, nodes 671 and 692 are connected by a switch. In this case of study, the switch is closed and its resistance and reactance is negligible. All nodes except 650 have an RL load, the value of such loads can be observed in Table II. The Generators are connected to busses 650, 645, 633, 611, 684, 652 and 680. The initial values for Kp and Kq

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⎛

−RB ⎜ −ωL ⎜ B ⎜ ⎜ M=⎜ ⎜ ⎜ ⎜ ⎝ ΓT

Γ

ωLB −RB 0 1/ωCB

−I

ΓT

N odes R(Ω) L(H)

650 71.9 9.55e−2

646 143.6 1.52e−2

645 85.6 2.16e−3

632 105.8 7.02e−2

−1/ωCB 0

633 137.5 2.81e−2

634 119.8 1.06e−2

I −I

611 55.8 2.30e−3

684 78.2 1.80e−3

⎞ Γ ⎟ ⎟ ⎟ ⎟ ⎟ I ⎟ ⎟ ⎟ ⎠

671 85.6 2.16e−3

(20)

692 539.5 4.77e−1

675 143.6 1.52e−2

652 94.6 6.61e−3

TABLE II: RL Loads

Line 1 2 3 4 5 6 7 8 9 10 11 12

F rom 650 645 632 632 632 633 684 671 684 671 671 692

To 632 646 645 633 671 634 611 684 652 692 680 675

R(Ω/mile) 0.3465 1.3294 1.3294 0.7526 0.3465 P.T. 1.3292 1.3238 1.3425 Switch 0.3465 0.7982

L(Ω/mile) 1.0179 1.3471 1.3471 1.1814 1.0179 P.T. 1.3475 1.3569 0.5124 Switch 1.0179 0.4463

C(S/mile) 6.2998 4.7097 4.7097 5.699 6.2998 P.T. 4.5193 4.6658 88.9912 Switch 6.2998 96.8897

TABLE I: Lines description are respectively 1.97e−5 (rad/W s) and 6.28e−6 (V /V Ar). The rated active and reactive power are 500kW and 0V Ar respectively and the LCL filter values can be seen in Table III. Lf (H) Rf (Ω) Cf (μF ) Lc (H) Rc (Ω)

1.52e−2 5.99e−2 928.0 1.52e−2 5.99e−1

TABLE III: LCL Filter parameters of droop characteristic based generators. Lf and Rf are the inductance and resistance of the filter inductance, the one connected to the converter side, Lc and Rc are the inductance and resistance of the coupling inductance, the one connected to the network side All calculations are made using the per unit system, and the bases are in Table IV Sb (V A) Vb (V ) Ib (A) Zb (Ω) ωb (rad/s)

5e6 4160 69.39 59.95 314

TABLE IV: Base magnitudes used in p.u. calculations. Tables V, VI and VII reflect the behaviour of the system with no communication, when only the distributed control of the power converters is working, and the changes when the central control runs the optimum power flow and gives the optimal Kp and Kq references to the power converters control. In Table V the data regarding generators can be observed. As

it was mentioned, for this case of study all generators have the same characteristics (P0 , Q0 , Kp , Kq ). When working in conventional droop mode all generators injects the same active power, since the droop Kp and the frequency are the same for all converters (60.84 Hz). This phenomenon does not occur with the reactive power, since, even when the Q0 and Kq are the same for all converters at the initial point, the actual reactive power depends on the voltage level at the connection point, and this voltage is not the same in all nodes. In Fig. 5 the voltage profile in the network before and after optimization is depicted. It can be observed that before optimization, the voltage profile of the top part of the network (nodes 650, 646, 645, 632, 633, 634) is lower than the voltage profile of the nodes situated at the bottom (nodes 611, 684, 671, 692, 675, 652, 680). In Fig. 4 the generated reactive power profile, after and before optimization, is shown. Due to droop Kq is the same for all converters, before optimization the net reactive power injected in the top part of the network is 1090.3kV Ar, and the reactive power consumed in the generators of the bottom part of the network is 937.2kV Ar. After optimization, the generated reactive power profile becomes flatter, and there is no generators consuming reactive power. Comparing the initial case with the optimized one, the voltage profile in the network is flattened even at node 646 that is a terminal node with no generation and connected to a generator through a high impedance line. The voltage in this node depends only on node 645 voltage and the active and reactive power demanded by the load situated at node 646. In this case the voltage in node 646 increases by 43.5V during the optimization process, and the voltage at node 645 increases 45.6V . This increment in node voltage causes a small augmentation in the active and reactive power demanded at node 646. That is why the current through the line connecting nodes 646 and 645 suffers a negligible variation (from 26.8A to 27.2A). The same effect can be observed in lines 6, 10 and 12 (see Table VII), such lines connect terminal nodes without generation with nodes where a generator is allocated, the current before and after optimization remains nearly constant. In the rest of the lines, the current is reduced a minimum of 50%. It must be remarked that the current in line 11, (connecting nodes 611−684) after optimization is nearly zero. In this case, this happens because generator at node 611 injects the active and reactive power demanded by the load at the same

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,

Generators Node 650 645 633 611 684 652 680 TOTAL

IG (A) No Opt. Opt. 78.0 64.7 188.0 83.3 144.9 80.1 79.2 73.7 77.8 73.4 172.1 50.7 105.2 51.9 – –

P (kW ) No Opt. Opt. 277.1 221.4 277.1 299.2 277.1 286.9 277.1 265.5 277.1 264.3 277.1 182.5 277.1 186.4 1940 1706.2

,

Q(kW ) No Opt. Opt. 44.2 71.9 609.0 20.0 437.1 29.2 -69.4 6.5 -44.0 9.2 -562.2 4.3 -261.6 11.7 153 152.8

kp( rad s /W ) No Opt. Opt. 1.97e−5 1.81e−5 1.97e−5 2.51e−5 1.97e−5 2.37e−5 1.97e−5 2.15e−5 1.97e−5 2.14e−5 1.97e−5 1.59e−5 1.97e−5 1.61e−5 – –

,

kq(V /V Ar) No Opt. Opt. 6.28e−6 3.93e−6 6.28e−6 6.28e−6 6.28e−6 6.28e−6 6.28e−6 6.28e−6 6.28e−6 6.28e−6 6.28e−6 1.53e−6 6.28e−6 6.28e−6 – –

TABLE V: Droop based generators behaviour (with and without optimization)

Loads Node 650 646 645 632 633 634 611 684 671 692 675 652

IL (A) No Opt. Opt. 51.0 51.1 26.9 27.2 47.4 48.0 37.3 37.5 29.6 29.8 33.8 34.1 73.8 73.7 52.7 52.6 47.7 47.8 7.2 7.2 28.3 28.3 44.0 43.6

PL (kW ) No Opt. Opt. 161.8 162.4 89.7 91.7 166.9 170.7 127.3 129.2 104.0 105.7 118.8 120.7 263.2 262.6 187.8 187.6 169.0 169.5 24.1 24.1 99.5 99.8 158.6 156.0

QL (kV Ar) No Opt. Opt. 82.0 82.5 3.6 3.7 1.6 1.7 32.3 32.8 8.1 8.3 4.0 4.1 4.1 4.1 1.7 1.7 1.6 1.6 8.1 8.2 4.0 4.1 4.2 4.2

Lines number 1 2 3 4 5 6 7 8 9 10 11 12

IdB (A) No Opt. Opt. -31.5 -15.9 26.7 27.1 10.1 -8.0 9.4 15.9 5.4 -3.4 -33.8 -34.1 -0.4 0.0 -19.9 -27.8 -3.0 7.0 -35.2 -35.1 68.3 51.7 -28.2 -28.3

IqB (A) No Opt. Opt. -10.7 -3.0 -2.5 -1.0 171.3 4.2 -120.6 -4.7 272.1 -3.1 1.9 1.1 -20.8 0.7 -195.7 3.3 159.5 -0.3 0.1 3.1 80.1 -3.3 -1.4 1.0

IB (A) No Opt. Opt. 33.3 16.2 26.8 27.2 171.6 9.0 120.9 16.6 272.2 4.6 33.8 34.1 20.8 0.7 196.7 28.0 159.5 7.0 35.2 35.3 105.2 51.8 28.3 28.3

TABLE VI: Loads current, active power and reactive power consumption before and after optimization

TABLE VII: Loads current, active power and reactive power consumption before and after optimization

node. It must be observed the state of line 5 after optimization, this line connects the upper part of the system with the bottom. The net active power consumption in the upper part is 768kW and generation is 807.5kW . In lower part, the active power generation is 898.7kW and consumption is 902, 2kW . That is power flowing through the line 5 is nearly zero and the current is reduced from 272.2A before optimization to 4.6A after optimization. Finally, total active power injected in the network by all generator was reduced from 1940kW to 1706.2kW . Total power consumed by the loads remains nearly the same before and after optimization, 1670.6kW and 1680kW respectively. This means that the active power losses were reduced in approximately 10 times, from 269.4kW to 26.2kW . The effect of this drop in the injected active power is a frequency rise from 60.84Hz to 60.96Hz. In order to validate the robustness of the method, 51 random cases were generated. All cases have 5 generators with the same characteristics of the above-described generator, and 12 different loads that were located randomly. In Fig. 6 the obtained results are summarized. In this figure, total active power losses in lines and generators and total active power consumed by the loads before and after optimization are depicted. With respect to the active power, it must be stated that the consumption after optimization is always higher or equal to the consumption before optimization. In the case of study, where all loads are RL type, this means that the voltage profile after

optimization is higher. In view of the losses reduction we can observe three different situations: • The first one, when zones in the network with similar levels of load demand and generation capacity, export or import active or reactive power from other zones, a high reduction in power losses can be achieved. This is the case studied. • The second one, moderate or low power losses reduction is achieved when generators are gather in a zone and the load is accumulated in a different zone. In such cases, the power losses are mainly produced in the lines connecting the two zones and can not be reduced in a significant manner through the optimization process. • The third one, when the demanded active and reactive power in most of the nodes are similar to the nominal values P0 and Q0 , a low power losses reduction is achieved. However, the probability of occurrence of this situation is very low. V. C ONCLUSION The proposed method consists on an hybrid control of the microgrid since combines the distributed and centralized control. The first one is based on conventional droop characteristic, and the second one uses a power flow tool to calculate the optimal power converter references to minimize power losses. This method combines the robustness of the distributed control, that guaranties a rapid load sharing, with the central control efficiency that calculates the optimum operating

LS7a.5-6

800

QG Opt. Q

600

G

kVAr

400 200 0 -200 -400 -600 650

645

633

611

984

652

680

node number

It must be mentioned that due to the nature of the droop control, the microgrid frequency and nodes voltage before and also after optimization, can differ from the nominal values. In this case, combining the above described power quality mode with the central control and the conventional droop mode, trough successive iterations, an optimum working point can be achieved, with less power losses and also with frequency network and a voltage profile near to the nominal. Further works will be focused in this line. Lastly, the effects of unbalances in non-transposed networks or loads should be studied in order to have a better comprehension of the effect of such unbalances over the method.

Fig. 4: Reactive Generated Power R EFERENCES 4200

node Voltage (V)

4150

4100

4050

4000

3950

3900

3850

650

646 645

632

633 634 611

684

671 692 675 652

680

node number

Fig. 5: Voltage profile without optimization (dotted line) and with optimization (solid line)

point minimizing losses. Under normal conditions, the central control keeps the microgrid working in a high efficiency level, by sending references to the power converters. The communication requirements are not too demanding because if the communication fails, the distributed control can keep the stability of the microgrid working in a less efficiency mode until the central control is restored. 1

MW

0,75 0,5

Losses Opt. Losses P L

Opt. P

L

0,25 0

case Fig. 6: Results obtained in 51 study cases randomly generated

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Pablo Arboleya received the M.Eng. and Ph.D. (with distinction) degrees from the University of Oviedo, Viesques, Spain, in 2001 and 2005, respectively, both in electrical engineering. Nowadays, he works as Associate Professor in the Departament of Electrical Engeneering at the University of Oviedo. He worked several years in the field of design of electrical machines and faults detection. Presently his main research interests are focused in the microgrid modeling and operataion techniques and combined AC/DC power flow.

Cristina Gonzalez-Moran received the M.Eng. and Ph.D. degrees from the University of Oviedo, Spain, in 2003 and 2010, respectively, both in electrical engineering. She is currently an Associate Professor at the University of Oviedo. Her areas of interest include renewable energies, distributed generation and microgrids modeling, simulation, design and optimization.

Manuel Coto was born in 1983 in Oviedo, Spain. He recived the M.Eng. degree from the University of Oviedo in 2007. He is currently pursuing the Ph.D. degree in the Departament of Electrical Engineering, University of Oviedo. His main research interests are in the area of Power-flow and AC/DC power systems modeling and simulation.

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